Research Article A Conceptual Design Approach of Coupled Shear Walls
Dipendu Bhunia1 Vipul Prakash2 and Ashok D Pandey 3
983089 Civil Engineering Group BIS Pilani 983091983091983091983088983091983089 India983090 Department of Civil Engineering II Roorkee Roorkee India983091 Department of Earthquake Engineering II Roorkee Roorkee India
Correspondence should be addressed to Vipul Prakash vipulprakashyahoocom
Received 983090983095 May 983090983088983089983091 Accepted 983094 July 983090983088983089983091
Academic Editors N D Lagaros and I Smith
Copyright copy 983090983088983089983091 Dipendu Bhunia et al Tis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Earthquake causes considerable damage to a large number o RCC high-rise buildings and tremendous loss o lie Tereoredesigners and structural engineers should ensure to offer adequate earthquake resistant provisions with regard to planning designand detailing in high-rise buildings to withstand the effect o an earthquake and minimize disaster As an earthquake resistantsystem the use o coupled shear walls is one o the potential options in comparison with moment resistant rame (MRF) and shearwall rame combination systems in RCC high-rise buildings Furthermore it is reasonably well established that it is uneconomicalto design a structureconsidering its linearbehaviorduring earthquake Hence an alternative design philosophy needs to be evolvedin the Indian context to consider the postyield behavior wherein the damage state is evaluated through deormation considerations
In the present context thereore perormance-based seismic design (PBSD) has been considered to offer signi1047297cantly improvedsolutions as compared to the conventional design based on linear response spectrum analysis
1 Introduction
Te growth o population density and shortage o land inurban areas are two major problems or all developing coun-tries including India In order to mitigate these two problemsthe designers resort to high-rise buildings which are rapidly increasing in number with various architectural con1047297gura-tions and ingenious use o structural materials Howeverearthquakes are the most critical loading condition or all
land based structures locatedin the seismically active regionsTe Indian subcontinent is divided into different seismiczones as indicated by IS 983089983096983097983091 (Part 983089) [983089] acilitating thedesigner to provide adequate protection against earthquakeA recent earthquake in India on January 983090983094th 983090983088983088983089 causedconsiderable damage to a large number o RCC high-risebuildings (number o storey varies rom 983092 to 983089983093) and tremen-dous loss o lie Te reasons were (a) most o the buildingshad sof and weak ground storey that provided open space orparking (b) poor quality o concrete in columns and(c) poordetailing o the structural design (httpwwwniceeorgeqe-iitkuploadsEQR Bhujpd ) Tereore this particular inci-dent has shown that designers and structural engineers
should ensure to offer adequate earthquake resistant provi-sions with regard to planning design and detailing in high-rise buildings to withstand the effect o an earthquake tominimize disaster
As an earthquake resistant system the use o coupledshear walls is one o the potential options in comparisonwith moment resistant rame (MRF) and shear wall ramecombination systems in RCC high-rise buildings MRF sys-tem and shear wall rame combination system are controlled
by both shear behavior and 1047298exural behavior whereas thebehavior o coupled shear walls system is governed by 1047298exuralbehavior However the behavior o the conventional beamboth in MRF and shear wall rame combination systemsis governed by 1047298exural capacity and the behavior o thecoupling beam in coupled shear walls is governed by shearcapacity During earthquake in1047297lled brick masonry cracksin a brittle manner although earthquake energy dissipatesthrough both inelastic yielding in beams and columns orMRF and shear wall rame combination systems whereasin coupled shear walls earthquake energy dissipates throughinelastic yielding in the coupling beams and at the base o the shear walls Hence amount o dissipation o earthquake
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983090 ISRN Civil Engineering
energy and ductility obtained rom both MRF and shearwall rame combination systems are less than those o coupled shear walls system in the high-rise buildings [983090ndash983089983089] However the Indian codes o practice governing theearthquake resistant design such as IS 983089983096983097983091 (Part 983089) [983089] andIS 983092983091983090983094 [983089983090] do not provide speci1047297c guidelines with regard
to earthquake resistant design o coupled shear walls On theother hand IS 983089983091983097983090983088 [983089983091] gives credence to the coupled shearwalls as an earthquake resistant option but it hasincorporated
very limited design guidelines o coupling beams that areinadequate or practical applications It requires urtherinvestigations and elaborations beore practical use
Further it is reasonably well established that it is uneco-nomical to design a structure considering its linear behaviorduring earthquake as is recognized by the Bureau o IndianStandards [983089 983089983090 983089983091] currently in use Hence an alternativedesign philosophy needs to be evolved in the Indian contextto consider the postyield behavior wherein the damage stateis evaluated through deormation considerations
In the present context thereore perormance-basedseismic design (PBSD)can be considered to offer signi1047297cantly improved solutions as compared to the conventional designbased on linear response spectrum analysis Perormance-based seismic design (PBSD) implies design evaluationand construction o engineered acilities whose perormanceunder common and extreme loads responds to the diverseneeds and objectives o owners tenants and societies atlarge Te objective o PBSD is to produce structures withpredictable seismic perormance In PBSD multiple levelso earthquake and corresponding expected perormancecriteria are speci1047297ed [983089983094] Tis aspect emphasizes nonlinearanalyses or seismic design veri1047297cation o any structure Tisprocedure gives some guidelines or estimating the possiblelocal and global damages o structures A retro1047297tted structurecan be evaluated with the help o PBSD Similarly economicsin the orm o lie-cycle cost along with construction cost o the structure is inherently included in PBSD [983090983089]
On the basis o the aoresaid discussion an effort has beenmade in this paper to develop a comprehensive procedure orthe design o coupled shear walls
2 Investigation of Coupling Beam
Coupled shear walls consist o two shear walls connectedintermittently by beams along the height Te behavior o coupled shear walls is mainly governed by the coupling
beams Te coupling beams are designed or ductile inelasticbehavior in order to dissipate energy Te base o theshear walls may be designed or elastic or ductile inelasticbehaviors Te amount o energy dissipation depends on theyield moment capacity and plastic rotation capacity o thecoupling beams I the yield moment capacity is too highthen the coupling beams will undergo only limited rotationsand dissipate little energy On the other hand i the yieldmoment capacity is too low then the coupling beams may undergo rotations much larger than their plastic rotationcapacities Tereore the coupling beams should be providedwith an optimum level o yield moment capacities Tesemoment capacities depend on the plastic rotation capacity
available in beams Te geometry rotations and momentcapacities o coupling beams have been reviewed based onprevious experimental andanalytical studies in this paper Ananalytical model o coupling beam has also been developedto calculate the rotations o coupling beam with diagonalreinorcement and truss reinorcement
983090983089 Geometry of Coupling Beam Te behavior o the rein-orced concrete coupling beam may be dominated by (1)shear orby (2) 1047298exureas per AC983092983088 [983089983094]FEMA 983090983095983091 [983089983092] andFEMA 983091983093983094 [983089983093] Shear is dominant in coupling beams when le 2 [983093] or 10383891103925 le 4
Tere are various types o reinorcements in RCC cou-pling beams described as ollows
983090983089983089 Conventional Reinforcement Conventional reinorce-ment consists o longitudinal 1047298exural reinorcement andtransverse reinorcement or shear Longitudinal reinorce-ment consists o top and bottom steel parallel to the longitu-
dinal axis o the beam ransverse reinorcement consists o closed stirrups or ties I the strength o these ties 90731710383891 ge 34required shear strength o the beam and the spacing these tiesle 11039253over the entire lengtho thebeam then stablehysteresisoccurs and such transverse reinorcement is said to beconorming to the type nowmandatory ornew constructionI the transverse reinorcement is de1047297cient either in strengthor spacing then it leads to pinched hysteresis and suchreinorcement is said to be nonconorming [983089983092ndash983089983094]
According to IS 983089983091983097983090983088 [983089983091] the spacing o transversereinorcement over a length o 21103925 ateither end o a beam shallnotexceed(a) 11039254 and (b) 983096 times the diameter o the smallestlongitudinal bar however it need not be less than 983089983088983088 mm
Elsewhere the beam shall have transverse reinorcement ata spacing not exceeding 11039252 Whereas the shear orce to beresisted by the transverse reinorcement shall be the maxi-mumo(1) calculated actored shear orce as per analysis and(2) shear orce due to ormation o plastic hinges at both endso the beam plus the actored gravity load on the span
983090983089983090 Diagonal Reinforcement Diagonal reinorcement con-sists o minimum our bars per diagonal It gives a betterplastic rotation capacity compared to conventional couplingbeam during an earthquake when 10383891103925 lt 15 as per Penelisand Kappos [983093] Te provisions or diagonal reinorcementaccording to different codes have already been shown in
able 983089 I the diagonal reinorcement is subjected to compres-siveloading it may buckle in which case it cannot be relied onto continue resisting compressive loading Under the actiono reversing loads reinorcement that buckles in compressionwith loading in one direction may be stressed in tensionwith loading in the opposite direction Tis action may lead to low-cycle atigue ailure so that the reinorcementcannot continue to resist tensile orces For this reasonit is necessary to ensure that this reinorcement does notbuckle o prevent buckling due to compressive loading thespacing between two adjacent diagonal bars should be greaterthan (1038389110392512) [based on buckling condition o a column]It has also been noticed rom Englekirk [983091] that diagonal
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983137983138983148983141 983089 Rotation capacities or coupling beams controlled by 1047298exure as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal Reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
Flexure dominant steel coupling beam2 le 52radic and ℎ907317 le 418radic 1 6 82 ge 65radic and ℎ907317 ge 640radic 025 2 3
reinorcement should not be attempted in walls that are lessthan 983089983094 in (983092983088983094983092 mm) thick Unless strength is an overridingconsideration diagonally reinorced coupling beams shouldnot be used
983090983089983091 russ Reinforcement russ reinorcement represents asigni1047297cant and promising departure rom traditional cou-pling beam reinorcements Te primary load transer mech-anism o the system is represented by the truss taken to itsyield capacity A secondary load path is created by the globalstrut and tie Te load transer limit state will coincide withthe yielding o all o the tension diagonals provided the so-produced compression loads do not exceed the capacity o the concrete compression strut Te yield strength o theprimary truss is governed by the tensile strength o its diag-onal whereas the primary truss transer mechanism mustinclude the shear travelling along the compression diagonalAccording to Penelis and Kappos [983093] and Galano and Vignoli
[983089983095] when 15 le 10383891103925 le 4 truss reinorcement offersbest seismic perormance in comparison with conventionaland diagonal reinorcements Tis type o reinorcement hasnot been used till now Detailing and placement problemsmust be careully studied i their use is contemplated Clearlyadditional experimentation is required because the systemappears to have merit especially in thin walls [983091]
When the postyield rotational level is much highercompared to rotational level or truss reinorcement thensteel beam can be provided as a coupling beam Tere are twotypes o steel beams which are provided as coupling beamsbased on the ollowing actors as per Englekirk [983091]AISC[983090983094]AISC [983090983095] and AISC [983090983096]
(a) Shear Dominant In this beam the shear capacity 9073171038389 isattained and the corresponding bending moment is equalto 9073171038389 times 2 which must be less than 983088983096 Te postyielddeormation is accommodated by shear and it is presumed le 169073171038389 where e = clear span o the coupling beam +983090 times concrete cover o shear wall = moment capacity o coupling beam and 9073171038389 = shear capacity o coupling beam
(b) Flexure Dominant In this beam the bending momentcapacity is attained and the corresponding shear orce isequal to 2which must be less than 9830889830969073171038389 Te postyielddeormation is accommodated by 1047298exure and it is presumed
ge 26
9073171038389
983090983090 Moment Capacity of Coupling Beam Te bendingmoment capacity o coupling beam depends on the geometry and material property o coupling beam Bending momentcapacity and shear orce capacity o the coupling beam arerelated with each other Englekirk [983091] Park and Paulay [983092]
Paulay [983090983097] Harries et al [983091983088] AISC [983090983094] AISC [983090983095] andAISC [983090983096] describe these capacities as ollows
983090983090983089 Reinforced Concrete Coupling Beam Shear capacity o coupling beam with conventional reinorcement can becalculated as
+ 2 852008 1038389 minus 1038389 852009 8520081103925minus1103925852009103838911039252
(983091)
where 103838911039251 = radic(10383892)2 + ( 1103925 minus1103925)2 and 103838911039252 =radic(1038389)2 + ( 1103925 minus1103925)2 All three shear capacities must
be less than equal to [(035(1103925 minus 1103925)103838911039250] or
[(035
(02510383891103925
)(1103925 minus 1103925
)10383891103925
0
] or
[(008
(1103925 minus 1103925
)0
]
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983092 ISRN Civil Engineering
983137983138983148983141 983090 Rotation capacities or coupling beams controlled by shear as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
which is basedon the statement that is capacity o a concretestrut in cylindrical elements will diminish to a level o 983091983088 to983091983093 o
as cracking increases where 0 is member overstrength actor o 983089983090983093
983090983090983090 Shear Dominant Steel Coupling Beam For I-sectiontype o steel coupling beam shear capacity (permissible shearresisted by web only) or shear dominant steel coupling beamis denoted as
9073171038389
= 06
907317
( minus 2
) and moment capacity
is = where is yield stress o structural steel 907317
is web thickness is the overall depth o the section is1047298ange thickness and is plastic section modulus
983090983090983091 Flexure Dominant Steel Coupling Beam Te transer-able shear orce (907317) or 1047298exure dominant steel couplingbeam is the lesser o 2 and9073171038389 where is the momentcapacity which is
983090983091 Rotational Capacity of Coupling Beam Te rotationcapacity in coupling beams depends upon the type o cou-pling beam When the rotational demand is greater than
rotational capacity o RCC coupling beam with conventional1047298exural and shear reinorcement then diagonal or trussreinorcement type o coupling beam could be provideddepending on the 10383891103925 ratio Te steel coupling beam couldbe used when the rotational limit due to lateral loadingexceeds the rotation capacity o RCC coupling beam withtruss reinorcement Various research works conducted by Paulay [983091983089 983091983090] Hindi and Sexsmith [983091983091] FEMA983091983093983094 [983089983093]Xuan etal [983091983092] describe these capacities AC 983092983088 [983089983094] FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli [983089983095] Chao etal [983091983093] and Englekirk [983091] describe the ollowing rotationalcapacities or various types o coupling beams considering thebehavior controlled by 1047298exure and shear during earthquake
ables 983089 983090 983091 983092 983093 and 983094 show these different rotationalcapacities or various coupling beams
Shear9073171038389907317radic or Shear9073171103925radic
le 3 or ge 6 is based
on the aspect ratio (10383891103925) o coupling beam and 2 le52radic and ℎ907317 le 418radic or 2 ge 65radic and
ℎ907317 ge 640radic are the conditions o the 1047298exure dominant
steel coupling beam to prevent local bucklingSpeci1047297cations in ables 983089 983090 983091 and 983092 can be questioned on
the basis o the ollowing observations
(983089) As per ables 983089 and 983090 the rotational capacities o beamdepends on size o wall (907317 1038389907317) which is illogical
(983090) When shear span to depth ratio le 2 or aspect ratio10383891103925 le 4 the behavior o RCC coupling beams iscontrolled by shear For this reason as aspect ratio(10383891103925) o diagonally reinorced beam is less than983089983093 it means that the behavior o diagonally rein-orced beam is controlled by shear Whereas ables983089 and 983091 show that diagonally reinorced couplingbeam behavior is controlled by 1047298exure which is notacceptable
(983091) Conventional longitudinal reinorcement with non-conorming transverse reinorcement is not acceptedor new construction
