INFORMATION TO USERS This manuscript has been reproduced trom the microfilm master. UMI films the text directJy tram the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. ln the unlikely event that the author did not send UMf a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing trom left to right in equal sections with small overlaps. ProQuest Information and leaming 300 North Zeeb Road, Ann Arbor, MI 48106-1346 USA 800-521-0600
Transcript
INFORMATION TO USERS
This manuscript has been reproduced trom the microfilm master. UMI films
the text directJy tram the original or copy submitted. Thus, some thesis and
dissertation copies are in typewriter face, while others may be from any type of
computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality illustrations
and photographs, print bleedthrough, substandard margins, and improper
alignment can adversely affect reproduction.
ln the unlikely event that the author did not send UMf a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand corner and continuing
trom left to right in equal sections with small overlaps.
ProQuest Information and leaming300 North Zeeb Road, Ann Arbor, MI 48106-1346 USA
800-521-0600
NOTE TO USERS
Page (s) not included in the original manuscript isunavailable trom the author or university. The
manuscript was microfilmed as received.
Pg 10-15 in Chapter 10
This reproduction is the best copy available.
UMIe
AN APPROACH TO SEISMIC DESIGN OFECCENTRICALLY BRACED FRAMES
by
Sanda Koboevic
A Thesis Submitted ta the Faculty of Graduate 5tudies and Researchin Partial Fulfilment of the Requirements of the Degree of Dactar af Philasophy
Department of Civil Engineering and Applied MechanicsMcGill University, Montreal, Canada
May, 2000
(Ç)Sanda Koboevic, 2000
1+1 National Ubraryof Canada
Acquisitions andBibliographie Services385 Welinglon Street0IIawa ON K1A 0N4C8nadIl
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The author retains ownership ofthecopyright in this thesis. Neither thethesis nor substantial extracts from itMaY he printed or otherwisereproduced witbout the author'spermission.
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L'autem conserve la propriété dudroit d'auteur qui protège cette thèse.Ni la thèse ni des extraits substantielsde celle-ci ne doivent être imprimésou autrement reproduits sans sonautorisation.
7.2.1 Deve10pment and application of the proposed design procedure 7-2
7.2.2 Study of EBF seismic behaviour using developed analytical tooIs 7-4
7.2.2.1 Proposed modifications of EBF design requirements in
CSA/CAN S16-1 7-4
7.2.2.2 Distribution of the lateral force 7-4
7.2.2.3 A..cial forces and moments for ductility design of columns 7-5
7.2.2.4 Seismic force reduction factors 7-5
7.2.2.5 Relationship between inelastic Ïnter-storey drift and
inelastic ün.k rotation 7-6
7.3 Concluding comments and recommendations for future work 7-6
7.4 Original conttlDutioQS 7-8
8. REFERENCES 8-1
9. APPENDIX A 9-1
10. APPENDIX B 10-1
xi
UST OF SYMBOLS• iiliiiiiii iiliiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii_..-liiiiiiiiiiiiiiiiliiiiiii_
A
AFr
AI
~.
a
oDAP
d
E
EBF
e
g
HSS
~
~
~
~
amplitude of the pulse
squashload
Arias intensity
area of the web
peak ground acceleration
factored compressive force in the link
nominal compressive resistance of the link
deadload
duration of the acceleration pulse
depth of the section
earthquakeload
eccentrically braced frame
length of the 1ink
concenttated force at the top of the structure to account for contribution of
higher modes
yield sttess of steel
scaling factor (Schiff"s method)
scaling factor (Schiff" s method)
acceleration due to gravity
hollow structural section
storey height
effective stiffness
effective length factor for in-plane action
effective length factor for out-of-plane action
ratio ofymax/~ evaluated for each storey
average value of Ky evaluated for each storey
ratio of Mdcl
X1l
L
~[
NAP
NBCC'inc:ar
NBCCmodaI
N1
NLTHA
NZC
P
Pr
PGA
PGV
PHA
PHV
PPS
PS~.
PSa
PLU
R
R
RMSA
average vaIue of~ evaIuated for each storey
span of the Iink beam; live load
bending moment in member; earthquake magnitude
maximum range of inelastic shear rotations
nominal bending resistance of the Iink
column plastic moment
faetored bending resistance of the member
effective mass
number of acce!eration pulses
NBCC linear lateraI force distribution
NBCC lateraI force distribution obtained from modal analysis for NBeC
design specttum
modified NBCC linear lateraI force distribution
number of pulses with the amplitude within the selected range
non-linear rime history anaIysis
number of zero crossings
axial force in member
factored axial force in link
peak ground acceleration
peak ground velocity
peak horizontal ground acceleration
peak horizontal ground velocity
predominant period of shaking
pseudo-velocity
pseudo-acceleration
equivalent horizontal forces to account for second order effects of dead and
live load acting on the deformed structure
force reduction factor; epicenttal distance
total reduetion factor factor, R*1lU
root mean square ofaccelerogram
redundancy factor
X1U
r
S
SHA
TP
U
UHS
v
v 1:,2".Il
V c,nonlIl
v nonlIl
overstrength factor
damping factor
ducti1ity factor
response ratio (demand-to-resistance ratio of the member)
seismic response factor of NBCC
seismic hazard analysis
pseudo-acceleration speetrum. intensity
pseudo-ve1ocîty speetrum intensity
square-root-sum-of-the-squares summation mIe
simple summation mIe
fundamental structural period
effective period
structural period using NBCC empirical formula
rime of the occurrence of the pulse
calibration factor
uniform hazard speetra
factor to account for moment gradient (bending about x axis) and for
second-order effects ofgravity load acting on the defonned member
shear force in member; design base shear force
design base shear at ma....wnum displacement
desÎgn lateral strength of the structure associated with seismic loading
elastic base shear
factored shear force in the 1ink
maximum shear force in the link induced by earthquake
nominal shear resistance of the 1ink
factored shear resistance of the link
ma..ximum lateral strength of the structure
elastic strength demand
maximum e1astic base shear obtained from push-over analysis at two percent
roof drift index
ma..ximum e1astic base shear obtained from NLTHA
maximum base shear obtained from NLTHA
xiv
V 1!.u
v
W
WWF
w
a
flfnmc:Il Y<I1·119rfr:unr:
latera1 strength of the strUcture obtained from push-over analysis at two
percent roof drift inde.x
peak ground velocity; zonal velocity ratio
wide t1ange section
welded wide Bange section
wind load (1 in 30 years)
thickness of the web
ratio oflink resistance to demand, Vr!Vf
integration parameter in Newmark's method; constant (m uoits length)
reIated to the expansion of the shear yield surface of the link due to isotropie
strain-hardening
inelastic shear rotation; integration parameter in Newmark's method
maximum inelastic shear rotation
storey drift
design displacement
inter-storey elastic drift
maximum inelastic displacement
maximum shear yield sttength of link after complete hardening
yield displacement
storey drift angle
mean value
overall ductility factor for multi-storey building
ductility displacement ratio associated with maximum ineIastic link rotation
just reaching the desÏgn limit of O.09rad
storey ductility displacement ratio
standard deviation
resistance factor
coefficient to account for increased bending resistance of a laterally
unsupponed beam segment when subjeet to a moment gradient
xv
UST OF TABLES._iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii~
Gravity loading (specified) on EBF 3-9
Seismic loading for EBF (Victo~B.q 3-10
Iink beam selection for initial structures 3-10
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Table 4.6
Table 4.7
Eight-storey frame: Initial and final section selection 3-11
Four-storey frame: Initial and final section selection 3-12
Fourteen-storer frame: Initial and final section selection 3-12
Contributions to seismic risk C%): PGV equal to O.3m/s 4-19
Summary of selected historie earthquake records 4-20
Scaling factors for earthquake records 4-21
Indices to charaeterise earthquake records: Law a/v records 4-22
Indices to charaeterise earthquake records: Intennediate a/v records 4-23
Charaeteristics ofacceleranon pulses: Low a/v records 4-24
Comparison of response of links ro historical and artificial records:
Low a/v records 4-25
Table 4.8 Comparison of response oflinks to hisrorical and artificial records:
Inrennediare a/l,r records 4-26
Table 4.9 Characteristic ground motion parameters: artificial records matching
new UHS for Canada (Atkinson et al, 1998) 4-27
Table 4.10 Indices to characterise earthquake records: artificial records matching
new UHS for Canada (Atkinson et al, 1998) 4-28
Table 4.U Link response parameters: artificial records matching new
UHS for Canada (Atkinson et al, 1998) 4-29
Table 4.12 Scaling factors Fab': artificial records matching new UHS for Canada
(Atkinson et al, t998) 4-30
Table 4.13 Link response parameters: Scaled artificial records matching
new UHS for Canada (Atkinson et al, 1998) 4-31
XVI
Table 5.6
Table 5.4
Table 5.5
Table 5.7
Table 5.8
Table 5.1
Table S.2
Table S.3
~
Seismic load calculation (Zone 5) 5-17
Wind load calculations 5-18
Four-storey frame: Ductility design - snmmary of selected sections
(current codified design procedure) 5-19
Eight-storey frame: Ductility design - summary of selected sections
(current codified design procedure) 5-19
Fourteen-storey frame: Ductility design - summary of seleeted
sections (current codified design procedure) 5-20
Fourteen-storey frame: Verification of sttength and inelastic inter-storey
Table 6.23 Weighting coefficients to calculate J,tfumc ••••••••..•.••••••••••••••••••••••••••.6-45
Table 6.24 Coefficients Ky based on ma."<Ïm.um ymax and maximum~ 6-47
Table 6.25 Coefficients Ky based on (J.1+<J) Ymax and (J.1+<J)~ 6-49
Table 6.26 Drift indexes associated with desired performances of the links 6-51
XIX
LIST OF FIGURES.liiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiil&
Fig 1.1
Fig 1.2
Fig 1.3
Fig 1.4
Fig 1.5
Fig 1.6
Fig 1.7
Fig 1.8
Fig 1.9
Fig 1.10
Fig 1.11
Fig 1.12
Fig 2.1
Fig 2.2
Fig 2.3
Fig 2.4
Fig 2.5
Fig 2.6
Fig 3.1
Fig 3.2
Fig 3.3
Fig 4.1
Fig 4.2
Typical EBF configurations 1-16
Typica1 force distributions in link beams under lateralload 1-16
Rigid-plastic collapse mechanism 1-16
Hysteretic behaviour of (a) unstiffened shear link and (b) stiffened shear
link (after Popov and Engelhardt, 1988) 1-17
Hysteretic behaviour of stiffened flexurallink (after Popov et al, 1989) 1-17
Static equilibrium of link (after Popov and Engelhardt, 1988) 1-17
Shear links with unequal end moments with (a) no axial force;
(b) axial force (after Popov and Engelhardt, 1988) 1-17
Link element with inelastic subhinges 1-18
Subhinge yield surfaces with resulting hinge force-deformation response 1-18
Force-defonnation relationship for (a) shear and (b) flexure to model
kinematic hardening of the links (after Rides et al., 1994) 1-19
Simplified static approach to calculate link shear forces 1-20
Link defonnations for 6 and 10-storey EBF subjected to 1.5 El Centre
and Chile earthquakes (after Popov et al., 1992) 1-20
Proposed design procedure: sequence of one iteration 2-17
l.\.fodelling of EBF 2-17
Typical interaction surface for beam-column element 2-17
Yiclding surfaces for clement groups (1), (2) and (3) 2-18
Modelling of rigid offsets 2-18
Modelling of beam-to-brace connection 2-18
Typicallayouts and clevations for four, eight and fourteen storeys EBFs 3-13
Stiffness and yielding surface dara are modified for aU member groups. A characteristic
yielding surface for shear links is presented in Fig. 1.4 in Chapter 1. Figures 2.4(a) and 2.4(b)
illustrate a typical shape of the yielding surfaces for groups (2), and (1) and (3) respeetîvely.
For the links and outer beam segments the modification of the yielding surface is
2-14
2.0UTLINE OF PROCEDURE AND DEVELOPMENT OF ANALYTICAL TOOLS
straightforward and involves oaly the update of the ultimate resistances. The combination of
tensile force and bending moment is judged criticalt for the outer beam segments and the
influence of the c1ass of the section on the shape of the upper portion of the yielding surface
is neglecred. For columns and hraces the combination of compressive force and bending
moment is usually goveming, thus the shape of the yielding surface is affected by the c1ass of
the section. To account for this, the locations of points A and B (see Fig. 2.4) for member
groups (1) and (3) are aIso updated, based on the class of the section in bending detennined
automatically by the program.
For member groups (2) and (3), the data modification program aIso revises infonnation on
the size of a brace-to-beam connection. It was assumed in this study that the link ends at the
intersection of brace and heam centerlines. In general, plastic hinges in frames will not fonn
at this location but rather near the faces of the joints. This effect cao he approximated in
AN5R-t by assuming rigid, infinitely sttong connecting links between the nodes and the
element ends, as illustrated in Fig. 2.5. The length of the connecting rigid links is defined
through the element end eccentricities, which vary depending on the brace and beam
sections and the angle of inclination between them. Using data from the input files 1 and 2,
the data modification program calculates the end eccentticities for the beam and the brace in
each storey, and updates the values in AN5R-l input file.
2.3.3.3 Program limitations
The data modification program was developed for Chevron-type EBFs not exceeding 35
storeys. It can be used to either update the existing ANSR-t input file for the sections
selected by the design program, or ta assist in the preparation of the input file for an
arbittary section selection. In bath cases, the template of the ANSR-t input file must be
available, as only the parts of the file related ta the element description cao he automatically
updated.
1 If, for a given compressive load, the beam section is Class 1, the contribution of the bendingmoment ta force-moment interaction is reduced by 2S percent. This is Dot the case if the axialload istensile. Since the beams are fully laterally supported, for bath Class 1 and Class 2 sectionscombinatian of moment and tensile force will always be criticaL
2-15
2.0UTLINE OF PROCEDURE AND DEVELOPMENTOF ANALYTICAL TOOLS
It is assumed that the elements of the frame are ammged in four main groups, columns,
beams, braces and links. The program requites that the beams be denoted as the second
group and the links as fourtb. Within each main group, elements can be divided into a
maximum of five subgroups. The number of subgroups is a variable specified by a user, but
it has to be equal for ail main element groups. If additional groups of elements are to be
specifiec:L their description should follow the link data. It should be noted that no provision
is made in the program to update properties of sucb additional groups.
It is further assumed that the number of stiffness types matches the number of the yielding
surfaces. For example, if two columns have the same cross-section but different effective
lengths, in general, they could be described specifying one stiffness type and two yielding
surfaces. The data modification progrant on the other hand would require specification of
two stiffness types, although the data for the two would be identical.
For member groups 2 and 3, the number of end eccentticity types is assumed to he twice the
number of stiffness types. The number of different end eccentricities types is limited by
ANSR-l to fifteen within one sub-group. Since the source code for the analysis program was
not available, it was not possible to increase this limit. Ir was decided instead to divide the
main groups of elements into subgroups and constrain the maximum. number of clements in
one subgroup to fourteen. As indicated in Fig. 2.6, in every storey, braces, columns and
outer beam segments in the left and right sides of the frame have identical stiffness type and
yield surface but a clifferent end eccentticity type. By limiting the number of the clements in
the subgroup to fourteen, the number of stiffness types and yielding surfaces is constrained
to seven, and the number ofend eccentricities types to fourteen.
2.4Summary
This Chapter bas inttoduced the proposed approach for seismic design of eccenttically
braced frames. The itetative method is based upon seismic response of the frame members,
and it incorporates non-linear time-history analysis direetly into the design process.
2-16
2.0UTUNE OF PROCEDURE AND DEVELOPMENTOFANALYTICAL TOOLS
The procedure is implemented by means of three computer programs. ANSR-l was selected
as the analysis module. Two computer programs have been written to integrate non-lïnear
cime history analysis into the design procedure for the Chevron-type of eccenttic bracing.
The purpose of the design module is to examine the forces in elements introduced by
earthquake loading, compare them with resistances and choose alternative sections if
resistance is exceeded. The data preparation module is developed to revise the input for the
analysis for the sections seleeted by the design program.
A complete iteration consists of mnning the analysis module, design module and data
modification module in sequence. The three steps are automatically repeated (with user
interaction when required) until there are no more section modifications. For further details
on developed programs, inc1uding flowcharts, formats of required output files and similar,
see Appendix B.
The automated design process described in this Chapter allows rapid design ofchevron type
EBFs and produces structures that conform to the desired seismic response attributes under
the 2-:rin !l of~hquake records selected for design.
2-17
1 (i) ANALYSIS MODULE
1(li )DESIGN MODULE
~-~
Ci) DATA PREARATIONMODULE
Fig. 2.1 Proposed design procedure: sequence of one itteration
M
Fig. 2.3 Typical interaction surface forbeam-column element
BeL - Beam-column elementsLK - Link elements
Fig. 2.2 rvlodelling of EBF
2-18
M
B
p -Class 1
-Class2
A
M
C
(a) Element group (2) (b) Element groups (1) and (3)
Fig. 2.4 Yielding surfaces for element groups (1), (2) and (3)
Rigid links
NODEj
Fig. 2.5 Modelling of rigid offsets
ST - stifness typeYT - yie/ding surface typeROT - rigid offsets type
ROTt: el. 3-4 : 0.0, -ex, 0.0, 0.0
ROT2: cl. 6-5 : 0.0, ex, 0.0, 0.0
ROT3: el. 1-4 : 0.0, -ex, 0.0, -ey
ROT4: el. 2-6: 0.0, ex, O.O,-ey
Fig. 2.6 ModeUing of beam-to-bnce cono.ection
2-19
Chapter 3
SENSITIVITY OF PROCEDURE TO INITIAL DESIGN......iiiiiiii_iiiiiiiiiiIiili__iiiiiiiiiiiiiiiiiiilliiliiiiiiiiiiiiii_iiiiiiiiiiiiiliiliiiliii_iiiiiiiiiiiiiiiiiiiiiiii_iiiiiiiiiiiiiiiiiiiiiii
Two important aspects need to be considered before the proposed design procedure can be
used efficiendy in practica1 applications. These are: (~ the sensitivity of the final sections
selection to the initial trial designy and (11) the selection of an earthquake record to use in the
analysis. This Chapter describes the study conducted to investigate the fonner aspect.
The sensitivity of the design procedure to initial section selection is examined for three
chevron type EBFs with fouryeight and fourreen storeys located in Zone 5. The approaches
to define the trial designs are discussed. For each &aIne height, at least two different initial
designs are used. The iterative procedure is then applied for a chosen earthquake record. The
final sets of sections obtained for each frame configuration are compared to assess the
influence of the trial design in their selection. Recommendations are then made regarding the
appropriate approach to generate the initial structure for design applications.
