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Tables
Table 1: Assumed preliminary data required for the analysis of the frame
Table 2: General data collection and condition assessments of building
Figures
S.No. List of the figures
1 Slab with columns
2 Solid Flat Slab
!offered Flat Slab
" Solid Flat Slab with #rop panels
$ Grid Floor System
% Grid Slab &lan 'iew
( Flat Slab &lane 'iew
) Grid Slab *# 'iew
+ Flat slab *# 'iew1, Grid Slab -leatoin
11 Flat Slab -leation
12 Grid Slab -leation and *# 'iew
1 Flat Slab -leation and *# 'iew
1" Geometry of the structure and also the sections
assigned
1$ /llustrates the -quialent static graity and
lateral loads Applied on the structure
1% /llustrates the lateral static load -0
1( /llustrates the use of seismic weight as masssource and the mass lumped at each story leel
1) odel load case set to calculate the mode
shapes
1+ Load cases set to perform the linear static
analysis
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ANALYSIS AND DESIGN OF MULTI-STORY UILDING FOR
FLAT AND GRID FLOOR SYSTEM USING ETAS
ASTRA!T
4ith the increase in population and deelopment of ciili5ation6 the demand for
789S/NG is increasing at a pea: rate. -specially in towns due to rapid industriali5ation6 the
demand is ery high. Adapting the construction of ulti*storeyed ;uilding not only matches
with demand but also decreases the price of the single house.
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7ence an -ngineer to be :nowledgeable about the planning and designing of such ulti*
storeyed ;uildings. Adancements of computer pac:ages hae gien many tools to the designer
towards achieing the best and accuracy in their wor:.
/n our prohe complete process of odeling6 Analysis of
whole structure is carried by using ->A;S &ac:ages and the designs of typical structural
elements ?beam6 column6 and slab@ are done by manually. >he typical flat slab is design in SAF-
by using finite element method.
&unching shear reinforcement is an efficient method to increase not only the strength but also the
deformation capacity of flat slabs supported by columns. -specially6 the increase in deformation
capacity is desired so that the load can be distributed to other supports preenting a total collapse
of the structure in the case of the occurrence of a local failure
"e# $%r&s Flat slab6 Grid floor6 ->A;S6 SAF-6 pinching shear6 graity and lateral loads.
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!'A(TER ) 1
INTRODU!TION
Ge*eral:
Now days6 there is an increase in housing requirement with increased population and
urbani5ation. >herefore6 building sector has gained increasing prominence. 7oweer6 the fact
that the suitable lands for buildingBconstruction* especially in the areas in which people lie
intensiely* are limited and e3pensie shows that there is a necessity for optimal ealuation of
these lands. Additionally6 continuously increasing prices leads to increase in building costsC so6
both dimensional and cost optimi5ation becomes necessary and een indispensable.
4hen a building is prohe slab directly rests on the column and load
from the slab is directly transferred to the columns and then to the foundation. >o support heay
loads the thic:ness of slab near the support with the column is increased and these are called
drops6 or columns are generally proided with enlarged heads called column heads or capitals.
Absence of beam gies a plain ceiling6 thus giing better architectural appearance and also less
ulnerability in case of fire than in usual cases where beams are used.
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asi, &ei*i+i%* % la+ slab
/n general normal frame construction utili5es columns6 slabs E ;eams. 7oweer it may
be possible to underta:e construction without proiding beams6 in such a case the frame system
would consist of slab and column without beams. >hese types of Slabs are called flat slab6 since
their behaior resembles the bending of flat plates.
A reinforced concrete slab supported directly by concrete columns without the use of beams
Fig 1.1 slabs with columns
!OM(ONENTS OF FLAT SLAS
DRO(S>o resist the punching shear which is predominant at the contact of slab and column
Support6 the drop dimension should not be less than one *third of panel length in t hat direction.
!OLUMN 'EADS!ertain amount of negatie moment is transferred from the slab to the
column at the support. >o resist this negatie moment the area at the support needs to be
increased .this is facilitated by proiding column capitalBheads.
Flat slabs are appropriate for most floor situations and also for irregular column layouts6
cured floor shapes6 ramps etc. >he benefits of choosing flat slabs include a minimum depth
solution6 speed of construction6 fle3ibility in the plan layout ?both in terms of the shape and
column layout@6 a flat soffit ?clean finishes and freedom of layout of serices@ and scope and
space for the use of flying forms.
>he fle3ibility of flat slab construction can lead to high economy and yet allow the
architect great freedom of form.
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-3amples areC solid flat slab6 solid flat slab with drop panel6 solid flat slab with column
head6 coffered flat slab6 coffered flat slab with solid panels6 banded coffered flat slab.
Fig 1.2 Solid Flat Slab Fig 1. !offered Flat Slab
Fig 1." Solid Flat slab with #rop &anels
A flat slab is a flat section of concrete. >hese slabs are classically used in foundations6
although they can also be used in the construction of roadways6 paths6 and other structures.
#epending on the si5e and comple3ity of a flat slab6 it may need to be designed by an engineer
who is familiar with the limitations and needs of slabs6 or it may be possible for a handy do it
yourself to ma:e one in an afternoon for a simple proypically6 a flat slab is made with reinforced concrete6 in which rebar is criss*crossed in
the forms to proide support and reinforcement once the concrete is poured and hardened. >he
slab design is designed to be reinforced in seeral directions so that it can withstand stresses suchas shifting ground6 earthqua:es6 frost6 and so forth. Failure to fully reinforce a flat slab can cause
it to crac: or gie along wea: lines in the concrete6 which will in turn cause instability.
For some sites6 a flat slab is poured in situ. /n this case6 the site is prepared6 forms for the
concrete are set up6 and the reinforcing rebar or other materials are laid down. >hen6 the concrete
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is mi3ed6 poured6 and allowed to cure before moing on to the ne3t stage of construction. >he
time required can ary considerably6 with si5e being a mahis may be done when conditions at the site do not facilitate an easy pour6 or when the
conditions for the slabs construction need to be carefully controlled. >ransportation of the slab
can be a challenge if it is especially large. ;arges6 cranes6 and flatbed truc:s may be required to
successfully moe it from the fabrication site to the site of the installation.
>he flat slab foundation is not without problems. /t can settle on uneen ground6 allowing
the structure to settle as well6 for e3ample6 and during seismic actiity6 a slab foundation cannot
hold up if the soils are subhe ease of the construction of formwor:.>he ease of placement of fle3ural reinforcement.
>he ease of casting concrete
>he free space for water6 air pipes6 etc between slab and a possible furred ceiling.>he free placing of walls in ground plan.
>he use of cost effectie pressurising methods for long spans in order to reduce slab
thic:ness and deflections as also the time needed to remoe the formwor:.>he reduction of building height in multi*storey structures by saing one storey height in
eery si3 storeyHs than:s to the elimination of the beam height.
>hese structural systems seem to attract global interest due to their adantages mainly in
countries in which the seismicity is low. >he application of flat*slab structures is restrained due
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to the belief that such structures are susceptible to seismic actions. oreoer6 it is :nown that in
!entral America6 at the beginning of 1+%,Hs6 flat*slab structures displayed serious problems
during earthqua:e actions.
GRID SLA
Grid floor systems consisting of beams spaced at regular interal in perpendicular
directions6 monolithic with slab. >hey are generally employed for architectural reasons for large
rooms such as auditoriums6 theatre halls6 show rooms of shop where column free spaced oid
formed in the ceiling is adantageously utili5ed for concealed architectural lighting. >he si5es of
the beam running in perpendicular directions are generally :ept the same. /nstead of rectangular
beam grid6 a diagonal.
Fig 1.1 Grid floor systems
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O.E!TI/E
>he main ob/*S>8I ;9/L#/NG F8 FLA> AN# G/# FL88
SIS>- 9S/NG ->A;S0 >he ->A;S stands for e3tended # ?>hree*#imensional@ Analysis of
;uilding Systems. >his is based on the stiffness matri3 and finite element based software. >he
analysis and design is done to satisfy all the chec:s as per /ndian standards. Finally data base is
prepared for arious structural responses.
S!O(E OF OR"
ANALIS/S AN# #-S/GN 8F 9L>/*S>8I ;9/L#/NG F8 FLA> AN# G/#
FL88 SIS>- 9S/NG ->A;S0 >he structure is analy5ed for both graity and lateral loads
?seismic and wind load@. >he indiidual structural elements are designed for worst load
combinations.