(983092) I the behavior o coupling beam is controlled by 1047298exure [aspect ratio (10383891103925) is greater than 983092] thelength o the coupling beam is quite larger Accordingto Munshi and Ghosh [983091983094] weakly coupled shearwalls can be obtained or larger span o the cou-pling beam and the design results o this type o coupled shear walls are inconsistent with regard to theductility and energy dissipation during earthquakemotion Hence it can be said that rotational capacity
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983137983138983148983141 983092 Rotation capacities or coupling beams controlled by shear as per AC 983092983088 [983089983094]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
o coupling beams controlled by 1047298exure as per AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] cannotbe accepted
Similarly speci1047297cations in ables 983093 and 983094 can also be ques-tioned on the basis o ollowing observation
For aspect ratio 10383891103925 = 15 Galano and Vignoli [983089983095]show different results regarding the ultimate rotation o
various RCC coupling beams in comparison with the resultsmade by Englekirk [983091]
983090983092 Analytical Program Te above study shows the incon-sistent modeling parameters and inconsistent evaluativeparameters However the behavior o coupled shear walls is
controlled by the characteristics o various coupling beamsTese characteristics depend on the ollowing parameters
(983089) Beam span to depth ratio
(983090) Reinorcement details
For this reason more study is required to investigate into thelimitations on behavior o coupling beams Since computerprogramme AENA983090D [983089983096] has some advantages in com-parison with other sofware packages like SAP V 983089983088983088983093 [983090983091]AENA983090D [983089983096] was considered to carry out this study Teadvantages as well as disadvantage o AENA983090D [983089983096] are asollows
983090983093 Advantages of AENA983090D Are
(i) Material element and reinorcement can be modeledindividually and
(ii) Geometric and material nonlinearity can be provided
983090983094 Disadvantage of AENA983090D Is
(i) Only static loading in one direction can be applied
983090983095 Reinforcement Layouts Tere were eighteen RCC cou-pling beams and three different reinorcement layouts con-sidered in the analytical program using AENA983090D [983089983096] (a)
longitudinal with conorming transverse ties (b) diagonalwith conorming transverse ties around themain bars and(c)truss with conorming transverse ties around the main barsFor each layout the cross section o the coupling beam wasconsidered as 983094983088983088 mm (depth 1103925) times 300mm (width ) andthe beam span-depth ratio (10383891103925) was considered as 983089 983089983093and 983090
983090983096 Materials Te concrete (M983090983088 grade) and steel (Fe 983092983089983093grade) were considered as two materials to model the coupledshear walls Te Poissonrsquos ratio was considered as 983088983090 Teunit-weight o concrete was considered as 983090983091 kNm3 and
the unit-weight o steel was considered as 983095983096983093 kNm3 Bothcoupling beam and shear wall elements were assigned as 983092-
noded quadrilateral elements material in coupling beam wasassigned as SBeta (inelastic) whereas material in shear wallwas assigned as plane stress elastic isotropic
983090983097 Investigative Model Figure 983089 and able 983095 describe theinvestigative models considered or AENA983090D [983089983096] analysisTe behaviors o all eighteen coupling beams were governedby shear Te load (F) was calculated based on the shear orcein beam and other parameters according to the provisions o FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
Te depth o the wall is considered as1038389907317 = 4m thicknesso the wall is considered as 907317 = 300mm and minimumreinorcement in the shear wall is taken as 983088983090983093 o its gross
area 983092983093983088 ccHere Youngrsquos modulus or concrete in beam = =224 times 104 MPa Youngrsquos modulus or steel in beam = 1038389 =21times105 MPa Youngrsquos modulus or concrete in wall = 907317 =224times104 MPa and Youngrsquos modulus or steel in wall= 1038389907317 =21 times 105 MPa
983090983089983088 Results and Discussions Te results using AENA983090D[983089983096] have been tabulated in able 983096 It shows the comparisono rotational limit at CP level among FEMA 983090983095983091 [983089983092] FEMA983091983093983094 [983089983093] and AENA983090D [983089983096] Tere are a lot o differencesamong the results o FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] andAENA983090D [983089983096] Te comparison has also been extended
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983137983138983148983141 983094 Rotation capacities or coupling beams as per Englekirk [983091]
ype o coupling beam Aspect ratio Rotation Capacity (Radians)10383891103925 max
983137983138983148983141 983095 (a) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (b) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (c) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]
983088983094 le983091 983093983096983093983092 983096ndash10 + 4ndash983090983088 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
ge983094 983089983090983092983095 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash10 + 4ndash983090983093 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash20 + 4ndash983091983093 as one diagonal 983090-legged 983090983093983090983088983088 cc
983088983094 le983091 983093983096983093983092 983096ndash10+4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash983090983088 + 4ndash983092983093 as one truss 983090-legged 983090983093983090983088983088 cc
983088983097 le983091 983094983090983091983093 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash983090983088 + 4ndash983092983088 as one truss 983090-legged 983090983093983090983088983088 cc
or considering AC 983092983088rsquos [983089983094] provisions Tere are also bigdifferences between the results o AC 983092983088 [983089983094] and AENA983090D[983089983096] shown in able 983097 It may be because o the limitations o AENA983090D [983089983096] sofware However it is unexpected in FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] that the rotationallimit is more or less same whereas theparameters consideredor calculation o shear strength are different Tereore itcan be said that the parameters given in FEMA 983090983095983091 [983089983092]FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] are questionable which
have already been discussed in this paper It has also beenobserved rom ables 983096 and 983097 that crack width in beam isquite signi1047297cant although the rotational values in AENA983090D[983089983096] are unexpectedly varyingwith FEMA 983090983095983091[983089983092]FEMA983091983093983094[983089983093] and AC 983092983088 [983089983094]
Hence the results obtained rom the above study usingAENA983090D [983089983096] were ound unsatisactory Tereore a new model has been created with some assumptions in themanner shown in Figure 983090 to carryout urther study
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ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
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983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
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ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 229
983090 ISRN Civil Engineering
energy and ductility obtained rom both MRF and shearwall rame combination systems are less than those o coupled shear walls system in the high-rise buildings [983090ndash983089983089] However the Indian codes o practice governing theearthquake resistant design such as IS 983089983096983097983091 (Part 983089) [983089] andIS 983092983091983090983094 [983089983090] do not provide speci1047297c guidelines with regard
to earthquake resistant design o coupled shear walls On theother hand IS 983089983091983097983090983088 [983089983091] gives credence to the coupled shearwalls as an earthquake resistant option but it hasincorporated
very limited design guidelines o coupling beams that areinadequate or practical applications It requires urtherinvestigations and elaborations beore practical use
Further it is reasonably well established that it is uneco-nomical to design a structure considering its linear behaviorduring earthquake as is recognized by the Bureau o IndianStandards [983089 983089983090 983089983091] currently in use Hence an alternativedesign philosophy needs to be evolved in the Indian contextto consider the postyield behavior wherein the damage stateis evaluated through deormation considerations
In the present context thereore perormance-basedseismic design (PBSD)can be considered to offer signi1047297cantly improved solutions as compared to the conventional designbased on linear response spectrum analysis Perormance-based seismic design (PBSD) implies design evaluationand construction o engineered acilities whose perormanceunder common and extreme loads responds to the diverseneeds and objectives o owners tenants and societies atlarge Te objective o PBSD is to produce structures withpredictable seismic perormance In PBSD multiple levelso earthquake and corresponding expected perormancecriteria are speci1047297ed [983089983094] Tis aspect emphasizes nonlinearanalyses or seismic design veri1047297cation o any structure Tisprocedure gives some guidelines or estimating the possiblelocal and global damages o structures A retro1047297tted structurecan be evaluated with the help o PBSD Similarly economicsin the orm o lie-cycle cost along with construction cost o the structure is inherently included in PBSD [983090983089]
On the basis o the aoresaid discussion an effort has beenmade in this paper to develop a comprehensive procedure orthe design o coupled shear walls
2 Investigation of Coupling Beam
Coupled shear walls consist o two shear walls connectedintermittently by beams along the height Te behavior o coupled shear walls is mainly governed by the coupling
beams Te coupling beams are designed or ductile inelasticbehavior in order to dissipate energy Te base o theshear walls may be designed or elastic or ductile inelasticbehaviors Te amount o energy dissipation depends on theyield moment capacity and plastic rotation capacity o thecoupling beams I the yield moment capacity is too highthen the coupling beams will undergo only limited rotationsand dissipate little energy On the other hand i the yieldmoment capacity is too low then the coupling beams may undergo rotations much larger than their plastic rotationcapacities Tereore the coupling beams should be providedwith an optimum level o yield moment capacities Tesemoment capacities depend on the plastic rotation capacity
available in beams Te geometry rotations and momentcapacities o coupling beams have been reviewed based onprevious experimental andanalytical studies in this paper Ananalytical model o coupling beam has also been developedto calculate the rotations o coupling beam with diagonalreinorcement and truss reinorcement
983090983089 Geometry of Coupling Beam Te behavior o the rein-orced concrete coupling beam may be dominated by (1)shear orby (2) 1047298exureas per AC983092983088 [983089983094]FEMA 983090983095983091 [983089983092] andFEMA 983091983093983094 [983089983093] Shear is dominant in coupling beams when le 2 [983093] or 10383891103925 le 4
Tere are various types o reinorcements in RCC cou-pling beams described as ollows
983090983089983089 Conventional Reinforcement Conventional reinorce-ment consists o longitudinal 1047298exural reinorcement andtransverse reinorcement or shear Longitudinal reinorce-ment consists o top and bottom steel parallel to the longitu-
dinal axis o the beam ransverse reinorcement consists o closed stirrups or ties I the strength o these ties 90731710383891 ge 34required shear strength o the beam and the spacing these tiesle 11039253over the entire lengtho thebeam then stablehysteresisoccurs and such transverse reinorcement is said to beconorming to the type nowmandatory ornew constructionI the transverse reinorcement is de1047297cient either in strengthor spacing then it leads to pinched hysteresis and suchreinorcement is said to be nonconorming [983089983092ndash983089983094]
According to IS 983089983091983097983090983088 [983089983091] the spacing o transversereinorcement over a length o 21103925 ateither end o a beam shallnotexceed(a) 11039254 and (b) 983096 times the diameter o the smallestlongitudinal bar however it need not be less than 983089983088983088 mm
Elsewhere the beam shall have transverse reinorcement ata spacing not exceeding 11039252 Whereas the shear orce to beresisted by the transverse reinorcement shall be the maxi-mumo(1) calculated actored shear orce as per analysis and(2) shear orce due to ormation o plastic hinges at both endso the beam plus the actored gravity load on the span
983090983089983090 Diagonal Reinforcement Diagonal reinorcement con-sists o minimum our bars per diagonal It gives a betterplastic rotation capacity compared to conventional couplingbeam during an earthquake when 10383891103925 lt 15 as per Penelisand Kappos [983093] Te provisions or diagonal reinorcementaccording to different codes have already been shown in
able 983089 I the diagonal reinorcement is subjected to compres-siveloading it may buckle in which case it cannot be relied onto continue resisting compressive loading Under the actiono reversing loads reinorcement that buckles in compressionwith loading in one direction may be stressed in tensionwith loading in the opposite direction Tis action may lead to low-cycle atigue ailure so that the reinorcementcannot continue to resist tensile orces For this reasonit is necessary to ensure that this reinorcement does notbuckle o prevent buckling due to compressive loading thespacing between two adjacent diagonal bars should be greaterthan (1038389110392512) [based on buckling condition o a column]It has also been noticed rom Englekirk [983091] that diagonal
8102019 161502
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ISRN Civil Engineering 983091
983137983138983148983141 983089 Rotation capacities or coupling beams controlled by 1047298exure as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal Reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
Flexure dominant steel coupling beam2 le 52radic and ℎ907317 le 418radic 1 6 82 ge 65radic and ℎ907317 ge 640radic 025 2 3
reinorcement should not be attempted in walls that are lessthan 983089983094 in (983092983088983094983092 mm) thick Unless strength is an overridingconsideration diagonally reinorced coupling beams shouldnot be used
983090983089983091 russ Reinforcement russ reinorcement represents asigni1047297cant and promising departure rom traditional cou-pling beam reinorcements Te primary load transer mech-anism o the system is represented by the truss taken to itsyield capacity A secondary load path is created by the globalstrut and tie Te load transer limit state will coincide withthe yielding o all o the tension diagonals provided the so-produced compression loads do not exceed the capacity o the concrete compression strut Te yield strength o theprimary truss is governed by the tensile strength o its diag-onal whereas the primary truss transer mechanism mustinclude the shear travelling along the compression diagonalAccording to Penelis and Kappos [983093] and Galano and Vignoli
[983089983095] when 15 le 10383891103925 le 4 truss reinorcement offersbest seismic perormance in comparison with conventionaland diagonal reinorcements Tis type o reinorcement hasnot been used till now Detailing and placement problemsmust be careully studied i their use is contemplated Clearlyadditional experimentation is required because the systemappears to have merit especially in thin walls [983091]
When the postyield rotational level is much highercompared to rotational level or truss reinorcement thensteel beam can be provided as a coupling beam Tere are twotypes o steel beams which are provided as coupling beamsbased on the ollowing actors as per Englekirk [983091]AISC[983090983094]AISC [983090983095] and AISC [983090983096]
(a) Shear Dominant In this beam the shear capacity 9073171038389 isattained and the corresponding bending moment is equalto 9073171038389 times 2 which must be less than 983088983096 Te postyielddeormation is accommodated by shear and it is presumed le 169073171038389 where e = clear span o the coupling beam +983090 times concrete cover o shear wall = moment capacity o coupling beam and 9073171038389 = shear capacity o coupling beam
(b) Flexure Dominant In this beam the bending momentcapacity is attained and the corresponding shear orce isequal to 2which must be less than 9830889830969073171038389 Te postyielddeormation is accommodated by 1047298exure and it is presumed
ge 26
9073171038389
983090983090 Moment Capacity of Coupling Beam Te bendingmoment capacity o coupling beam depends on the geometry and material property o coupling beam Bending momentcapacity and shear orce capacity o the coupling beam arerelated with each other Englekirk [983091] Park and Paulay [983092]
Paulay [983090983097] Harries et al [983091983088] AISC [983090983094] AISC [983090983095] andAISC [983090983096] describe these capacities as ollows
983090983090983089 Reinforced Concrete Coupling Beam Shear capacity o coupling beam with conventional reinorcement can becalculated as
+ 2 852008 1038389 minus 1038389 852009 8520081103925minus1103925852009103838911039252
(983091)
where 103838911039251 = radic(10383892)2 + ( 1103925 minus1103925)2 and 103838911039252 =radic(1038389)2 + ( 1103925 minus1103925)2 All three shear capacities must
be less than equal to [(035(1103925 minus 1103925)103838911039250] or
[(035
(02510383891103925
)(1103925 minus 1103925
)10383891103925
0
] or
[(008
(1103925 minus 1103925
)0
]
8102019 161502
httpslidepdfcomreaderfull161502 429
983092 ISRN Civil Engineering
983137983138983148983141 983090 Rotation capacities or coupling beams controlled by shear as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