3.1 General considerations
Low sensitivity of the proposed iterative procedure to the choice of the initial frame
structure is desirable. Ideallyy for the same modeling assumptions and earthquake record
chosen, the convergence should always be toward a unique structure regardless of the initial
member selection. A study was can:ied out to investigate whether the initial selection
influences the member sections in the final structure designed using the iterative procedure
and if so, to what extent. Attention was a1so directed towards the identification of an
appropriate method to select the initial frame members for practical design applications.
3-1
3. SENSITIVITY OF PROCEDURE TO INITIAL DESIGN
To realize the latter objective, it was necessary to detennine logical approaches to select the
initial structure. A number of basic design requirements impose limitations on the seemingly
limitless choice of sections. In the following paragraph, seIected design criteria are discussed
in light of their impact on the selection ofsections for different member groups of the frame
This study focuses on EBFs with pure shear links and thus the following criteria should be
adopted in the design, as discussed in section 1.3.2: for a selected link length, ooly the
sections for which the ratio of factored bending resistance (MJ ta factored shear resistance
CVJ is less than 1.6 can be selected; Vr should be as close as possible ta the force demand
CV?J to limit forces transmitted to the other members of the frame; the ratio a =Vr!Vr is
maintained as constant as possible over the height of the building; the same section should
he rnaintained through the whole length of the link beam, and the link beam should he at
least Class 1 section, while columns and hraces have to comply with Class 1 or 2
requirements. In addition, the selected frame sections must provide adequate strength for aIl
serviceahility and ultimate limit states under aIl loading combinations inc1ucling wind and
earthquake, and an economical structure should result.
3.2 Selection of the trial design
3.2.1 Approaches to select a trial design
The above limitations were taken into account when defining the initial frame sections. Two
different approaches to choosing the initial design were adopted. The first approach is more
suited for studies that evaluate the adequacy of present code provisions for chis structural
system. The second approach is more appropriate for practical applications, since it is
simpler and less rime consuming for a designer.
In the fust approach, a trial design is in strict conformity with Canadian design provisions
for EBFs. Sections are selected on the basis of the seismic loacling and duetility requirements
and subsequendy verified for al1 other relevant load combinations inclucling second order
effects. The duetility design is cattied out using an EBF seismic design program (EBFSD)
deveIoped by Han, Redwood and Kasai (1997). Verification of the strength and the stiffness
3-2
3. SENSITIVITY OF PROCEDURE TO INITIAL DESIGN
of the frames for the relevant load combinations is done using program SODA (Acronym
Software Inc., 1996)). The main features of both programs are explained in more detail in
Cbapter 5. This approacb is referred to as Design Case1.
In the second approach, link beam sections are selected first to bave adequate inelastic shear
resistance for forces introduced by the NBCe seismic load. Other members of the frame are
then selected to comply with sttength and stiffness requirements. Thus, only the links fully
satisfy ductility requirements of Clause 27.6. Similarly to Design Case 1, link sections are
selected with the belp of the program EBFSD. Design of other members of the frame and
verification of seleeted link sections is then carried out by SODA. This approacb is referred
to as Design Case 2.
Previous studies of an eight-storey EBF (Koboevic and Redwood 1997) bave indicated that
in severe seismic zones it is possible ta achieve a design compliant with ail ducrility
requirements, that at the same rime has very high response ratios for forces arising from
tradirional load combinations used in strength and stiffness design. In other words, it can
happen that the differences between the initial designs obtained following these two
approaches are not too pronouncecl, and therefore the sensitivity of the procedure to the
choice of initial structure cannot he fully investigated. For these reasons, another trial design
denoted as Design Case 3 was also studied. Sections selected in this case are anticipated to
be very different frOID those of the final structure. Since mioimizing the link oversttength is
a design objective, the same link sections as those of Design Cases 1 and 2 were adopted.
For columns and hraces on the other hand, Design Case 3 assigns the same sections in ail
storeys, these corresponding to the ones required in the first storey of Design Case 2.
3.2.2 Initial member selection
3.2.2.1 Building features and loadiDg
The structures are located in Zone 5. Typical layouts and elevanons are shown in Fig. 3.1.
Gravity and seismic loading was calculated in accordance with NBeC (1995), and a snmmary
of the loads for ail three frames is given in Tables 3.1 and 3.2 respectively. The selected
building layouts and load calculanons are described in more detail in Chapter 5.
3-3
J. SENSITIVITY OF PROCEDURE ro INITIAL DESIGN
3.2.2.2 Link beam selection for initial structures
For each frame configuration studie~ 1ink beams in Design Cases 1,2, and 3 had the same
cross-sections since their selection was based on the same requirements. The chosen sections
are listed in columns (a), (c) and (e) of Table 3.3. This table also indicates the values of link
resistance-to-force demand ratio (a).
Comparing the values for a listed in columns (b), (d) and (f) of Table 3.3, two observations
can be made. The top storey link for all three configurations has somewhat greater a than
the links in other storeys. For the four and eight-storey frames, strength requirements
govemed the link design in the top storey, and this cao explain the larger section being
sdected at this location. For the fourteen-storey frame, while gravity load played a role, the
heavier top link beam was also necessary to ensure the selection of pure shear link. For the
fourteen-storey frame, a is in general larger than for the other two frame configurations.
This is mosdy the result of the attempt to have a uniform distribution of Cl over the height
of the structure.
3.2.2.3 Selection ofbraces and columns in trial design
Columns (a), (c) and (e) of Table 3.4 snmmarize the initial selection of brace and column
sections in the eight-storey frame for Design Cases 1,2 and 3 respectivdy. Sections sdeeted
for the four and fourteen starey frames are presented in columns (a) and (c) of Tables 3.5
and 3.6. For these [wo frame configurations, oaly Design Cases 2 and 3 were studied.
Selection of braces and columns was mainly based on the required strength for the
traditional goveming load combinations, including second order effects. In the case of taller
frames however, design cao be significandy influenced by sorne other requirements,
particularly inter-storey plastic drift limitations. Keeping in mind the objective of this study,
this requirement was neglected in the design of 14 storey EBF in order ta provide a
consistent comparison, based on stren~of the results for all three frame configurations.
3.3 Selection ofearthquake record and modeling assurnptions
A systematic approach ta selection of earthquake records will he discussed in Chapter 4. For
the purpose of the study discussed in this Chapter, component N21E of the Taft
3-4
3. SENSITIVITY DF PROCEDURE rD INITIAL DESIGN
ea.rthquake, recorded in Lincoln School on June 12, 1952 was seleeted as the input
acceleration record. In a previous study (Koboevic and Redwood, 1997) this record was
identified as one of the records causing the most severe disttess in an 8-storey sttueture
designed for Zone 5. The rime history of the record and elastic response speetrum are
illusttated in Fjgs. 3.2 and 3.3 respectively.
The analysis was carIÎed out for the situation in wbich yielding is permitted in links and
accepted to a smaller extent in outer beam segments (see 2.3.2.1). Acceptance of yield in the
outer beam segment implies that the srability of this member must be ensured. Links and
outer beam segments were therefore assumed to be fully laterally supported and could thus
he modeled as inelastic elements. Because of this modelling approach, the link beam sections
were not modified during the iterative procedure; hence, the final 1ink beam selection is
equivalent to the initial section described in Table 3.3.
Modeling of other elements and post-analysis verification for stability followed the
approaches discussed in more detail in Chapter 5.
3.4 Final section selection obtained in iterative design procedure
3.4.1 Eight storey structure
Final selection of sections obtained in the iterative procedure for aIl three design cases is
indicated in columns (b), (d), and (t) ofTable 3.4. Two iterations were necessary to converge
ta solution in Design cases 1 and 2 and three in Design case 3. The resulting designs are in
confomùty with modelled behaviour, that is, the inelastic activity is confined primari1y to the
links, limited yie1ding is observed in outer beam segments (maximum accumulated inelastic
rotation less chan 0.1 rad) and braces and columns responded elastically without 10ss of
stahility.
The final sttuctures obtained in each of the three cases show remarkable similarity. The
variation of the mass is less than 3%, and aIl structures have simiIar fundamental period
(1.86s in Design cases 1 and 2, and 1.85s in Design case 3). A somewhat heavier column
3-5
3. SENSITIVITY OF PROCEDURE ro INITIAL DESIGN
section in the top rier was selected in the Design case 3, and a smaIl difference was observed
in brace sections at leve1s 5 and 6. 1bis variation is due to the range of acceptable response
ratios set in the design module to define an economical selection. For the same combination
of loads, different sections MaY he satisfactoty and the difference in section resistances could
yield up to 25% of difference in response ranos. For example, the maximum response ratio
for the brace at level 5 in Design case 2 (HSS30SX203X8) is 0.99, while the ma.XÏlnum
response ratio of the brace at the same level in Design cases 1 and 3 (HSS30SX203XI0) is
0.86. The examination of the history of selected sections within each iteration cycle showed
that it was in faet possible to conduet the selection so as to obtain identical structures in all
three cases.
3.4.2 Four and fourteen storey structures
Final section selection for the four- and fourteen-storey structures is summarized in columns
(b) and (d) of Tables 3.5 and 3.6 respectively. For the four-storey structure, the procedure
yielded the same final design in both cases studied. The final design was obtained after five
cycles for Design case 2, and three cycles for Design case 3.
For the fourteen-storey structure, the procedure converged in three and four iterations for
Design cases 2 and 3 respectively. The two final designs had aImost identical fundamental
periods ([14=3.05s) and less than two percent difference in mass. A smaller variation of
brace sections is observed in storeys 1, 9,10 and Il for the two final designs. Analogously to
the eight-storey structure, this cao be associated with the limits imposed on response ratios
for economical reasons.
3.5 Discussion of the results
Results presented in the previous section indicate very smal1 differences in the final designs
in all cases studied for the different frame configurations. These variations are due to the
range of response ratios imposed by the design module to ensure economical section
selection. The selected sections could have up to 25 percent difference in response ratios for
the same loading conditions. The narrower the accepted range, the less difference in the final
designs would be observed. For engineering applications the observed differences are small
3-6
3. SENSITIVITY OF PROCEDURE rD INITIAL DESIGN
and can he neglected. Bearing this in mind, it can be concluded that for widely different
initial frame members, for a given geometty and earthquake record, the iterative procedure
yields the same structure. The study demonsttated that the proposed procedure is not
sensitive to the initial memher selection of the frame.
The approach leading to Design case 2 was identified to he the Most appropriate way to
select the initial structure when the iterative procedure is used as design tooL In this
approach, members are designed following common methods used in limit states design, and
only the links requite special verification for inelastic shear. A designer does not have to
apply capacity design principles to select the initial structure. The approach is practica1 and
rime saving.
T0 provide consistent comparison of results, the inter-storey drift limitation was neglected as
a design requitement in initial section selection for the fourteen-storey frame. However, if
the procedure is to be used for design of taller frames, it is recommended that inter-storey
drift limitations be incorporated into the initial member selection, since their influence on
the size of members may be significant.
The modeling case in which the elastic behaviour of outer beam segments is anticipated was
also e..xamined. This approach however led to significant increase of Iink sections, which in
tum affected the sizes of other members of the frame and resulted in heavier design.
3.6 Summary
In this Chapter, a study of the sensitivity of the iterative procedure to the initial design bas
been described. The primary objective was to detennine whether, for a given earthquake
record and frame geometty, different strUctures seleeted to initiate the iterative design
process yielded the same final design. In addition, an attempt was made to identify the Most
suitable approach to initial member selection when the iterative procedure is used as design
tooL
3-7
3. SENSITIVITY OF PROCEDURE TO INITiAL DESIGN
The study focused 00 four, eight and fourteeo storey EBFs located in Zone 5. For the
chosen earthquake record the iterative procedure was carried out to produce inelastic
behaviour of links and stable elastic response of braces and columns. For each frame height,
the iterative procedure was initiated for different initial structures, and the final section
selections were compared. Oo1y small variations in seleeted sections were observed, aIl
within the limits judged acceptable for engineering application. Thus, it was demonstrated
that the proposed procedure is not sensitive to the initial member selection. The approach to
initial member selection, in which the columns, braces and outer beam segments are seleeted
according to sttength and stiffness requirements and the links are verified to have adequate
inelasric shear resistance for seismic load, is recommended as the most suitable for design
SELECTION OF DESIGN EARTHQUAKE RECORD._iiiIiiIiiiiiiiilliiiiliiil-----IiiiiIIiiIiII~iiiiiiiiiii-iiiliiiiiii&ii&iiiiiiiiiiiiiiiiiiiiliii-iiiiiiii--..
This Chapter describes the methodology used to select the earthquake record for the
iterative design procedure. Artificial records mat would reflect relevant local seismic
conditions are generated for a seiected design location in Western Canada. The
combinations of earthquake magnitudes (M) and epicenttal distances (R) that contribute
most significantly to the peak ground parameters at the site are obtained from seismic huard
analysis. Historical records, with the appropriate combination of ~I and R are seiected, and
elastic response spectra are determined. The artificial acceleration records are then generated
to match mese spectra. Comparison of historie and simulated records is performed to
evaluate if the simuIated records can he considered representative of a Western North
American seismic event.
4.1 Introduction
The proposed design procedure is criticalIy dependent on adequate representation ofground
motion. The characteristics of appropriate acceleration records such as intensity, frequency
content, duration etc, should he similar to those expected at the design location for the levels
of risk associated with the design limit state under consideration. In addition, to limit the
design effort it is desirable to define a unique acceleration record.
The characteristics of earthquakes that influence structural response the most, are frequency
content and the duration of stIong shaking. These two parameters depend on both the level
of seismic motion and the seismo-teetonic environment at the specific location. Seismo
tectonic conditions are usually descrihed by the magnitude (M) and epicentral distance (R).
Based on field measurements, attenuation relationships that relate intensity parameters to
4-1
4. SELECTION OF DESIGN EARTHQUA/ΠRECORD
magnitude and distance have been developed for specific regions taking into account the
effects of the local geology and of fault mechanisms likely to be involved. Frequency content
and duration of an eatthquake are a1s0 reIated to magnitude and distance. Seismic events
with larger magnitudes recorded doser to the source of the earthquake are usually shoner in
duration and richer in high frequencies compared to those recorded at a larger distance. 1bis
aU indicates that the prediction of the characteristics of ground motions of interest in
structural engineeing cao he made hased on the magnitude and epicentral distance.
In NBCC (1995), the severity of the expected ground motion at the specific location is
expressed for design purposes through peak horizontal ground acceleration (PRA) and peak
horizontal ground velocity (PHV). They are obtained from the seismic hazard analysis (SHA)
for a selected site and for a specific probability of exceedance. These calculations are based
on the assessment of magnitude-recurrence relationships for a panicu1ar seismo-tectonic
region and on appropriate attenuation Iaws. Since SHA integrates the contribution of aU
possible earthquakes, the seismic hazard curves cao be decomposed for a seleeted design
location to detennine the magnitudes and epicenttal distances that make dominant
contributions to the ground motion parameter at the speci.fied probability ofexceedance.
4.2 Proposed methodology to define a design acceleration record
4.2.1 Oudine of the method
Heiderbrecht and Naumoski (1988) suggested that the decomposition of seismic hazard
eurves obtained for PHA. and PHV at a selected location could be used to assist selection of
the actual sttong motion records to indude in the dynamic analysis. The records are chosen
to match the combination of M and R that dominates the seismic hazard at the design
location. This approach has been adopted in the present study, as the tirst step of the
method used to generate the design acceleration record for the iterative procedure. Historical
records selected in this way are specific to the and reflect the local seismic conditions.
These records are used to define appropriate spectta, based on which artificial records are
generated. Validation of artificial records is then carried out by comparison of their intrinsic
4-2
4. SELECTION OF DESIGN EARTHQUAKE RECORD
properties with those of the historica1 records and by comparisons of structural response
parameters.
In the following sections, each of these steps is described in more detail and the application
of the proposed methodology is illustrated for a seleeted site in Western Canada (Victoria,
B.C).
4.2.2 Determination ofM and R for initial selection ofhistorie records
The initial scanning of historic acceleration records is based on the magnitudes and
epicenttal distances that make dominant contributions to the ground motion parameter at
the specified probability of exceedance. Peak horizontal ground velocity, rather than peak
horizontal ground acceleration is selected as the appropriate ground motion parameter, since
the structures considered in this study have fundamental periods in the velocity-sensitive
region of specttum, i.e., T>O.Ss.
4.2.2.1 A computer program for assessment ofseismic hazard
A computer program EQDES developed by Tremblay (1994) was used to obtain the
distribution of seismic risk as a funetion of magnitudes and distances for PHA and PHV.
The distribution is ohtained for ground motion parameters equal to those specified for the
site. The calculations are performed according to the probabilistic approach originally
developed by Comell (1968). In this approach, the occurrence of future seismic eveats is
predicted based on seismic sources for which magnitude-recurrence relationships are known,
and the amplitude of the ground motion parameter at a given site is obtained using
attenuation relationships derived for the region.
The numerical scheme adopted in the program EQDES is similar to the one in the program
EQRISC (McGuire et al. 1976). The latter was used by Basham et al (1982, 1985) for
establishing the seismic maps provided in NBCC (1995). The same database as the one used
by Basham is adopted for this study. The database contains information regarding the
characteristics of the seismic source zones (location, depth and recuuence formula), a list of
4-3
4. SELECTION OF DESIGN EARTHQUAKE RECORD
the source zones to consider for a selected location and the attenuation relationship. Source
zones commonly considered for Westem Canada are illusttated in Fig. 4.1.
4.2.2.2 Assessing the distribution ofseismic huard for Victoria, B.C.
The decomposition of the seismic hazard curve for PHV was carried out for Victoria, B.C.
For comparison, the distribution of seismic hazard was aIso examined for PHA. Program
EQDES requites the specification of location in tenns of longitude and latitude and the
value of the ground motion parameter for a specified probability of exceedance. NBCC
(1995) allocates Victoria to seismic zone 5 with respect to both PHV and PHA. In this zone,
these two parameters take on values of 0.3 mis and 0.3g respectively with 10 percent
probability of exceedence in 50 years.
The distribution of seismic hazard in tenns of magnitudes and epicentral distances obtained
for PHV and PHA is illusttated in Fig.4.2 and 4.3 respeetively. As indicated in Fig. 4.2,
earthquakes with magnitudes between 6.5 to 7.0, at epicentral distances in the range of 25 to
75 km contributed most significandy to PHV. Table 4.1 gives a percentage of contribution
to seismic hazard for magnitude and epicenttal distance within these ranges. The analysis
aIso indicated that eighty percent of the total contribution to PHV originated &om the
adjacent earthquake source of Puget Sound (pGT on the map). The remaining twenty
percent originated from Cascadia and Northem Vancouver Island source zones.