!'A(TER ) 2
LITERATURE
;ASJAAN ?2,,(@ has wor:ed on irregular flat slabs designed according to structural
membrane approach. Flat slabs are less labor intensie6 simplify the installation of serices and
can accommodate more floors within restricted heights. 7oweer6 the span influencing their
design is the longest and they require more steel compared to two*way slabs. 8ther drawbac:s of
flat slabs are ulnerability to punching shear failure and higher deflections. >o aoid punchingshear failure drop panels6 column heads or shear reinforcement are used. /f span in flat slabs is
reduced then both deflection and punching shear problems can be aoided. 7oweer6 architects
prefer to hae few e3posed columns in usable areas. >his ineitably leads to columns in an
irregular layout6 hidden inside partitions or walls. Flat slab construction with columns in an
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irregular layout is a iable solution in constructing buildings that satisfy their functional
requirements in urban enironments.
7isabe has wor:ed on Fatigue Life -3tension of #amaged ! Slabs by Strengthening with
!arbon Fiber Sheets Attaching ethod. A series of wheel truc:ing fatigue tests were conducted
on the intentionally damaged reinforced concrete slabs of highway bridges strengthened with
carbon fiber sheets attached by the grid bonding method. As a result of this e3periment6 it was
found that grid*bonding method where carbon fiber sheets were bonded with interals on the
bottom surface of concrete dec:s was roughly 1, times higher than that of a non*strengthened
! slab6 and there was no problem in adhesieness in grid bonding parts.
Graf ?1++2@ has wor:ed on analysis and testing of a flat slab concrete building. A 1"*storey
reinforced concrete flat slab concrete building in southern !alifornia was assessed for earthqua:e
ris:. >he mid*1+%,Hs design uses frame action between the slab and columns for lateral
resistance. 9nli:e other flat slab buildings damaged in past earthqua:es6 this building has large6
deep6 pyramid*shaped drop panel to reinforce the critical slab*column estes at the uniersity of
!alifornia6 Ger:elty campus inestigated the ductility of the slab*column connection6 and
proided data for analytical model refinement. esults showed stiffness degradation as e3cepted6
but loss of strength with in anticipated ma3imum drifts was negligible.
George has wor:ed on applications of flat*slab rBc structures in seismic regions. /t is :nown that
the Gree: codes allow flat*slab structural systems6 howeer they proide specific compliance
criteria. /n the present study an e3tended parametric inestigation was carried out in order to
identify the seismic response of structural systems consisting of a@ slabs*columns b@ columns*
parametric beams c@ columns shear walls*slabs d@ columns*shear walls*slabs and parametric
beams. >he aforementioned systems were studied for all possible storey heights in Greece bymeans of F.-.. !ode SA&2,,, er.+. >he compliance criteria proided by the Gree: !ode for
earthqua:e resistance are related to second order effects6 torsion fle3ibility6 capacity design and
the sensitiity of masonry infill. !onclusions were e3tracted concerning the number of storey
which can be applied to each case.
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Altug ?2,,"@ has wor:ed on Fragilityanaly sis of flat*slab structures. Flat*slab ! buildings
e3hibit seeral adantages oer conentional moment*resisting frames. 7oweer6 the structural
effectieness of flat*slab construction is hindered by its alleged inferior performance under
earthqua:e loading. Although flat*slab systems are widely used in earthqua:e prone regions of
the world6 fragility cures for this type of construction are not aailable in the literature. >his
study focuses on the deriation of such fragility cures using medium*rise flat*slab buildings
with masonry infill walls. >he study employ ed a set of earthqua:e records compatible with the
design spectrum selected to represent the ariability in ground motion. /nelastic response*history
analysis was used to analy5e the random sample of structures subhe fragility cures deeloped from this study were compared with the fragility cures
deried for moment*resisting ! frames. >he study concluded that earthqua:e losses for flat*slab
structures are in the same range as for moment*resisting frames. #ifferences6 howeer6 e3ist. >he
study also showed that the differences were
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precise definition of its properties attains great importance6 especially when e3isting buildings
are inoled.
Faya5uddin ?2,12@ has wor:ed on !omparatie Analysis of Flat &late ultistoried Frames 4ith
and 4ithout Shear 4alls under 4ind Loads. AbstractKFlat plate is the term used for a slab
system without any column flares or drop panels. Although column patterns are usually on a
rectangular grid6 flat plates can be used with irregularly spaced column layouts. /n flat plate
loads directly to supporting columns6 which is different from other two way systems by the lac:
of beams6 column capitals6 and drop panels /n tall multistoried structures the flat plate floor
system has wee: resistance to lateral loads li:e wind6 hence special features li:e shear walls6
structural 4alls are to be proided if they are to be used in 7igh rise constructions. /n the present
inestigation numerical studies for 2,6",6%,6), storied for frames with normal conentional
beam supported slab system6 flat plate floor system6 flat plate floor system with Shear walls has
been conducted. A !omparison the !ritical !olumn A3ial Forces6 !olumn moments6 Lateral
#rift ?in mm@ due to static and wind loads on the structures located at 7yderabad at a basic wind
speed of "" mBs has been obsered during analysis.
Sandesh ?2,12@ has wor:ed on #ynamic Analysis of Special oment esisting Frame ;uilding
with Flat Slab and Grid Slab. A popular form of concrete building construction uses a flat
concrete slab ?without beams@ as the floor system. >his system is ery simple to construct6 and is
efficient in that it requires the minimum building height for a gien number of stories.
9nfortunately6 earthqua:e e3perience has proed that this form of construction is ulnerable to
failure6 when not designed and detailed properly6 in which the thin concrete slab fractures around
the supporting columns and drops downward6 leading potentially to a complete progressie
collapse of a building as one floor cascades down onto the floors below. Grid floor system
consisting of beam spaced at regular interals in perpendicular directions6 monolithic with
slab .>hey are generally employed for architectural reasons for large room such as6 auditoriums6
theaters halls6 show room of shops. Analysis and #esign of flat slabs are still the actie areas of
research and there is still no general agreement on the best design procedure. >he present day
/ndian Standards !odes of &ractice outline design procedures only for slabs with regular
geometry and layout. ;ut in recent times6 due to space crunch6 height limitations and other
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factors6 deiations from a geometry and regular layout are becoming quite common. Also
behaior and response of flat slabs during earthqua:e is a big question.
Jiran ?2,1@ has wor:ed on 8ptimum #esign of einforced !oncrete Flat Slab with #rop &anel.
/n this present study optimum design of reinforced concrete flat slab with drop panel according
to the /ndian code ?/S "$%*2,,,@ is presented. >he obhe cost of each structural element coers that
of material and labor for reinforcement6 concrete and formwor:. >he structure is modeled and
analy5ed using the direct design method. >he optimi5ation process is done for different grade of
concrete and steel. >he comparatie results for different grade of concrete and steel is presented
in tabulated form. 8ptimi5ation for reinforced concrete flat slab buildings is illustrated and the
results of the optimum and conentional design procedures are compared. >he model is analysed
and design by using A>LA; software. 8ptimi5ation is formulated is in nonlinear
programming problem ?NL&&@ by using sequential unconstrained minimi5ation technique
?S9>@.
'iswanathan ?2,12@ has wor:ed on Shear stress distribution of flat*plate using Finite -lement
Analysis. >he deelopment of a linear numerical model of flat*plate to predict shear stress
distribution around slab column connection is presented in this paper. An attempt is made to
model the slab6 fle3ural reinforcement and shear reinforcement using three dimensional solid
elements. >he proposed finite element model has been proed to be capable of simulating the
shear behaior of slab*column connection and to be suitable for analysis of structural
performance of flat plate structures. Numerical results obtained from this model hae good
agreement with the aailable results of other researcherHs numerical model with one dimensional
rebar element.
Sable ?2,12@ has wor:ed on !omparatie Study of Seismic ;ehaior of ultistory Flat Slab and
!onentional einforced !oncrete Framed Structures. >all commercial buildings are primarily aresponse to the demand by business actiities to be as close to each other6 and to the city centre
as possible6 thereby putting intense pressure on the aailable land space. Structures with a large
degree of indeterminacy is superior to one with less indeterminacy6 because of more members
are monolithically connected to each other and if yielding ta:es place in any one of them6 then a
redistribution of forces ta:es place. >herefore it is necessary to analy5e seismic behaior of
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building for different heights to see what changes are going to occur if the height of conentional
building and flat slab building changes.
Jandale?2,1@ has wor:ed on !omparatie study of ectangular &restressed !oncrete Flat Slab
and !! Flat Slab A simple prestressed flat slab is generally supported by a networ: of columns
without beam. >he design of a typical simple flat slab inoles the analysis of moments in the
two principal directions so that cables may be arranged to resist these moments. >he slab is
analy5ed as a one way slab and the total number of cables required to resist the moments in each
of the two principal directions are determined. >he column strips being stiffer than the middle
strips6 greater percentage of the tendons are housed in the column strips. >he proportioning of the
tendons between the column and middle strips may be based on the proision of codes6 such as
/S "$% and ;S )11,6 where column strips share a higher proportion of the total moment. Since
it is not generally possible to ary the spacing of cables for positie and negatie moments in
either the column or the middle strips6 the total number of cables required in any direction is
apportioned in the ratio of %$ and $ percent between the column and middle strips.