which is basedon the statement that is capacity o a concretestrut in cylindrical elements will diminish to a level o 983091983088 to983091983093 o
as cracking increases where 0 is member overstrength actor o 983089983090983093
983090983090983090 Shear Dominant Steel Coupling Beam For I-sectiontype o steel coupling beam shear capacity (permissible shearresisted by web only) or shear dominant steel coupling beamis denoted as
9073171038389
= 06
907317
( minus 2
) and moment capacity
is = where is yield stress o structural steel 907317
is web thickness is the overall depth o the section is1047298ange thickness and is plastic section modulus
983090983090983091 Flexure Dominant Steel Coupling Beam Te transer-able shear orce (907317) or 1047298exure dominant steel couplingbeam is the lesser o 2 and9073171038389 where is the momentcapacity which is
983090983091 Rotational Capacity of Coupling Beam Te rotationcapacity in coupling beams depends upon the type o cou-pling beam When the rotational demand is greater than
rotational capacity o RCC coupling beam with conventional1047298exural and shear reinorcement then diagonal or trussreinorcement type o coupling beam could be provideddepending on the 10383891103925 ratio Te steel coupling beam couldbe used when the rotational limit due to lateral loadingexceeds the rotation capacity o RCC coupling beam withtruss reinorcement Various research works conducted by Paulay [983091983089 983091983090] Hindi and Sexsmith [983091983091] FEMA983091983093983094 [983089983093]Xuan etal [983091983092] describe these capacities AC 983092983088 [983089983094] FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli [983089983095] Chao etal [983091983093] and Englekirk [983091] describe the ollowing rotationalcapacities or various types o coupling beams considering thebehavior controlled by 1047298exure and shear during earthquake
ables 983089 983090 983091 983092 983093 and 983094 show these different rotationalcapacities or various coupling beams
Shear9073171038389907317radic or Shear9073171103925radic
le 3 or ge 6 is based
on the aspect ratio (10383891103925) o coupling beam and 2 le52radic and ℎ907317 le 418radic or 2 ge 65radic and
ℎ907317 ge 640radic are the conditions o the 1047298exure dominant
steel coupling beam to prevent local bucklingSpeci1047297cations in ables 983089 983090 983091 and 983092 can be questioned on
the basis o the ollowing observations
(983089) As per ables 983089 and 983090 the rotational capacities o beamdepends on size o wall (907317 1038389907317) which is illogical
(983090) When shear span to depth ratio le 2 or aspect ratio10383891103925 le 4 the behavior o RCC coupling beams iscontrolled by shear For this reason as aspect ratio(10383891103925) o diagonally reinorced beam is less than983089983093 it means that the behavior o diagonally rein-orced beam is controlled by shear Whereas ables983089 and 983091 show that diagonally reinorced couplingbeam behavior is controlled by 1047298exure which is notacceptable
(983091) Conventional longitudinal reinorcement with non-conorming transverse reinorcement is not acceptedor new construction
(983092) I the behavior o coupling beam is controlled by 1047298exure [aspect ratio (10383891103925) is greater than 983092] thelength o the coupling beam is quite larger Accordingto Munshi and Ghosh [983091983094] weakly coupled shearwalls can be obtained or larger span o the cou-pling beam and the design results o this type o coupled shear walls are inconsistent with regard to theductility and energy dissipation during earthquakemotion Hence it can be said that rotational capacity
8102019 161502
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ISRN Civil Engineering 983093
983137983138983148983141 983092 Rotation capacities or coupling beams controlled by shear as per AC 983092983088 [983089983094]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
o coupling beams controlled by 1047298exure as per AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] cannotbe accepted
Similarly speci1047297cations in ables 983093 and 983094 can also be ques-tioned on the basis o ollowing observation
For aspect ratio 10383891103925 = 15 Galano and Vignoli [983089983095]show different results regarding the ultimate rotation o
various RCC coupling beams in comparison with the resultsmade by Englekirk [983091]
983090983092 Analytical Program Te above study shows the incon-sistent modeling parameters and inconsistent evaluativeparameters However the behavior o coupled shear walls is
controlled by the characteristics o various coupling beamsTese characteristics depend on the ollowing parameters
(983089) Beam span to depth ratio
(983090) Reinorcement details
For this reason more study is required to investigate into thelimitations on behavior o coupling beams Since computerprogramme AENA983090D [983089983096] has some advantages in com-parison with other sofware packages like SAP V 983089983088983088983093 [983090983091]AENA983090D [983089983096] was considered to carry out this study Teadvantages as well as disadvantage o AENA983090D [983089983096] are asollows
983090983093 Advantages of AENA983090D Are
(i) Material element and reinorcement can be modeledindividually and
(ii) Geometric and material nonlinearity can be provided
983090983094 Disadvantage of AENA983090D Is
(i) Only static loading in one direction can be applied
983090983095 Reinforcement Layouts Tere were eighteen RCC cou-pling beams and three different reinorcement layouts con-sidered in the analytical program using AENA983090D [983089983096] (a)
longitudinal with conorming transverse ties (b) diagonalwith conorming transverse ties around themain bars and(c)truss with conorming transverse ties around the main barsFor each layout the cross section o the coupling beam wasconsidered as 983094983088983088 mm (depth 1103925) times 300mm (width ) andthe beam span-depth ratio (10383891103925) was considered as 983089 983089983093and 983090
983090983096 Materials Te concrete (M983090983088 grade) and steel (Fe 983092983089983093grade) were considered as two materials to model the coupledshear walls Te Poissonrsquos ratio was considered as 983088983090 Teunit-weight o concrete was considered as 983090983091 kNm3 and
the unit-weight o steel was considered as 983095983096983093 kNm3 Bothcoupling beam and shear wall elements were assigned as 983092-
noded quadrilateral elements material in coupling beam wasassigned as SBeta (inelastic) whereas material in shear wallwas assigned as plane stress elastic isotropic
983090983097 Investigative Model Figure 983089 and able 983095 describe theinvestigative models considered or AENA983090D [983089983096] analysisTe behaviors o all eighteen coupling beams were governedby shear Te load (F) was calculated based on the shear orcein beam and other parameters according to the provisions o FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
Te depth o the wall is considered as1038389907317 = 4m thicknesso the wall is considered as 907317 = 300mm and minimumreinorcement in the shear wall is taken as 983088983090983093 o its gross
area 983092983093983088 ccHere Youngrsquos modulus or concrete in beam = =224 times 104 MPa Youngrsquos modulus or steel in beam = 1038389 =21times105 MPa Youngrsquos modulus or concrete in wall = 907317 =224times104 MPa and Youngrsquos modulus or steel in wall= 1038389907317 =21 times 105 MPa
983090983089983088 Results and Discussions Te results using AENA983090D[983089983096] have been tabulated in able 983096 It shows the comparisono rotational limit at CP level among FEMA 983090983095983091 [983089983092] FEMA983091983093983094 [983089983093] and AENA983090D [983089983096] Tere are a lot o differencesamong the results o FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] andAENA983090D [983089983096] Te comparison has also been extended
8102019 161502
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983094 ISRN Civil Engineering
983137983138983148983141 983094 Rotation capacities or coupling beams as per Englekirk [983091]
ype o coupling beam Aspect ratio Rotation Capacity (Radians)10383891103925 max
983137983138983148983141 983095 (a) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (b) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (c) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]
983088983094 le983091 983093983096983093983092 983096ndash10 + 4ndash983090983088 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
ge983094 983089983090983092983095 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash10 + 4ndash983090983093 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash20 + 4ndash983091983093 as one diagonal 983090-legged 983090983093983090983088983088 cc
983088983094 le983091 983093983096983093983092 983096ndash10+4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash983090983088 + 4ndash983092983093 as one truss 983090-legged 983090983093983090983088983088 cc
983088983097 le983091 983094983090983091983093 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash983090983088 + 4ndash983092983088 as one truss 983090-legged 983090983093983090983088983088 cc
or considering AC 983092983088rsquos [983089983094] provisions Tere are also bigdifferences between the results o AC 983092983088 [983089983094] and AENA983090D[983089983096] shown in able 983097 It may be because o the limitations o AENA983090D [983089983096] sofware However it is unexpected in FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] that the rotationallimit is more or less same whereas theparameters consideredor calculation o shear strength are different Tereore itcan be said that the parameters given in FEMA 983090983095983091 [983089983092]FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] are questionable which
have already been discussed in this paper It has also beenobserved rom ables 983096 and 983097 that crack width in beam isquite signi1047297cant although the rotational values in AENA983090D[983089983096] are unexpectedly varyingwith FEMA 983090983095983091[983089983092]FEMA983091983093983094[983089983093] and AC 983092983088 [983089983094]
Hence the results obtained rom the above study usingAENA983090D [983089983096] were ound unsatisactory Tereore a new model has been created with some assumptions in themanner shown in Figure 983090 to carryout urther study
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ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
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983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
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ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
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Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 329
ISRN Civil Engineering 983091
983137983138983148983141 983089 Rotation capacities or coupling beams controlled by 1047298exure as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal Reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
Flexure dominant steel coupling beam2 le 52radic and ℎ907317 le 418radic 1 6 82 ge 65radic and ℎ907317 ge 640radic 025 2 3
reinorcement should not be attempted in walls that are lessthan 983089983094 in (983092983088983094983092 mm) thick Unless strength is an overridingconsideration diagonally reinorced coupling beams shouldnot be used
983090983089983091 russ Reinforcement russ reinorcement represents asigni1047297cant and promising departure rom traditional cou-pling beam reinorcements Te primary load transer mech-anism o the system is represented by the truss taken to itsyield capacity A secondary load path is created by the globalstrut and tie Te load transer limit state will coincide withthe yielding o all o the tension diagonals provided the so-produced compression loads do not exceed the capacity o the concrete compression strut Te yield strength o theprimary truss is governed by the tensile strength o its diag-onal whereas the primary truss transer mechanism mustinclude the shear travelling along the compression diagonalAccording to Penelis and Kappos [983093] and Galano and Vignoli
[983089983095] when 15 le 10383891103925 le 4 truss reinorcement offersbest seismic perormance in comparison with conventionaland diagonal reinorcements Tis type o reinorcement hasnot been used till now Detailing and placement problemsmust be careully studied i their use is contemplated Clearlyadditional experimentation is required because the systemappears to have merit especially in thin walls [983091]
When the postyield rotational level is much highercompared to rotational level or truss reinorcement thensteel beam can be provided as a coupling beam Tere are twotypes o steel beams which are provided as coupling beamsbased on the ollowing actors as per Englekirk [983091]AISC[983090983094]AISC [983090983095] and AISC [983090983096]
(a) Shear Dominant In this beam the shear capacity 9073171038389 isattained and the corresponding bending moment is equalto 9073171038389 times 2 which must be less than 983088983096 Te postyielddeormation is accommodated by shear and it is presumed le 169073171038389 where e = clear span o the coupling beam +983090 times concrete cover o shear wall = moment capacity o coupling beam and 9073171038389 = shear capacity o coupling beam
(b) Flexure Dominant In this beam the bending momentcapacity is attained and the corresponding shear orce isequal to 2which must be less than 9830889830969073171038389 Te postyielddeormation is accommodated by 1047298exure and it is presumed
ge 26
9073171038389
983090983090 Moment Capacity of Coupling Beam Te bendingmoment capacity o coupling beam depends on the geometry and material property o coupling beam Bending momentcapacity and shear orce capacity o the coupling beam arerelated with each other Englekirk [983091] Park and Paulay [983092]
Paulay [983090983097] Harries et al [983091983088] AISC [983090983094] AISC [983090983095] andAISC [983090983096] describe these capacities as ollows
983090983090983089 Reinforced Concrete Coupling Beam Shear capacity o coupling beam with conventional reinorcement can becalculated as
+ 2 852008 1038389 minus 1038389 852009 8520081103925minus1103925852009103838911039252
(983091)
where 103838911039251 = radic(10383892)2 + ( 1103925 minus1103925)2 and 103838911039252 =radic(1038389)2 + ( 1103925 minus1103925)2 All three shear capacities must
be less than equal to [(035(1103925 minus 1103925)103838911039250] or
[(035
(02510383891103925
)(1103925 minus 1103925
)10383891103925
0
] or
[(008
(1103925 minus 1103925
)0
]
8102019 161502
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983092 ISRN Civil Engineering
983137983138983148983141 983090 Rotation capacities or coupling beams controlled by shear as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
which is basedon the statement that is capacity o a concretestrut in cylindrical elements will diminish to a level o 983091983088 to983091983093 o
as cracking increases where 0 is member overstrength actor o 983089983090983093
983090983090983090 Shear Dominant Steel Coupling Beam For I-sectiontype o steel coupling beam shear capacity (permissible shearresisted by web only) or shear dominant steel coupling beamis denoted as
9073171038389
= 06
907317
( minus 2
) and moment capacity
is = where is yield stress o structural steel 907317
is web thickness is the overall depth o the section is1047298ange thickness and is plastic section modulus
983090983090983091 Flexure Dominant Steel Coupling Beam Te transer-able shear orce (907317) or 1047298exure dominant steel couplingbeam is the lesser o 2 and9073171038389 where is the momentcapacity which is
983090983091 Rotational Capacity of Coupling Beam Te rotationcapacity in coupling beams depends upon the type o cou-pling beam When the rotational demand is greater than
rotational capacity o RCC coupling beam with conventional1047298exural and shear reinorcement then diagonal or trussreinorcement type o coupling beam could be provideddepending on the 10383891103925 ratio Te steel coupling beam couldbe used when the rotational limit due to lateral loadingexceeds the rotation capacity o RCC coupling beam withtruss reinorcement Various research works conducted by Paulay [983091983089 983091983090] Hindi and Sexsmith [983091983091] FEMA983091983093983094 [983089983093]Xuan etal [983091983092] describe these capacities AC 983092983088 [983089983094] FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli [983089983095] Chao etal [983091983093] and Englekirk [983091] describe the ollowing rotationalcapacities or various types o coupling beams considering thebehavior controlled by 1047298exure and shear during earthquake
ables 983089 983090 983091 983092 983093 and 983094 show these different rotationalcapacities or various coupling beams
Shear9073171038389907317radic or Shear9073171103925radic
le 3 or ge 6 is based
on the aspect ratio (10383891103925) o coupling beam and 2 le52radic and ℎ907317 le 418radic or 2 ge 65radic and
ℎ907317 ge 640radic are the conditions o the 1047298exure dominant
steel coupling beam to prevent local bucklingSpeci1047297cations in ables 983089 983090 983091 and 983092 can be questioned on
the basis o the ollowing observations
(983089) As per ables 983089 and 983090 the rotational capacities o beamdepends on size o wall (907317 1038389907317) which is illogical
(983090) When shear span to depth ratio le 2 or aspect ratio10383891103925 le 4 the behavior o RCC coupling beams iscontrolled by shear For this reason as aspect ratio(10383891103925) o diagonally reinorced beam is less than983089983093 it means that the behavior o diagonally rein-orced beam is controlled by shear Whereas ables983089 and 983091 show that diagonally reinorced couplingbeam behavior is controlled by 1047298exure which is notacceptable
(983091) Conventional longitudinal reinorcement with non-conorming transverse reinorcement is not acceptedor new construction