Sîmilar observations were made regarding PHA. Fig. 4.3 shows that PHA is mosdy the result
of the nearby events (25 to 50 km) with magnitudes varying between 6.0 and 7.0. AgaÏn,
Most of the contributing earthquakes are &om Puget Sound source zone (90%).
4.2.3 Selection of historical strong motion records
4.2.3.1 Search strategy
To proceed with the selection of representative historica1 strong motion records for a
selected location a search strategy and a set of selection criteria were defined. The ranges of
magnitudes and epicenttal distances that contribute most strongly to PHV at the design
location were identified as essential search parameters. As descnbed above the seismic
4-4
4. SELECTION OF DESIGN EARTHQUAKE RECORD
events with magnitude range 6.5 ta 7.0 and epicentral distance range from 25 to 75 km were
used for the study.
Another search entenon considered was the ratio of the peak ground acceleration of the
record, a, and peak ground velocity, v. It was demonstrated by Tso et al (1992) that the
acceleration-to-velocity (a/v) ratio provided useful information regarding the relative
frequency content and duration of sttong shaking for ground motions from different seismic
environments. Earthquake records are commonly divided into three groups based on their
a/v ratio, low a/v group (a/v < 0.8, with a normalized by g and v in mis), intermediate a/v
group (1.2<a/v<0.8), and high a/v group (a/v>1.2). The zonal a/v ratios used in NBCC
(1995) for seismic regionalization indicate that in Western Canada ground motions are
typically expected to be in either low or intennediate a/v ratio groups characterized by low
frequency content, high amplitudes and long duration. Thus, limiring a/v ratio ta values
below 1.2 was the second search criterion used in selection of the bistorical sttong motion
records.
In order to eliminate the effects of local site amplification on the characteristics of the sttong
motion records the search was aIso confined to accelerograms recorded on finn ground.
Wherever possible, free-field records were selected, otherwise the structural records obtained
on building ground floors were induded.
4.2.3.2 Description of the database
An ensemble of historical records was selected &om the Earthquake Sttong Motion
Database (NGOC, 1996).2 The main infonnation about each record in the database are
summarized in the catalogue contained in S~ICAT (1996), a data inventory package
2 The database contains over 15000 digitized and processed accelerograph records, dating from 1933
to 1994, from bath the United States and other seismicaIly active countties in the worId The
accelerographs are recorded in a variety of structural and geologica1 environments. The strong
motion data are organized into sets grouped by either triggering events or geographic regions. Most
of the data sets include three types of processed records: uncorrected, correeted and response
spectra.
4-5
4. SELECTION OF DESIGN EARTHQUAKE RECORD
developed for PC-DOS platfoon. These include the trigger events, recording sites,
magnitudes, epicenttal distances, peak ground motion parameteI5 etc. SMCAT allows the
user aIso to search the catalogue according to a specified set of parameteI5 and to rettieve
the acceleration records from the database.
4.2.3.3 Selected historical records for Victoria, B.C.
Infonnation on historical records seleeted from the Earthquake Sttong Motion Database is
SlImmarized in Table 4.2. These include the general characteristics of the records and data on
peak horizontal acceleration and peal ground velocity. Six records were seleeted from low
a/v ratio group, and eight from the intermediate a/v ratio group.
4.2.3.4 Scaling of the eanhquake records
For easier comparison of structural response to different historical records, accelerograms
are usually scaled so that they have similar levels of intensity. If the record is used to examine
the seismic design requirements, its intensity level should aIso correspond to that dcfined by
NBCC (1995). Earthquake records can he scaled based either on ground motion parameteI5,
or on response quantities. In this study two scaling approaches were examined, one using
the peak ground velocity as a normaliziog parameter, and the other using the speettum
intensity.
In the first approach, the peak ground velocity of the record is matched to PHV specified
for the seismic zone under consideration and accelerations are scaled accordingly,
maintaining unchanged the a/v ratio of the historica1 record. Resulting scaling factors for the
set of selected historical records are given in column Ca) ofTable 4.3. The study by Tso et al.
(1992) has demonsttated that nonnaliziog acceleration records with respect to the peak
ground velocity yields much less dispersion in elastic response spectra for earthquake records
with different a/v, particularly in the velocity-sensitive range.
In the second approach, the elastic response spectra of acceleration records are used to
detennine scaling factors. Sïnce the maximum strain energy stored in a linear elastic system is
proportional to the pseudo..velocity (pS\"), the speettum itself cao be considered a measure of
4-6
4. SELECT/ON OF DES/GN EARTHQUA/ΠRECORD
the severity of the earthquake. The speetrum intensity is defined by Housner (1959) as the
area under the pseudo-velocity curve between 0.1 and 2.5 s. Nau et al (1984) found that this
scaling approach can reduce dispersion of both elastic and inelastic spectra for low to
moderate ductility.
The scaling factors are calculated in a two step procedure~ as proposed by Schiff (1988). In
the first step, the earthquake records are normalized to have identical specttum intensity, SI".,
in the velocity sensitive range. Five percent of damping was assumed in calculation of S~ for
reasons of compatibility with the NBCC design specttum. The integration limits were set to
0.5 and 3 s, as these couelate with the fundamental periods of the structures investigated.
Scaling factors FI were found by dividing S~ of each record by the maximum value of SI... in
the group. Resulting factors are shown in column (c) of Table 4.3. When scaled by the factor
FI. the spread between the elastic response spectra of different records is reduced in the
medium to long period range.
The absolute ordinate of the spectra is detennined in the second step, which shifts the
spectra as a group and anchors it to NBCC design speetrum. The scaling factor F2J unique
for ail records, was computed by dividing the pseudo-acceleration spectral intensity, SIu of
NBCC desÏgn specttum. by the average of SIa for historical records scaled by FI. SIa was
calculated as an area under the pseudo-acceleration spectral curve for 5% damping, between
0.25 and 0.5 s. These limits roughly correspond to the acceleration-sensitive region of
specttum. The value of F2 and the final scaling factors F1xF2 are listed in column (d) and (e)
ofTable 4.3.
Comparison of columns Ca) and Ce) of Table 4.3 indicates that both methods yielded similar
scaling factors. It was decided therefore, to proceed with the first scaling method described,
based on PHV. This method is simpler~ and is more commonly used among researchers. It
was !ater found that the records exhibiting the greatest difference between columns Ca) and
(e) were among the least influenrial in causing damage.
4-7
4. SELECTION OF DESIGN EARTHQUAKE RECORD
4.2.4 Elastic speetra for historical records
The elastic response spectra were obtained for the seleeted historical records, scaled with
factors shown in column (a) of Table 4.3. lbree percent damping was used for reasons
explained in section 2.3.1.3. Response spectta for pseudo-ve1ocity obtained for the whole set
of selected historical records are shown in Fig. 4.4. Response speetra were also derived for
low and intermediate a/v records separately and the results are presented in Figs 4.5 and 4.6
respectively. The NBCC pseudo-velocity design specttum for Victoria, B.C. is indicated in all
figures.
Response spectra for the low and intermediate a/v group of records show significant
difference in shape. For the low a/v group, larger amplification of PS\. is observed in the
period range from 1 to 2 sec which coincides with the expected first natural periods for
eight- and four-storey EBFs. The shape of the specttum in this region is "pulse-like", which
may indicate higher potential for inelastic damage. For intermediate a/v records, the shape
of the spectrum is more jagged and larger amplitudes of PS,.. are observed at lower periods,
from 0.4 to 1.2s, reaching the maximum at around 0.5s. The second natural periods for eight
and fourteen storey EBF are expected to faIl into this range. Because of this pronounced
difference in spectral shapes, it was decided to treat separately groups of records with
different a/v ratio. The decision was also made to use mean PS~ spectra as the target spectra
for generation of artificial acceleration records, as this correlated better with the NBCC
design spectrum.
The locally weighted linear least squares procedure proposed by Cleveland (1979) was used
to obtain a non-parametric estimate of the mean value of the spectral ordinates as a funetion
of the period. In non-parametric procedures, the prior knowledge of a functional
dependence hetween periods and spectral ordinates is not required, and the impact of
different degrees of smoothness on the estimates cao he easily investigated. Estimates of the
uncertainty on the non-parametric regression can aIso he obtained, in general as a function
of the period.
4-8
4. SELECTION OF DESIGN EARTHQUAKE RECORD
An advanrage of the locally weighted linear least squares procedure over other non
parametric smoothing procedures is that peaks and valleys are not overly smoothed by the
procedure. Smoothness is conttolled through a kemel or weighting function, commonly
taken as the normal distribution function. The degree of smoothness in this case is
controlled by the standard deviation of the distribution. In the extteme, when the standard
deviation approaches infinity, the results are identical to those of linear regression. Objective
functions based on cross-validation can be defined to select the optimal degree of
smoothness; however, a visual assessment is often sufficient in practice.
The smoothed PS... response spectta obtained for both groups of records are illustrated in
Figs 4.7 and 4.8 along with the original PS... spectra. The optimal degree of smoothness was
achieved for a standard deviation equal to 0.3.
4.2.5. Indices to characterize earthquake records
Elastic and inelastic response of structures to earthquake excitation is influenced by a
number of ground motion characteristics such as (i) amplitude of the motion, (u) frequency
content of the excitation, (w) duration and rime of occurrence of the maxima, and (iv)
number and charaeteristics of important acceleration pulses. To understand better these
characteristics, and thus facilitate the generation of artificial record representative of Western
Canada the following ground motion indices were examined as suggested by Christopoulos
(1998) and Tajebi (1994):
(i) Peak ground acceleratioo (pGA) (g)
(u) Time ofoccurrence ofPGA (5)
(tii) Root mean square of accelerogram, RMSA
(iv) Number of zero crossings (Nzq, used to calculate: Ca) oumber of acceleration pulses
(NAP =NZC-l) and (b) predominant period of shaking (pPS =total duration of the
record divided by the O.5NZq
(v) Arias intensity, AI
(Vl) Mc-Caon and Shaw duration: the rime span between the upper cut-off rime (rime
beyond which the derivative of the cumulative root mean square of accelerogram is
4-9
4. SELECTION OF DESIGN EARTHQUA/ΠRECORD
always decreasing) and the lower eut-off rime (rime beyood whicb the reverse
derivative of the cumulative root mean square of accelerogram is always decreasing)
(vil) Bracketed duratioo: the rime betweeo the first and the Iast excursioo of absolute value
of acceleratioo above the eut-off acceleration (set in this study to O.OSg)
(viU) Hudser duratioo: rime oecessary to attain 5% and 90% of total eoergy (aIl based on the
Arias Intensity)
(lx) Trifunac-Brady duration: the rime necessary to accumulate between 5% and 95% of
total energy (based on Arias Intensity)
(x) Spectral inteosity based 00 pseudo-acceleration: in this study takeo as the area under
the pseudo-acceleratioo spectral curve for 3% of damping between periods 0.25sec ta
O.ssec.
(Xl) Specttal intensity based 00 pseudo-velocity: in this study takeo as the area under the
pseudo-velocity spectral curve for 3% ofdamping between periods O.Ssec to 3.0sec.
Results expressed in terms of Mean and standard deviation obtained for low and
intermediate a/v groups of records are presented in columns (a) and (b) of Tables 4.4 and
4.5 respecrlvely.
4.2.6 Generation of the artificial acceleration records
4.2.6.1 Short description ofprogram SIMQKE
Program SIMQKE (Gasparini et al., 1976) was employed to geoerate statistically
independeot accelerograms compatible witb smooth spectra shown in Figg. 4.7 and 4.8. For
each specttum, three different accelerograms were created.
The basis for the spectrum-compatible motion generation is the relationship between the
respoose spectrum values for selected damping and the Ilexpected" Fourier amplitudes of the
ground motioo. Eartbquakes are synthesized by superimposing sinusoidal componeots with
fixed amplitudes and randomly varying phase angles. followed by the multiplication of the
resulting stationary trace by a user-specified intensity function representiog the variation of
ground motion with rime.
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4. SELECTION OF DESIGN EARTHQUAKE RECORD
Each earthquake simulation is unique as the seed number used for generation of the phase
angle is changed for every simulation. The response specttum corresponding ta the
synthesized motion is computed next and compared to a target speettum. The procedure is
repeated severa! times until a good agreement between target and response spectta for the
generated record is obtained. The final result is an accelerogram with desired peak ground
acceleration and frequency content, and with pseudo-velocity response spectrum matching
the desired input speetrum.
4.2.6.2 Input data
Beside the targeted pseudo-velocity spectnun, input data for program SIMQKE include the
desired peak ground acceleration and the range of frequency, description of intensity
function etc. Based on the analysis of the frequency content of historical records, the
frequeney range up to 5Hz was selected for the simulation. The intensity functions were
defined following recommendations by Christopoulos (1998). The duration of strong
shaking was estimated based on Trifunac-Brady definition of strong motion duration
evaluated for historical records. Selected intensity functions are illustrated in Figs 4.9 and
4.10.
To avoid any scaling, an attempt was made to obtain simulated records with peak ground
velocity equal to the one of the site (pGV=0.3m/s). In addition, the desired peak ground
accelerations were set so that the a/v ratios of simulated records would he within the limits
of the genera1ly accepted ranges used in classification (1.2<a/v<0.8 and a/v<O.8 for low and
intennediate groups respectively).
The rime-histories of generated accelerograms matching response spectra for low and
intennediate a/v group of records are shown in Fig. 4.11 and 4.12 respectively.
4.3 Comparison ofhistorical and generated records
4.3.1 Comparison of earthquake indices
The set of indices described in section 4.2.5 was evaluated for the simulated records and is
given in Tables 4.4 and 4.5 for low and intermediate a/v records respectively. Mean and
4-11
4. SELECTION OF DESIGN EARTHQUAKE RECORD
standard deviation for the historical records are also given. The difference between the
parameter obtained for each simulated record and the historical mean is expressed as a
multiple of the standard deviation of the historical record in columns (f)~ (g) and (h) of the
tables.
The characteristics of acceleration pulses along with the duration of strong shaking may have
a significant impact on the inelastic dynamic response of structural systems. Chopra and
Lapez (1979) define an acceleration pulse as a segment of the accelerogram between any two
successive zero-crossing points. A single pulse with bigh acceleration may introduce large
deformations in a structure, and repeated application of long, intense pulses may lead to low
cycle fatigue and incremental collapse. Since in the present study, the records generated were
intended for use in non-linear analysis, the acceleration pulses were studied in more detail.
The following pulse characteristics were examined: the amplitude of the pulse, A (mm/sl,
duration of the pulse, D AP (s), the rime of the occurrence of the pulse Tp (s), the total
number of pulses (NAP), and the number of pulses with the amplitude within the selected
range (Nt~ N so, N too, N2f)J, NochJ, where the amplitude ranges are defined as fol1ows: Nt: A
S10 mm/52; Ns: 10 mm/s2 < A S 50 mm/52; N IO: 50 mm/52 < A S 100 mm/s2; N20: 100
mm/52 < A S 200 mm/5
2; and Nocher: A ~ 200 mm/s2. Results obtained for historical and
generated records for both a/v groups of records are summarized in Table 4.6.
4.3.1.1 Low a/v records
Two out of three simulated records have maximum PGA matching closely the mean PGA
for historical records. It would have been possible to achieve even better agreement since
the desired PGA was incorporated into the generation process, but a compromise had to he
made to obtain a resulting accelerogram with a/v ratio within the preferred range. The
maximum PGA occurs sooner for generated records. As can be seen from Table 4.4, very
good matches were ohtained for Trifunac-Brady and Hudser durations of sttong shaking,
somewhat poorer agreement was achieved for bracketed durations, while Mc-Cann-Shah
durations for ail generated records were found to he significandy higher than the Mean
obtained for historical records.
4-12
4. SELECTION OF DESIGN EARTHQUAKE RECORD
Spectral intensities evaluated both for PSOI
and PSv show very good agreement, which
indicates an excellent spectrum compatibility achieved in the process of artificial records
generation. Higher values of AI and RMSA were observed for simulated records. On
average, accelerations cross the zero line more often for generated records and the
predominant periods are slighdy lower which MaY indicate the presence of higher
frequencies in the artificial records than in the historical ones. However, the consistency of
the frequency content was ensured, since modeIing of the appropriate frequencies (up to
5Hz) has been incorporated into the generation process.
As can be seen from the Table 4.6, the total number of acceleration pulses is higher for the
artificial records, the differences being of 5imilar magnitude for pulses with amplitudes up to
200 mm/52. The numbers of large pulses, with amplitudes between 200 and 500 mm/52 are
comparable. Unlike the historical records, the artificial records have largest acceleration
pulses which are aIso the longest. For both historical and simulated records, the amplitudes
and duration of the highest amplitude pulses are comparable. On the other band, the longest
pulses of the artificial records have higher amplitudes and shorter duration.
4.3.1.2 Intermediate a/v records
Comparison of columns (a) and (b) of Tables 4.4 and 4.5, shows that the intrinsic
charactetÏstics of law and intennediate a/v groups of histarical records are different. The
latter group bas somewhat higher PGA, shorter duration of strong shaking, higher number
of zero crossings, lower predominant period, higher AI and RlvISA, and smaller spectral
intensities for bath PSa and PSv' These observations further justify separate consideration of
the two groups, and the generation ofartificial records ta match two different spectra.
Table 4.5, indicates in general a good agreement between the historical and artificial records
from the intermediate a/v group. Compared to the low a/v group, hetter agreement was
observed for duration of strong shaking, number of zero crossing and predominant period.
Similarly to the low a/v group, AI and RMSA were found to he higher for generated
records.
4-13
4. SELECTION OF DESIGN EARTHQUAKE RECORD
Table 4.6 shows that the total numbers of acceleration pulses compare weil for historical and
generated records. Historical records have somewhat higher number of low-amplitude pulses
(A< 10 mm/s~, and smaller number of pulses with amplitude ranging berween 10 and 200
mm/s2• The number of high-amplitude puIses (200mm/s2<A<SOOmm/s1 is similar.
Observations regarding the amplitudes and durations of the largest and longest acceleration
pulses are identical to those made for low a/v group, except that the amplitude of the largest
pulse is higher for the historical records.
4.3.1.3 S~oIJsis
For both groups of records, the comparison of intrinsic characteristics of historical and
generated records showed in general good agreement berween the two. Just as selected
historical records are considered representative for the design location, so can he the
artificially generated records. Since the generation process included the speetrum
compatibility, similar structural response is e.~1Jeeted, particularly in the elastic range.