Gupta?2,12@ has wor:ed on Seismic ;ehaiors of ;uildings 7aing Flat Slabs with drops.
As flat slab building structures are significantly more fle3ible than traditional concrete
frameBwall or frame structures6 thus becoming more ulnerable to seismic loading. >herefore6 the
characteristics of the seismic behaior of flat slab buildings suggest that additional measures for
guiding the conception and design of these structures in seismic regions are needed. >o improe
the performance of building haing flat slabs under seismic loading6 proision of part shear walls
is proposed in the present wor:. >he obheir !ost
!omparison.>he FLA> slab system of construction is one in which the beam is used in the
conentional methods of construction done away with the directly rests on column and the load
from the slabs is directly transferred to the columns and then to the foundation. #rops or
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columns are generally proided with column heads or capitals. Grid floor systems consisting of
beams spaced at regular interals in perpendicular directions6 monolithic with slab. >hey are
generally employed for architectural reasons for large rooms such as auditoriums6 estibules6
theatre halls6 show rooms of shops where column free space is often the main requirement. >he
aimof the prohe proposed construction site is Ne3us point apposite to
'idhan;haan and beside N! office6 Nagpur. >he total length of slab is1.) m and width is
2(.22 m. total area of slab is )$".1% sqm. /t is designed by using $ Grade concrete and Fe"1$
steel. Analysisof the flat slab and grid slab has been done both manually by /S "$%*2,,, and by
using software also. Flat slab and Grid slab hasbeen analy5ed by S>AA# &8. ates hae been
ta:en according to N..!. !.S./t is obsered that the FLA> slab with drop is more economical
than Flat slab without drop and Grid slabs.
NG9I-N*/N7 has wor:ed on punching shear resistance of steel fiber reinforced concrete flat
slabsthis paper deals with behaior and capacity of steel fiber reinforced concrete ?SF!@ flat
slabs under punching shear force. A total of twele small*scale flat slabs of different dimensions
that consisted of nine SF! and three control steel reinforced concrete ?S!@ ones were tested.
-ffect of steel fibers amount on punching shear crac:ing behaior and resistance of the slabs was
inestigated. >he results show a significant increase of the punching shear capacity and
considerable improement of crac:ing behaior as well as good integrity of column*slab
connection of the slabs with fibers. >he slabs without fibers failed suddenly in ery brittle
manner6 while6 the fiber reinforced ones collapsed in more ductile type. At sericeability limit
state6 a strong reduction of aerage crac: width up to appro3imately (,.)M of the SF! slabs in
comparison with S! ones was obsered. /n addition6 based on e3perimental data obtained from
the authorHs study and literature6 the paper performed an ealuation of accuracy of e3isting
models and formulas in preious studies that used to predict punching shear resistance of SF!
slabs. >he results from the ealuation show that the e3isting formulas gae inaccurate results
with a large scatter in comparison with the testing results6 and thus6 a new formula should be
proposed for more accurate estimation of punching shear resistance of SF! slabs.
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!'A(TER-
MET'ODLOGY
INTRODU!TION
An earthqua:e is a sudden tremor or moement of the earthHs crust6 which originates
naturally at or below the surface. >he word natural is important here6 since it e3cludes shoc:
waes caused by nuclear test6 man*made e3plosions6 etc. About +,M of all the earthqua:es
results from tectonic eents6 primarily moements on the faults. >he remaining is related to
olcanism6 collapse of subterranean caities or manmade effects. >ectonic earthqua:es are
triggered when the accumulated strain e3ceeds the shearing strength of the roc:s.
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>he destruction an earthqua:e causes depends on its magnitude and duration6 or the
amount of sha:ing that occurs. A structureHs design and the materials used in its construction also
effects the amount of damage the structure incurs. -arthqua:e aries from small6 imperceptiblesha:ing to large shoc:s felt oer thousands of :ilometers. -arthqua:e can deform the ground6
ma:e buildings and other structures collapse6 and create tsunamis ?large sea waes@. Lies may
be lost in the resulting destruction.
ASI! ELEMENTS OF EART'3UA"E
Structures on the earth are generally subA>/! AN##INA/!. Static loads are constant with time while dynamic loads are time arying. /n
general6 the mahe effects of dynamic load are not considered because the structure is
rarely subhis feature of neglecting the dynamic forces may
sometimes become the cause of disaster6 particularly in case of earthqua:e.
Nowadays there is a growing interest in the process of designing !iil -ngineering structures
capable to withstand dynamic loads6 particularly6 earthqua:e induced loads.
STATI! AND DYNAMI! E3UILIRIUM:
>he basic equation of static equilibrium under displacement method of analysis is gien by6
F?e3t@:y
4here6 F?e3t@ is the e3ternal applied static force
: is the stiffness resistance and
y is the resulting displacement
>he resisting force ?:y@ resists the applied force 6 F?e3t@.
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Now6 if the applied static force changes to dynamic force or time arying force the equation of
static equilibrium becomes one of the dynamic equilibrium and has the form
F?>@my=cy=:y
4here6 my is the inertia forces acting in the direction opposite to that of the seismic
motion applied to the base of the structure6 whose magnitude is the mass of the structure times
its acceleration.
cy is the damping force acting in a direction opposite to that of seismic motion.
:y is the restoring force.
#ynamic analysis shall be performed to obtain the design seismic force6 and its distribution to
different leels along the height of the building and to the arious lateral load resisting elements
>he dynamic force may be an earthqua:e force resulting from rapid moement along the plane
of faults within the earth crust. >his sudden moement of the faults releases great energy in the
form of seismic waes6 which are transmitted to the structure through their foundation6 and
causes motion in the structure. >hese motions are comple3 in nature and induced abrupt
hori5ontal and ertical oscillations in structure6 which result accelerations6 elocity and
displacement in the structure. >he induced accelerations generate inertial forces in the structure6
which are proportional to acceleration of the mass and acting opposite to the ground motion.
>he energy produced in the structure by the ground motion is dissipated through internal friction
within the structural and non*structural members. >his dissipation of energy is called damping.
>he restoring forces in the structure is proportional to the deformation induced in the structure
during the seismic e3citation. >he constant of proportionality is referred as stiffness of structure.
INERTIA FOR!ES IN STRU!TURES
-arthqua:e causes sha:ing of the ground. So a building resting on it will e3perience motion at its
base. From NewtonHs First Law of otion6 een though the base of the building moes with the
ground6 the roof has a tendency to stay in its original position. ;ut since the walls and columns
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are connected to it6 they drag the roof along with them. >his is much li:e the situation that you
are faced with when the bus you are standing in suddenly startsC your feet moe with the bus6but
your upper body tends to stay bac: ma:ing you fallbac:wardsOO >his tendency to continue to
remain in the preious position is :nown as inertia. /n the building6 since the walls or columns
are fle3ible6 the motion of the roof is different from that of the ground ?Figure 1@.
!onsider a building whose roof is supported on columns ?Figure 2@. !oming bac: to the
analogy of yourself on the bus when the bus suddenly starts6 you are thrown bac:wards as if
someone has applied a force on the upper body. Similarly6 when the ground moes6 een the
building is thrown bac:wards6 and the roof e3periences a force6 called inertia force. /f the roof
has a mass and e3periences an acceleration a6 then from NewtonHs Second Law of otion6 the
inertia force F/ is mass times acceleration a6 and its direction is opposite to that of the
acceleration. !learly6 more mass means higher inertia force. >herefore6 lighter buildings sustain
the earthqua:e sha:ing better.
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EFFE!T OF DEFORMATIONS IN STRU!TURES:
>he inertia force e3perienced by the roof is transferred to the ground ia the columns6
causing forces in columns. >hese forces generated in the columns can also be understood in
another way. #uring earthqua:e sha:ing6 the columns undergo relatie moement between their
ends. /n Figure 26 this moement is shown as quantity u between the roof and the ground. ;ut6
gien a free option6 columns would li:e to come bac: to the straight ertical position6 i.e.6
columns resist deformations. /n the straight ertical position6 the columns carry no hori5ontal
earthqua:e force through them. ;ut6 when forced to bend6 they deelop internal forces. >he
larger is the relatie hori5ontal displacement 9 between the top and bottom of the column6 the
larger this internal force in columns. Also6 the stiffer the columns are ?i.e.6 bigger is the column
si5e@6 larger is this force. For this reason6 these internal forces in the columns are called stiffness
forces. /n fact6 the stiffness force in a column is the column stiffness times the relatie
displacement between its ends.
FLO OF INERTIA FOR!ES TO FOUNDATION:
9nder hori5ontal sha:ing of the ground6 hori5ontal inertia forces are generated at leel of
the mass of the structure ?usually situated at the floor leels@. >hese lateral inertia forces are
transferred by the floor slab to the walls or columns6 to the foundations6 and finally to the soil
system underneath ?Figure "@.