(983092) I the behavior o coupling beam is controlled by 1047298exure [aspect ratio (10383891103925) is greater than 983092] thelength o the coupling beam is quite larger Accordingto Munshi and Ghosh [983091983094] weakly coupled shearwalls can be obtained or larger span o the cou-pling beam and the design results o this type o coupled shear walls are inconsistent with regard to theductility and energy dissipation during earthquakemotion Hence it can be said that rotational capacity
8102019 161502
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ISRN Civil Engineering 983093
983137983138983148983141 983092 Rotation capacities or coupling beams controlled by shear as per AC 983092983088 [983089983094]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
o coupling beams controlled by 1047298exure as per AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] cannotbe accepted
Similarly speci1047297cations in ables 983093 and 983094 can also be ques-tioned on the basis o ollowing observation
For aspect ratio 10383891103925 = 15 Galano and Vignoli [983089983095]show different results regarding the ultimate rotation o
various RCC coupling beams in comparison with the resultsmade by Englekirk [983091]
983090983092 Analytical Program Te above study shows the incon-sistent modeling parameters and inconsistent evaluativeparameters However the behavior o coupled shear walls is
controlled by the characteristics o various coupling beamsTese characteristics depend on the ollowing parameters
(983089) Beam span to depth ratio
(983090) Reinorcement details
For this reason more study is required to investigate into thelimitations on behavior o coupling beams Since computerprogramme AENA983090D [983089983096] has some advantages in com-parison with other sofware packages like SAP V 983089983088983088983093 [983090983091]AENA983090D [983089983096] was considered to carry out this study Teadvantages as well as disadvantage o AENA983090D [983089983096] are asollows
983090983093 Advantages of AENA983090D Are
(i) Material element and reinorcement can be modeledindividually and
(ii) Geometric and material nonlinearity can be provided
983090983094 Disadvantage of AENA983090D Is
(i) Only static loading in one direction can be applied
983090983095 Reinforcement Layouts Tere were eighteen RCC cou-pling beams and three different reinorcement layouts con-sidered in the analytical program using AENA983090D [983089983096] (a)
longitudinal with conorming transverse ties (b) diagonalwith conorming transverse ties around themain bars and(c)truss with conorming transverse ties around the main barsFor each layout the cross section o the coupling beam wasconsidered as 983094983088983088 mm (depth 1103925) times 300mm (width ) andthe beam span-depth ratio (10383891103925) was considered as 983089 983089983093and 983090
983090983096 Materials Te concrete (M983090983088 grade) and steel (Fe 983092983089983093grade) were considered as two materials to model the coupledshear walls Te Poissonrsquos ratio was considered as 983088983090 Teunit-weight o concrete was considered as 983090983091 kNm3 and
the unit-weight o steel was considered as 983095983096983093 kNm3 Bothcoupling beam and shear wall elements were assigned as 983092-
noded quadrilateral elements material in coupling beam wasassigned as SBeta (inelastic) whereas material in shear wallwas assigned as plane stress elastic isotropic
983090983097 Investigative Model Figure 983089 and able 983095 describe theinvestigative models considered or AENA983090D [983089983096] analysisTe behaviors o all eighteen coupling beams were governedby shear Te load (F) was calculated based on the shear orcein beam and other parameters according to the provisions o FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
Te depth o the wall is considered as1038389907317 = 4m thicknesso the wall is considered as 907317 = 300mm and minimumreinorcement in the shear wall is taken as 983088983090983093 o its gross
area 983092983093983088 ccHere Youngrsquos modulus or concrete in beam = =224 times 104 MPa Youngrsquos modulus or steel in beam = 1038389 =21times105 MPa Youngrsquos modulus or concrete in wall = 907317 =224times104 MPa and Youngrsquos modulus or steel in wall= 1038389907317 =21 times 105 MPa
983090983089983088 Results and Discussions Te results using AENA983090D[983089983096] have been tabulated in able 983096 It shows the comparisono rotational limit at CP level among FEMA 983090983095983091 [983089983092] FEMA983091983093983094 [983089983093] and AENA983090D [983089983096] Tere are a lot o differencesamong the results o FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] andAENA983090D [983089983096] Te comparison has also been extended
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983094 ISRN Civil Engineering
983137983138983148983141 983094 Rotation capacities or coupling beams as per Englekirk [983091]
ype o coupling beam Aspect ratio Rotation Capacity (Radians)10383891103925 max
983137983138983148983141 983095 (a) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (b) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (c) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]
983088983094 le983091 983093983096983093983092 983096ndash10 + 4ndash983090983088 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
ge983094 983089983090983092983095 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash10 + 4ndash983090983093 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash20 + 4ndash983091983093 as one diagonal 983090-legged 983090983093983090983088983088 cc
983088983094 le983091 983093983096983093983092 983096ndash10+4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash983090983088 + 4ndash983092983093 as one truss 983090-legged 983090983093983090983088983088 cc
983088983097 le983091 983094983090983091983093 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash983090983088 + 4ndash983092983088 as one truss 983090-legged 983090983093983090983088983088 cc
or considering AC 983092983088rsquos [983089983094] provisions Tere are also bigdifferences between the results o AC 983092983088 [983089983094] and AENA983090D[983089983096] shown in able 983097 It may be because o the limitations o AENA983090D [983089983096] sofware However it is unexpected in FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] that the rotationallimit is more or less same whereas theparameters consideredor calculation o shear strength are different Tereore itcan be said that the parameters given in FEMA 983090983095983091 [983089983092]FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] are questionable which
have already been discussed in this paper It has also beenobserved rom ables 983096 and 983097 that crack width in beam isquite signi1047297cant although the rotational values in AENA983090D[983089983096] are unexpectedly varyingwith FEMA 983090983095983091[983089983092]FEMA983091983093983094[983089983093] and AC 983092983088 [983089983094]
Hence the results obtained rom the above study usingAENA983090D [983089983096] were ound unsatisactory Tereore a new model has been created with some assumptions in themanner shown in Figure 983090 to carryout urther study
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ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
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983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
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ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
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Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 429
983092 ISRN Civil Engineering
983137983138983148983141 983090 Rotation capacities or coupling beams controlled by shear as per FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
Diagonal reinorcement NA 983088983088983088983094 983088983088983089983096 983088983088983091983088
which is basedon the statement that is capacity o a concretestrut in cylindrical elements will diminish to a level o 983091983088 to983091983093 o
as cracking increases where 0 is member overstrength actor o 983089983090983093
983090983090983090 Shear Dominant Steel Coupling Beam For I-sectiontype o steel coupling beam shear capacity (permissible shearresisted by web only) or shear dominant steel coupling beamis denoted as
9073171038389
= 06
907317
( minus 2
) and moment capacity
is = where is yield stress o structural steel 907317
is web thickness is the overall depth o the section is1047298ange thickness and is plastic section modulus
983090983090983091 Flexure Dominant Steel Coupling Beam Te transer-able shear orce (907317) or 1047298exure dominant steel couplingbeam is the lesser o 2 and9073171038389 where is the momentcapacity which is
983090983091 Rotational Capacity of Coupling Beam Te rotationcapacity in coupling beams depends upon the type o cou-pling beam When the rotational demand is greater than
rotational capacity o RCC coupling beam with conventional1047298exural and shear reinorcement then diagonal or trussreinorcement type o coupling beam could be provideddepending on the 10383891103925 ratio Te steel coupling beam couldbe used when the rotational limit due to lateral loadingexceeds the rotation capacity o RCC coupling beam withtruss reinorcement Various research works conducted by Paulay [983091983089 983091983090] Hindi and Sexsmith [983091983091] FEMA983091983093983094 [983089983093]Xuan etal [983091983092] describe these capacities AC 983092983088 [983089983094] FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli [983089983095] Chao etal [983091983093] and Englekirk [983091] describe the ollowing rotationalcapacities or various types o coupling beams considering thebehavior controlled by 1047298exure and shear during earthquake
ables 983089 983090 983091 983092 983093 and 983094 show these different rotationalcapacities or various coupling beams
Shear9073171038389907317radic or Shear9073171103925radic
le 3 or ge 6 is based
on the aspect ratio (10383891103925) o coupling beam and 2 le52radic and ℎ907317 le 418radic or 2 ge 65radic and
ℎ907317 ge 640radic are the conditions o the 1047298exure dominant
steel coupling beam to prevent local bucklingSpeci1047297cations in ables 983089 983090 983091 and 983092 can be questioned on
the basis o the ollowing observations
(983089) As per ables 983089 and 983090 the rotational capacities o beamdepends on size o wall (907317 1038389907317) which is illogical
(983090) When shear span to depth ratio le 2 or aspect ratio10383891103925 le 4 the behavior o RCC coupling beams iscontrolled by shear For this reason as aspect ratio(10383891103925) o diagonally reinorced beam is less than983089983093 it means that the behavior o diagonally rein-orced beam is controlled by shear Whereas ables983089 and 983091 show that diagonally reinorced couplingbeam behavior is controlled by 1047298exure which is notacceptable
(983091) Conventional longitudinal reinorcement with non-conorming transverse reinorcement is not acceptedor new construction
(983092) I the behavior o coupling beam is controlled by 1047298exure [aspect ratio (10383891103925) is greater than 983092] thelength o the coupling beam is quite larger Accordingto Munshi and Ghosh [983091983094] weakly coupled shearwalls can be obtained or larger span o the cou-pling beam and the design results o this type o coupled shear walls are inconsistent with regard to theductility and energy dissipation during earthquakemotion Hence it can be said that rotational capacity
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ISRN Civil Engineering 983093
983137983138983148983141 983092 Rotation capacities or coupling beams controlled by shear as per AC 983092983088 [983089983094]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
o coupling beams controlled by 1047298exure as per AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] cannotbe accepted
Similarly speci1047297cations in ables 983093 and 983094 can also be ques-tioned on the basis o ollowing observation
For aspect ratio 10383891103925 = 15 Galano and Vignoli [983089983095]show different results regarding the ultimate rotation o
various RCC coupling beams in comparison with the resultsmade by Englekirk [983091]
983090983092 Analytical Program Te above study shows the incon-sistent modeling parameters and inconsistent evaluativeparameters However the behavior o coupled shear walls is
controlled by the characteristics o various coupling beamsTese characteristics depend on the ollowing parameters
(983089) Beam span to depth ratio
(983090) Reinorcement details
For this reason more study is required to investigate into thelimitations on behavior o coupling beams Since computerprogramme AENA983090D [983089983096] has some advantages in com-parison with other sofware packages like SAP V 983089983088983088983093 [983090983091]AENA983090D [983089983096] was considered to carry out this study Teadvantages as well as disadvantage o AENA983090D [983089983096] are asollows
983090983093 Advantages of AENA983090D Are
(i) Material element and reinorcement can be modeledindividually and
(ii) Geometric and material nonlinearity can be provided
983090983094 Disadvantage of AENA983090D Is
(i) Only static loading in one direction can be applied
983090983095 Reinforcement Layouts Tere were eighteen RCC cou-pling beams and three different reinorcement layouts con-sidered in the analytical program using AENA983090D [983089983096] (a)
longitudinal with conorming transverse ties (b) diagonalwith conorming transverse ties around themain bars and(c)truss with conorming transverse ties around the main barsFor each layout the cross section o the coupling beam wasconsidered as 983094983088983088 mm (depth 1103925) times 300mm (width ) andthe beam span-depth ratio (10383891103925) was considered as 983089 983089983093and 983090
983090983096 Materials Te concrete (M983090983088 grade) and steel (Fe 983092983089983093grade) were considered as two materials to model the coupledshear walls Te Poissonrsquos ratio was considered as 983088983090 Teunit-weight o concrete was considered as 983090983091 kNm3 and
the unit-weight o steel was considered as 983095983096983093 kNm3 Bothcoupling beam and shear wall elements were assigned as 983092-
noded quadrilateral elements material in coupling beam wasassigned as SBeta (inelastic) whereas material in shear wallwas assigned as plane stress elastic isotropic
983090983097 Investigative Model Figure 983089 and able 983095 describe theinvestigative models considered or AENA983090D [983089983096] analysisTe behaviors o all eighteen coupling beams were governedby shear Te load (F) was calculated based on the shear orcein beam and other parameters according to the provisions o FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
Te depth o the wall is considered as1038389907317 = 4m thicknesso the wall is considered as 907317 = 300mm and minimumreinorcement in the shear wall is taken as 983088983090983093 o its gross
area 983092983093983088 ccHere Youngrsquos modulus or concrete in beam = =224 times 104 MPa Youngrsquos modulus or steel in beam = 1038389 =21times105 MPa Youngrsquos modulus or concrete in wall = 907317 =224times104 MPa and Youngrsquos modulus or steel in wall= 1038389907317 =21 times 105 MPa
983090983089983088 Results and Discussions Te results using AENA983090D[983089983096] have been tabulated in able 983096 It shows the comparisono rotational limit at CP level among FEMA 983090983095983091 [983089983092] FEMA983091983093983094 [983089983093] and AENA983090D [983089983096] Tere are a lot o differencesamong the results o FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] andAENA983090D [983089983096] Te comparison has also been extended
8102019 161502
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983094 ISRN Civil Engineering
983137983138983148983141 983094 Rotation capacities or coupling beams as per Englekirk [983091]
ype o coupling beam Aspect ratio Rotation Capacity (Radians)10383891103925 max
983137983138983148983141 983095 (a) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (b) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (c) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]
983088983094 le983091 983093983096983093983092 983096ndash10 + 4ndash983090983088 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
ge983094 983089983090983092983095 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash10 + 4ndash983090983093 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash20 + 4ndash983091983093 as one diagonal 983090-legged 983090983093983090983088983088 cc
983088983094 le983091 983093983096983093983092 983096ndash10+4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash983090983088 + 4ndash983092983093 as one truss 983090-legged 983090983093983090983088983088 cc
983088983097 le983091 983094983090983091983093 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash983090983088 + 4ndash983092983088 as one truss 983090-legged 983090983093983090983088983088 cc
or considering AC 983092983088rsquos [983089983094] provisions Tere are also bigdifferences between the results o AC 983092983088 [983089983094] and AENA983090D[983089983096] shown in able 983097 It may be because o the limitations o AENA983090D [983089983096] sofware However it is unexpected in FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] that the rotationallimit is more or less same whereas theparameters consideredor calculation o shear strength are different Tereore itcan be said that the parameters given in FEMA 983090983095983091 [983089983092]FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] are questionable which
have already been discussed in this paper It has also beenobserved rom ables 983096 and 983097 that crack width in beam isquite signi1047297cant although the rotational values in AENA983090D[983089983096] are unexpectedly varyingwith FEMA 983090983095983091[983089983092]FEMA983091983093983094[983089983093] and AC 983092983088 [983089983094]
Hence the results obtained rom the above study usingAENA983090D [983089983096] were ound unsatisactory Tereore a new model has been created with some assumptions in themanner shown in Figure 983090 to carryout urther study