However, sorne discrepancies hetween historical and generated records were observed in the
characterisrics ofacceleranon pulses (both groups of records) and duration of strong shaking
(low a/v group). Since bath of these parameters may have significant impact on the inelastic
structural response, it was decided to further evaluate the generated records based on the
results of non-lïnear analysis for an EBF structure.
4.3.2 ComlJarison of structural inelastic resIJonse
The dynamic response to aIl historical and generated records was studied for an eight-storey
EBF fully compliant with strength, stiffness and ducrility requirements of Canadian design
codes (see Sections 3.2.1 and 3.2.2). The ineIastic behaviour of links was examined in tenns
of maximum. induced shear forces nonnalized by the nominal shear resistance Clmu/V~, and
the rruL~um range of shear deformations, max y ange (i.e. the sum of the maximum positive
and maximum negative shear strains). Tables 4.7 and 4.8 snmmarize results obtained for low
and intermediate a/v groups. Mean and standard deviation for historical records are given
while those for simulated accelerograms are shown for cach record separately. The
4-14
4. SELECTION OF DESIGN EARTHQUA/ΠRECORD
differences between the laner results and the mean of the bistorical records, expressed as a
multiple of the standard deviation, provide a basis for comparison.
As illusttated in Figs. 4.12 and 4.13, the distribution of mean CVmu/VJ and mean (ma.~ y ansJover the height of the frame has a different trend for the two groups of historical records.
For both groups, the largest forces occurred at the top storeys, but the ratio of the maximum
induced shear force ta resistance is more uniform for low a/v records. The variation of
defonnations over the height was much more pronounced for the intennediate a/v records.
The shear deformations observed at the top storey were two rimes the deformations found
for low a/v records in the same storey, but their magnitudes significandy decreased in the
mid-portion of the frame.
The same figures illustrate aIso the distribution of forces and deformations obtained for each
simulated record. In generaL good agreement between response parameters for historical
and simulated records was observe~ particularly regarding maximum induced forces. A
somewhat poorer match was achieved for shear defonnations for the low a/v group, but the
general trend was still weIl captured, and the data of columns (t) to (h) of Table 4.7 confirm
that these differences alllie within about one standard deviation.
The study of ineIastic response had demonstrated that the selected structure responded in a
similar manner to historical and generated records, in spite of sorne differences observed in
the characteristics ofacceleration pulses and duration of stroog shaking.
4.3.3 Generated records selected for design
Based on the study of intrinsic charaeteristic and comparison of inelastic structural response
described above, two of the generated records, one for each a/v ratio group, were chosen
for use in the iterative procedure for design location considered. They corresponded most
closely to the historical records, based 00 their intrinsic characteristic and response
parameters. The rime histories of selected records are illustrated in Figs 4.11(a) and 4.12 (a).
4-15
4. SELECTION OF DESIGN EARTHQUAKE RECORD
4.4 Comments on artificial records matching new unifonn hazard spectra
for Canada
The Geological Survey of Canada (Adams et al, 1996) bas developed new national seismic
hazard maps. In addition to ground motions, the maps give unifonn hazard spectra (UHS)
for major ciries developed for finn ground with 10% probability of exceedence in 50 years.
It is anticipated that these maps will provide the seismological basis for earthquake design
requiremeots for the next edition of the National Building Code ofCanada.
Atkinson and Beresnev (1998) have simulated a set of ground-motion rime histories
compatible with the UHS for number of different cities in Canada including Victoria, B.C.
The objective was to provide appropriate accelerograms to engineers wishing to perform
dynamic analysis based on the time-history method. To match short and long period parts of
UHS, for each city two horizontal acceleranoo records were generated for a moderate nearby
earthquake, and two for a large earthquake farther away. For cities in British Columbia,
records were aIso simulated for an earthquake on the Cascadia subduction zone. AlI
generated records reflect appropriate magnitude-distance range and tectomc environment.
It was of interest to see whether these simulated ground motions could be used for the
iterative design procedure proposed herein. For Victoria, a total of eight records was
available, two rnatching short-period UHS (M=6 and R=20km), (Wo matching long-period
event (r\f=7.2 and R=70km), and four for Cascadia events (M=8.5). The characteristic
ground motion parameters are given in Table 4.9.
Selected intrinsic properties, shown in Table 4.10, were calcuIated and compared to those of
the historical records used herein. Simulated records representing Cascadia events have large
duration of strong shaking (frifunac definition), exceeding twice the value found for low a/v
historical records. Records matching UHS for Victoria, have shorter durations of strong
shaking compared to historical records of appropriate a/v ratio, the difference being
particularly pronounced for the (Wo simulated records matching the short-period part of
UHS. The predominant period for all simulated records is around 0.2s which compares well
4-16
4. SELECTION OF DESIGN EARTHQUAKE RECORD
with the value found for intermediate a/v historica1 records, but is somewhat smaller than
the value found for low a/v records (0.3s). The difference is aIso observed in the spectral
intensity (SIJ. With the exception of two records representing Cascadia events, spectral
intensity was significandy smaller for simulated records.
IneIastic response of the eight-storey EBF discussed in the previous section was aIso
examined for all simulated records. Results obtained for maximum inelastic shear forces in
links, and maximum range of the inelastic shear defonnations are shown in Table 4.11. With
exception of one Cascadia record, the forces and deformations are smaller than those
observed for the bistorical records.
While simulated records were generated to match the new UHS (spectral accelerations) for
Victoria, historical records were selected on the basis of PHV prescribed by NBCC (1995).
Levels of earthquake load obtained for UHS do not necessarily have to match those of
NBCC, unless appropriate scaIing factors are applied (Humar and Rahgorzar ,1996). This
may partially explain the differences in results for inelastic response obtained for simulated
and historical records.
It should be noted that the peak ground velocities for accelerograms generated by Atkinson
and Beresnev (1998), do not correspond to PHV expected at the site according to
NBCC(1995). The scaling procedure used in the present study (see Section 4.2.3.4) would
requite adjustment of the accelerations so that the PGV matches PHV of the site. The
resulting scaling factors for sùnulated records are listed in column (a) ofTable 4.12. Column
(b) shows values of spectral intensity (SIv) determined for scaled records. These values
compare much better to results obtained for historical records. As cao be see from Table
4.13, a better agreement cao aIso be observed in terms of inelastic response, if these scaling
factors are applied.
4.5 Summary
This chapter bas presented the methodology used to define the earthquake record for the
proposed iterative design procedure. The objective was to define a unique acceleratioo
4-17
4. SELECTION OF DESIGN EARTHQUAKE RECORD
record, specific to the site. The following steps have been suggested for structures with
fundamental periods in the velocity-sensitive region of the specttum: (i) find earthquake
magnitude and distances that conttibute Most significandy to the peak ground velocity at the
design locatio~ (u) select historical records to match detennined magnitude and distance
ranges, and (m) generate artificial record to match smoothed elastic response speetra derived
for selected historical records.
Typical western Canadian seismic events are expected to have low or intermediate a/v ratios.
Two sets of historical records where thus selected. The analysis of their intrinsic
characteristics and elastic response spectra bas demonstrated significant differences between
the two sets. Artificial records with elastic spectra compatible to smooth response spectra
were generated for each of the two groups. The evaluation of the simulated records was
accomplished through the comparison of relevant characteristics of the accelerograms to
those of the historical ones. Special attention was devoted to the examination of acceleration
pulses, as these influence the inelastic response of structures to a large extent.
In general, the results obtained showed good agreement between historica1 and generated
records. However, sorne discrepancy was observed in the characteristics of acceleration
pulses and duration of strong shaking, and additional study was undertaken to investigate in
more detail their impact on the inelastic structural response. The results of the non-linear
analysis carried out for a typical eight-storey EBF confirmed similarity in the inelastic
response of the structure when subjected to histoncal and artificial records of the same a/v
ratio group.
The proposed methodology thus yielded two artificial accelerograms, one for each a/v ratio
group. These can be considered representative of the chosen design location and are
appropriate for use in the iterative design procedure described in Cbapter 2.
4-18
e
Table 4.1 Contributions to seismic risk (%): PGV equal to O..3m/s
Fig 4.14 Comparison of structural rcsponsc to historical and gcncrated records: Maximum range of link inclastic shear deformations
Chapter 5
APPLICATION OF THE PROCEDURE AS DESIGN TOOL......_iiiiiiiiliiiiiiliiiiiiiiiiiiili_iiiiiiiiiiili__iiiiiiiiiliiiiiiiiiiiiiiiiiiiiiiiiiiiliii_liiiiiliiiiiiiiiilliiiiiiilliiiiiiiiiiiiiiiiiiiiiiiiiiiiliilliiiiiiliiiiiiiiiiii&
1bis Chapter describes the use of the proposed iterative procedure for seismic design of
EBFs. The application is illustrated wough e.xamples of three Chevron-type EBFs, these
having four, eight and fourteen storeys and located in Victoria, B.e. The initial frame
members are selected based on sttength, stiffness and ductility requirements of the Standard
(CSA 1994), thus following current Canadian design practice. The propased iterative
procedure is carried out for two generated acceleration records obtained fallawing the
methodology described in the previous Chapter. Ta evaluate the extent to which the iterative
procedure achieved the desired frame behaviour, the inelastic response of members is
examined for the set of historical acceleration records described in Chapter 4. The response
parameters for the final structures are compared to those obtained for the initial structures
for the same set of acceleration records. The current Canadian design procedure and the
proposed iterative procedure are then examined in the Iight of these results.
5.1 Design of initial structures
It was demonstrated in Chapter 3 that the iterative procedure was not sensitive ta the initial
design. Structures to initiate the iterative procedure were thus selected following the present
codified procedure for seismic design of EBFs in Zone 5, to provide a basis for comparison
of the two design procedures.
Details of designs of three initial frames with four, eight and fourteen storeys are described
in the following sections. In aIl cases, frame members were first seleeted to camply with
ductility requirements, and subsequendy verified for sttength and stiffness. This sequence is
appropriate for zones with severe seismic loading.
5-1
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
5.1.1 Building layouts and frames elevations
Typical building Iayouts and framing arrangements considered are illustrated in Fig. 3.1. The
Iayout for the eight-storey frame is based on Chien (1987), while those for four and fourteen
storey frame were adopted from Wong (1997). These layouts represent typical commercial
building structures. For each building height, the lateral resistance in one horizontal direction
was provided by two single-bay EBFs located in the central core. For four and fourteen
storey buildings the same late..ral system was provided in the other horizontal direetio~ while
the eight-storey building had two peripheral moment-resisting frames in that direction.
5.1.2 Load calculations
5.1.2.1 Gravity load
The eight-storey frame was subjected to gtavity load specified by Chien (1987). Gravity loads
for the foUI- and fourteen-storey frame were determined following recommendations by
Wong (1997) (see aIso Han(1998». A summaty of dead and live load for aU three frames is
given in Table 3.1. Loads were applied as unifonnly distributed loads on the beams and
concentrated loads on the columns.
5.1.2.2 Seismic Joad
Summary of the seismic load calculation is shown in Table 5.1. The design base shear, V,
was calculated according to NBCC (1995) as follows:
[5.1] V=(Vc:/R)U = (vSIFW/R)U
where S=1.5/VT (for T > 0.5s); T=0.09~VOs; ~ is the height of the structure in meters; Ds
is the width of the braced bay in meteIS; v is the zonal velocity ratio; U is the calibration
factor, W is the weight of the structure +25% snow, and R is the force reduction factor for
EBFs. AIl relevant parameters are summarized in Table 5.1 for all three frames.
As the fondamental natura! period of many steel structures exceeds the code formula vaiue,
the design was carried out using a base shear on the building of 80% of the value shawn in
5-2
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
Table 5.1, as permitted by NBCC (1995). The period of the structures designed was
subsequendy found to he high enough to justify this procedure.
The base shear was diswbuted over the height of the buildings according to requirements of
NBCC (1995). No change in base shear magnitude was made to account for torsion in order
to maintain the consistency between the design and the dynamic analysis performed !ater.
Total seismic load on each single EBF (i.e. one-half of that on the structure) applied at each
storey is given in Table 5.1.
5.1.2.3 Wind Joad
\Vind loads were determined according to NBCC(1995). The specified extemal pressure, p,
is given by:
where q is a reference velocity pressure, Cc: is exposure factor, Cg is gust effect factor and Cp
is extemal pressure coefficient. Summary of wind load calcuIations for 1/10 and 1/30 years
wind for all three frames is given in Table 5.2.
5.1.3 Ductility design
5.1.3.1 General
The ductility design was camed out using an EBF seismic design program (EBFSD)
developed by Han, Redwood and Kasai (1997). The program incorporates the requirements
of Clause 27 of CAN/CSA-S16.1-94 cliscussed previously in the Chapter 2. Some
procedures that go beyond the current Canadian provisions cao aIso be used, such as the
design of members of frame other than links using different amplification factors and
inclusion of moments in column design.
The program EBFSD is briefly described in the following. Shear forces in links are
calculated following the procedure shown in Fig. 1.11. Axial forces induced by earthquake
loading in other frame members are detennined using an approximate statie approach
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5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
(Redwoo~ 1995) illustrated in Fig. 5.1. The effeets of the appropriately scaled gtavity loads
(1.00 and O.5L) on hraces and columns are subsequendy included. The effect of the gtavity
load comhination (1.25D+l.5L) is also considered for column design since it may he critical
for the top tier columns. Bending moments in heams and hraces are calculated using
expressions developed by Kasaï and Han (1997). Bending moments in columns are included
using equation 1.1 (see section 1.4.2). A more detailed description of the EBFSD program
can be found in Han, Redwood and Kasaï (1997).
5.1.3.2 Modeling assumptions and section selection
Link beams were chosen from Class 1 W sections and assumed fully laterally supported.
Selected sections are shown in column (a) of Tables 5.3, 5.4 and 5.5 for four, eight and
fourteen storey frames respectively. The link resistance-to-force demand ratios (a) are listed
in column (b) of the same tables.
Braces were designed as Class 1 or 2 HSS sections. The effective lengtb factor for in-plane
action, K, was taken as 1.0, as required by the Standard while for the out-of-plane action, Ky
equal to 0.9 was selected, relying on the stiff laterai and torsional bracing required at the link
ends. Columns were selected from Class 1 or 2 W or WWF sections, and the same cross
section was maintained in two storey segments. Columns were assumed continuous and
laterally unsupported between storeys. Effective length factors, I<x and Ky, were taken as 1.0.
It should he noted that aIl the calculations were done with the resistance factor, tP, equal to
1.0, as specified in CSA (1994). Selected brace and column sections are given in columns (c)
and (d) of Tables 5.3, 5.4 and 5.5. The total mass of the structures and fundamental periods
are also included.
5.1.4 Sttength verification
Sttength verification was carried out using the program SODA (Waterloo Engineering
Software 1991). In addition to performing analysis and verification of structures for North
American code requirements, SODA can aIso he used to automatically design steel frames
for static loads while oprirnizing the structural weight.
5-4
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
The following loading combinations were considered in strength verification of the three
EBFs:
(1) 1.25D+1.5L
(2) 1.25D+1.5W1/ JO
(3) 1.25D+0.7(1.5L+ 1.5W,/JtJ
(4) 1.0D+0.5L+1.0E+P.â2
For seismic loads P-â effects must be based on elastic deflections multiplied by ~ and the
automated second-order routines available in SODA could not be employed as they are not
based on such amplified defonnations. Therefore, equivalent latera1loads PL12 were used to
account for these effects in loading combination (4).
For the four-storey frame, no further modification of sections was required ta satisfy
strength requirements. For eight-storey frame, beams in storey 3 and 5 were increased by
one size (W530X74 and W460X67 with (X equal to 1.18 and 1.11 respectively), resulting in
increase of structural mass of less than one percent. In gen~ the sections in eight-storey
frames were better utilized compared ta the four-storey frame. The beams had particularly
high response ratios (between 0.90 and 0.98), columns somewhat Iower (0.8 to 0.85) while
brace sections were the least efficient (response ratios between 0.6 to 0.8). For the four
storey frame, response ratios for all member groups varied between 0.65 and 0.75.
Strength requirements imposed more important section modifications in the fourteen-storey
frame. Halfof the heam sections were increased, as weIl as braces in the rwelfth storey. In an
effoIt to maintain the parameter (X as uniform as possible over the height of the frame, sorne
additional modifications of beams were aIso necessary. Nevertheless, the increase of
structural mass was ooly about four percent. The final sections seleeted ta camply with
sttength requirements are shown in coIumns (a), (c) and (d) of Tahle 5.6.
5-5
5. APPUCATION OF THE PROCEDURE AS DESIGN TOOL
5.1.5 Stiffness verification
Inter-storey plastic~ evaluated based on the elasttc deformations multiplied by R, was
aIso checked for aIl frames. The acceptable Iimit for regular structures under seismic loads is
defined by NBCC (1995) as (WO percent of the storey height (O.02hJ. The eight storey frame
just satisfied this requirement, whereas the four storey frame exhibited maximum inter
storey drift of about one-half of the limit. In both cases, the top storey was the crirical
location.
For the fourteen-storey frame, the inter-storey plastic drift reached 0.03 ~ in the top aine
storeys thereby exceeding the codified value by 50 percent. Hence, it was necessary to
further revise the frame design. For taller frames, a..xial deformations of the columns
contribute more significandy to lateral storey defonnattons as compared to lower &antes, for
which hrace contributions are predominant. Increasing bottom column sections was
confirmed as the most efficient way to control inter-storey drift in upper storeys. "Fine
tuningft of column and braced sizes in storeys with excessive drift was then made. The
snmmary of revised sections is given in columns (e) and (f) ofTahle 5.6. The structural mass
of this desigü iùcre~ed by 30 percent compared to the design complying with ductiIity and
strength requirements, described in the previous section.
5.1.6. Verification of the link inelastic shear deformation, y
The Iink shear defonnarion, y, is limited by the provisions of Clause 27.6.4 to 0.09 radians
for shear links. To finalize the design, the plastic link rotations were calculated as described
in Section 1.3.1 and compared to the codified limits. The storey drift angle, 9drift used to
calculate y is related to the fust-order elastic drift amplified by O.SR.
VaIues of y obtained for each of three frames in ascending order of the heights were
O.OSrad, O.08Srad and O.089rad, all being within acceptable limits. The three designs were
thus in full conformity with Canadian requirements for ductiIity, strength and stiffness. Note
that an allowance for column moments following Iink yie1ding bas aIso been included, a
feature not specified in CSA (1994).