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Again6 let us go bac: to the rope swings on the tree if you sit at one end of the cradle6 it twists
?i.e.6 moes more on the side you are sitting@. >his also happensP sometimes when more of your
friends bunch together and sit on one side of the swing. Li:ewise6 if the mass on the floor of a
building is more on one side ?for instance6 one side of a building may hae a storage or a
library@6 then that side of the building moes more underground moement ?Figure @. >his
building moes such that its floors displace hori5ontally as well as rotate.
Similarly6 in buildings with unequal ertical members ? i.e.6 columns andBor walls@ also
the floors twist about a ertical a3is ?Figure "b@ and displace hori5ontally. Li:ewise6 buildings6
which hae walls only on two sides ?or one side@ and thin columns along the other6 twist when
sha:en at the ground leel ?Figure "c@. ;uildings that are irregular shapes in plan tend to twist
under earthqua:e sha:ing. For e3ample6 in a propped oerhanging building
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?Figure $@6the oerhanging portion swings on the relatiely slender columns under it.
EFFE!T OF TIST TO UILDING MEMERS:
>wist in buildings6 called torsion by engineers6 ma:es different portions at the same floor leel to
moe hori5ontally by different amounts. >his induces more damage in the columns and walls on
the side that moes more ?Figure %@. any buildings hae been seerely affected by this
e3cessie torsional behaiour during past earthqua:es. /t is best to minimi5e ?if not completely
aoid@ this twist by ensuring that buildings hae symmetry in plan ?i.e.6 uniformly distributed
mass and uniformly placed ertical members@. /f this twist cannot be aoided6 special
calculations need to be done to account for this additional shear forces in the design of buildingsC
the /ndian seismic code ?/S 1)+6 2,,2@ has proisions for such calculations. ;ut6 for sure6
buildings with twist will perform poorly during strong earthqua:e sha:ing.
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EART'3UA"E DESIGN ('ILOSO('Y
EART'3UA"E RESISTANT UILDINGS:
>he engineers do not attempt to ma:e earthqua:e proof buildings that will not get damaged een
during the rare but strong earthqua:eC such buildings will be too robust and also too e3pensie.
/nstead6 the engineering intention is to ma:e buildings earthqua:e resistantC such buildings resist
the effects of ground sha:ing6 although they may get damaged seerely but would not collapse
during the strong earthqua:e. >hus6 safety of people and contents is assured in earthqua:e*
resistant buildings6 and thereby a disaster is aoided. >his is a ma
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>he consequences of damage hae to be :ept in iew in the design philosophy. For e3ample6
important buildings6 li:e hospitals and fire stations6 play a critical role in post*earthqua:e
actiities and must remain functional immediately after the earthqua:e. >hese structures must
sustain ery little damage and should be designed for a higher leel of earthqua:e protection.
!ollapse of dams during earthqua:es can cause flooding in the downstream reaches6 which itself
can be a secondary disaster. >herefore6 dams ?and similarly6 nuclear power plants@ should be
designed for still higher leel of earthqua:e motion.
-arthqua:e*resistant buildings6 particularly their main elements6 need to be built with ductility in
them. Such buildings hae the ability to sway bac:*and*forth during an earthqua:e6 and to
withstand earthqua:e effects with some damage6 but without collapse. #uctility is one of the
most important factors affecting the building performance. >hus6 earthqua:e*resistant design
stries to predetermine the locations where damage ta:es place and then to proide good
detailing at these locations to ensure ductile behaiour of the building.
EART'3UA"E RESISTANT DESIGN OF UILDINGS:
For e3ample6 consider the common urban residential apartment construction D the multi*storey
building made of reinforced concrete. /t consists of hori5ontal and ertical members6 namely
beams and columns. >he seismic inertia forces generated at its floor leels are transferred
through the arious beams and columns to the ground. >he correct building components need to
be made ductile. >he failure of a column can affect the stability of the whole building6 but the
failure of a beam causes locali5ed effect. >herefore6 it is better to ma:e beams to be the ductile
wea: lin:s than columns. >his method of designing ! buildings is called the strong column
wea:*beam design method ?Figure "@.
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;y using the routine design codes ?meant for design against non*earthqua:e effects@6 designers
may not be able to achiee a ductile structure. Special design proisions are required to help
designers improe the ductility of the structure. Such proisions are usually put together in the
form of a special seismic design code6 e.g.6 /S 1+2,*1++ for ! structures. >hese codes also
ensure that adequate ductility is proided in the members where damage is e3pected.
EART'3UA"E EFFE!T ON R! UILDING:
A typical ! building is made of hori5ontal members ?beams and slabs@ and ertical members
?columns and walls@6 and supported by foundations that rest on ground. >he system comprising
of ! columns and connecting beams is called a ! Frame. >he ! frame participates in
resisting the earthqua:e forces. -arthqua:e sha:ing generates inertia forces in the building6
which are proportional to the building mass. Since most of the building mass is present at floor
leels6 earthqua:e*induced inertia forces primarily deelop at the floor leels. >hese forces trael
downwards * through slab and beams to columns and walls6 and then to the foundations from
where they are dispersed to the ground. As inertia forces accumulate downwards from the top of
the building6 the columns and walls at lower storeys e3perience higher earthqua:e*induced
forces ?Figure 1@ and are therefore designed to be stronger than those in storeys aboe.
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Floor slabs are hori5ontal plate*li:e elements6 which facilitate functional use of buildings.
9sually6 beams and slabs at one storey leel are cast together. /n residential multi*storey
buildings6 thic:ness of slabs is only about 11,*1$,mm. 4hen beams bend in the ertical
direction during earthqua:es6 these thin slabs bend along with them ?Figure 2a@. And6 when
beams moe with columns in the hori5ontal direction6 the slab usually forces the beams to moe
together with it. /n most buildings6 the geometric distortion of the slab is negligible in the
hori5ontal planeC this behaiour is :nown as the rigid diaphragm action ?Figure 2b@.
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After columns and floors in a ! building are cast and the concrete hardens6 ertical spaces
between columns and floors are usually filled*in with masonry walls to demarcate a floor area
into functional spaces ?rooms@. Normally6 these masonry walls6 also called infill walls6 are not
connected to surrounding ! columns and beams. 4hen columns receie hori5ontal forces at
floor leels6 they try to moe in the hori5ontal direction6 but masonry walls tend to resist this
moement. #ue to their heay weight and thic:ness6 these walls attract rather large hori5ontal
forces ?Figure @.
7oweer6 since masonry is a brittle material6 these walls deelop crac:s once their ability to
carry hori5ontal load is e3ceeded. >hus6 infill walls act li:e sacrificial fuses in buildingsC they
deelop crac:s under seere ground sha:ing but help share the load of the beams and columnsuntil crac:ing. -arthqua:e performance of infill walls is enhanced by mortars of good strength6
ma:ing proper masonry courses6 and proper pac:ing of gaps between ! frame and masonry
infill walls.
'ORI4ONTAL EART'3UA"E EFFE!T:
Graity loading ?due to self weight and contents@ on buildings causes ! frames to bend
resulting in stretching and shortening at arious locations. >ension is generated at surfaces that
stretch and compression at those that shorten ?Figure "b@. 9nder graity loads6 tension in the
beams is at the bottom surface of the beam in the central location and is at the top surface at the
ends. 8n the other hand6 earthqua:e loading causes tension on beam and column faces at
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locations different from those under graity loading ?Figure "c@C the relatie leels of this tension
?in technical terms6 bending moment@ generated in members are shown in Figure "d. >he leel of
bending moment due to earthqua:e loading depends on seerity of sha:ing and can e3ceed that
due to graity loading. >hus6 under strong earthqua:e sha:ing6 the beam ends can deelop
tension on either of the top and bottom faces. Since concrete cannot carry this tension6 steel bars
are required on both faces of beams to resist reersals of bending moment. Similarly6 steel bars
are required on all faces of columns too.
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STRENGT' 'IERAR!'Y:
For a building to remain safe during earthqua:e sha:ing6 columns ?which receie forces from
beams@ should be stronger than beams6 and foundations ?which receie forces from columns@
should be stronger than columns. Further6 connections between beams E columns and columns
E foundations should not fail so that beams can safely transfer forces to columns and columns to
foundations.
INDIAN SEISMI! DESIGN !ODES
IM(ORTAN!E OF SEISMI! DESIGN !ODES:
Ground ibrations during earthqua:es cause forces and deformations in structures.
Structures need to be designed to withstand such forces and deformations. Seismic codes help to
improe the behaiour of structures so that they may withstand the earthqua:e effects without
significant loss of life and property. !ountries around the world hae procedures outlined in
seismic codes to help design engineers in the planning6 designing6 detailing and constructing of
structures. An earthqua:e resistant building has four irtues in it6 namely
?a@ Good Structural !onfiguration /ts si5e6 shape and structural system carrying loads are such
that they ensure a direct and smooth flow of inertia forces to
the ground.