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ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
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983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
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ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
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983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
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Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 529
ISRN Civil Engineering 983093
983137983138983148983141 983092 Rotation capacities or coupling beams controlled by shear as per AC 983092983088 [983089983094]
ype o coupling beam Conditions Plastic Rotation Capacity (Radians)
o coupling beams controlled by 1047298exure as per AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] cannotbe accepted
Similarly speci1047297cations in ables 983093 and 983094 can also be ques-tioned on the basis o ollowing observation
For aspect ratio 10383891103925 = 15 Galano and Vignoli [983089983095]show different results regarding the ultimate rotation o
various RCC coupling beams in comparison with the resultsmade by Englekirk [983091]
983090983092 Analytical Program Te above study shows the incon-sistent modeling parameters and inconsistent evaluativeparameters However the behavior o coupled shear walls is
controlled by the characteristics o various coupling beamsTese characteristics depend on the ollowing parameters
(983089) Beam span to depth ratio
(983090) Reinorcement details
For this reason more study is required to investigate into thelimitations on behavior o coupling beams Since computerprogramme AENA983090D [983089983096] has some advantages in com-parison with other sofware packages like SAP V 983089983088983088983093 [983090983091]AENA983090D [983089983096] was considered to carry out this study Teadvantages as well as disadvantage o AENA983090D [983089983096] are asollows
983090983093 Advantages of AENA983090D Are
(i) Material element and reinorcement can be modeledindividually and
(ii) Geometric and material nonlinearity can be provided
983090983094 Disadvantage of AENA983090D Is
(i) Only static loading in one direction can be applied
983090983095 Reinforcement Layouts Tere were eighteen RCC cou-pling beams and three different reinorcement layouts con-sidered in the analytical program using AENA983090D [983089983096] (a)
longitudinal with conorming transverse ties (b) diagonalwith conorming transverse ties around themain bars and(c)truss with conorming transverse ties around the main barsFor each layout the cross section o the coupling beam wasconsidered as 983094983088983088 mm (depth 1103925) times 300mm (width ) andthe beam span-depth ratio (10383891103925) was considered as 983089 983089983093and 983090
983090983096 Materials Te concrete (M983090983088 grade) and steel (Fe 983092983089983093grade) were considered as two materials to model the coupledshear walls Te Poissonrsquos ratio was considered as 983088983090 Teunit-weight o concrete was considered as 983090983091 kNm3 and
the unit-weight o steel was considered as 983095983096983093 kNm3 Bothcoupling beam and shear wall elements were assigned as 983092-
noded quadrilateral elements material in coupling beam wasassigned as SBeta (inelastic) whereas material in shear wallwas assigned as plane stress elastic isotropic
983090983097 Investigative Model Figure 983089 and able 983095 describe theinvestigative models considered or AENA983090D [983089983096] analysisTe behaviors o all eighteen coupling beams were governedby shear Te load (F) was calculated based on the shear orcein beam and other parameters according to the provisions o FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]
Te depth o the wall is considered as1038389907317 = 4m thicknesso the wall is considered as 907317 = 300mm and minimumreinorcement in the shear wall is taken as 983088983090983093 o its gross
area 983092983093983088 ccHere Youngrsquos modulus or concrete in beam = =224 times 104 MPa Youngrsquos modulus or steel in beam = 1038389 =21times105 MPa Youngrsquos modulus or concrete in wall = 907317 =224times104 MPa and Youngrsquos modulus or steel in wall= 1038389907317 =21 times 105 MPa
983090983089983088 Results and Discussions Te results using AENA983090D[983089983096] have been tabulated in able 983096 It shows the comparisono rotational limit at CP level among FEMA 983090983095983091 [983089983092] FEMA983091983093983094 [983089983093] and AENA983090D [983089983096] Tere are a lot o differencesamong the results o FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] andAENA983090D [983089983096] Te comparison has also been extended
8102019 161502
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983094 ISRN Civil Engineering
983137983138983148983141 983094 Rotation capacities or coupling beams as per Englekirk [983091]
ype o coupling beam Aspect ratio Rotation Capacity (Radians)10383891103925 max
983137983138983148983141 983095 (a) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (b) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (c) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]
983088983094 le983091 983093983096983093983092 983096ndash10 + 4ndash983090983088 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
ge983094 983089983090983092983095 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash10 + 4ndash983090983093 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash20 + 4ndash983091983093 as one diagonal 983090-legged 983090983093983090983088983088 cc
983088983094 le983091 983093983096983093983092 983096ndash10+4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash983090983088 + 4ndash983092983093 as one truss 983090-legged 983090983093983090983088983088 cc
983088983097 le983091 983094983090983091983093 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash983090983088 + 4ndash983092983088 as one truss 983090-legged 983090983093983090983088983088 cc
or considering AC 983092983088rsquos [983089983094] provisions Tere are also bigdifferences between the results o AC 983092983088 [983089983094] and AENA983090D[983089983096] shown in able 983097 It may be because o the limitations o AENA983090D [983089983096] sofware However it is unexpected in FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] that the rotationallimit is more or less same whereas theparameters consideredor calculation o shear strength are different Tereore itcan be said that the parameters given in FEMA 983090983095983091 [983089983092]FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] are questionable which
have already been discussed in this paper It has also beenobserved rom ables 983096 and 983097 that crack width in beam isquite signi1047297cant although the rotational values in AENA983090D[983089983096] are unexpectedly varyingwith FEMA 983090983095983091[983089983092]FEMA983091983093983094[983089983093] and AC 983092983088 [983089983094]
Hence the results obtained rom the above study usingAENA983090D [983089983096] were ound unsatisactory Tereore a new model has been created with some assumptions in themanner shown in Figure 983090 to carryout urther study
8102019 161502
httpslidepdfcomreaderfull161502 729
ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
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983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
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ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 629
983094 ISRN Civil Engineering
983137983138983148983141 983094 Rotation capacities or coupling beams as per Englekirk [983091]
ype o coupling beam Aspect ratio Rotation Capacity (Radians)10383891103925 max
983137983138983148983141 983095 (a) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (b) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093] (c) investigative model o coupling beam in AENA983090D [983089983096] as per IS 983089983091983097983090983088 [983089983091] IS 983092983093983094 [983089983097] SP-983089983094 [983090983088] FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]
983088983094 le983091 983093983096983093983092 983096ndash10 + 4ndash983090983088 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
ge983094 983089983090983092983095 983096ndash20 + 4ndash983091983088 as one diagonal 983090-legged 983090983093983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash10 + 4ndash983090983093 as one diagonal 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash20 + 4ndash983091983093 as one diagonal 983090-legged 983090983093983090983088983088 cc
983088983094 le983091 983093983096983093983092 983096ndash10+4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983089983095983089 983096ndash983090983088 + 4ndash983092983093 as one truss 983090-legged 983090983093983090983088983088 cc
983088983097 le983091 983094983090983091983093 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 cc
983089983090 le983091 983094983094983089983095 983096ndash983089983088 + 4ndash983091983088 as one truss 983090-legged 983089983094983090983088983088 ccge983094 983089983091983090983091 983096ndash983090983088 + 4ndash983092983088 as one truss 983090-legged 983090983093983090983088983088 cc
or considering AC 983092983088rsquos [983089983094] provisions Tere are also bigdifferences between the results o AC 983092983088 [983089983094] and AENA983090D[983089983096] shown in able 983097 It may be because o the limitations o AENA983090D [983089983096] sofware However it is unexpected in FEMA983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] that the rotationallimit is more or less same whereas theparameters consideredor calculation o shear strength are different Tereore itcan be said that the parameters given in FEMA 983090983095983091 [983089983092]FEMA 983091983093983094 [983089983093] and AC 983092983088 [983089983094] are questionable which
have already been discussed in this paper It has also beenobserved rom ables 983096 and 983097 that crack width in beam isquite signi1047297cant although the rotational values in AENA983090D[983089983096] are unexpectedly varyingwith FEMA 983090983095983091[983089983092]FEMA983091983093983094[983089983093] and AC 983092983088 [983089983094]
Hence the results obtained rom the above study usingAENA983090D [983089983096] were ound unsatisactory Tereore a new model has been created with some assumptions in themanner shown in Figure 983090 to carryout urther study
8102019 161502
httpslidepdfcomreaderfull161502 729
ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
8102019 161502
httpslidepdfcomreaderfull161502 829
983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
8102019 161502
httpslidepdfcomreaderfull161502 929
ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
8102019 161502
httpslidepdfcomreaderfull161502 1129
ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 729
ISRN Civil Engineering 983095
where V is shear force in the beam
WallBeam
F
F
Lw LwLb
hs = 3 mV =
F times L w
Lw + L b
F983145983143983157983154983141 983089 Initial sketch o the analytical model
db
2 times b
db
2 times b
Lb
db
F983145983143983157983154983141 983090 Schematic diagram o coupling beam
983090983089983089 Assumptions
(i) Te effect o gravity loads on the coupling beams hasbeen neglected
(ii) De1047298ection o the coupling beam occurs due to lateralloading
(iii) Contra 1047298exure occurs at the mid-span o the couplingbeam
(iv) Te con1047297ned concrete due to the con1047297ning action isprovided by closely spaced transverse reinorcementin concrete is assumed to govern the strength
otal elongation in the horizontal direction (Figure 983090) due tolateral loading can be written as
Δ1038389 = 1103925 times (983092)
and strain in the concrete
= Δ10383891038389
(983093)
Hence considering (983092) and (983093) the ollowing equation can bewritten as
coupling beam rotation = times 1038389
1103925
(983094)
Te results considering (983094) with maximum strain in con1047297nedconcrete (cu) o 983088983088983090 (Con1047297ning action is provided by closely spaced transverse reinorcement in concrete as per AC 983092983088[983089983094]) have been tabulated in able 983089983088
It can be observed rom able 983089983088 that the values obtainedasper(983094) have similar trend with the values speci1047297ed by AC983092983088 [983089983094] FEMA 983090983095983091 [983089983092] FEMA 983091983093983094 [983089983093] Galano and Vignoli[983089983095] and Englekirk [983091]
Based on the above study able 983089983089 has been preparedcontaining modi1047297ed parameters governing the couplingbeam characteristics which are also considered or thedevelopments o the design technique discussed below Asdesign technique is based on collapse prevention (CP) levelo structure plastic rotation capacity given in able 983089983089 is orCP level only
3 Proposed Design Technique
In this paper an attempt hasbeen made to develop a techniqueto design coupled shear walls considering its ideal seismicbehavior (stable hysteresis with high earthquake energy dis-sipation) For preparing this design technique symmetricalcoupled shear walls have been considered Designcapacity curve o coupled shear walls is obtained at the collapsemechanism o the structure based on this technique Tistechnique is applied to both 1047297xed base and pinned basecoupled shear walls o start with this technique is useul inselecting the preliminary dimensions o symmetrical coupledshear walls and subsequently arrives at a 1047297nal design stageFurther this technique is particularly useul or designerconsultant and practicing engineer who have no access tosophisticated sofware packages A case study has been doneimplementing the technique with the help o Microsof ExcelSpreadsheet and the results have also been validated
983091983089 Proposed Formulation In Figure 983091 the coupled shearwalls are subjected to a triangular variation o loading withamplitude 1 at the roo level Te value o 1 is obtainedcorresponding to the CP level o structure Subsequently thebase shear and roo displacement can be determined Teprocedure involving Figure 983091 the assumptions steps andmathematical calculation with initial value o 1 as unity havebeen illustrated as in Figure 983091
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983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
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ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 829
983096 ISRN Civil Engineering
T 983137 983138 983148 983141 983096 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n d
N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h F E M A 983090 983095 983091 [ 983089 983092 ] a n
d F E M A 983091 983093 983094 [ 983089 983093 ]
L o n g i t u d i n a
l r e i n
f o r c e m e n t a n
d
t r a n s v e r s e r e i n
f o r c e m e n t
S h e a r 907317 1038389
907317 radic
R o t a t i o
n a l
l i m i t a t c o
l l a p s e p r e v e n t i o n
l e v e l
( C P )
i n r a d i a n s
C r a c k w i d t h i n c o u p
l i n g
b e a m
a t C P l e v e l i n
m e t e r s
b y
A T E N A
983090 D [ 983089 983096 ]
M e m
b e r c o n t r o l l e d
b y
1047298 e x u r e
M e m
b e r c o n t r o l l e d
b y s h e a r
A T E
N A 983090 D [ 983089 983096 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
F E M A
983090 983095 983091 [ 983089 983092 ]
F E M A
983091 983093 983094 [ 983089 983093 ]
1038389
= 0 6
m
1038389 =
0 9
m
1038389
= 1 2
m
1038389
= 0 6
m
1038389
= 0 9
m
1038389
= 1 2
m
C o n v e n t i o n a
l l o n g i t u d i n a l r e i n
f o r c e m e n t
w i t h c o n
f o r m i n g t r a n s v e r s e r e i n
f o r c e m e n t
le 983091
983088 983088
983090 983093
983088 983088
983090 983093
983088 983088
983089 983093
983088 983088
983090 983088
983088 983088
983088 983088 983096 983096 983089
983088 983088 983088
983089 983088 983092
983088 983088
983088 983090 983091 983090 983093
983088 983088
983088 983088 983090 983094 983091
983088 983088 983088 983088 983091 983088 983094
983088 983088
983088 983088 983093 983093 983097
ge 983094
983088 983088
983089 983093
983088 983088
983090
983088 983088
983089 983088
983088 983088
983089 983094
983088 983088
983088 983091 983092 983096
983088 983088 983088
983093 983090 983096
983088 983088
983088 983096 983096 983094
983088 983088
983088 983088 983095 983089 983090 983093
983088
983088 983088 983089 983095 983090 983094
983088 983088
983088 983091 983089 983090 983092
D i a g o n a
l
le 983091
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983091 983093
983088 983088 983089 983089
983088 983088
983089 983089 983089
983088 983088
983088 983088 983092 983097 983092
983088 983088
983088 983092 983091 983089 983093
983088 983088
983088 983091 983095 983090
ge 983094
983088 983088
983091
983088 983088
983091
mdash
mdash
983088 983088
983088 983090 983097 983090
983088 983088 983088
983096 983091 983091
983088 983088
983088 983097 983095 983096
983088 983088
983088 983088 983093 983095 983090 983092
983088 983088 983088 983090 983097 983094 983089
983088 983088
983088 983091 983090 983090 983096
T r u s s
le 983091
N A
N A
N A
N A
983088 983088
983088 983089 983089 983095 983094
983088 983088 983088
983088 983092 983090 983090
983088 983088
983088 983088 983097 983091
983088 983088
983088 983088 983091 983089 983092 983092
983088 983088
983088 983088 983089 983088 983094 983094
983088 983088
983088 983088 983090 983088 983092
ge 983094
N A
N A
N A
N A
983088 983088
983088 983089 983092 983089 983091
983088 983088 983088
983090 983097 983095
983088 983088
983088 983090 983097
983088 983088
983088 983088 983091 983092 983092
983088 983088
983088 983088 983095 983093 983089 983092
983088 983088
983088 983088 983094 983094
8102019 161502
httpslidepdfcomreaderfull161502 929
ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
8102019 161502
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
8102019 161502
httpslidepdfcomreaderfull161502 1229
983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
8102019 161502
httpslidepdfcomreaderfull161502 1329
8102019 161502
httpslidepdfcomreaderfull161502 1429