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5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
5.2 Final designs
The iterati.ve procedure was then applied for the two generated records discussed in Chapter
4. Final designs were fust obtained for the artificial record from the low a/v group and then
verified for the artificial record from the intennediate a/v group.
The analysis was carried out assuming that beam segments outside the links could exlubit
sorne yielding as long as the stability of these members was ensured. In general, this
approach yields greater economy, since the strict avoidance of ine1astic behaviour in outer
beam segments causes a significant increase of section size, which in tom affects the size of
other members of the frame.
Based on the previous srudies (Koboevic and Redwood, 1997), P-â effects were not
accounted for in the analysis. These srudies demonstrated that second arder forces had
much less effect on inelastic structural respoose than what was suggested by their impact in
the design process.
~fodelling of links and other members of the frame followed the details described in sections
2.3.1.2, 2.3.1.3 and 5.1.3. Special attention was giveo to inclusion of the gravity load since the
program ANSR-1 does not feature the option to specify the unifonnly distributed loads on
the beam-column elements. The gravity forces were thus applied as concentrated loads on
columns at each storey level, while the effects on beams and braces were taken into account
for through initial forces. These forces are used to initialize the element end actions and are
not converted into loads on the nodes. The ooly effect they have on the behaviour of the
system is to influence the onset of plasticity and to affect geomettic sriffness, if considered
Initial forces were specified as bending moment for beams at the beam to brace jonction and
the axial force for braces.
The procedure converged in three, five and two iterations for four-, eight- and fourteen
storey frames respectively. The members seleeted for the low a/v record exhibited
satisfactory behaviour for the intermediate a/v record. The ooly exception was the top
column tier in the eight-storey frame, which was subsequeody increased by one size. The
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5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
final selection for brace and column sections is given in Table 5.7. Link beam sections are
not listed; they are identical to those of the initial designs.
5.3 Study of the inelastic response
5.3.1 General
To evaluate the success of the two design methods in producing structures with the desired
seismic behavioUIy the inelastic response of initial and final designs was examined. To
facilitate discussion in the following sections, the two designs are denoted as "Set 1" and
"Set 2" structures respectively. For the fourteen-storey frame, the iterative procedure
imposed only the modification of one brace section in the first storey. This minor change
was not expected to influence the dynamic response in any significant way and therefore for
this frame height only the behaviour of the initial design was studied. The non-lïnear
dynamic analysis was carried out for the fourteen bistorical records described in Section
4.2.3.3. With a/v ratios in the low and intermediate ranges, these records are representative
ofwestern Canadian seismic events.
The results presented hereinafter pay particular attention to; (i) location of the inelastic
activity, (u) number and duration of inelastic excursions, (m) maximum induced shear forces
and shear deformations of the linksy (VI) maximum inelastic rotations of outer beam
segments and (vil) inter-storey drift. For each record within the same a/v group the
maximum values of the response parameter considered are found at every storey, and the
mean and mean plus one standard deviation are evaluated for each of the two record groups.
Comparison with design limits prescribed in the Standard, discussed in the following
sections, was in ail cases clone with respect to the mean plus one standard deviation.
5.3.2 Response of the initial structures (Set 1)
5.3.2.1 Four-storey &ame
As foreseen in both design procedures, a considerable amount of yielding took place in the
links. The fOUI-storey frame was equally affeeted by both a/v groups of records.
Simultaneous yielding of al1 four links was frequendy observed for twelve of the fourteen
records. As indicated in Table 5.8, the energy dissipation took place mosdy in the three
5-8
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
bottom links, an~ for both groups of records, the contnbution of the bottom storey link
was the most signifiant.
The maximum induced shear force was normaIized by the nominal shear resistance of the
Iink CYp= 0.5s~y) and the results are illustrated in Fig. 5.2. All1inks developed shear forces
of similar magnitudes, with peak values slighdy higher for intennediate a/v record group.
The overload value assumed in design (1.35V~ was exceeded in all storeys up to a maximum
of about 25 percent. Detailed results are listed in Table 5.8.
As can be seen from the same table, alllinks experienced significant inelastic shear rotations.
The limit prescribed by the Standard (O.09rad) was exceeded in all but one storey, with the
maximum reaching about 0.17 rad in the top storey for both groups of records. However,
with the exception of the top storey link, the maximum range of shear deformations, max
YratlgI:' as defined in section 1.2.1, was within 0.18 rad. The range was identified by Kasaï and
Popov (1986b) as the important parameter in characterizing link ductile behaviour. The same
study has demonstrated that a proper1y stiffened short link can safely sustain a shear
deformation range of this magnitude.
The extent of overload of columns and braces is shown in Table 5.9. This is expressed as the
summation of the number of rime increments (each of 0.04s, chis being the frequency with
which the output was saved) during which any column or brace in the frame was subjected
to forces greater than the nominal resistance for a particular earthquake record. Instability of
braces and columns was observed for all records. With the exception of one record, the
columns in the top storey and the second storey were not affected. Compared to lowa/v
records, the intennediate a/v records cause more frequent loss of stability in braces. The
least affected braces for both groups of records were chose at level two.
Columns (a) and (b) of Table 5.10 snmmarize results for the inelastic rotations of the outer
beam segments. The maximum absolute rotation within one rime step and the absolute
maximum accumulated inelastic rotation are identical, which indicates that the critical outer
5-9
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
beam segment yielded ooly once during the loading history. The magnitudes of inelasric
rotations are all weIl below O.Dlcad.
Results for inter-storey drift are shown in columns (e) and ID of Table 5.8. The location and
the magnitude of the maximum. drift varied with the particular record. On average slighdy
higher values were obtained for intermediate a/v records. For both groups of records the
codified limit of O.D~ (equal to 74 mm) was exceeded in the top storey, and reachcd
maximum values of about 80 mm. Note that a sttong correlation between the maximum.
inter-storey inelastic drift and maximum inelasttc shear rotation was evident in both location
and magnitude.
5.3.2. 2 Eigbt-storey &ame
Low a/v records induced much more yielding in the links of eight-storey frame than the
intermediate a/v records. While for the first group all eight links were often observed to
yield simultaneously, for the second group, the top storey link yielded most frequendy, and
the maximum number of links yielding at the same rime did not exceed five.
As illustrated in Fig 5.3, distribution of maximum shear force over the height of the
structure was different for the two groups of records. For low a/v records, links in ail
storeys developed shear forces of similar magnitudes with slighdy higher values observed in
the top three storeys. The overload value anticipated in the Standard was exceeded in ail
storeys by the same margin found for the four storey structure (about 20 percent). For
intermediate a/v records, ooly the top two storey links attained shear forces comparable to
those caused by low a/v records. Shear forces observed in aIl other links were within the
predicted limits.
As can he seen from Table 5.11, maximum shear defonnations followed the trends found
for the shear forces. In general, links in the eight-storey frame underwent smaller
defonnations compared to those of the four-storey structure, with the exception of the top
storey link where the maximum of0.205 rad was observed for intermediate a/v records. For
this record group, this was the only storey where the limit of 0.09 rad was exceeded While
5-10
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
the shear deformations were concentrated in the top storey for intennediate a/v records,
they were more equally spread betweeo the storeys for low a/v records. In three storeys the
recorded value was higher than the design limit, with maximum excess of about 30 percent.
In ail cases but one, the maximum range of shear deformations was within the acceptable
range for both groups of records.
As indicated in Table 5.12, loss of the stability of braces and columns was predicted for ail
but one record. Unlike in the four-storey structure, the observed damage in braces and
columns was mainly concentrated in the upper two storeys, this being the case for both
groups of records.
Results for the inelastic rotations of outer beam segments are summarized in columns (c)
and (cl) of Table 5.1O. ~Iagnitudes of observed inelastic rotations were larger than those in
the four-storey frame. The ma..'CÎmum inelastic rotation within any rime step slighdy exceeded
0.015rad, and the maximum accumulated inelastic rotation was O.025rad. The ductility
demand 00 these beam segments was assessed using the analogy with long EBF links
predominantly vielding in flexure. For this type of 1ink, CSA (1994) imposes a rotation limit
ofO.03rad to insure stable hysteretic behaviour. Thus, it was judged that the inelastic rotation
of the outer beam segment smaIler or equal to 0.03 rad could be considered acceptable.
Results for the inter-storey drift are given in columns (e) and G) of Table 5.11. Similarly to
the four-storey frame, the maximum. values occurred in the same storey as the maximum.
inelastic shear rotations, and the distributions of the two over the height of the frame had
similar trends for both groups of records. The design limit (72mm) was exceeded oaly in the
top storey for the intennediate a/v group.
5.3.2.3 Founeen-storey &ame
Of the three Set 1 structures studied, the fourteeo-storey frame experienced the least
inelastic activity in the links for ail records. The maximum number of simultaneously yie1ding
links was e1even but this was for only two of the fourteen records; for all the others, the
maximum number did not exceed six. For both groups of records, very little inelastic aetivity
5-11
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
was observed in the top storey link. Most of the energy was dissipated in the bonom link,
however for intermediate a/v records significant energy dissipation occurred aIso in the Il th,
12th and 13th storeys.
As shown in Fig. 5.4, similar distributions of shear force were obtained for bath groups of
records. In general, higher forces developed in the top and the bottom part of the frame.
The abrupt change of shear force magnitude was observed in the top storey link. It should
be noted that this link had the largest a (see Table 5.7) amongst all the links in frames
examined, for reasons of providing the pure shear link at that location.
The link shear force magnitude distributions were slighdy more uniform for low a/v records.
For bath groups of records, the largest forces were observed in the twelfth storey, exceeding
the overload value anticipated in design by 20 and 25 percent for low and intennediate a/v
records respectively. To a smaller extent, the design limit (1.35V~ was aIso exceeded in the
bottom of the frame. The maximum shear forces in all other links were within the limits for
both groups of records.
Columns (b) and (c) of Table 5.13 summarize the results for inelastic shear rotations.
Maximum values slighdy surpassed the design limit (0.09rad) in one storey for low a/v
records, and in four storeys for intermediate a/v records. Maximum deformations were
concenttated in the upper part of the structure, varying between 0.09 to O.l2rad. They are
significandy smaller than those found for four and eight storey frames. The maximum range
of shear defonnations was well within the admissible limits, and did not exceed O.14rad for
any of the records studied.
For five of the fourteen records, sorne instability of braces was predieted, aIl of this in the
first storey and was of significandy smaller scope than for the four- and eight-storey frames
(see Table 5.14). AIl of the columns had the desired elastic response.
5-12
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
As shown in columns (e) and (f) of Table 5.10. outer beam segments developed some very
restricted yielding with IDa...wnum. ine1astic rotations of ooly O.OO2rad The inter-storey~
shown in columns (e) and G) ofTable 5.13. was well below the design limit (74mm), reaching
a maximum value of 50mm. The correlation between the Înter-storey drift and maximum.
inelastic shear rotation found for the {\VO other frames was also observed.
5.3.3 Response of the final structures (Set 2)
5.3.3.1 Response of the links
The amount of yielding observed in links of the Set 2 structures was similar to that observed
in the links of Set 1 structures. The location of inelastic activity as weIl as the number of
links yielding simultaneously were comparable for all records studied. This was anticipated,
since the link sections of final and initial desjgns were the same.
Table 5.15 shows the distnbution of the ma.,Qmum induced shear forces for the four- and
eight-storey frames. For the four-storey frame the iterarive procedure was effective in
reducing peak values (mean plus one standard deviation), although slighdy higher values
were observed in a few cases for the Set 2 structures. A more uniform distribution of forces
was also achieved. For the eight-storey frame, little difference was observed in the shear
force magnitudes for the initial and final designs.
The results obtained for inelastic shear rotations are summarized in Tables 5.16 and 5.17.
While the links in the Set 2 four-storey frame deformed less for low a/v records compared
to those of the initial design, the defonnations of the latter slighdy increased for the
intennediate a/v records. The design limit of 0.09rad was exceeded in the same storeys as in
the initial frame. The peak value of the ma..~ yrange for low a/v records was reduced to 0.15rad,
whereas for the intermediate a/v records the peak value of max Yange still remained weIl
above the acceptable limit of O.18rad.
For the eight-storey frame, the procedure was more successfui in controIling the ine1astic
shear rotations. The peak values were significandy reduced for links in the Set 2 structure for
both groups of records, exceeding the design limit ooly by a small margin. In addition, the
5-13
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
distribution of y became more uniform, which was particularly noticeable for the
intennediate a/v records.
The improved behaviour of links in Set 2 structures was mainly achieved in tenns of more
uniform distribution of maximum Iink shear forces and defonnations. Overall response of
links in Set 1 and 2 eight-storey frame was monitored through coefficients l:l:Vdiff/l:ny and
~~ydiff/l:ny, where l:l:Vdàrr/~nV is the sum of differences between the actual Iink shear force
and 1.35Vpt l:l:Ydiff/l:ny is the sum of the differences between the actuallink ine1astic shear
rotations and 0.09rad, while Lny and ~ny represent the number of rime steps in which the
links shear forces and inelastic rotations exceeded 1.35Vp and O.09rad respectively.
Summation was done for links in aIl storeys at instances when yielding of Iinks occurred, and
results are expressed as mean values for each a/v group of records. As indicated in Table
5.18, in aIl cases, smaller values of these coefficients were observed for Set 2 structure.
5.3.3.2 Response ofother members of the frame
The desired elastic response of columns and braces can he guaranteed ooly for the records
which were used in the iterative design procedure. Thus, for the historical records used in
this response study sorne instability of these elements can be anticipated. The study of the
inelastic response of the Set 2 structures confirmed that the iterative procedure was
particularly successful in decreasing stability problems of columns and braces. The results
obtained for these structures are summarized in Table 5.19.
The overaIl ductility demand on the outer beam. segments has a1s0 decreased for the Set 2
structures. The results for four- and eight- storey frame are illustrated in Table 5.20.
Somewhat larger rotational demand on the Set 2 eight-storey frame was observed for one
record ooly, this still being below 0.03rad
5-14
5. APPLICATION OF THE PROCEDURE AS DESIGN TOOL
5.3.3.3 Inter-storey drift
Results obtained for inelastic inter-storey drift for Set 2 structures are given in Table 5.21. In
aIl cases, the procedure successfully reduced this drift, and the maximum exceeded the
design limits only by a very small margin.
5.4 Comparison of two design procedures
The following observations are based on the results presented in previous sections:
(i) For taller structures the two design procedures yielded almost identical structures. For
these frame height, the goveming design requirement of the current design procedure
was the inter-storey inelastic drift;
(u) In both approaches, for all three frames, the overload in links exceeded the value of
1.35 VP' used in the current design procedure;
(w) Although the beams were identical for the two sets of structures, the link overload was
in genera1 slightly smaller in the structure obtained by the iterative procedure, and the
distribution of the maximum shear forces was more uniform;
(Iv) High values of inelastic shear defonnations were observed for structures produced by
both procedures;
(v) In general, inelastic shear deformations exceeded the present design limit of O.09rad by
a sma1ler margin for structures designed using the iterative procedure;
(Vl) Strong positive correlation was observed between maximum inelastic shear rotations
and inter-storey drift;
(VÏJ.) Maximum inter-storey drift was doser to the design limit (2% of storey height) and
better controlled for structures obtained by the iterative procedure;
(vÜ1) For both procedures, the outer beam segments underwent small inelastic rotations;
(L"'C) Signïficant reduction of column and brace distress (loss of stability) was observed in
the structures designed following the iterative procedure.
It should he noted that the columns in the initial structures were in fact designed with an
aIlowance for the effeets of bending moments as suggested by Kasaï and Han (1997).
Without this additional constraint, which is not a part of cun:ent Canadian procedure,
columns would have experienced even more distress.
5-15
5. APPUCATION OF THE PROCEDURE AS DESIGN TOOL
5.6 Summary
This Chapter bas applied the proposed iterative procedure for seismic design of EBFs to
three frames with four, eigbt and fourteen storeys. The procedure was iniriated with the
designs fully complying with the present codified requirements. While for the lower frames,
the brace and column sections of initial and final designs differed, for taller frames, both
approaches yielded almost identica1 structures.
The success of the two design approaches in producing EBF structures with the desired
seismic response was evaluated by comparing the dynamic response of corresponding pairs
of designs for the selected histoncal records. For both design approaches, high shear forces
and deformations were observed, particularly for the lowest frame. The overloads in links
exceeded values anticipated in the current Canadian design procedure. The proposed
method however, in general, conttibuted to a more unifonn distribution of link shear force
over the height of the frame, and resulted in slighdy reduced overload. The maximum
inelastic sbear rotations were better conttolled in these structures, and 50 was the inter-5torey
drift. The most significanc improvement in the behaviour was observed in the response of
hrnce~ ~"d t:'oh.!mns, wmch exhibited much less disttess compared to those of the structures
Fig. 5.3 Eight-storey frame, Set 1: l\rla.ximum nonnalized link shear forces
.. - - i............ / 1.,.,- ~
-~~ !
~- 1
/ ....1
./" r. :1 -.- L.ow-.,v !~ ~ -- (ntermediare a/v 1
............ "" . i""-. ~ !~-- .... ;
!
14131211109
f ~en 6
54321o
1.0 1.2 1.6 1.8
Fig. 5.4 Fourteen-storey frame, Set 1: Ma.ximum nonnalized link shear forces
5-39
Chapter 6
STUDY OF THE SEISMIe SERAVIOUR OF EBF'S._-----~-iiiiiIiIiiiiiii8llli----------..
Developed analytical tools are used to investigate further and understand better the seismic
behaviour of EBFs and the relevant findings of those studies are described in this Chapter.
Modifications of seismic design requirements proposed for the new edition of CAN/ CSA
S16.1 are examined fust. The ineIastic response of the eight-storey EBF designed following
these modified requirements is compared to that of the structure designed using the iterative
procedure. Attention is then directed to seismic force profiles, magnitudes of axial forces
and moments for ductility design of columns, fôrce modification factors and relationship
between inelastic inter-storey storey drifts and inelastic Iink deformations.
6.1 Future EDF seismic design requirements: proposai for CAN/CSA
S16.1
6.Ll Summary ofproposed modifications
In this section, a draft proposaI (Redwood, 1999) for revisions to the Canadian standard for
steel structures, CAN/CSA-S16.1, is examined. Important modifications of the seismic
requirements of Clause 27 are anticipated, induding those affecting design procedures for
EBFs.
The current Canadian requirements for the design of EBFs, specified in CAN/CSA-S16.1
94 were discussed in Section 1.3.2. In the following, sorne of the proposed design
requirements are summarized and differences between the !Wo are outlined (typescript in
italics gives an outline of the new proposaIs).