?b@ Lateral Strength >he ma3imum lateral ?hori5ontal@ force that it can resist is such that the
damage induced in it does not result in collapse.
?c@ Adequate Stiffness /ts lateral load resisting system is such that the earthqua:e induced
deformations in it do not damage its contents under low*to moderate sha:ing.
?d@ Good #uctility /ts capacity to undergo large deformations under seere earthqua:e sha:ing
een after yielding6 is improed by faourable design and detailing strategies. Seismic codes
coer all these aspects.
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INDIAN SEISMI! !ODES:
Seismic codes are unique to a particular region or country. >hey ta:e into account the local
seismology6 accepted leel of seismic ris:6 building typologies6 and materials and methods used
in construction. Further6 they are indicatie of the leel of progress a country has made in the
field of earthqua:e engineering.
>he first formal seismic code in /ndia6 namely /S 1)+6 was published in 1+%2. >oday6 the
;ureau of /ndian Standards ?;/S@ has the following seismic codes
/S 1)+ ?&art /@6 2,,26 /ndian Standard !riteria for -arthqua:e esistant #esign of Structures
?$th eision@
/S "2%6 1++6 /ndian Standard !ode of &ractice for -arthqua:e esistant #esign and
!onstruction of ;uildings ?2nd eision@
/S 1)2(6 1++6 /ndian Standard Guidelines for /mproing -arthqua:e esistance of -arthen
;uildings
/S 1)2)6 1++6 /ndian Standard Guidelines for /mproing -arthqua:e esistance of Low
Strength asonry ;uildings
/S 1+2,6 1++6 /ndian Standard !ode of &ractice for #uctile #etailing of einforced !oncrete
Structures Subhe regulations in these standards do not ensure that structures suffer no damage during
earthqua:e of all magnitudes. ;ut6 to the e3tent possible6 they ensure that structures are able to
respond to earthqua:e sha:ings of moderate intensities without structural damage and of heay
intensities without total collapse.
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/S 1)+
/S 1)+ is the main code that proides the seismic 5one map ?Figure 1@ and specifies
seismic design force. >his force depends on the mass and seismic coefficient of the structureC the
latter in turn depends on properties li:e seismic 5one in which structure lies6 importance of the
structure6 its stiffness6 the soil on which it rests6 and its ductility.
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!'A(TER-I/
!ASE STUDY
>he Layout of plan haing "" . >he buildings considered are einforced concrete ordinary
moment resisting space frames of 11storey symmetric . Stiffness of the infill is neglected in order
to account the Nonlinear ;ehaior of Seismic demands. All these buildings has been analy5ed by
Seismic coefficient method. >he storey height is :ept uniform of m for all :ind of building
models which are as below. >he analysis illustrates the step*by*step procedure for determination
of forces.
>able ".1 Assumed &reliminary data required for the Analysis of the frame
Grid slab
Sl0*% /ariable Da+a
1 >ype of structure oment esisting Frame
2 Number of Stories 11
Floor height m
" Lie Load ., :NBm2
$ #ead load 1., :NBm2 and wall load of 12JNBm
% aterials!oncrete ?2,@ and einforced with 7IS# bars
?Fe"1$@
(
Si5e of !olumns
$,,$,, mm
) Si5e of ;eams
,,32,mm
+ #epth of slab 1$,mm thic:
1, Specific weight of !! 2$ :NBm
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11 Qone //
12 /mportance Factor 1
1 esponse eduction Factor $
1" >ype of soil edium
Flat slab
Sl0*% /ariable Da+a
1 >ype of structure oment esisting Frame
2 Number of Stories 11
Floor height m
" Lie Load ., :NBm2
$ #ead load 1., :NBm2 and wallload of 1$JNBm
% aterials!oncrete ?2,@ and einforced with 7IS# bars
?Fe"1$@
(
Si5e of !olumns
$,,$,, mm
) Si5e of ;eams
,,32, mm
+
#epth of slab
>hic:ness of #rop
1$,mm thic:
2,,mm thic:
1, Specific weight of !! 2$ :NBm
11 Qone //
12 /mportance Factor 1
1 esponse eduction Factor $
1" >ype of soil edium
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Grid Slab plan iew
Flat Slab plan iew
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Grid Slab *# 'iew
Flat Slab *# 'iew
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Grid Slab -leation iew
Flat Slab -leation iew
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-leation and *# iew of Grid slab
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Figure. ".) Geometry of the structure and also the sections assigned.
502 DATA !OLLE!TION
>he building models are 11 storeyHs located in 5one //. >ables "., and >able ".2present asummary of the building parameters.
>able ".2 General data collection and condition assessment of building
Sl.No
.#escription /nformation
emar:s
1
;uilding height
a 11*storey m /ncluding the
foundation leel
2Number of basements below
ground,
****
8pen ground storey Ies ****
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" Special ha5ards None ****
$ >ype of buildingegularB/rregula
r Space frames
/S 1)+2,,2
!lause (.1
% 7ori5ontal floor system ;eams and slabs ****
( Software used -tabs2,1 ****
50 ANALYSIS MET'ODS
Analysis methods are broadly classified as linear static6 linear dynamic6 nonlinear static and
nonlinear dynamic methods. #uring earthqua:e loads the structural loading will reach to collapse
load and the material stresses will be aboe yield stresses. so in that case material nonlinearity
and geometric nonlinearity should be incorporated into the analysis to get better results. >hese
methods also proide information on the strength6 deformation and ductility of the structures as
well as distribution of demands.
5001 E6ui7ale*+ S+a+i, Me+h%&
-quialent static method of analysis is a linear static procedure6 in which the response of
building is assumed as linearly elastic manner. >he analysis is carried out as per /S1)+*2,,2
?&art "@.
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Grid and Flat slab load patterns
Figure ".12 /llustrates the -quialent static graityE lateral loads Applied on the Structure0
Flat and Grid slab seismic load patterns
Figure ".1 /llustrates the lateral static Load -q 3.
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Grid and Flat slab 4ind load
Figure ".1" /llustrates the use of seismic weight as mass source and the mass lumped at each
storey leel.
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Figure ".1% odal load case set to calculate the mode shapes.
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Figure ".1( Load cases set to perform the linear static analysis.
!'A(TER-/
RESULTS AND DIS!USSIONS
>he esults obtained are of different parameters such as Storey drifts6 ;ase shear 6odal &eriod 6
Shear force6 moments6 lateral loads6A3ial loads6 shear storey8
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0 2 4 6 8 10 12 140
0
0
0
0
0
0
Maximum story Drifts in EQX
Flat slab
Grid slab
Story level
Drifts
Figure $.1 Storey #rifts in *#irection comparison for Flat and Grid Slabs.
0 2 4 6 8 10 120
10
20
30
40
Shear forces in Exterior columns
Flat slab
Grid slab
Story level
Shear
Figure $.2 Shear force comparison for Flat and Grid Slabs for e3terior column.
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0 2 4 6 8 10 120
10
20
30
40
50
60
70
Shear forces in Interior columns
Flat slab
Grid slab
Story level
Shear
Figure $. Shear force comparison for Flat and Grid slabs for interior column.
0 2 4 6 8 10 120
10
2030
40
50
60
70
Moments in Exterior columns
Flat slab
Grid slab
Story level
Monents
Figure $." oment force comparison for Flat and Grid slabs for e3terior column.
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0 2 4 6 8 10 12
-15
-10
-5
0
5
10
15
Moments in Interior columns
Flat slab
Grid slab
Story level
Monents
Figure $.$ oment force comparison for Flat and Grid slabs for interior column.
0 2 4 6 8 10 120
500
1000
1500
2000
Axial force in Exterior columns
Flat slab
Grid slab
Story level
AXial force
Figure $.% A3ial force comparison for Flat and Grid slabs for e3terior column.
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0 2 4 6 8 10 120
500
1000
1500
2000
2500
Axial force in Interior columns
Flat slab
Grid slab
Story level
AXial force
Figure $.( A3ial force comparison for Flat and Grid slabs for interior column.
0 2 4 6 8 10 12 14
-120
-100
-80
-60
-40
-20
0
Shear story in EQX
Flat slab
Grid slab
Story level
Shear
Figure $.) Shear Storey in *#irection comparison for Flat and Grid slabs.
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0 2 4 6 8 10 12 140
5
10
15
20
25
30
Lateral loads in EQX
Flat slab
Grid slab
Story level
Loads
Figure $.+ Lateral load in *#irection comparison for Flat and Grid slabs.
0 2 4 6 8 10 12 140
5
1015
20
25
30
Lateral load in EQX
Flat slab
Grid slab
Story level
Lateral load
Figure $.+ Lateral load to story comparison for Flat and Grid slabs.