983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 929
ISRN Civil Engineering 983097
T 983137 983138 983148 983141 983097 C o m p a r e t h e M o
d e l i n g P a r a m e t e r s a n
d N u m e r i c a
l A c c e p t a n c e C r i t e r i a w i t h A T C 983092 983088 [ 983089 983094 ]
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
8102019 161502
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
8102019 161502
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983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1029
983089983088 ISRN Civil Engineering
Wall 2
Wall 1
F1
F1 times (Hminus hs)H
F1 times (H minus 2hs)H
F1 times (H minus 3hs)H
F1 times (H minus 4hs)H
F1 times (H minus 5hs)H
F1 times (H minus (Nminus 3i)hs)H
F1 times (H minus (Nminus 2i)hs)H
F1 times (H minus (Nminus i)hs)H
I A
I A
db
hs
H
i
Lw LwLb
(a)
l
Mid-point of L b
CL of wall 1 CL of wall 2
1038389F1 V
V
V
VV
V
V
V
V
1103925F1
Wg
Wg
H
x
MMVw Vw
B
T C = T
A
(b)
F983145983143983157983154983141 983091 (a) Coupled shear walls (b) Free body diagram o coupled shear walls
983137983138983148983141 983089983088 Maximum rotations in radians
ype o reinorcement
10383891103925 Value as per (983094) Galano and
Vignoli [983089983095] Englekirk [983091]
AC983092983088 [983089983094] FEMA983090983095983091 [983089983092] and FEMA
(983092) Te axial deormation o the coupling beam isneglected
(983093) Te effect o gravity loads on the coupling beams isneglected
(983094) Te horizontal displacement at each point o wall983089 is equal to the horizontal displacement at eachcorresponding point o wall 983090 due to the presence o coupling beam
(983095) Te curvatures o the two walls are same at any level
(983096) Te point o contra 1047298exure occurs at mid-point o clear span o the beam
(983097) Te seismic design philosophy requires ormation o plastic hinges at the ends o the coupling beamsAll coupling beams are typically designed identically with identical plastic moment capacities Being lightly loaded under gravity loads they will carry equal shear
orces beore a collapse mechanism is ormed All
coupling beams are thereore assumed to carry equalshear orces
(983089983088) In the collapse mechanism or coupled shear wallsplastic hinges are assumed to orm at the base o thewall and at the two ends o each coupling beam Inthe wall the elastic displacements shall be small incomparison to the displacements due to rotation atthe base o the wall I the elastic displacements inthe wall are considered negligible then a triangulardisplaced shape occurs Tis is assumed to be thedistribution displacementvelocityacceleration alongthe height Te acceleration times the massweightat any 1047298oor level gives the lateral load Hence the
distribution o the lateral loading is assumed as atriangular variation which conorms to the 1047297rst modeshape pattern
983091983091 Steps Te ollowing iterative steps are developed in thisthesis or the design o coupled shear walls
(983089) Selection o a particular type o coupling beam anddetermining its shear capacity
(983090) Determining the ractions o total lateral loadingsubjected on wall 983089 and wall 983090
(983091) Determining shear orces developed in couplingbeams or different base conditions
8102019 161502
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ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
8102019 161502
httpslidepdfcomreaderfull161502 1229
983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1129
ISRN Civil Engineering 983089983089
983137983138983148983141 983089983089 Modi1047297ed parameters governing the coupling beam characteristics controlled by shear
ype o couplingbeam
Shear span to depth ratio 10383891103925 ype o detailing Plastic Rotation Capacity (Radians)
(983096) Calculating base shear and roo displacement
(983097) Modiying the value o 1 or next iteration startingrom Step (2) i Step (7) is not satis1047297ed
983091983092 Mathematical Calculation Te stepswhich aredescribedabove have been illustrated in this section as ollows
Step 983089 Te type o coupling beam can be determined asper able 983089983089 and shear capacity can be calculated as perSection 983090983090
Step 983090 In Figure 983091(b) ree body diagram o coupled shearwalls has been shown and are ractions o total lateralloading incident on wall 983089 and wall 983090 respectively such that
+ = 10 (983095)
For symmetrical coupled shear walls moments o inertiaso two walls are equal or equal depths and thicknesses atany level Further curvatures o two walls are equal at any level Hence based on the Assumption (7) equation (983095) canbe written as = = 05 (983096)
Step 983091 In this step it is explained how to calculate the shear
orce developed in the coupling beams or different typeso boundary conditions CSA [983090983093] and Chaallal et al [983091983095]de1047297ned the degree o coupling which is written as
DC = times ot
(983097)
where = 1038389907317 + 1038389 is the axial orce due to lateral loadingand ot is total overturning moment at the base o the wallproduced due to lateral loading For 1047297xed base condition DC
varies rom 983088 to 983089 and (983097) can also be written as
DC = 9830801103925983081
9830801038389907317
983081
times 9830801038389
983081 (983089983088)
983137983138983148983141 983089983090 Values o constant and exponents and
Te above equation (983089983088) is proposed by Chaallal et al [983091983095] is the total number o storeys is constant and and are exponents which are given in able 983089983090So based upon the above criteria and considering (983097) and(983089983088) shear orce developed in the coupling beam could bedetermined as ollows
For 1047297xed base condition ollowing equation can be
written as
= = 991761=1
907317 = ot times 98308011039259830819830801038389907317983081 times 9830801038389983081 (983089983089)
whereot is totaloverturning moment at the base due to thelateral loading
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983090)
Pinned Base Condition In this study pinned base condi-tion has been introduced as one o the possible boundary conditions or coupled shear walls It can be constructedby designing the oundation or axial load and shear orcewithout considering bending moment It is expected thatstable hysteresis with high earthquake energy dissipation canbe obtained or considering this kind o base condition
DC is 983089 or pinned base condition rom (983097) Hence theequation can be written as
= = 991761=1
907317 = ot (983089983091)
8102019 161502
httpslidepdfcomreaderfull161502 1229
983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1229
983089983090 ISRN Civil Engineering
Tereore based on the Assumption (9) shear orce incoupling beam at each storey is
907317 = sum=1907317 (983089983092)
Step 983092 Afer obtaining and 907317 at each storey or theparticular value o 1 bending moment values in each storey could be determined or each wall Subsequently curvaturediagram or each wall is generated by using moment areamethod as adopted in the Microsof excel spreadsheet whichis required to determine the wall rotation in each storeyTe ollowing equations are considered to calculate the wallrotation
Overturning moment at a distance ldquordquo rom base withrespect to each wall can be written as
ot () = minus991761=0
104869905 times 1
983080 minus ℎ1038389983081 983080minusminusℎ10383899830811048701 (983089983093)
where is storey number and it is considered rom the baseas 01 23
Resisting moment in wall due to shear orce in thecoupling beam at a distance ldquordquo rom base can be written as
wr () = 10383899073172 + 10383892 991761=
907317 (983089983094)
where net moment in the wall at a distance ldquordquo rom basegenerated due to overturning moment and moment due toshear orce in the coupling beam can be written as
net () = ot () minus wr () (983089983095)
Wall rotation at th storey or 1047297xed base can be written as
907317 = intℎ
0 net () 1103925 (983089983096)
where
= 907317 times 1038389390731712 (983089983097)
For plastic hinge rotation at the 1047297xed base o wall or rotation
at the pinned base o wall (983089983096) could be written as
907317 = intℎ
0 net () 1103925 + 9073170 (983090983088)
where9073170 is the plastichinge rotation atthe 1047297xed base o wallor rotation at the pinned base o wall
Step 983093 Consider (i) ensile orces at the base o wall 983089 ()as well as compressive orces at the base o wall 983090 () arecalculated due to lateral loading
(ii) Compressive loads at the bases o wall 983089 and wall 983090 arecalculated due to gravity loading
Lw Lb Lw
wi
wibi
Lb
2
F983145983143983157983154983141983092 Deormed shape o a th storey symmetricalcoupledshearwalls
(iii) Net axial orces at the bases o wall 983089 and wall 983090 arecalculated that is Net axial orce = ensile or Compressiveorce due to lateral loading ( or ) plusmn Compressive load dueto gravity loading
(iv) Ten according to these net axial orces or the
particular values o 1103925 and the yield moment valuesat the bases o wall 983089 and wall 983090 can be determined rom- interaction curve [983090 983089983097] Where 1103925 and areyield strength o concrete breadth o a section depth o thatsection and percentage o minimum reinorcement in thatparticular section respectively and is the axial orce and is the moment here net axial orce is considered as inthe - interaction curve
(v) Tereore i calculated bending moment value at any base o the two walls is greater than yield moment valueplastic hinge at that base would be ormed otherwise noplastic hinge would be ormed
Step 983094 Te rotation o coupling beam in each storey isdetermined in Figure 983092
Rotation o coupling beam at th storey or symmetricalwalls [983091] as per Figure 983092 is given by
= 907317 1 + 10383899073171038389
(983090983089)
where 907317 is rotation o wall at th storey and can becalculated as per (983089983096) 1038389907317 = depth o wall 1038389 = length o coupling beam
For plastic hinge rotation at the 1047297xed base o wall or realhinge rotation atthe pinned base o wall (983090983089) could be writtenas
= 1038389907317 983163907317983165 (983090983090)
where 907317 can be calculated as per (983090983088) or 1047297xed base o wallor or pinned base o wall and
1038389907317 = 1 + 10383899073171038389
(983090983091)
Step 983095 Te rotational limit or collapse prevention level o different types o RCC coupling beams and steel beams aregiven in able 983089983089 Te task was to check whether the rotationso beams attained their rotational limit o CP level at thecollapse mechanism o the structure simultaneously
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1329
8102019 161502
httpslidepdfcomreaderfull161502 1429
983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
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983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
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983089983092 ISRN Civil Engineering
Coupling beam
Rigid link
05Lw Lb 05Lw
F983145983143983157983154983141 983094 Modeling in SAP V 983089983088983088983093 [983090983091] and DRAIN-983091DX [983090983090]
B a s e s h e a r
Roof displacement
Capacity
VByield
Ki
o
Area a1
Area a2
Δroofyield
ΔroofCP
F983145983143983157983154983141 983095 Bilinear representation or Capacity Curve
representation is prepared in the manner shown in Figure 983095based on the concepts given in AC 983092983088 [983089983094]
It can be seen rom Figure 983095 that bilinear representationcan be due to the basis o initial tangent stiffness and equalenergies (Area a1 = Area a2) Subsequently ductility o thecoupled shear walls has been calculated as
Δ = Δ roo CPΔ roo yield (983090983095)
whereΔ roo CP andΔ roo yield canbe calculatedrom (983090983092)Δ isthe ductility which represents how much earthquake energy dissipates during an earthquake
983091983095 Results and Discussions Coupled shear walls at sectionldquoa-ardquo as shown in Figure 983093 are considered or conducting thestudy
983091983096 RCC Coupling Beam with Conventional Longitudinal Reinforcement and Conforming ransverse Reinforcement
983137983138983148983141 983089983092 Ductility o coupled shear walls considering differentapproaches
SAP V 983089983088983088983093 [983090983091] 983094983097983090 983095983092983095
RCC coupling beam with Conventional longitudinal rein-orcement and conorming transverse reinorcement in eachstorey has been selected as per Step 983089 or the study Te resultso this study or 1047297xed base as well as pinned base conditionshave been shown in Figure 983096 and able 983089983092
983091983096983089 Discussions of Numerical Results Figure 983096(b) showsthat the results obtained rom proposed design technique orpinned base conditions are almost similar with the results
obtained rom DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091]Whereas Figure 983096(a) is showing a bit differences about theresults obtained rom proposed design technique DRAIN-983091DX [983090983090] and SAP V 983089983088983088983093 [983090983091] although same dimensionssame material properties and same loading were consideredin all the three techniques However the differences werenot very high (983093ndash983089983088) able 983089983092 is showing the results aboutductility obtained or 1047297xed and pinned base conditions withthe help o the Figures 983096(a) and 983096(b) and Section 983091983094983092 It isnoticed that ductilityor pinnedbase condition is greater than1047297xed base conditionsIt means that stable hysteresiswith highearthquake energy dissipation can be obtained or coupledshear walls with pinned base
Te results obtained rom the proposed design techniquearesatisactoryHowever it is necessary to 1047297nd the limitationso the proposed design technique Tereore in the ollowingsection parametric study is elaborately discussed to detectthe limitations o the proposed design technique
4 Parametric Study
It has been observed rom the CSA [983090983093]andChaallaletal[983091983095]that the behavior o the ductilecoupled shear walls depend ondegree o coupling where degree o coupling depends upondepth and length o the coupling beam as well as depth andheight o the coupled shear walls [983092 983089983088]
Tereore this study has been restricted on length o thecoupling beam and number o stories as basic variables andother parameters are considered as constant Tese param-eters have been considered in proposed method to makeout effect on the behavior o coupled shear walls Furthermodi1047297cations to achieve ideal seismic behavior according tothe proposed method have been included in this study
983092983089 Model for Parametric Study A typical building withsymmetrical coupled shear walls is shown in Figures 983097(a)and 983097(b) Coupled shear walls at section ldquoa-ardquo have beenconsidered to carry out the parametric study
8102019 161502
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ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
8102019 161502
httpslidepdfcomreaderfull161502 1629
983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
8102019 161502
httpslidepdfcomreaderfull161502 1729
ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
8102019 161502
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
8102019 161502
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1529
ISRN Civil Engineering 983089983093
0 01 02 03
1500
1000
500
0
SAP V 1005
Drain-3DX
Design technique
Roof displacement (m)
B a s e
s h e a r
( k N )
(a)
SAP V 1005
Drain-3DX
Design technique
0 01 02 03
900
600
300
0
Roof displacement (m)
04
B a s e
s h e a r
( k N )
(b)
F983145983143983157983154983141 983096 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983097 (a) Plan view o building with symmetrical coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
983092983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asper the suggestions made by in Chaallal et al [983091983095] otalgravity loading on coupled shear walls at section ldquoa-ardquo hasbeen calculated as the sum o dead load plus 983090983093 LL as per IS983089983096983097983091 (part 983089) [983089] or 1047298oor however in case o roo only deadload is considered
983092983091 Parameters able 983089983093 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the parametric study
983092983092 Analysis Using Proposed Design echnique Te abovemen-tioned building has been studied by the design tech-nique Te results or different parameters have beendescribed in this section
983092983093 Observed Behavior o study the in1047298uence o length o the coupling beam (1038389) on the behavior o coupled shearwalls length o the coupling beam is considered as 983089 m 983089983093 m
983137983138983148983141 983089983093 Dimensions and material properties o coupled shearwallsor parametric study
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m 983089983093 m and 983090 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983089983088 983089983093 and 983090983088
Wall thickness (907317) 983091983088983088 mmWidth o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Yield strength o steel () 983092983089983093 MPa
and 983090 m or both 1047297xed and pinned base conditions RCCcoupling beam with conventional longitudinal reinorcementwith conorming transverse reinorcement has been selectedShear capacity in the coupling beam is calculatedas per Step 983089Te rotational limit o coupling beam has been selected as perStep 983095 Te study has been perormed or coupled shear walls
8102019 161502
httpslidepdfcomreaderfull161502 1629
983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
8102019 161502
httpslidepdfcomreaderfull161502 1729
ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 1829
983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 1929
ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 2029
983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
8102019 161502
httpslidepdfcomreaderfull161502 2129
ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1629
983089983094 ISRN Civil Engineering
with number ostories983090983088 983089983093and983089983088 or both 1047297xedand pinnedbase conditions