6-1
6. STUDY OF EBF'S SEISMIC BEHAVIOUR
(i) Beam segments outside of the links are designed for link forces calculated based on
the nominal strength ofthe link (0.55 wdFyfor shear links) multiplied by 1.3Ry- When
subject to these forces, the beam resistance can be taken as Ry times the nominal
resistance. R, ;s a factor by wh;ch the specified minimum yield stress is multiplied to
give the expectedyield stress. Unless obtained directly form material coupon tests, R,
;s ta be ta!œn as 1.1, but the product RyE'y should not exceed 385MPa.
In the current Standar~ the factored resistance of the link 0'r = epO.55wdF'f for shear links,
where ep=0.9), calculated using the specified minimum yield stress (00 1\ factor), is
multiplied by the amplification factor 1.5 ta 0 btain design forces in the outer beam
segments. The beam resistance is taken as the nominal value, but is detennined using the
specified minimum yield stress.
(U) Forces in the braces are found using the same amplification factor as the one in
design ofthe outer beam segments (J.3R,), applied ta the nominal strength ofthe Unie.
Braces must have adequate factored res;stance to support these forces, calculated
using the specifled minimum yield stress.
Similarly ta the outer beam segments, in the cw:rent Standard, forces in braces are evaluated
using the amplified link forces of 1.5Vr• Braces are then selected 50 that they have an
adequate nominal resistance ta support those loads.
(Ui)To calculate axialforees in columns due to yielding and strain-harden;ng in links, the
nominal strength ofthe link is multiplied by 1.15R,. For the top two storeys, however,
the amplification factor of J.3R, is used The cumulative effect ofyielding links is
combined wilh the gravity loads. Columns should have adequate factored resistance
to support these loads, calculated using the specified minimum yield stress. The right
hand side ofthe interaction equation ofClauses 13.8.1 and 13.8.2 must be reduced to
0.85 to accountfor the moment contribution.
6-2
6. STUDYOF EBF'SSEISMIC BEHAVIOUR
In the current Standar~ axial forces in columns are ca1culated using the amplification factor
of 1.25 applied to the factored resistance of the 1ink. The same amplification factor is
specified for links in aIl storeys. No provision is made to include bending moments resulting
from column continuity and relative storey drift. l'hus, the right band side of the interaction
equations mentioned above is 1.0, as originally specified in the Standard. Column resistance
is taken as the nominal value.
(iv) The inelastic rotation of the link segment relative 10 the resl of the beam. y, is
calculated at a frame drift of (R-I) times the elastic drift determined for factored
seismic loading. The resulting values shall not exceed the following limits: (a) 0.09
radians for links with length of1.6M~p or less and (b) 0.03 radians/or links with
length of2.6M,lVp or greater. For links with lengths between the above values. the
limits are obtained by linear interpolation.
In the current Standar~ the inelastic Iink rotation, "f, is calcuIated at the frame drift of O.5R
rimes the elastic drift detennined for faetored seismic loading. Acceptable limits for "f, are
unchanged
6.1.2 Evaluation ofproposed design requirements
To assess the effectiveness of the proposed designed requirements m overconung
deficiencies identified in the current codified design procedures, three chevron-type EBFs
\vith four, eight and fourteen storeys were designed to comply with the proposed
requirements, and their inelastic response was studied for the set of historical ground
motions. The geometty of the frames, loading conditions and acceleration records used in
the analysis were identical to those reported in Chapter 5.
For alI three frame heights, members were first seleeted based on duetility requirements, and
subsequendy examined for sttength and inter-storey plastic drift. Verifications of inelastic
Iink rotations were included in the ductility design phase. Subsequendy in this Chapter, the
structures compliant with the proposed Standard are designated as Design A.
6-3
6. SroDYOF EBF'SSE/SMIC BERAV/OUR
Non-linear response of Design A was monitored separate1y for low and intermediate a/v
records by tracing the maximum shear forces and deformations of links, numher of rime
increments in which columns or braces experienced 1055 of stability and inter-storey drift.
For each group of records, the results are presented in terms of mean plus one standard
deviation. Comparison is then made with the results obtained for the structures designed in
compliance with the current Standard (Design B) and the those designed using the iterative
procedure (Design q.
6.1.2.1 Four-storey &ame
A list of the sections selected to satisfy ductility requirements is shown in Table 6.1. No
additional modifications of sections were necessary to satisfy strength or inelastic drift
requirements. The following observations can be made when comparing this design to
Designs B and C (see Table 5.2 and columns Ca) and (d) of Table 5.6):
(i) In ail cases, link beams sections are similar, with sorne slighdy larger sections seleeted in
the Design A frame. AlI three approaches would have yie1ded exacdy the same sections
for the link itself, since the requirements are unchanged. Observed differences in section
sizes thus arose from the revised design requirements for the outer beam segments. The
link forces used to compute Ioads in these segments are effectively slighdy lower in the
new proposai compared to the current Standard (1.30Vp and 1.35Vp respective1~.
However, the limits for Class 1 sections are more severe in the former case, since they
are calculated based on Rf/, this therefore being the reason for some slighdy increased
sections.
(11) Brace sections of Designs A and C are comparable, although those se1ected in Design C
had slighdy higber resistances. For all storeys, brace sections of Design B were in general
one size smaller compared to those of the two other designs.
l In the current Standard, beam forces are calculated based on lin.k force of 1.S'Vp, where ,=0.9,which gives 1.35Vp• In the proposed Standard, the calculation is based on 1.3RyVp- This needs to befurther adjusted, since the beam resistance in the former case is based on Fr, while in the latter case itis based on RrF)". Thus, for consistent comparison 1.3R.yVp should be divided by R,., which yields linkforce of 1.30Vp.
4 A recent revision to this proposai suggests that Rf be included in these limits only if Ry>l.1.
6-4
6. STUDY OF EBF'S SEISMIC BEHAVIOUR
(m) Design B has in genera1 the smaIlest column sizes. The bottom column tier of Designs A
and C is comparable, but a somewhat larger column section was selected for the top
column tier in Design C.
(IV) Designs A and C have similar structural mass, which is about 20% greater than Design
B.
(v) Largest ine1astic 1ink rotations were predicted in Design A with a maximum of O.07rad in
the top storey link (see Table 6.2(a».
(VI) With the exception of one storey, the smallest inter-storey ine1astic drift (R rimes the
elastic drift) was predicted in Design C (see Table 6.2(b».
Tables 6.3 to 6.5 summarize results of non-linear time-history analysis carried out for Design
A. For easier comparison with Designs B and C, the maximum shear forces and
defonnations for aIl three designs are plotted in Figs 6.1 and 6.2, while Table 6.6 allows a
comparison of the inter-storey drift responses. The following observations can be made:
(i) Similarly to Design C, Design A decreased the peak values of link shear forces (up to
5%) compared with Design B. More uniform distribution of the forces over the height
of the frame was aIso achieved, but the design limit was still exceeded by up to 20
percent.
(ii) Design A was the most successful of the three in conttolling the link inelastic shear
rotations, y. With the exception of the top storey link, where excessively high rotation
was observed for intennediate a/v records (O.214rad), y was rather uniformly distnbuted
and exceeded the allowable design limit ooly by one percent. With exception of this one
storey, max Yange was aIso the smallest observed among the three designs.
6-5
6. SruDY OF EBF'S SE/SMIC BEHAV/OUR
(m) Design A was not as effective as Design C in decreasing buce and column distress. In
fact, the 10ss of stability of these elements observed in Design A was comparable to that
of Design B.
(lV) The analysis has shown that the inter-storey drift exceeded the values foreseen in design
for aIl three structures, particularly in the top storey of Design A for intermediate a/v
records where a drift of 2.8 rimes the predieted value was observed (30 percent larger
than design limit of O.02hJ. In other cases, the observed values were 1.25 to 2.5 rimes
higher than predicted.
6.1.2.2 Eight-storey frame
Table 6.7 summarizes the sections of Design A before the verification of inelastic link
rotations was conducted. At this stage, Designs A and Chad almost identical structural mass,
exceeding the mass of Design B by about eight percent. However, the verification of
inelastic link rotations, y, for Design A indicated that the design limit was violated in top five
storeys by up to 25 percent. Thus, further revisions were necessary.
The estimate of y is proportional to the elastic inter-storey drift. The most effective inter
storey drift reduction was achieved br increasing the sizes of the two bottom column tiers
and the top three buces. As a result of these modifications, the structural mass increased by
17 percent, thus making the Design A the heaviest of the three. No further adjustments were
needed to satisfy inter-storey inelastic drift requirements, in fact, predicted values were weIl
below the aIlowable limits. The design was aIso compliant with strength requirements.
Results from non-lineat analysis for Design A are presented in Tables 6.8 to 6.10.
Comparative plots of maximum shear forces and defonnations obtained for aIl three designs
are shown in Figs 6.3 and 6.4, while Table 6.11 shows observed and predicted values of
inter-storey inelastic drift. Examination of these results indicates the following:
(i) Compared to Designs Band C, bottom storeys links of Design A deve10ped somewhat
smaller shear forces for low a/v records, but design limits were still exceeded by 25
6-6
6. STUDYOF EBF'S SEISMIC BEHAYIOUR
percent on average. The peak force observed at storey 7 for an three designs remained
unchanged. For intermediate a/v records, links of an three designs deve10ped very
similar forces, with maximum of 10 percent variation observed at storey 2. The
maximum shear forces were noted in the top storey link, and in the top four storeys
design Iimits were exceeded by a maximum of 30 percent.
(u) For low a/v records, the most favorable results for ine1astic link rotations were obtained
for Design C. Although Design A was more effective in reducing the peak y, ovetall, the
design limit of 0.09 radians was violated to a lesser extend in Design C. For intennediate
a/v records all three designs showed similar link deformations. The peak y of Design B,
observed in the top storey, was reduced by 20 percent in Design A and by 14 percent in
Design C, but still remained well above the acceptable limits.
Cm) Both Designs A and C exhibited more desirable response of columns and braces
compared to Design B. In general, the smaller amount of column and brace disttess was
observed for Design C, but the difference between Designs A and C was less
pronounrerf than in the case of the four storey structure.
(iv) Low a/v records generated higher inter-storey drifts chen predicted in the bottom
storeys of all three designs, while for intermediate a/v higher inter-storey drifts chan
predicted were observed in the top storey. With these exceptions, in general, the
predicted and observed values for all three designs are in better agreement than in the
case of the four-storey structure.
Cv) Similar trends were observed for predieted and observed inelastic shear rotations of the
link, that is y was under-predicted it bonom storeys for low a/v records, and in the top
storeys for intermediate a/v records.
6.1.2.3 Founeen-storey &ame
Table 6.12 Sllmmarizes sections of Design A se1eeted following ductility requirements,
before inelastic shear rotations were verified against the codified limits. Since ÏDter-storey
6-7
6. STUDY OF EBF'S SE/SMIC BEHAV/OUR
plastic drift was identified as a critical factor for Design B, the evaluation of this parameter
was conducted on Design A prior to verifications of y. It was found mat the largest drift,
observed in the second storey from the top, had just met the design requirement (2% of
storey height). Thus, this stage of Design A could be considered comparable to Design B.
Indeed, the examination of the structural mass of two designs indicated about 10 percent
difference.
Although the inter-storey ineIastic drift requirement was the goveming factor in Design B,
link defonnations, y, were ooly just within the allowable limits. In other words, ooly very
small modifications of a structure compliant with y requirementsS were needed to satisfy the
inter-storey drift requirement. However, for Design A, the maximum predieted value of y
(calculated as R-1 rimes the e1astic drift) reached the value of O.17rad, thus exceeding the
design limit by a large margine
Significant changes in section sizes were required to reduce inter-storey drift so that the
calculated value of y remained bellow O.09rad. It was demonstrated that an increase in beam
size does not have sufficient impact to justify the resulting increase of forces ttansmitted to
braces and columns. Hence, brace and column sections were modified. With the largest HSS
braces (305X305X13) in all storeys, and significant increase of bottom five column tiers
(WWF650X864), it was still not possible to obtain satisfactory y values. The solution was
finally obtained by using W shapes for brace sections combined with increased column sÎ2es.
The summary of selected sections is shown in columns (e) and (t) ofTable 6.12.
The inspection of structural mass indicates 50 percent increase compared to Design B. Many
sections were highly undemtilized under traditional load combinations, and the predicted
ine1astic inter-storey drifts were weil bellow design limits.
It was established in section 5.3.2.3 that the inelastic response of the founeen storey frame
designed according to the current design procedure (Design B) was in genera1 satisfactory. In
a few cases, maximum shear forces and deformations exceeded the design limits by a very
5 In the cwrent Standard, the limit on y correponds ta O.SR times the e1astic drift.
6-8
6. STUDY OF EBF'S SEISMIC BEHAVIOUR
small margin. Columns responded e1astically for aIl records studied, and very limited
instabilities were observed in braces. Thus it is not anticipated that the ine1astic response of
Design A would improve significandy enough to justify such a large increase of mass
compared to Design B.
6.1.3 Summary
The objective of the study described in this section was to examine the modifications of
seismic design requirements for EBFs proposed for incorporation in the next edition of
CSA/CAN-S16.t. The inelastic response of three chevron-type EBFs with four, eight and
fourteen storeys (Design A) was studied for selected acceleration records, and compared to
that of the structures desjgned Ci) following the provisions of the current Standard (Design
B) and (u) using the iterative procedure proposed in this study (Design q.
AIl three designs yielded similar beam sections for all frame heights. More variation was
observed in brace and colunm sections; compared to structures compliant with current
Standard, heavier column and brace sections were in general selected in Designs A and C.
This in turn led to the overall increase in structural mass. For the four- and eight-storey
frame, Designs A and Chad similar mass exceeding that of Design B by about twenty
percent. For the fourteen-storey frame, for which Design B and C were almost identical, the
mass of Desjgn A was substantially increased, approximately by fifty percent.
This important increase of section sizes for fourteen storey frame of Design A was entirely
the result of the effort to maintain ine1astic shear rotations of links below the allowable limits
in the ductility phase of design. Assuming equal frame geometty and elastic inter-storey drift,
y calcuIated by the proposed modifications of the Standard is 1.5 times larger than the one
calculated using current provisions. For the design of lower or medium height frames,
satisfying the y limit does not seem to impose great difficulty, and in sorne ways MaY
improve the overall behaviour of the frame. For taller frames, however, the y limit is very
difficult to meet and results in uneconomical design without significandy improved seismic
behaviour.
6-9
6. SroDY OF EBF'S SE/SMIC BEHA V/OUR
The Most significant improvement in behaviour of Design A compared to Designs B and C
was observed in the response of the links of the four-storey frame, which deve10ped rather
uniform defonnations over the frame height. However, the excessive top storey link
defonnation in response to inteanediate a/v records remained a problem. In addition, the
instability of columns and braces was observed as &equendy as in the design based on the
current Standard. For the eight-storey frame, the seismic behaviour of Designs A and C was
comparable and superior to that of Design B.
Similarly to the iterative procedure, modified requirements of the new proposais were not
fully successful in reducing the peak values of link shear forces and deformations, but in
general, more unifonn distribution over the height of the frame was achieved than for
Design B.
6.2 Study of the lateraI force distribution
6.2.1 General
The minimum base shear for seismic design of structures in Canada and the distribution of
the lateral force over the height of the structure are specified in NBCC (1995). In
detenniniog the lateral force profiles two approaches cao be used:
(i) The first approach is simpler and appropriate for reguIar buildings. The force
distribution is based on the assumption that for the ttanslational vibrations, the majority
of reguIar buildings respond in the first mode; thus, the linear distribution of lateral
forces is appropriate. For buildings with longer periods, where the increased
contribution of the higher modes is expected, a redistribution of forces is accounted for
by applying a portion of the base shear as a concenttated force on the top of the
structure. The magnitude of this force varies with the fundamental period of the
structure, starting &om zero for periods of 0.75 and less, and not exceeding 25 per cent
of the design base shear. The distribution of the forces obtained following this approach
is denoted hereinafter as NBCCIinear0
6-10
6. STUDYOF EBF'SSEISM/C BEi/AV/OUR
(u") The second approach is recommended for the buildings with significant irregularities,
discontinuities in mass or stiffness or varying eccentticities between the center of mass
and center of stiffness, but may be used otherwise. In this approach, modal analysis is
used to obtain design storey shears and other design quantities of interest. Structural
response in each mode is determined for the appropriately sca1ed NBCC design
spectrum. AIl modal contnbutions are adjusted so that the total modal base shear
obtained by combining the individual modal base shears is equal to the Code base shear.
The resulting distribution of the forces is denoted further in the text as NBCCmodal•
The buildings examined in dUs project were quite regular; thus, the selection of NBCCIinc::at
lareraI force distribution to design EBFs studied was a natural choice. The results of the
dynamic analysis presented in Chapter 5 indicated that higher shear forces and defonnarions
developed in the upper storeys of these frames, particularly in response to intermediate a/v
records. This may result from more significant contnbutions of higher modes in the
structural response than foreseen by the Code. Hence, a study was conducted with the
objective of examining the suitability of the lateraI force distribution assumed in design.
Attention was directed to the foUI, eight and fourteen storey frames designed in compliance
with the present Standard. (Design B, given in Chapter 5). Frames obtained using the
iterative procedure were aIso examined, but since little difference in results was observed,
ooly the results for frames compliant with current codified design requirements are
presented in this section.
For each frame height, the lateraI force profiles were obtained as follows:
(i) Envelopes ofstorey shears (maximum positive and maximum negative) were found from
the non-lïnear time-history analysis (NLTHA) for all historical records from low and
intermediate a/v groups. For each group of records, the storey shears corresponding to
the Mean plus one standard deviation were ca1culated oext, and the lateraI force was
detennined as the difference between the shears at two subsequent storeys. It should be
noted that, for a selected earthquake record, the values of lateral forces obtained in this
6-11
6. STUDY OF EBF'S SE/SMIC BEHAV/OUR
way do not correspond to the maximum value observed at that storey during the
complete time-history. However, they are more appropIÏate than the latter since the
objective is to study the lateral force distribution.
(n) NBCCmodal distribution was aIso detennined from the response spectrum. analysis, carried
out using program SAP2000 (1997). In addition, for the eight-storey frame, latera1 forces
were aIso detennined for the smooth pseudo-acceleration speetta derived for low and
intennediate a/v records (see Section 4.2.4). These speetra are illustrated in Figs 6.5 (a)
and (b).
To provide consistent comparison, all the results were scaled 50 that the total base shear
force obtained from (i) and (n) matched that prescribed by NBCC for each frame
considered.