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0 2 4 6 8 10 12 140
5
10
15
20
Displacement for diaphragm in EQX
Flat slab
Grid slab
Story level
load
Figure $.+ #isplacements for diaphragm comparison for Flat and Grid slabs.
0 2 4 6 8 10 12 140
0.5
11.5
2
2.5
3
Modal Periods and freuency
Flat slab
Grid slab
Modal
!ime
Figure $.+ odal &eriods and frequency comparison for Flat and Grid slabs.
!%lu9* Desig*
!olumn si5e $,,3$,,
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fc: 2, NBmm2
fy "1$ NBmm2
A3ial load of the column6 &u 1$2).)(% JN
Self weight of column ,.$,3,.$,32$
%.2$ 3 ?ht. of column@
1).($ JN
Factor of safety 1.$31).($
2).12$ JN
>otal load 1$2).)(%=2).12$
1$$( JN
-ffectie length of the column ,.),3l
,.),3*,.2T
2.21%m
221%mm
Mi*i9u9 e,,e*+ri,i+#:
-ccentricity in 3* direction LB$,,=#B,
,,,B$,,=$,,B,
22.%(mm
,.,2m
oment due to eccentricity
oment about 3*a3is 3 &ue3
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1$2).)(%3,.,2
$.1%" JNm
oment about y*a3is y &uey
1$2).)(%3,.,2
$.1%" JNm
!he, %r sle*&er*ess ra+i%:
Le3B# 221%B$,, "."2 U 12
LeyB# 221%B$,, "."2 U 12
So6 design column as short column
>otal design moment6 3 e3=a3
$.1%" JNm
>otal design moment6 y ey=ay
$.1%" JNm
Desig* % i-a;ial be*&i*g ,%lu9*:
? &uBfc:b #@ ?1$2).)(%31,,,@B?2,3$,,3$,,@
,.,%
?&uBfc:@ 1B2, ,.,$
Assuming 2,mm bar
Area of 2,mm bar ast B" 32,2 1".1%mm
-ffectie coer for column ",mm
-ffectie coer = dB2 ",=2,B2
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+,,
&u5 2.$,,31,%N
2$,, JN
Substitute &u5in
,.%%(=1.%%( &uB&u5
,.%%(=1.%%( ?1$2).)(%31,,,@B?2$,,31,,,@
1.%+
Substitute this alue in aboe equation
?u3Bu31@=? uyBuy1@
1.,
?$.1%"B22$@1.%+=?$.1%"B22$@1.%+1.,
,.,)%1.,
7ence Safe.
AstBast+,,B?B"3122@
(.+%
No. of bars are )
ea9 Desig*
;eam si5e ,,32,
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fc: 2, NBmm2
fy "1$NBmm2
#ead load of slab ,.1$ 3 2$ .($ JNBm2
Lie load
Floor finished load 1
>otal load (.($
Slab load (.($31.$
11.%2$ JNBm2
4all load ?*,.2@31)3,.2
+.+(
Self weight of beam ,.3,.232$
1.(2$JN
>otal load 2.2 JNBm
For shorter beam wl3B
2.23$B
).)(JNm
a3imum bending moment wl2B12
u ).)(3$2B12
),.+(JNm
Shear force wlB2
).)(3$B2
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!he, %r shear rei*%r,e9e*+ :
Nominal shear reinforcement 6 'uBbd
?+(.1($31,,,@B?,,32,@
1."1 JN
&ermissible shear stress 6uBbd2 1
&t 1,,AstBbd
1,,3)3B"3122B,,32,
1.1M
For &t 1.1M E fc: 2, NBmm2
From /S "$%
c ,.%)2
R c
7ence shear reinforcement should be designed
#esign for shear reinforcement 6 'u 'uc='us
'uc cbd
,.%)23,,32,
"(,$) N
"(.,%JN
;y using S&*1%
'us 'uD'uc
+(.1($*"(.,%
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$,.12 JN
Spacing for stirrups 'usBd
$,.12B?B"3)2@
,.++(
From S&*1%6 for 'us E ,.++( we get the spacing as follows
So6 &roide 2 legged )mm bars spacing of 2,,mm !B!
Slab Desig*
l3 $m
ly $m
l3Bly$B$1U2
#esign two way slab
fc3 2, NBmm2
fy "1$ NBmm2
From /S "$% 6 # lB$3,.)
# effectie shorter spanB$3,.)
-ffectie coer ,.2
-ffectie shorter span $=,.2B2=,.2B2
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From /S "$%6
uBd ,.")
From S&*1%6
uBfc:bd2 ,.1)
22.%B2,31,,,3d2,.1)
d +,mm
&roide oerall depth ?#@ +,=1$=1,B2
11,mm
So6 proide oer all depth of 1$,mm
Ast required in shorter direction
u3Bbd2 22.%31,%B1,,,31,2 1."JNBmm2
From S&*1%6
&t ,.$)" for u3Bbd2 1." JNBmm2
&t 1,,AstBbd2
Ast &t31,,,31,B1,,
,.$)"31,,,31,B1,,
($+mm
Dis+ribu+i%* s+eel:
inimum steel ,.12bdB1,,
,.1231,,,31,B1,,
1$% mm2
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Spacing astBAst31,,,
?B"3)2B($+@31,,,
%%.2mm
($mm
So6 proide )mm bars V ($mm !B!
As+i* l%*ger &ire,+i%* :
uyBbd2 22.%31,%B1,,,31,2
1."NBmm
2
From S&*1% 6
&t ,.$)" for uyBbd2 1." NBmm2
Ast &t31,,,31,B1,,
,.$)"31,,,31,B1,, ($+mm
inimum steel ,.1231,,,31,B1,,
1$%mm2
Spacing astBAst31,,,
?B"3)2B($+@31,,,
%%.2mm
($mm
So6 proide )mm bars V ($mm !B!
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F%%+i*g Desig*
A3ial load & 1$2).)(% JN
Self weight of footing 1$2).)(%B1,
1$2.))(%JNBm2
>otal load 1%)1.(%JNBm2
Soil bearing capacity ?S;!@ 1),JNBm2
Area of footing total loadBS;!
1%)1.(%B1),
+."m2
l .,%m 6 b .,%m
Soil reaction for the factored load6 qu 1.$&B;3;
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1.$31$2).)(%B.,%3.,%
2"".+2JNBm2
,.2"$ JNBm2
Dep+h % %%+i*g :
!onsideration of shear6 depth of the footing should be proided.
!onsidering a section 3*3 V a distance d from face of the column
'u soil pressure from shaded area
qu;?;*bB2*d@
,.2"$3,%,?,%,*,,B2*d@
("+.(?1),*d@
Assuming ,.2M steel 6 for 2,grade of concrete
c ,.+" NBmm2
inimum depth required cbd
,.+"3,%,3d ("+.(?1),*d@
d $2+mm
&roide %,,mm
!he, %r be*&i*g :
ulimit ,.%fc:;3ulimit?d*,."23ulimit@
,.%fc:;3ulimitBd?1*,."23ulimitBd@d2
ulimitBd ,.")
ulimit ,.1)fc:bd2
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,.1)32,3,%,3%,,2
,",."231,%N*mm
u qu;?;*b@2B)
,.2"$3,%,?,%,*,,@2B)
(1.)%31,%N*mm
uU ulimit
So6 proide depth is safe.
!he, %r +$% $a# shear :
!ritical section is at a distance dB2 from the face of column
&erimeter of critical section "?b=d@
"?,,=%,,@
%,,mm
Area of critical section %,,3d %,,3%,,
21%,,,,mm2
>wo way shear stress upward pressure in shaded areaBArea of critical section
qu;3;*W?b=d@?b=d@XTBArea of critical section
,.2"$? ,%,3,%,@*?+,,3+,,@B%,,3%,,
,.+(,2NBmm2
a3imum shear stress permitted ,.2$fc:
1.11)NBmm2R ,.+(,2NBmm2
7ence safe in shear.
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As+re6uire& :
u ,.)(fyAstd1*?AstfyB;3d3fc:@T
(1.)% 31,% ,.)(3"1$3Ast3%,,1*?Ast3"1$B,%,3%,,32,@T
""+$,(2.$Ast2D .+((2%)31,11= 1.1,%"%+%31,1$ ,
Ast "2) mm2
9sing 2, mm bar
No. of bars AstBast
"2)BB"32,2
1"
Spacing ?B"32,2B"2)@31,,,
(".2mm
&roide 2, mm bars V $,mm !B!
&tproided ?B"32,2B$,3%,,@31,,
,.)$
cfrom /S "$%6
c ,.$)"
'uBbd ,.2"$3,%,W?,%,*,,B2@*%,,XB,%,3%,,
,.1)$
U c
7ence shear reinforcement is safe.