983092983093983089 For Number of Stories = 20 For more details seeFigures 983089983088 983089983089 983089983090 and 983089983091
983092983093983090 Discussion of Results for = 20 Te de1047298ection orthe case o pinned base condition is much higher than thecase o 1047297xed base (Figure 983089983088) however the base shear or thecase o pinned base condition is lower than the case o 1047297xedbase (Figure 983089983091) It shows satisactory results based on thebehavior o coupled shear walls Because coupled shear wallswith pinned base de1047298ected more subjected to lesser lateralloading in comparison with the coupled shear walls with 1047297xedbase andbase shear is directly varying with the lateral loading(983090983094) Since wall rotation is directly varying with the lengtho the beam (Figure 983089983089) and de1047298ection is the summation o the wall rotation (983090983093) de1047298ection is directly varying with thelength o the beam (Figure 983089983088) It has been also observed
that all beams reach to their rotational limit o CP level orpinned base condition however very ew beams reach totheir rotational limit o CP level or 1047297xed base condition(Figure 983089983090) Hence it can be said that coupled shear walls arebehaving as a rigid body motion or pinned base conditionwhich is expected Te explanations or 1047297xed base condition(Figure 983089983090) are given in the ollowing manner
(i) Te rotation o the cantilever wall is maximum at theree end o the wall Tis rotation decreases towardsthe base o the wall and is zero at the base or 1047297xity
(ii) Fixed base coupled shear walls with short span cou-pling beam is behaving as a cantilever wall (1038389 =1
m o Figure 983089983089) It is also one o the behaviors o a coupled shear walls However 1047297xed base coupledshear walls with long span coupling beam does notshow cantilever wall (1038389 = 15m and 1038389 = 2m o Figure 983089983089) behavior
(iii) Beam rotation is proportional to the wall rotation
Tereore it can be said rom the above observations thatcoupled shear walls with short span coupling beam (1038389 =1m) can be acceptable in comparison with the long spancoupling beam (1038389 = 15m and 1038389 = 2m) although thebehavior o all three coupling beams is governed by shearaccording to able 983089983089
With the help o Section 983091983094983092 and Figure 983089983091 ductility or
pinned base condition and 1047297xed base condition has beencalculated in able 983089983094
It has been observed rom able 983089983094 that ductility is moreor pinned base condition in comparison with the 1047297xed basecondition and ductility increases with increase in length o the coupling beam ((983090983092) and (983090983095) Figures 983089983088 983089983089 and 983089983091)
983092983093983091 For Number of Stories = 15 For more details seeFigures 983089983092 983089983093 983089983094 and 983089983095
983092983093983092 Discussion of Results for = 15 With the help o Section 983091983094983092 and Figure 983089983095 ductility or pinned base condi-tion and 1047297xed base condition has been calculated in able 983089983095
983137983138983148983141 983089983094 Ductility o coupled shear walls or = 20
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983091983091983091
983089983093 m 983092983096
983090 m 983094983091
Pinned983089 m 983093983089983089
983089983093 m 983094983091983093
983090 m 983095983089
983137983138983148983141 983089983095 Ductility o coupled shear walls or = 15
Base condition Length o the coupling beam (1038389) Values
Fixed
983089 m 983090983097983091
983089983093 m 983092983088
983090 m 983093983097
Pinned
983089 m 983092983093
983089983093 m 983093983096983093
983090 m 983094983096983095
It has been observed rom Figures 983089983092 to 983089983095 and able 983089983095that the results obtained or = 15 are similar with theresults o = 20 or 1047297xed base condition and pinned basecondition
983092983093983093 For Number of Stories = 10 For more details seeFigures 983089983096 983089983097 983090983088 and 983090983089
983092983093983094 Discussion of Results for = 10 Figures 983090983088 and983090983089 show that beam rotation and capacity curve reach CP
level or the case o 1038389 = 1m with pinned base conditiononly However beam rotation and capacity curve do notreach the CP level or the other cases while shear capacitiesin all coupling beams have been achieved It means thatideal seismic behavior (stable hysteresis with high earthquakeenergy dissipation) o coupled shear walls has only beenachieved or 1038389 = 1m with pinned base condition Proposeddesign technique does not show ideal seismic behavior o coupled shear walls or 1038389 = 1m 983089983093m and 983090 m with 1047297xedbase condition and 1038389 = 15m and 983090 m with pinned basecondition Now remedial action has been considered in theollowing manner to obtain the ideal seismic behavior
983092983093983095 Remedial Action for = 10 Te remedy or the caseso 1038389 = 1m 983089983093 m and 983090 m with 1047297xed base condition and1038389 = 15m and 983090 m with pinned base condition to achieveCP level is mentioned in (Figures 983090983090 983090983091 983090983092 and 983090983093) o obtainthe CP level it is required to increase the wall rotation Sincewall rotation ((983089983096) and (983089983097)) is inversely varying to the 10383893907317it is required to decrease the 1038389907317 It has been observed romFigure 983090983093 that the ideal seismic behavior o coupled shearwalls has been achieved
983092983093983096 Discussion of the Above Results Figures 983090983092 and 983090983093show that beam rotation and capacity curve reach CP levelor all cases although the results are not satisactory or
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ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
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ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1729
ISRN Civil Engineering 983089983095
S t o r
e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(a)
S t o r e y
h e i g h t ( m )
0 01 02 03 04
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
(b)
F983145983143983157983154983141 983089983088 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
24
48
72
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983089 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o r e y
h e i g h t ( m )
0 001 002 003
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
24
48
72
S t o
r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983090 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 1829
983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 1929
ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 2029
983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
8102019 161502
httpslidepdfcomreaderfull161502 2129
ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 2229
983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
8102019 161502
httpslidepdfcomreaderfull161502 2329
ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1829
983089983096 ISRN Civil Engineering
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
600
1200
B a s e s h e a r
( k N )
0 02 04
Roof displacement (m)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
375
750
B a s e s h e a r
( k N )
0 01 02 03 04 05
Roof displacement (m)
(b)
F983145983143983157983154983141 983089983091 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
54
S t o r e y
h e i g h t ( m )
0 01 02 03 04 05 06
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
54
S t o r e y
h e i g h t ( m )
0 028 056
Displacement (m)
Lb
= 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983092 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0002 0004 0006 0008
Wall rotation (rad)
(b)
F983145983143983157983154983141 983089983093 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 1929
ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
8102019 161502
httpslidepdfcomreaderfull161502 2029
983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
8102019 161502
httpslidepdfcomreaderfull161502 2129
ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
8102019 161502
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 1929
ISRN Civil Engineering 983089983097
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r e y
h e i g h t ( m )
0 0008 0016 0024
Beam rotation (rad)
(a)
Lb = 1 m
Lb = 15 m
Lb = 2 m
0
18
36
54
S t o r
e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
(b)
F983145983143983157983154983141 983089983094 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
0
500
1000
1500
2000
B a s e s h e a r
( k N )
0 01 02 03
Roof displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
Roof displacement (m)
0 02 040
375
750
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983095 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
0
18
36
S t o r e y
h e i g h t ( m )
0 0006 0012
Displacement (m)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Displacement (m)
0 004 008 012
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983096 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
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983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
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983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
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ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2029
983090983088 ISRN Civil Engineering
0
18
36
S t o r e y
h e i g h t ( m )
0 00004 00008
Wall rotation (rad)
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
Wall rotation (rad)
0 00055 0011
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983089983097 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0002 0004
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(a)
0
18
36
S t o r e y
h e i g h t ( m )
0 0016 0032
Beam rotation (rad)
Lb = 1 mLb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983088 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
B a s e s h e a r
( k N )
0 0006 0012 0018
Roof displacement (m)
0
500
1000
Lb = 1 m
Lb = 15 m
Lb = 2 m
(a)
B a s e s h e a r
( k N )
0 011 022
Roof displacement (m)
0
425
850
Lb = 1 m
Lb = 15 m
Lb = 2 m
(b)
F983145983143983157983154983141 983090983089 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
8102019 161502
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ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
httpslidepdfcomreaderfull161502 2429
983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
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ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2129
ISRN Civil Engineering 983090983089
S t o r e y
h e i g h t ( m )
0 02 04 06
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
0
18
36
(a)
S t o r
e y
h e i g h t ( m )
0
18
36
0 012 024
Displacement (m)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983090 (a) Storey displacement or 1047297xed base condition at CP level (b) Storey displacement or pinned base condition at CP level
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 001
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
S t o r e y
h e i g h t ( m )
0
18
36
0 0006 0012
Wall rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinnedLb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983091 (a) Wall rotation or 1047297xed base condition at CP level (b) Wall rotation or pinned base condition at CP level
S t o r
e y
h e i g h t ( m )
0
18
36
0 0015 003
Beam rotation (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(a)
Beam rotation (rad)
S t o r
e y
h e i g h t ( m )
0
18
36
0 0008 0016 0024
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983092 (a) Beam rotation or 1047297xed base condition at CP level (b) Beam rotation or pinned base condition at CP level
8102019 161502
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983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
8102019 161502
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ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
httpslidepdfcomreaderfull161502 2429
983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
httpslidepdfcomreaderfull161502 2529
ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
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983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2229
983090983090 ISRN Civil Engineering
B a
s e s h e a r
( m )
0
500
1000
0 03 06
Roof displacement (rad)
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and Lw = 3 m
Lb = 2 m and L w = 3 m
(a)
B a
s e s h e a r
( m )
Roof displacement (rad)
0
425
850
0 01 02 03
Lb = 1 m and L w = 2 m for 1047297xed and 4 m for pinned
Lb = 15 m and L w = 3 m
Lb = 2 m and L w = 3 m
(b)
F983145983143983157983154983141 983090983093 (a) Capacity curve or 1047297xed base condition (b) Capacity curve or pinned base condition
983137983138983148983141983089983096 Dimensions and material properties o coupledshear wallsor nonlinear static analysis
Depth o the wall (1038389907317) 983092 m
Length o beam (1038389) 983089 m
Depth o beam (1103925) 983096983088983088 mm
Number o stories () 983090983088 and 983089983093
Wall thickness (907317) 983091983088983088 mm
Width o coupling beam () 983091983088983088 mm
Storey height (ℎ1038389) 983091983094 m
Modulus o concrete () 983090983090983092 GPa
Modulus o steel (
1038389) 983090983088983088983088 GPa
Steel yield strength () 983092983089983093 MPa
1047297xed base condition according to the explanations given inSection 983092983093983089
Hence it can be said rom theabove results that proposeddesign technique is useul to design the coupled shear wallsduring earthquake motion o con1047297rm it more nonlinearstatic analysis is considered in the ollowing manner to assessthe proposed design technique
5 Assessment of Proposed Design Technique
Using Nonlinear Static Analysis
In this paper nonlinear static analysis is carried out todetermine the response reduction actors o coupled shearwalls at different earthquake levels
983093983089 Design Example Te ollowing design example is pre-sented or carrying out the nonlinear static analysis o coupled shear walls Tese walls are subjected to triangular
variation o lateral loading Te base o the walls isassumed as 1047297xed able 983089983096 mentions the different parameterswith dimensions and material properties which have beenconsidered to carry out the study Figures 983090983094(a) and 983090983094(b)
show the plan and sectional elevation o the coupled shearwall building respectively Te placeconsidered or this study is Roorkee and soil type or this place is medium (ype II)maximum considered earthquake (MCE) level and designbasis earthquake level (DBE) are considered or the study
983093983090 Loading Consideration Dead loads (DL) o 983094983095 kNm2
and live loads (LL) o 983090983092 kNm2 have been considered asgiven in Chaallal et al [983091983095] otal gravity loading on coupledshear walls at section ldquoa-ardquo has been calculated as the sum o dead load plus 983090983093 LL as per IS 983089983096983097983091 (part 983089) [983089] or 1047298oor
however in case o roo only dead load is considered
983093983091 Results and Discussions Te results and discussions aredescribed in Figure 983090983095
983093983091983089 Calculation of Performance Point Place consideredhere is Roorkee which belongs to the seismic zone IV andZ is 983088983090983092 as per IS 983089983096983097983091 (part 983089) [983089] 983093 damped elasticresponse spectra as per IS 983089983096983097983091 (part 983089) [983089] are consideredhere as demand curve DBE and MCE levels are consideredor calculation o perormance point (pp) Capacity curvesare already obtained in Figure 983090983095 Te perormance point has
been calculated with the help o capacity spectrum method o AC 983092983088 [983089983094] which is shown in Figure 983090983096
In this case modal mass co-efficient 1 = 0616 andMode participation actor PF1 = 151 derived with the help o modal analysis in SAP V 983089983088983088983093 [983090983091] Figure 983090983096 shows that ppis the perormance point Te base shear at the perormancepoint (pp) 907317bpp = 11731 kN and roo displacement at theperormance point (pp) Δ roo pp = 031m
In this case modal mass co-efficient1 = 0616 andModeparticipation actor PF1 = 151 Figure 983090983097 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 9576 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0097m
8102019 161502
httpslidepdfcomreaderfull161502 2329
ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
httpslidepdfcomreaderfull161502 2429
983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
httpslidepdfcomreaderfull161502 2529
ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
httpslidepdfcomreaderfull161502 2629
983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2329
ISRN Civil Engineering 983090983091
9 m 9 m 9 m 9 m
5 m
5 m
a
a
Lw
Lw
Lb
(a)
Wall 2
Wall 1
Lw LwLb
I A
I A
db
hs
H
(b)
F983145983143983157983154983141 983090983094 (a) Plan view o building with coupled shear walls (b) Coupled shear walls at section ldquoa-ardquo
0
200
400
600
800
1000
1200
1400
B a s e s h e a r
( k N )
0 01 02 03 04Roof displacement (m)
(a)
B a s e s h e a r
( k N )
0 01 02 03Roof displacement (m)
0
500
1000
1500
2000
(b)
F983145983143983157983154983141 983090983095 (a) Capacity curve or = 20 (b) Capacity curve or = 15
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09
Sd
pp
Straight linetangent to thecapacity curve
5 demandresponse spectra
Capacity curve
Reduced demandspectra
F983145983143983157983154983141 983090983096 Perormance point at the MCE level or = 20
8102019 161502
httpslidepdfcomreaderfull161502 2429
983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
httpslidepdfcomreaderfull161502 2529
ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
httpslidepdfcomreaderfull161502 2629
983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2429
983090983092 ISRN Civil Engineering
pp
Straight linetangent to theCapacity curve
5 demand responsespectra
Capacity curve
Reduced demandresponse spectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983090983097 Perormance point at the DBE level or = 20