6.2.2 Discussion of the results
6.2.2.1 Four storey frame
Figs 6.6 (a) and (b) illusttate the lateral force distribution obtained from NLTHA for low
and ÏDtermediate a/v records respeetivdy. For both groups of records, very similar
distributions of the forces were obtained, with slighdy higher forces observed at the top two
storeys for intermediate a/v records, and at the bottom two storeys for low a/v records. For
each group of records, the maximum positive and negative values of lateral forces were
comparable.
NBCClincu distribution is aIso indicated in Fig 6.6 for comparison. In general, a good
agreement was observed between the two distributions for both groups of records. At the
top storey however, the Iateral force from NLTHA exceeded the Code speci.fied vaIue by
about 25 and 40 percent for low and inteanediate records respeetively. As cao be seen in
Fig. 6.76, in the top storey, an improved match was achieved using NBCCmocbl distnbution
instead of NBCCIincw particu1arly for the inteanediate a/v records. In the bottom storey,
6 The distnbution of lateral force from NLTHA is shown in this figure in terms of absolutemaximum Iateral force (positive or negative).
6-12
6. STUDY OF EBF'S SElSMIC BEHAVlOUR
however, forces obtained from NBCCIinc2r and NBCCmodal distributions were aImost identical,
and about 30 percent smaller than those observed from NLTHA for low a/v records.
As mentioned in the previous section, the contnbution of higher modes in the NBC~
distnbution is a function of the fundamental period, T, for an structures with T larger than
0.7s. The Code fonnula used to determine T (see Section 5.1.22) usually yields a first natural
period that is smaller in magnitude than that obtained analytically. For the four-storey frame,
for instance, TNBCC was 0.58s, compared to the analytical value of 1.01s. Since TNBCC was less
than 0.7s, the NBCC procedure made no allowance for bigher mode contributions, that is,
no concenttated force was specified at the top of the structure. However, had the structural
period been taken as 1.01s, a concentrated force would have been assigned. The need for the
higher lateraI force at the top of the four-storey frame is confirmed by the analytical results,
both from the non-linear and response-speetrum analysis.
A sample calcuIation was performed, in which the concentrated force at the top of the frame
was determined using the Code fonnula (Ft=O.071V), but T NBCC was replaced by the
analytical value. The design base shear force, V, was still computed in accordance with
NBCC requirements, and thus was a function of T NBCC (see Section 5.1.2.2). The remainiog
portion of the shear force, V-Ft, was distributed following NBCC provisions. ResuIting
lateraI forces obtained from this modified procedure (NBCClinor ~ are shown in Table
6.13. Forces obtained from non-linear analysis, and NBCCIincar and NBCCmocbI distributions
are aIso shown. It cao be seen that in general, the modified approach yielded a lateraI force
distribution that models more realistically the dynamic response of the structure.
6.2.2.2 Eight-storey frame
Lateral force distributions obtained from NLTHA are illustrated in Figs 6.8 (a) and (b). For
both groups of records, ma.~um positive and negative lateraI force envelopes were very
similar. For low a/v records, the distribution compares weil to NBC~ with the
maximum difference observed in the top storey where the lateraI force from the NBCCIineu
distribution was exceeded by 15 percent. A poorer match was noted for intermediate a/v
records; NBC~ distribution over-predieted the forces in the mid-portion of the frame,
6-13
6. STUDYOF EBF'SSEISMIC BEHAVIOUR
and under-predicted those in the two bottom storeys and at the top. While the lateral force
observed at the top and the second storey e."<ceeded the NBCCIinc2r value by about 40
percent, in the bottom storey the NBCC!incar force was exceeded by a much larger margin
(about three rimes).
The NBCCmodaI distribution is indicated in Fig. 6.9. While in the mid-portion of the frame the
forces in the NBCCmodal distribution are somewhat smaller than the NBC~ forces, the
reverse cao be observed in the top and the bottom storeys. Thus, for the intermediate a/v
records, this distribution follows distribution the force profile obtained frOID the non-Iïnear
analysis better than NBCC1ineat• Still, at the top storey, NBCCmodaI predicted forces about 20
percent smaller than those observed in NLTHA, while in the bottom storey the difference
was about 25 percent.
The distribution of the lateral force for the eight-storey frame was investigated further by
performing the modal analysis for two design spectra that were constructed in Chapter 4,
representattve of low and intermediate a/v records in Zone 5. In response to the lowa/v
spectta, lateral forces developed were very similar to those found in NLTHA and modal
analysis for the NBCC spectmm. Fig 6.10 illusttates the force distribution obtained for
intennediate a/v spectra. A clear departure from the first-mode response cao he observed
and the influence of the third mode is quite distinct. The third natural period of this
structure is 0.39s, and as cao be seen from Fig 6.5 (b), this corresponds precisely to the peak
values in the pseudo-acceleratioo spectrum.
The force profile shown in column (e) of Table 6.14 was obtained using the modified
approach described in the previous section to ca1culate the top lateral force. When compared
with other distributions given in columns Ca) to (d), it cao be seen that overall, the modified
distribution (NBCClinc2r~ reflects better the dynamic response of the structure than
NBCCIine:ar. The modified approach however, could ooly improve the conditions at the top
storey. In fact, increasing the top storey force and maintaining the same base shear further
decreased the forces at the bottom storey, but by a small margin (about 5 percent). A lateral
6-14
6. STUDYOF EBF'S SE/SMIC BEHAV/OUR
distribution in better accorclance with the dynamic response of the structure would be
obtained if the lateraI force were maintained uniform in the !wo bottom storeys.
6.2.2.3 Founeen storey frame
Distributions obtained from the non-linear analyses aIong with the NBCCIincat and NBCCmodal
lateraI force profiles are illustrated in Figs 6.11 and 6.12. Results show similar trends to those
for the eight-storey structure; both NLTHA and modal analysis assigned larger forces to the
bottom storey and smaIler forces to the mid-portion of the frame compared to the
NBCCIineu distribution. However, differences were observed with respect to the location of
the largest force. In the NBCCIineu profile, the largest lateraI force was assigned at the top of
the frame. The two analyses on the other hand, identified the second storey &om the top as
the one with the largest force, with magnitude simiIar to that of NBCCIineu in the top storey.
In light of results &om NLTHA and modal analysis, a modification of the procedure ta
define NBCCIinc:ar force profile was examined. As for the four and eight storey frames, the
concentrated force was determined using the analytica1 fundamental period (2.76s). This
force was distnbuted between the top two storeys sa that the totallateral forces7 applied at
those locations were equivalent. As cao be seen in Table 6.15 this distribution better matches
the force profile obtained in non-linear and modal analysis in the upper portion of the frame,
but the lateraI force applied at the bottom storey still remains largely under-predicted. It
appears that the lateraI force distnbution, as illustrated in Fig. 6.13, with uniform forces at
the bottom four to SL,"< storeys would match better the one found in non-linear analysis.
6.2.3 Summuy
The study presented in this section was conducted ta examme the statie lateraI force
distribution defined by NBeC (NBC~caJ that provided basis for design of aIl EBFs stuclied
in this report. Lateral force profiles were obtained both from NLTHA and modal analysis
(NBCCrnodaÙ and compared with the NBCC1inear distnbution. For aIl frame heights it was
7 Force V-Ft is ditributed Iinearly using NBCC approa~ giving forces Ft3 and f t4 at fourteen andfourteen level respeetive1y. Ft determined U5ing analytical period T is man disttibuted between thelevel thirteen and fourteen 50 that F13+Ft13 is equal ta Ft4+Ft14.
6-15
6. STUDY OF EBF'S SElSM/C BEHAVIOUR
found that the NBCCIinat distribution over-estimated forces in the mid-portion of the
frames, but by only a small margine At the top and bottom storeys, however, forces
predicted by the NBCCIineu distnbution were significandy exceeded, indicating the possibility
that the effects ofhigher modes were not appropriately accounted for.
Compared to NBCC~ the NBCCmodaJ distribution in general more close1y matched that
obtained from NLTHA and would be preferred for use in design. However the NBCCIinc2r
distribution is simplet to obtain and is more likely to he used by praeticing engjneers.
Therefore, a modification of this procedure was examined, in which a concentrated force,
applied at the top of the structure to account for higher mode effects, was calculated using
the fundamental periods detennined analytically instead of employing the Code empirical
fonnula. The total base shear and the overall distribution of the remaining force were
unchanged.
It was found that the resulting distribution obtained using the modified approach
(NBCClinc:u~ is in better agreement with the observed dynamic response of the frames. In
ail cases, this modification improved the lateraI force profile in the top storeys of the frame
while not producing significant change in the force magnitudes in the bottom storeys.
Dynamic analysis indicates that in this region a uniform force profile would be more
appropriate than the linearly varying one.
6.3 Column axial forces and moments
6.3.1 General
Clause 27 of CSA/CAN S16.1 provides requirements for ductility design of columns in
EBFs. The amplification factor of 1.25 is applied on the factored shear resistance of the link
ta evaluate column axial forces at individual storeys. Simple summation is used to estimate
the cumulative effects of yielding links in storeys above the column under consideration.
This approach seems reasonable, since achieving simultaneous yielding of the links in all
storeys is a design objective. The reduced amplification factor (1.25) is justified by the lower
probability that all the links would attain their maximum forces (l.SVJ at the same rime. No
6-16
6. STUDY OF EBF'S SE/SMIC BEHAV/OUR
provision in the current Standard is made to inc1ude the column end moments arising from
the relative storey movements and column continuity in the ductility phase of design.
Proposed modifications of duetility design requirements for the next edition of the Standard
were discussed in Section 6.1. They incorporate observations of recent analYtica1 studies and
account for: (i) presence of bending moment in columns, by reserving a 15 percent of the
column capacity for hending, and (u) likelihood that the top columns would he affected by
the full force developed in the strain-hardened link, by assigning amplification factor of 1.5
to calculate forces in the top two columns.
It was demonsttated in Chapter 5 and first section of Chapter 6 that neither current codified
requirements, nor the proposed ones were fully successful in achieving the desired seismic
response of columns, particularly in the upper storeys of the frame. The study was therefore
undertaken to examine in more detail the following: (i) appropriate amplification factors to
use in column design, (n) combination rules to realistically estimate axial forces inttoduced
by yielding links, and (m) magnitudes and distributions ofcolumn end moments.
Results presented in this section were compiled from the non-lïnear analysis carried out for
four-, eight- and fourteen-storey frames designed using the proposed iterative procedure,
since the columns of these frames experienced very little instahility in response to the
selected set of historical records. These structures were described in detail in Chapter 5.
6.3.2 Column axial forces
6.3.2.1 Axial forces &om non-linear analysis
Since the output from the non-linear analysis for columns includes both axial force and
moment, the decision had to he made as ta what should he considered as representative axial
force in the column. Two approaches were e.umined. In the first approach, for each
acceleratioo record within the same a/v ratio group, the maximum axial force from the
complete time-history was found for the columns in each storey. In the second approach,
the maximum. column response ratio resulting from the combined action of axial force and
6-17
6. sruDYOF EBF'SSEISMIC BEHAYIOUR
bending moment during the rime history was found, and the corresponcling a.~ force was
taken as the represenrative force.
By inspection of the results, it was found that the two values of the axial force were very
close, and in many cases identicaL The maximum differences observed were about 10
percent for the four- and eight-storey frame, and 15 percent for the fourteen-storey frame,
these heing for oo1y one record and in one storey. It was decided therefore, to consider
column axial forces corresponding to the maximum response ratio.
For each group of historica1 records, the axial column forces are expressed in terms of mean
plus one standard deviation as shown in columns (a) and (b) ofTahle 6.16. In general, smaIl
coefficients of variation were observed (maximum 10 percent). For aIl three heights,
intermediate a/v records induced larger forces in the columns of the upper half of the frame,
and low a/v records in the bottom half. The final axial force distribution given in column (c)
of Table 6.16 was obtained by combining the results for both record groups 50 that the
maximum force was selected in each storey. Link amplification factors for column duetility
design and force combination mIes were then e.umined in Iight of these resu1ts.
6.3.2.2 CombinatioD mies
In a well-designed EBF, simultaneous yielding of alllinks is a desjgn objective and using
simple summation ta evaluate column a.w forces introduced by links presents itself as a
natura! choice. To account for the Iower probability that aU the links would develop their
ultimate forces (l.SVr) at the same rime, two approaches are possible: (i) use a simple
summation mIe, but reduce ultimate forces, or (ù) use ultimate forces, but change the
combination mIe.
Redwood and Channagiri (1990) have proposed the calculation of column loads in ductility
design of concenttically braced frames using the summation of: (i) maximum brace force
componeat at any level above the column in consideration, and [11) the square root of the
sum of t!le squares of the maximum brace force contnbution in all other storeys above this
6-18
6. STUDY OF EBF'S SEISMIC BEHAVIOUR
leveL This approach, denoted as SRSS*, was e..umined in the context of EBF for the eight
and fourteen storey frames and compared to the simple summation rule (55).
As shown in Table 6.17, it was found that the SRSS* combination mIe yie1ded in general
significandy smaller forces than SS mIe, particularly for the founeen storey frame. Much
Iarger ultimate link forces would have been needed to get comparable results, and even then,
the predieted forces wouId have under-estimated those observed in non-linear analysis.
Although experimental evidence of more significant sttain-hardening deve10ping in shear
links exists (Hames et al., 1997, Englehart & Popov 1988), 1.5Vp (1.67VJ is commonly
accepted as the upper bound on the uItimate link force. Thus, in this study the SS ruIe was
identified as the appropriate ruIe to evaluate a.oo forces in the ductility design of columns.
6.3.2.3 Amplification factors
Table 6.18 snmmarizes the column a.~ forces obtained assuming different uItimate shear
forces in the links. The following amplification factoIS applied to the shear resistances of the
links were considered: (i) 1.25 in aIl storeys, (n) 1.5 in aIl storeys and (w) 1.65 in top (Wo
storeys and 1.3 in aIl other storeys. For each case, the comparability with results from the
non-lïnear analysis is evaluated by comparing the square root of the sum of the squares of
relative erroIS. These are indicated in the Jast row of Table 6.18.
For four- and eight-storey frames, column forces calcuIated in accordance with the current
Standard showed the poorest match. In aIl storeys, forces were under-predicted by up to 20
percent. For amplification factors as described in (n) and (m), good compatibility with results
from non-lînear analysis was observed in both cases, although case (m) was slighdy superior.
For the fourteen-storey frame, the best match overall was obtained considering the ultimate
link forces as defined in the euttent Standard In seven storeys the forces observed in oon
linear analysis were exceeded, but by a smaII margin (maximum 7 percent). Approaches (n)
and (m) under-predieted the column axial forces in a smaller number of storeys and by
smaller margin, but they over-estimated column axial forces in the top of the &ante by 15
and 17 percent respeetively.
6-19
6. STUDY OF EBF'S SEISMIC BEHAVIOUR
6.3.3 Column bending moments
6.3.3.1 Bending moments &om nOD-linear analysis
The current Standard provides no guidance regarding the inclusion of the bending moments
into the ductility design of columns. Severa! studies (Koboevic and Redwood (1997), Kasai
and Han (1997)), previously reported on the presence of significant column end moments in
chevron-type EBFs, which should not he negleeted in the ductility design phase. Based on
the results of analytica1 studies, Kasai and Han suggest allocating 15 percent of column
resistance to the bending. These recommendatioos were incorporated in the design of
frames descnoed in the present study; however, the desirable response of columns was not
always achieved. This may he partially attributed ta higher response moments compared ta
thase used in the design. For this reason, the magnitudes and distributions of column end
moments obtained from non-lïnear analysis in the present study were examined in more
detail.
Similarly ta axial forces, for each historical record, two bending moments were considered
for each selected column tier: (i) maximum bending moment, and (11) bending moment in
combination with the axial force that caused the Iargest response ratio in the complete time
history. It was found that, in large number of cases, these two moments were identicaL The
results presented hereinafter are for the moments (11), this being the more realistic loading
condition for the column.
Resulting moments obtained for each a/v group of records are summarized in Table 6.19.
~fean values are given to provide the consistent comparison with the study reported by
Kasaï and Han. As can be seen from Table 6.19, in generai, the intennediate a/v records
induced larger moments than low a/v records. Compared to axial forces, much higher
coefficients of variation were observed for moments particularly in the top column tier for
all three frames. These variations cao he expected since the columns moments are very
sensitive to relative storey movements and these change significandy for cach individual
record.
6-20
6. STUDY OF EBF'S SE/SMIC BEHAVIOUR
In spite of these differences, very similar trends in moment distributions were observed for
aIl three frames. Columns in the top storey developed the Iargest hending moments with
magnitudes reaching about 40 percent of column plastic moments (MpC; as shown in Table
6.20. In the next two storeys, a moment of about 20 percent of Mpcol was observed, while in
all other storeys the maximum value did not exceed 10 percent of Mpcol
•
In view of these results, the assumption of moments urilizing 15 percent of column
resistance in an storeys does not seem appropriate. Larger hending should he considered in
the design of the top storey columns. Although the analysis also indicated slighdy larger
moments in columns of the two storeys below, aIlocating 15 percent of column resistance ta
bending may he justifiable coosidering the fact that the axial forces may be slighdy over
predicted in these locations (see Tables 6.16 and 6.18). The same may be accepted in other
storeys, however this approach yields somewhat conservative estimates of column bending
moments in these lower locations.
6.3.4 Summary
This section has described a study of column axial forces and bending moments ta use in the
ductility phase of EBF design. Simple summation of forces arising &om yielding and strain
hardening links was identified as the appropriate combination rule to evaluate column axial
forces. For low to medium height frames, the best agreement with analytical results was
obtained assuming link shears of 1.65Vr (1.49Vp) in the top two storeys, and 1.3Vr (1.17Vp)
in the others. For higher frames, however, this approach somewhat overestimated column
forces in the lower parts of the frame, although this has a small impact on the design.
It was aIso demonsttated that the uniform contribution of moment ta axial force-moment
interaction might lead ta unconservative esrimates of column end moment in the top
column tier. At this location, bending moments as high as 40 percent of the section plastic
moment could he expected. In other storeys magnitudes of hending moments vary between
0.1 and O.~, and a 15 percent assumption appears to he justifiable.
6-21
6. STUDY OF EBF'S SEISMIC BEHAV10UR
6.4 Study of the seismic force modification factor
6.4.1 General
The minimum base shear for seismic design of structures in Canada is given in NBCC(1995)
as V=V/U/R, where R is a force modification factor, and U a calibration factor. The force
modification factor, R, accounts for the ability of structural system ta dissipate energy by
damping and ine1astic action, while the calibration factor, U, is specified ta provide the ''level
of protection" equivalent to that from the previous editions of the Code. Depending on the
structural system, R ranges from 1 to 4 (R=4 for EBFs), while U is assigned a constant value
of 0.6. Thus, in design of EBF, the elastic base shear is reduced by a total factor,
R=(R*1/U),of6.67.