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Seis9i, Resp%*se Spe,+ru9
7eight between the floor m
Lie load JNBm2
#ead load 1JNBm2
Floor finish 1JNBm2
4eight of the partition load 2 JN
!olumn si5e $,,3$,,
fc: 2, NBmm2
fy "1$ NBmm2
Slab thic:ness ,.1$m
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;eam ,.3,.2
Area 1$31$
22$ m2
!alculation of beam ,.3,.232$
1.(2$JN
>otal length of the beam ?1$31$@31.(2$
)).12$JNm2
!olumn ,.$3,.$32$
%.2$JN
>otal length of the column 1%33%.2$
,,JNm2
Slab ,.1$32$ .($JNBm
>otal length of slab .($31$31$
)".($JNm
4all load >otal length of the wall 3 thic:ness 3 story height 3 unit weight of
asonary.
?$31$=$31%@3,.2,332,
1)%,JN
Load on the floor self weight of the slab=floor finish=2$M of imposed load=wall
load =dead load
/mposed load ,.2$
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1=1=,.2$3
2.($JNBm2
)".($=,,=)).12$=1)%,=?2.($322$@
",1,.%2$JN
oof slab load=1B2column load=1B2wall load
)".($=,,B2=1)%,B2
1+2.($JN
>otal seismic load of the building ?",1,.%2$31,@= 1+2.($
"2,,JN
Fu*&a9e*+al *a+ural peri%&=Ta> :
/t is the first modal time period of ibration of the structure
>a ,.,($h,.($ for !! frame structures 6 without bric: infill
>a ,.,)$h,.($ for steel structures6 without bric: infill
>a ,.,+hBd with infill
4here h height of the building
d base dimension of the building
>a ,.,+3311B1$
,.(%( sec
7ori5ontal seismic coefficient6 Ah Q / SaB23g
SaBg 1.%B>
1(.(
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Qone factor6 Q ,.1, for Qone //
/mportant factor6 / 1
esponse reduction factor6 $
Ah ,.1,3131(.(B23$
,.1((
;ase shear Ah3total seismic weight
,.1((3"2,,
("$1.+1+ JN
ass No. 4i JN 7 m 4ih2
4ih2B4ih2 0';34ih2B4i
h2
1 1+2.($ 2,+"+%.($ ,.1(1+ ++%."%2(,,+
2 ",1,.%2$ , %,+$%2.$ ,.2,+" 1(1%.)(%%($
",1,.%2$ 2( 2+2("$.%2$ ,.1)%%2 1+,.%(,1,(
" ",1,.%2$ 2" 21,12, ,.1"("$21 1,+).),1,(2
$ ",1,.%2$ 21 1(%)%)$.%2$ ,.112)+,1,% )"1.2%+$(,+
% ",1,.%2$ 1) 12++""2.$ ,.,)2+"2 %1).,($%,1
( ",1,.%2$ 1$ +,2+,.%2$ ,.,$($+)$ "2+.21+1%))
) ",1,.%2$ 12 $(($, ,.,%)%, 2(".(,,2%)
+ ",1,.%2$ % 1"")2.$ +.21$(%31,* %).%($,%(,1
1, ",1,.%2$ %,+$.%2$ 2.,+"31,* 1(.1%)(%%($
11 ",1,.%2$ *** , , ,
>otal 1$%%%+1).($
Flat slab
!%lu9* Desig*
!olumn si5e $,,3$,,
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fc: 2, NBmm2
fy "1$ NBmm2
A3ial load of the column6 &u 1%1,.",1 JN
Self weight of column ,.$,3,.$,32$
%.2$ 3 ?ht. of column@
1).($ JN
Factor of safety 1.$31).($
2).12$ JN
>otal load 1%1,.",1=2).12$
1%)."(JN
-ffectie length of the column ,.),3l
,.),3*,.2T
2.21%m
221%mm
Mi*i9u9 e,,e*+ri,i+#:
-ccentricity in 3* direction LB$,,=#B,
,,,B$,,=$,,B,
22.%(mm
,.,2m
oment due to eccentricity
oment about 3*a3is 3 &ue3
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1%1,.",13,.,2
(.," JNm
oment about y*a3is y &uey
1%1,.",13,.,2
(.," JNm
!he, %r sle*&er*ess ra+i%:
Le3B# 221%B$,, "."2 U 12
LeyB# 221%B$,, "."2 U 12
So6 design column as short column
>otal design moment6 3 e3=a3
(.," JNm
>otal design moment6 y ey=ay
(.," JNm
Desig* % i-a;ial be*&i*g ,%lu9*:
? &uBfc:b #@ ?1%1,.",131,,,@B?2,3$,,3$,,@
,.22
?&uBfc:@ 1B2, ,.,$
Assuming 2,mm bar
Area of 2,mm bar ast B" 32,2 1".1%mm
-ffectie coer for column ",mm
-ffectie coer = dB2 ",=2,B2
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d1 $,mm
d1B# $,B$,, ,.1
d1Bb $,B$,, ,.1
From S&*1% 6
d1B# ,.1
!onsidering d1B# ,.2, 6 fc:2, NBmm26 fy"1$ NBmm
26?uB fc:b #@ ,.,+
u ,.,+32,3$,,3$,,2
22$31,%Nmm
22$ JNm
u3 22$ JNm
uy 22$ JNm
!he, %r i-a;ial be*&i*g :
From /.S. "$%
?u3Bu31@=? uyBuy1@
1.,
?,.%%(=1.%%( &uB&u5@
&u5 ,."$fc:Ac= ,.%(fyAs
,."$32,3$,,3$,,=,.%(3"1$3+,,
2.$,,31,%
JN
Assuming 1M of bar
&t 1,, AstBbd
Ast 13$,,3$,,B1,,
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+,, mm2
&u5 2.$,,31,%N
2$,, JN
Substitute &u5in
,.%%(=1.%%( &uB&u5
,.%%(=1.%%( ?1%1,.",131,,,@B?2$,,31,,,@
1.("
Substitute this alue in aboe equation
?u3Bu31@=? uyBuy1@
1.,
?(.,"B22$@1.("=?(.,"B22$@1.("1.,
,.,)%%1.,
7ence Safe.
AstBast+,,B?B"3122@
(.+%
No. of bars are )
ea9 Desig*
;eam si5e ,,32,
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+(.1($ JN
!he, %r ee,+i7e &ep+h:
u ,.1)fc:bd2
-ffectie depth of the beam6 d ?),.+(31,%B,.1)32,3,,@
12.(1mm
8er all depth # d=coer=?dB2@
12.(1=2$=?1%B2@
< "$.(1mm
So6 proide ,,3$, mm
uBbd2 ),.+(31,%B,,32,2
$.1,NBmm2
From S&*1%6
For uBbd2 $.1,Nmm6 fc: 2,NBmm
26 fy "1$NBmm2
&t ,.+M
Ast &t3bdB1,,
Ast ?,.+3,,3$,@B1,,
+"$ mm2
&roide 12mm bars
No of bars AstBast +"$BB"3122
).%
) bars of 12 mm is proided
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$,.12 JN
Spacing for stirrups 'usBd
$,.12B?B"3)2@
,.++(
From S&*1%6 for 'us E ,.++( we get the spacing as follows
So6 &roide 2 legged )mm bars spacing of 2,,mm !B!
la+Slab Desig*
/nterior panel $3$m
Lie load JN
Floor finished load 1 JN
fc: 2,NBmm2
fy "1$NBmm2
!olumn si5e $,,3$,,
Thi,*ess % slab :
>hic:ness of slab ",6 if mild steel
26 if fy"1$ or fy$,,
>hic:ness of slab6 d spanB2
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$,,,B2
d 1%,mm
>a:e coer as ",mm
d 1%,=1$, 1,mm
# d=", 2,,mm
#rop 1B3span
1B3$
1.%)m
&roide drop of 2m32m
&roide a drop of 1$,mm thic:
>otal thic:ness slab=drop
# 2,,=1$,
$,mm
Self weight of slab ,.$32$
).($ JNBm2
Floor finished load 1 JNBm2
Lie load JNBm2
>otal load ).($=1= 12.($ JNBm2
#esign factored load6 4u 1.$312.($ 1+.12$ JNBm2
!lear span $*,.$ ".$m
#esign load6 4o 4u3le3l3
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1+.12$3$3".$
4o ",.1JN
#esign total moment6 o 4l3B)
",.13".$B)
2"2.,$ JNm
Negatie design moment ,.%$3o
&ositie design moment ,.$3o
>otal negatie moment ,.%$32"2.,$
1$(.2$JNm
>otal positie moment ,.$32"2.,$
)".(1JNm
4idth of column strip width of middle strip 2,,,mm 2m
!olumn strip iddle strip
Negatie moment ,.($31$(. 11(.+JNm ,.2$31$(. +.JNm
&ositie moment ,.%,3)".(1 $,.)2%JNm ,."3)".(1 .))JNm
ulimit ,.1)fc:bd2
,.1)32,32,,,31,2
$,."(231,%Nmm
$, JNm
ulimit $, JNm
u 2"2JNm
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ulimit R u
7ence thic:ness is safe and sufficient.