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
1
2
3
4
5
6
7
S a
0 01 02 03 04 05 06 07 08 09Sd
pp
F983145983143983157983154983141 983091983088 Perormance point at the MCE level or = 15
pp
Straight line tangent to thecapacity curve
5 demand responsespectra
Capacity curve
Reduced demand responsespectra
0
05
1
15
2
25
3
35
S a
0 005 01 015 02 025 03 035 04 045
Sd
F983145983143983157983154983141 983091983089 Perormance point at the DBE level or = 15
8102019 161502
httpslidepdfcomreaderfull161502 2529
ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
httpslidepdfcomreaderfull161502 2629
983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2529
ISRN Civil Engineering 983090983093
983137983138983148983141 983089983097 Response Reduction Factors or DBE and MCE levels
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983088 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 14553 kN and roo displacement at theperormance point (pp)
Δroo pp
= 0259m
In thiscasemodal mass co-efficient1 = 0644 and Modeparticipation actor PF1 = 1485 Figure 983091983089 shows that pp isthe perormance point Te base shear at the perormancepoint (pp) 907317bpp = 12515 kN and roo displacement at theperormance point (pp) Δ roo pp = 0101m
983093983091983090 Calculation of Response Reduction Factor at the Per- formance Point able 983089983097 shows different response reductionactors or MCE and DBE levels Tese are calculated atdifferent perormance points (Figures 983090983096ndash983091983089)
From able 983089983097 response reduction actoro coupled shearwalls is varying between 983089983090983090 to 983090983088983093 or maximum consid-
ered earthquake (MCE) level which is almost same as theprovision o CSA [983090983093] or coupling beam with conventionalreinorcement
6 Conclusions
From the above studies the ollowing recommendations havebeen made or the design o coupled shear walls underearthquake motion
(i) Design technique should be adopted or 1047297xing thedimensions o coupled shear walls
(ii) Coupled shear walls with ge 15 with equal storey height ℎ1038389 = 36m can be designed with an optimumratio o 10383891038389907317 = 025 or 10383891103925 = 125 and = 8times10minus03 to obtainconsistencybetween the behaviorwithrespect to the wall rotation and earthquake energy dissipations
(iii) Pinned base condition can be provided at the baseo the shear wall as this type o base condition offersbetternonlinear behavior in compare to the 1047297xed basecondition
(iv) Te behavior o coupling beam should be governed by shear
Notations
Area o symmetrical coupled shear walls907317 Area o concrete section o an Individual pierhorizontal wall segment or coupling beam
resisting shear in in2 as per ACI 983091983089983096 [983091983097]
Gross area o concrete section in in2 For ahollow section is the area o the concreteonly and does not include the area o the
void(s) as per ACI 983091983089983096 [983091983097]1038389 Reinorcing steel in one diagonal as per
Englekirk [983091] 1038389 Area o nonprestressed tension reinorcementas per Englekirk [983091] 10383891103925 Reinorcement along each Diagonal o Coupling beam as per IS 983089983091983097983090983088 [983089983091]
V 1103925 otal area o reinorcement in each group o diagonal bars in a diagonally reinorced
coupling beam in in2 as per ACI 983091983089983096 [983091983097]
Width o coupling beam Flange width o I-beam as per FEMA 983090983095983091 [983089983092]and FEMA 983091983093983094 [983089983093]907317 Web width o the coupling beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093] Compressive axial orce at the base o wall 983090
CP Collapse prevention level Overall depth o the steel I-coupling beamsection
DC Degree o couplingDL Dead loadsDBE Design basis earthquake
1103925 Effective depth o the beam
1103925 Depth o the coupling beam1103925 Distance rom extreme compression 1047297ber tocentroid o compression reinorcement as perEnglekirk [983091]Δ Displacement at 907317Δ Elastic displacement (rArr 907317)Δ Displacement at limiting responseΔ roo Roo displacementΔ roo CP Roo displacement at CP levelΔ roo yield Roo displacement at yield levelΔ Displacement at ultimate strength capacity Δ Displacement at yield strength capacity
Δ1038389 Actual displacement at
9073171038389
8102019 161502
httpslidepdfcomreaderfull161502 2629
983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2629
983090983094 ISRN Civil Engineering
c Modulus o elasticity o concrete Youngrsquos modulus or concrete in beamcw Youngrsquos modulus or concrete in wallEPP Elastic-perectly-plasticEQRD Earthquake resistant design
1038389 Modulus o elasticity o steel as per FEMA 983090983095983091
[983089983092] and FEMA 983091983093983094 [983089983093]1038389 Youngrsquos modulus or steel in beam1038389907317 Youngrsquos modulus or steel in wall Clear span o the coupling beam + 983090 times concretecover o shear wall as per Englekirk [983091] Strain in concrete Force1 Maximum amplitude o triangular variation o loading
FEMA Federal emergency management agency Ultimate orce Yield stress o structural steel
Speci1047297ed compressive strength o concrete
cylinder Characteristic compressive strength o concretecube Speci1047297ed yield strength o reinorcement Overall height o the coupled shear wallsℎ Distance rom inside o compression 1047298ange toinside o tension 1047298ange o I-beam as per FEMA983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]ℎ1038389 Storey height Moment o inertia o symmetrical coupledshear walls Moment o inertia o coupling beam
IO Immediate occupancy level
Storey number Unloading stiffness1 Postyield stiffness Elastic stiffness Initial stiffnesssec Secant stiffness1038389 Length o the coupling beam10383891103925 Diagonal length o the member
LL live loadsLS Lie saety level1038389907317 Depth o coupled shear walls Distance between neutral axis o the two walls
0 Member over strength actor as per Englekirk
[983091] Moment o symmetrical coupled shear walls1 Moment at the base o the wall 9830892 Moment at the base o the wall 983090MCE Maximum considered earthquakeMDOF Multi-degree o reedom Nominal 1047298exural strength at section in lb-in as
per ACI 983091983089983096 [983091983097] Moment capacity o coupling beam as perEnglekirk [983091]ot otal overturning moment due to the lateralloading
MRF Moment resistant rame
Displacement ductility capacity relied on in thedesign as per NZS 983091983089983088983089 [983092983088]Δ Ductility Δ1 Energy based proposal or ductility undermonotonic loading and unloading
Δ2 Energy based proposal or ductility under
cyclic loading otal number o storeysNA Not applicableNEHRP National earthquake hazard reduction programNSP Non-linear static procedure Axial orce as per IS 983092983093983094 [983089983097]PBSD Perormance based seismic design Percentage o minimum reinorcement Shear span to depth ratiopp Perormance point Response reduction actorRCC Reinorced cement concrete1103925 Ductility related orce modi1047297cation actor
Ductility actor Redundancy actor1038389 Overstrength actor Spectral acceleration1103925 Spectral displacementSDOF Single-degree o reedom ensile axial orce at the base o wall 9830891 ensile strength o One diagonal o a diagonal
reinorced coupling beam1103925 ensile strength o truss reinorced couplingbeamrsquos diagonal as per Englekirk [983091] Te residual chord strength as per Englekirk [983091]
Flange thickness o steel I-coupling beam as per
Englekirk [983091] Inclination o diagonal reinorcement incoupling beam Coupling beam rotation Rotational value at ultimate pointmax Maximum rotational value907317 Wall rotation Yield rotation as per FEMA 983090983095983091 [983089983092] and FEMA983091983093983094 [983089983093]907317 Wall thickness907317 Web thickness o steel I-coupling beam907317 Shear orce in the coupling beam
9073171 Te shear or vertical component o one
diagonal in a primary truss travelled along thecompression diagonal as per Englekirk [983091]9073172 Te shear in a secondary truss produced by theresidual tension reinorcement activated theload transer mechanism as per Englekirk [983091]907317 Base shear907317 Non-actored design base shear9073171103925 Factored design base shear may be less than orgreater than 9073171038389907317 Base shear or elastic response907317 Base shear at limiting response907317 Nominal shear strength in lb as per ACI 983091983089983096[983091983097]
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
8102019 161502
httpslidepdfcomreaderfull161502 2929
Submit your manuscripts at
httpwwwhindawicom
8102019 161502
httpslidepdfcomreaderfull161502 2729
ISRN Civil Engineering 983090983095
907317 Te transerable shear orce or 1047298exuredominant steel coupling beam as per Englekirk [983091]9073171038389 Shear capacity o coupling beam as perEnglekirk [983091]
90731710383891 Shear strength o closed stirrups as per AC 983092983088
[983089983094] FEMA 983090983095983091 [983089983092] and FEMA 983091983093983094 [983089983093]907317 Capacity corresponding to Δ (may be themaximum capacity)9073171 Factored shear orce as per IS 983089983091983097983090983088 [983089983091]9073172 Factored shear orce at section in lb as per ACI983091983089983096 [983091983097]907317907317 Shear orce at the base o the shear wall9073179073171 Shear orce at the base o wall 9830899073179073172 Shear orce at the base o wall 983090907317 Base shear at idealized yield level9073171038389
Actual 1047297rst yield level
V otal nominal shear stress in MPa as per NZS983091983089983088983089 [983092983088]
otal gravity loading or symmetrical coupledshear walls Compressive strut width as per Englekirk [983091] Zone actor Plastic section modulus o steel coupling beam
References
[983089] Bureau o Indian Standards ldquoCriteria or earthquake resistantdesign o structures part 983089 general provisions and buildingsrdquoech Rep IS-983089983096983097983091 part 983089 Bureau o Indian Standards New Delhi India 983090983088983088983090
[983090] A K Jain Reinforced Concrete Limit State Design Nem Chand
amp Bros Roorkee India 983089983097983097983097[983091] R E Englekirk Seismic Design of Reinforced and Precast
Concrete Buildings John Wiley New York NY USA 983090983088983088983091
[983092] R Park and Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 983089983097983095983093
[983093] G G Penelis and A J Kappos Earthquake-Resistant ConcreteStructures EampFN SPON New York NY USA 983089983097983097983095
[983094] B S Smith and A Coull all Building Structures (Analysis and Design) John Wiley and Sons New York NY USA 983089983097983097983089
[983095] P J Fortney and B M Shahrooz ldquoBoundary detailing o coupled core wall system wall piersrdquo Advances in Structural Engineering vol 983089983090 no 983091 pp 983090983097983097ndash983091983089983088 983090983088983088983097
[983096] K A Harries and D S McNeice ldquoPerormance-based design
o high-rise coupled wall systemsrdquo Structural Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983096983097ndash983091983088983094 983090983088983088983094
[983097] S El-awil K A Harries P J Fortney B M Shahrooz and YKurama ldquoSeismic design o hybrid coupled wall systems stateo the artrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp983089983092983093983091ndash983089983092983093983096 983090983088983089983088
[983089983088] Paulay and M J N Priestley Seismic Design of Reinforced Concrete and Masonry Buildings John Wiley amp Sons New YorkNY USA 983089983097983097983090
[983089983089] F Naiem Te Seismic Design Handbook Kluwer AcademicBoston Mass USA 983090983088983088983089
[983089983090] Bureau o Indian Standards ldquoEarthquake resistant design andconstruction o buildingsmdashcode o practicerdquo ech Rep IS-983092983091983090983094 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983091] Bureau o Indian Standards ldquoDuctile detailing o reinorcedconcrete structures subjected to seismic orcesmdashcode o prac-ticerdquo ech Rep IS-983089983091983097983090983088 Bureau o Indian Standards New Delhi India 983089983097983097983091
[983089983092] Federal Emergency Management Agency ldquoNEHRP guidelinesor the seismic rehabilitation o buildingsrdquo ech Rep FEMA-983090983095983091 Federal Emergency Management Agency WashingtonDC USA 983089983097983097983095
[983089983093] Federal Emergency Management Agency ldquoPrestandard andcommentary or the seismic rehabilitation o buildingsrdquo echRep FEMA-983091983093983094 Federal Emergency Management AgencyWashington DC USA 983090983088983088983088
[983089983094] Applied echnology Council ldquoSeismic evaluation and retro1047297to concrete buildingsrdquo ech Rep AC-983092983088 Applied echnology Council Redwood City Cali USA 983089983097983097983094 Volume I
[983089983095] L Galano and A Vignoli ldquoSeismic behavior o short couplingbeams with different reinorcement layoutsrdquo ACI Structural Journal vol 983097983095 no 983094 pp 983096983095983094ndash983096983096983093 983090983088983088983088
[983089983096] AENA983090D Version 983091983091983088983091 Nonlinear Finite Element Integrated Analysis Cervenka Consulting Praha Czech Republic 983090983088983088983094
[983089983097] Bureau o Indian Standards ldquoPlain and reinorced concretemdashcodeo practicerdquo ech Rep IS-983092983093983094 Bureau o Indian StandardsNew Delhi India 983090983088983088983088
[983090983088] Bureau o Indian Standards IS-983092983093983094 ldquoDesign aids or reinorcedconcreterdquo ech Rep SP-983089983094 Bureau o Indian Standards New Delhi India 983089983097983095983096
[983090983089] V Prakash ldquoWhither perormance-based engineering inIndiardquo ISE Journal vol 983092983089 no 983089 pp 983090983088983089ndash983090983090983090 983090983088983088983092
[983090983090] V Prakash G H Powell and S Campbell DRAIN-983091DX Base Program User Guide Version 983089983089983088 Structural EngineeringMechanics and Materials Department o Civil Engineering UCBerkeley Cali USA 983089983097983097983091
[983090983091] SAP983090983088983088983088 Advanced 983089983088983088983093 Static and Dynamic Finite Element
Analysis of Structures Computers and Structures Inc BerkeleyCali USA 983090983088983088983094
[983090983092] S M Pore PerformanceBased SeismicDesign of Low to MediumRise RC Framed Buildings for India Department o EarthquakeEngineering II Roorkee Roorkee India 983090983088983088983095
[983090983093] Canadian Standards Association ldquoDesign o concrete struc-tures or buildingsrdquo CSA CAN983091-A983090983091 983091-M983097983092 Canadian Stan-dards Association Rexdale Canada 983089983097983097983092
[983090983094] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983089983097983097983095
[983090983095] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings Supplement No 983090 AmericanInstitute o Steel Construction Inc Chicago Ill USA 983090983088983088983088
[983090983096] American Institute o Steel Construction Inc Seismic Provi-sions for Structural Steel Buildings American Institute o SteelConstruction Inc Chicago Ill USA 983090983088983088983093
[983090983097] Paulay ldquoTe design o ductile reinorced concrete structuralwalls or earthquake resistancerdquo Earthquake Spectra vol 983090 no983092 pp 983095983096983091ndash983096983090983091 983089983097983096983094
[983091983088] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response o steel beams coupling concrete wallsrdquo Journal of Structural Engineering vol 983089983089983097 no 983089983090 pp 983091983094983089983089ndash983091983094983090983097983089983097983097983091
[983091983089] Paulay ldquoA displacement-ocused seismic design o mixedbuilding systemsrdquo Earthquake Spectra vol 983089983096 no 983092 pp 983094983096983097ndash983095983089983096 983090983088983088983090
8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
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httpslidepdfcomreaderfull161502 2929
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8102019 161502
httpslidepdfcomreaderfull161502 2829
983090983096 ISRN Civil Engineering
[983091983090] Paulay ldquo Te displacement capacity o reinorced concretecoupled wallsrdquo Engineering Structures vol 983090983092 no 983097 pp 983089983089983094983093ndash983089983089983095983093 983090983088983088983090
[983091983091] R A Hindi and R G Sexsmith ldquoA proposed damage model orRC bridge columns under cyclic loadingrdquo Earthquake Spectra vol 983089983095 no 983090 pp 983090983094983089ndash983090983096983089 983090983088983088983089
[983091983092] G Xuan B M Shahrooz K A Harries and G A RassatildquoA perormance-based design approach or coupled core wallsystems with diagonally reinorced concrete coupling beamsrdquo Advances in Structural Engineering vol 983089983089 no 983091 pp 983090983094983093ndash983090983096983088983090983088983088983096
[983091983093] S Chao K Khandelwal and S El-awil ldquoDuctile web ractureinitiation in steel shear linksrdquo Journal of Structural Engineering vol 983089983091983090 no 983096 pp 983089983089983097983090ndash983089983090983088983088 983090983088983088983094
[983091983094] J A Munshi and S K Ghosh ldquoDisplacement-based seismicdesign or coupled wall systemsrdquo Earthquake Spectra vol 983089983094no 983091 pp 983094983090983089ndash983094983092983090 983090983088983088983088
[983091983095] O Chaallal D Gauthier and P Malenant ldquoClassi1047297cationmethodology or coupled shear wallsrdquo Journal of Structural Engineering vol 983089983090983090 no 983089983090 pp 983089983092983093983091ndash983089983092983093983096 983089983097983097983094
[983091983096] I A Macleod Lateral Stiffness of Shear Walls with OpeningsDepartment o Civil Engineering Glasgow University GlasgowUK 983089983097983094983094
[983091983097] American Concrete Institute ldquoBuilding code requirements orreinorced concrete and commentaryrdquo ech Rep ACI 983091983089983096-983088983093ACI 983091983089983096R-983088983093 American Concrete Institute FarmingtonHills Mich USA 983090983088983088983093
[983092983088] New Zealand Standard ldquoTe design o concrete structuresrdquoech Rep NZS 983091983089983088983089 (part 983089) New Zealand Standard Welling-ton New Zealand 983089983097983097983093