!he, %r shear :
!ritical section is at distance dB2 1,B2 1$$mm
/t is square in si5e column si5e =1$$=1$$
$,,=1$$=1$$
)1,mm
' >otal load D 4o3,.)1,3,.)1,
1+.12$3$3$ D 1+.12$3,.)1,3,.)1,
"%$.$JN
Nominal shear6 "%$.$31,,,B"3)1,31,
,."% NBmm2
Shear strength Jsc
Js ,.$=c
c L1BL2 $B$ 1
Js 1
c ,.2$fc: ,.2$2, 1.11)NBmm2
cR
7ence slab is safe in shear.
Rei*%r,e9e*+ :
F%r *ega+i7e 9%9e*+ i* ,%lu9* s+rip :
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u 11(.+JNm
d 1,mm
u ,.)(fyAstd1*AstfyBbdfc:T
11(.+31,% ,.)(3"1$3Ast31,1*Ast3"1$B2,,,31,32,T
111+2$.$ Ast1* AstB2+)(+.$T
Ast 1,+.,mm2
4idth 2,,,mm
9sing 12mm bar spacing requirement is
S ?B"3122B1,+@32,,,
2,%.+"mm
&roide 12mm bars at 2,, mm !B!.
F%r p%si+i7e 9%9e*+ ,%lu9* s+rip :
u $,.)231,%JNmm
d 1%,mm
u ,.)(fyAstd1*AstfyBbdfc:T
$,.)231,% ,.)(3"1$3Ast31%,1*Ast3"1$B2,,,31%,32,T
$((%) Ast1 D 2,.($AstB2,,,,T
Ast +(mm2
9sing 1,mm bar spacing requirement is
S ?B"31,2B+(@32,,,
1%(.(1mm
&roide 12mm bars at 1$, mm !B!.
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F%r *ega+i7e 9%9e*+ i* 9i&&le s+rip :
u +.JNm
d 1%,mm
u ,.)(fyAstd1*AstfyBbdfc:T
+.31,% ,.)(3"1$3Ast31%,1*Ast3"1$B2,,,31%,32,T
$((%) Ast1* 2,.($AstB2,,,,T
Ast (1mm2
4idth 2,,,mm
9sing 1,mm bar spacing requirement is
S ?B"31,2B(1@32,,,
22,.mm
&roide 1,mm bars at 2,, mm !B!.
F%r p%si+i7e 9%9e*+ 9i&&le s+rip :
u .))31,%JNmm
d 1%,mm
u ,.)(fyAstd1*AstfyBbdfc:T
.))31,% ,.)(3"1$3Ast31%,1*Ast3"1$B2,,,31%,32,T
$((%)Ast1 D 2,.($AstB2,,,,T
Ast %1,mm2
9sing 1,mm bar spacing requirement is
S ?B"31,2B%1,@32,,,
2$(.$mm
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&roide 12mm bars at 2$, mm !B!.
F%%+i*g Desig*
A3ial load & 1%1,." JN
Self weight of footing 1%1,.",1B1,
1%1.,"JNBm2
>otal load 1((1.(JNBm2
Soil bearing capacity ?S;!@ 1),JNBm2
Area of footing total loadBS;!
1((1.(B1),
+.)"m2
l .1"m 6 b .1"m
Soil reaction for the factored load6 qu 1.$&B;3;
1.$31%1,.,",1B.,%3.,%
2$(.+2JNBm2
,.2$(JNBm2
#epth of footing
!onsideration of shear6 depth of the footing should be proided.
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!onsidering a section 3*3 at a distance d from face of the column
'u soil pressure from shaded area
qu;?;*bB2*d@
,.2$(3,%,?,%,*,,B2*d@
()%."2?1),*d@
Assuming ,.2M steel 6 for 2,grade of concrete
c ,.+"NBmm2
inimum depth required cbd
,.+3,%,3d ()%."2?1),*d@
d $"$mm
&roide %,,mm
!he, %r be*&i*g :
ulimit ,.%fc:;3ulimit?d*,."23ulimit@
,.%fc:;3ulimitBd?1*,."23ulimitBd@d2
ulimitBd ,.")
ulimit ,.1)fc:bd2
,.1)32,3,%,3%,,2
,",."231,%
N*mm
u qu;?;*b@2B)
,.2$(3,%,?,%,*,,@2B)
(").)31,%N*mm
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uU ulimit
So6 proide depth is safe.
!he, %r +$% $a# shear :
!ritical section is at a distance dB2 from the face of column
&erimeter of critical section "?b=d@
"?,,=%,,@
%,,mm
Area of critical section %,,3d %,,3%,,
21%,,,,mm2
>wo way shear stress upward pressure in shaded areaBArea of critical section
qu;3;*W?b=d@?b=d@XTBArea of critical section
,.2$(? ,%,3,%,@*?+,,3+,,@TB%,,3%,,
1.,2NBmm
2
a3imum shear stress permitted ,.2$fc:
1.11)NBmm2R 1.,2NBmm2
7ence shear is safe.
As+re6uire& :
u ,.)(fyAstd1*?AstfyB;3d3fc:@T
(").)31,% ,.)(3"1$3Ast3%,,1*?Ast3"1$B,%,3%,,32,@T
""+$,(2.$Ast2D .+((2%)31,11= 1.(")$1))31,1$ ,
Ast %, mm2
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9sing 2, mm bar
No. of bars AstBast
%,BB"32,2
12
Spacing ?B"32,2B%,@31,,,
(,.%2mm
&roide 2, mm bars V $,mm !B!
&tproided ?B"32,2B$,3%,,@31,,
,.)$
cfrom /S "$%6
c ,.$)"JNBmm2
'uBbd ,.2$(3,%,W?,%,*,,B2@*%,,XB,%,3%,,
,."1JNBmm2
U c
7ence shear reinforcement is safe.
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!ON!LUSIONS !'A(TER-/I
?01 !ON!LUSIONS
>he choice of the system for slab in the tall building is ery important toresist the internal forces and stability
;ase shear of flat slab building is less than the base shear in grid slab building in both
and I* directions.
A3ial force in end columns of flat slab building is less as compared to grid slab building
A3ial force in intermediate columns of flat slab building is same as compared to grid
slab building.
;uilding drift in grid slab building is less as compared to flat slab buildingin each story in both and I*directions.
>he natural time period increases as the height of building ? No. of stories@increases6 irrespectie of type of building i5. conentional structure6 flat slabstructure
/n comparison of the conentional .!. building to flat slab building6 the timeperiod is less for conentional building than flat slab building because of
monolithic construction.
Story drift in buildings with flat slab construction is significantly more ascompared to conentional .!.! building. As a result of this6 additional momentsare deeloped. >herefore6 the columns of such buildings should be designed byconsidering additional moment caused by the drift.
Shear force in e3terior and interior column in flat slab is more compared to gridslab.
oment in e3terior column in flat slab is more compared to grid slab.
oment in interior column in flat slab is less compared to grid slab.
Lateral loads in -0 are less in flat slab compared to grid slab
Shear story in -0 are more in flat slab compared to grid slab.
#isplacement of diaphragm is more in flat slab compared to grid slab.
?02 S!O(E FOR FURT'ER STUDY
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NON LINEAR STATI !"S#O$ER ANAL%SIS &'r (at a)d *rid slab. A)al+ti,al Ar'a, t' St/d+ E,t '& Sar all ') Flat Slab Grid Slab . 'arati St/d+ '& R a)d !rstrssd '),rt Flat Slabs.
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REFEREN!ES
si*) '& Ri)&'r,d '),rt Str/,t/rs b+ A. . ai)
Ill/stratd dsi*) '& ri)&'r,d ,'),rt b/ildi)*s b+ r.$.L. Sa
r.S.R.ar
9asi, !ri),ils '& A)al+sis a)d si*) '& a) R Frad Str/,t/rs byProf. H. R.
Surya Prakash S. Krishna Murthy
si*) '& R.. str/,t/ral l)ts b+ S.S. 9ai:atti
si*) '& R.. slabs b+ ..ai)
R.. si*) a)d ra;i)* b+ Nla Sara
Tras/r '& R.. si*)s b+ S/sil :/ar
si*) '& R.. str/,t/rs b+ r'&.N.ris)a Ra
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/S 1)+?part*1@ 2,,2 criteria for earthqua:e resistant design of structures &art*1 general
proision E buildings !riteria for -arthqua:e esistant #esign of Structures &art 1 General &roisions and
;uildings ?Fifth eision@ /S 1)+?part1@2,,2.
/ndian standard Y&lain E einforced !oncrete !ode of &racticeZ Fourth eision /S"$%2,,,.
#uctile #etailing of einforced !oncrete Structures to Seismic Forces /S 1+2,1++ $T
.Anitha6 ;.0.ahman6 [[.'i