Although R has major impact in seismic design of structures, to date, the values assigned to
this factor are mainly founded on experience and engineering judgment, and have very Iittle
technical basis (Whittaker et aI, 1999). In the 1980's at Berkeley, hased on experimental data,
researchers suggested that R he described as a product of three factors Rs, ~ and ~,
accounting for reserve of sttength, ductility and added viscous damping respectively. In th.is
formulation, ~ was typicaIly set to 1.0. In experiments conducted on a dual system
comprising a moment-resisring frame and an EBF (Whittaker et al., 1987) R. and ~ were
evaluated as 2.85 and 2.12 respectively, this resulting in R equal to about six. In a revised
formulation of R in the USA (ATC 1995) ~ is abandoned and a redundancy factor, RR' is
added. This is intended to quantify the improved reliahility of seismic framing systems that
use multiple lines ofvertical seismic framing.
The study descrihed in this section is conducted to understand better and evaluate the
modification factor R currendy used in NBCC (1995) for EBFs. As suggested by Uang
(1991), R was taken herein to be a product of oversttength factor, Rs, and ductility factor
R.a. This fonnulation works weil within the framework of NBCC, in which R and I/U
correspond approximate1y to R.a and R. respective1y. The two factors can he defined using
the general force-displacement response of a structure idealized by the linear-perfecdy plastic
6-22
6. STUDY OF EBF'S SElSM/C BEHA VIOUR
curve as illustrated in Fig. 6.14. 1bis type of relationship for each of the frames considered
(four-, eight- and fourteen-storey frames compliant with cutrent Standard, see Chapter 5)
was developed using nonlinear static analysis (pushover analysis) for monotonically
increasing NBCC1incar seismic forces. Resulting curves describing the relation between the
base shear and the roof displacement are illusttated in Figs. 6.15 (a) to (c). For comparison,
factors Rs and~ were aIso calculated using the results from non-lïnear time-history analysis.
6.4.2 Overstrength factor, IlsThe maximum lateraI sttength of the building, Vu, would commonly exceed the design lateral
sttength, Vd, associated with seismic loading. SeveraI reasons contribute to this situation
including resistances of selected members exceeding design forces; material sttengths
exceeding nominal sttengths; sorne other requirements goveming the design (e.g. ineIastic
drift, wind load, gtavity load) etc. The level of overstrength in the structure can be measured
by the oversttength factor, Rs, defined as the ratio ofVu and Vd (see Fig, 6.14).
In the context of the NBCC, Vd indicated in Fig. 6.14 corresponds to the seismic design base
shear V. To define Vu two approaches were considered: Ci) Vu was taken as the base shear
obtained from the pushover analysis at 2 percent roof drift index 01u1!"j, and (n) for each a/v
group of the selected historicaI records, Vu was detennined from the NLTHA as mean plus
one standard deviation of the maximum response base shear force 01uno;.
Column (a) of Table 6.21 shows results obtained for Rs from the pushover analysis. Rssv'med between 1.8 and 2, the former correspanding ta the eight-storey frame and the latter
to four- and faurteen-storey frames. The results from NLTHA for Iow a/v group of records,
given in coIumns (b) of the same table show the similar trend. In bath cases, the variation of
Rs in function of structural period was about fifteen percent maximum. For intermediate a/v
group of records slighdy larger variations in Rs were observed, mainly due to the Iower Rsvalue obtained for eight-storey frame.
Note that in three cases, the smallest values of Rs were obtained for eight-storey frame. This
is consistent with observations made in Chapter 5 regarding the utilization of sections of
6-23
6. STUDY OF EBF'S SEISMIC BEHAVIOUR
frames with different heights. It was demonstrated in that Chapter that the sections of the
eight-storey frame had very high response ratios bath for Code specified loads and for
forces arising from links, 50 it could be anticipated that this frame would have the least
oversttength. The higher ~ for other two frames may he due to drift influencing the design
of the fourteen-storey frame, and the gravity loads affecting the four-storey frame design.
It is thus concluded that in the range of periods studied (1s to 35), the factor Rs is not
significandy dependent on structural periode For consistent comparison between Rs and
1/U, the later should be divided by 0.8 8, thus the value assigned by NBCC seems realistic
for these EBFs. However, a considerable period dependence and higher values of~ could
be expected in the shorter period ranges (Fischinger and Fajfar (1994); see also Fig. 6.16).
6.4.3 Ductility factor,~
The duetility factor ~ is a measure of a global nonlinear response of a framing system and it
can be defined as the ratio of the elastic sttength demand, Vuf:, ta inelastic sttength demand
Vu, associated with a certain displacement ductility ratio J.1 (see Fig. 6.14 for definitions ofVuf:
and VJ. For single-degree-of-freedom systems, J.1 is defined as the ratio of maximum
inelastic displacement, ~, ta the yield displacement, L\. It is a weil established fact that the
relationship between~ and J.1 is sensitive to the variety of factors, such as structural period,
soil conditions, strain-hardening, magnitude of fl, differences in duetility demands for single
and multiple-degrees of freedom systems and similar. (Whittaker et al, 1999). NBCC (1995)
however stipulates that that magnitudes of R~ and ,... are equal over the whole range of
common structural periods.
Similarly to &.s, both pushover analysis and NLTHA were used to detennine factor~. The
procedure to obtain Vu was described in the section 6.4.2. The same method was used to
8 The ine1astic base shear used to design frames in this study was furtber reduced by the factor of 0.8,to account for the conservative estimates of structural period using Code empirical formula. NBCaIlows the use of other calculation methods to detem1Ïne the structural period, but the base shearobtained in this way must not be less than 80 percent of that corresponding to empirical estimate ofstructural period. Thus, for consistent comparison between Rs obtained herein and l/U, the larersbould he divided by 0.8.
6-24
6. STUDY OF EBFtS SE/SMIC BEHA V/OUR
detennine Vue ~.e both Vu~· and Vue,nonI) but assuming elastic behaviour of all frame
members induding links.
The results for~ are Sllmmarized in columns (a) to (d) ofTable 6.22. Unlike Rs, ~ showed
dependency on the structural perio~ with pushover analysis giving magnitudes increasing
from 2.86 to 4.63 with decrease in structural period. This trend is consistent with previous
findings reported in the literature (Bolin and Rides (1991), Han (1998». NLTHA gave lower
values of~ ranging between 2.39 and 3.759 with decreasing period.
It was demonstrated in the previous section that the maximum inelastic base shears obtained
form the pushover analysis and NLmA 01uZ'. and Vuno) were comparable. Since the lateral
force profiles and thus displacement profiles are imposed on the structure in pushover
analysis, when responding elastically, the structure is likely to develop Iarger base shears in
pushover analysis than in response to a selected earthquake recordto• 1bis cao explain the
higher values of~ from pushover analysis and justify why the magnitudes of~ obtained
from NLTHA are probably more realistic. In all cases, ~ was smaller than R given in
NBCC, the difference increasing from about 6 percent for the four-storey frame to 40
percent for the fourteen-storey frame.
Since the ductility factor ~ is reIated to the dispIacement ductility ratio, Jl., the latter
parameter was aIso monitored. While for single storey buildings, â max and âv cao be clearly
defined as the roof leve1 dispIacements, the use of this definition to evaluate J.L for multi
storey buildings CJ.LfnrnJ presents sorne inherent difficulties. For example, by inspection it was
found that for a numher of earthquake records studie~ frames did not respond
predominandy in the first mode, thus, calculation of Jl fr:une based on the roof displacements
is questionable.
9 The numbers correspond to the maximum of~ low a/v and~ intem'll:diaœ a/v for each frame.10 The idea is based on the analogy with Rayleigh's method for estimating natura! period ofvtbration.The approximate period is always smaller than the exact value, since the assumptien is made teapproximate the exact mode shape, i.e. the displacement profile is imposed 1bis in a way isequivalent te having a c'stiffer" structure, thus the natural period is always smaller than the exactvalue.
6-25
6. STUDY OF EBF'S SE/SMIC BEHAVIOUR
Newmark and Hall (1982) postulated that J.Lfr:ame is in general some weighted average of the
storey ductility displacement ratios CJ.lstorey), where the weighting function is best defined
considering a particular pattern of displacements corresponcling to the preferred mode of
defonnations of the structure. Following this idea, an alternative approach to detennine Jlfr:ame
was examined herein. The preferred pattern of displacement was selected so that at every
storey, the inelastic inter-storey drift was equal to the design limit (2 percent of storey
height). This displacement profile was then compared to maximum inelastic storey drifts
obtained from NLTHA and the weighting coefficients were detennined. These are given in
Table 6.23.
For each frame considered, the displacement ductility ratio at every storey (flslorq.) was
determined first, and the global displacement ductility ratio, J.1famc:' was then found as the
weighted average value. J.Ls[O~ was calcuIated as the ratio of the maximum inelastic inter
storey drift and the inter-storey drift at first yie1d of the link at the storey under
consideration. Both drifts were obtained from the NLTHA. A Mean plus one standard
deviation of J!srocq- was found for each alv record group, and the larger of the two was
retained to caIcuIate Jlfame. Results for Jlfame are indicated in column (e) ofTahle 6.22.
Similarly to R.., J,Lframc was aIso found to be period-dependent with magnitudes increasing
from 2.64 ta 5.40 with decreasing period. Comparison of results obtained for ~ and Jlframc
shows very little difference hetween the two parameters for the fourteen-storey frame,
suggesting the equal displacement rule applies (i.e. ~=J.L) . However, for the four- and eight
storey frames, the equal energy rule (Rp=(2J.L -1)1/~ describes better the relationship between
~ and Jl. For the two available values, the results can be approximated by R.p =1.2(2J.1fnmc
1)112.
It was mentioned earlier in this section that the R factor specified in NBCC (1995)
corresponds roughly to ~ and that NBCC assumes that~ and J.1 are equal ovec the whole
range of common structural periods. The above discussion confinns this assumption for the
6-26
6. STUDY OF EBF'S SE/SMIC BEHAV/OUR
fourteen-storey frame ([14=2.765), but not for four- and eight-storey frames (T=1.01s and
r=1.89s) where J.1 exceeded RJl by 45 and 20 percent respective1y.
Although, with the exception of the four-storey frame, I.lfamc was be10w the design target
ductility of 4, larger ductility demands were in general seen in the upper and lower storeys
compared with the middle storeys (see Fig. 6.17). 1bis pattem could he re1ated to the higher
mode response contnbutions. In aIl cases, the links in the storeys with highest duetility
demands deve10ped the largest inelastic rotations, often exceeding the design limit of
O.09rad. A further investigation was therefore conducted with the objective of establishing
the global duetility displacement ratio of the frame at which the link with the largest inelastic
rotation y just reaches the design limit (J.1fnmcy<o_~
I.lrnmcY<O.09 was found from NLTHA following the same approach used to determine I.lfr:unc. To
do this, f.1srottyr<O.09 values were fust found as the ratio of inter-storey inelastic drift at the
instant when the link in that storey first reached the inelastic rotation of 0.09rad, to the inter
storey inelastic drift corresponding to the first link yielding in that storey. The weighted
average of these value.4il gave Jlfr.uneY<D.09 equal to 4.1, 3.3 and 3.7 in ascending order of frame
heights. As can he seen, Jlfr.unc ~'"{ceeded Jlfr.uncY<O.09 for the four- and eight-storey frames. It was
reported in Chapter 5, that links of these frames develop inelastic rotations in excess of the
design limite It appears that, had the global ductility displacement ratio been below four and
three for the four and eight storey frames respectively, the violation of the link rotation limit
would have been less severe.
6.4.4 Summuy
This section has investigated the response modification factor, R=R*1 lU, eurrendy in use in
NBCC for seismic design of EBFs. R was represented as a product of two factors, the
overstrength factor, Rs, and ductility factor ~. In the period range considered (ls to 3 sec),
Rs was found not to he significandy influenced by structural period with magnitudes
corresponding fairly weil ta 1lU. ~. on the other hand, increased as the structural period
decreased, and for the four-storey frame exceeded the value of R specified in NBCC for
6-27
6. STUDY OF EBF'S SE/SMIC BERAVIOUR
EBFs (R=4). The relationship between duetility factor and displacement ducrility ratio, J.1fame
was also investigated. It was found that the assumption made in NBCC that the two
parameters are equal was justified for the founeen-storey frame, but for other two frame
heights, J.1fr.une was found to be larger than ~. Ir the case of four- and eight-storey frames,
where NLTHA indicated large inelastic link defonnation, J.1famc also exceeded the duetility
demand associated with link rotations at the design limit.
6.5 Relationship between the inelastic link deformation r. and inter
storey drift li
6.5.1 General
In the current Standard, the inelastic link deformation, "(, is evaluated as a function of inter
storey drift and the geometty of the frame. 1bis relationship is commonly approximated
from a rigid plastic mechanism (see Fig 1.3). For Chevron-type EBF "(=(A/h)*~../e), where A
is the inter-storey drift calculated as O.SR rimes the elastic inter-storey drift determined for
factored loading, and L, e and h describe the geometty of the frame. The Standard requires
that the value ofy does not exceed O.09rad for links yielding in shear.
The results of non-linear time-history analysis presented in Chapter 5 indicate that, for a
number of records, maximum inelastic Iink deformations exceeded those predicted in the
design. This puts into question the current Standard procedures to predict inelastic shear
deformations of the link. The study was therefore undertaken to examine: (i) whether the
relationship between the inelastic inter-storey drifts and the inelastic shear defonnations can
be detennined from the simple rigid-plastic mechanism and (u) does the link reach an
ine1astic-shear defonnation of 0.09 rad at an inelastic inter-storey drift equal to O.SR rimes
the elastic drift.
Results from the non-linear analysis time-history analysis discussed in this section are those
for four-, eight- and founeen-storey frame designed according to the current Standard (see
Chapter 5 or Chapter 6 - Design B), responding to the set of selected historical records.
6-28
6. STUDY OF EBF'SSEISMIC BEHAVIOUR
6.5.2 Relationship between the maximum y and maximum A
For each record of the two a/v ratio groups maximum inelastic link rotation Ytm:6.J and
maximum inelastic drift, ~, were determined at each storey for aIl three frames studied. In
aIl cases, a very sttong positive correlation was observed between the two parameters. AIso
for a given record and frame height, the ymax corresponded to ~J regarding both the
location and the rime of occurrence. This further confinned the physical connection
between the two parameters.
Columns Ca) ta (d) of Tables 6.24 and 6.25 summarize values of Ytm:6. and~ obtained from
non-linear analysis. While Table 6.24 gives the absolute maximum values found at a given
storey for any record within one a/v group, in Table 6.25 the results are expressed in tenns
of mean plus one standard deviation. Coefficients Ky, defined as the ratio of the Ymu/~ are
listed in columns Ce) and (t) of the same tables for low and intennediate a/v records
respectively. For each storey, the maximum of columns Ce) and Ct) is found and the resulting
Ky is given in column (g). Kytiame for each individual frame is then obtained by calcularing
mean and Mean plus one standard deviation of values given in column (g). For comparison,
for each frame height, the value of coefficients Ky and Kytiame were evaluated at each storey
assuming that the frame behaves as the rigid-plastic mechanism. They are denoted as KyRP
,
and K/nrneRP and are listed in column (h) ofTable 6.24.
As seen in Tables 6.24 and 6.25, very similar values of Kyfnmc were obtained for aIl frame
heights, aIl very close ta 0.002. These correspond fairly weil ta results obtained using the
approach from the Standard, parricularly in the first storey of the frames. In other storeys,
rigid-plastic mechanism yielded more conservative results for a1l three frame heights. Note
that Ky varied significandy over the height of the frames. The rigid-plastic mechanism does
not capture these variations, but nevertheless, for a given inelastic inter-storey drift, the
values of y predicted by the Standard are more conservarive compared to those obtained
from the analysis. Thus, it is concluded that the relationship between inelastic shear
defonnation of the link and inelastic inter-storey drift approximated from rigid-plastic
mechanism is acceptable.
6-29
6. STUDY OF EBF'SSE/SMIC BEHAVIOUR
6.5.3 Drift lim.its to controllink behaviour
In the current Standard, inelastic inter-storey drift corresponding to link reaching the
maximum shear defonnation of O.09rad is calculated by multiplying the elastic inter-storey
drift by 0.5R. As shown previously in mis Chapter, the displacement ductility ratio, Jl, was
approximately equal to the ductility factor ~ (which corresponds to NBCC's force
reduction factor R) only for the 14-storey frame, while for the 4- and 8-storey frames R~
exceeded J.l. Both parameters varied with the structural periode Thus, it is rather unlikely that
the inelastic inter-storey drift associated with link deformation design limit can he predicted
on basis of elastic frame defonnations and the force reduction factor. A more direct
approach was therefore adopted, in which the values inter-storey drifts, corresponding to the
desired perfoanance of the links, were set based on results from NLTHA.
This difficulty to predict a complex relationship between peak elastic and inelastic
displacements of the structural system is one of the limitations of a spectral acceleration
based design method, otherwise known as a "force-based method", which provides the basis
for seismic design of structures in most current seismic codes, including NBCC (1995). This
design approach treats displacements and defonnations in rather superficial ways, although
they are generally accepted as much better indicators of potential damage than forces.
If "strains and deformations are the best indicators ofpotential damage, then it would appear
Ihat a design approach that attempts to design a structure which would achieve, rather than be
bOlmded by, a given iimit state under a given seismic intensity would be desirable" (priesdey,
1998). Designing a structure for a specified target displacement is the central concept of
design approach known as the direct displacemeot-based design method Fundamentals of
the method as proposed by Priesdey (1993,1998) are illustrated in Fig. 6.18.
In direct displacement-based design the structure is charaeterized by a secant stiffness at
maximum displacement and a level ofequivalent v;scous damping appropriate to the hysteretic
energy absorbed during inelastic response (Figs 6.18(b) and (c». The structure is represeoted
as an equivalent snOF oscilator (substitute structure) with known effective mass ml! and
unknown effective period Te and unlcnown effèctive stiffness ke (Fig. 6.18 (a»). For a design
6-30
6. SruDY OF EBF'S SE/SMIC BEHAV10UR
disp/acement 41, and the damping selected based on the expeeted ductility deman~ the
effective period Ttt is obtained from the design displacement spectta as shown in Fig. 6.18
(d). For known Te and IDc, effective stiffness can be found from the formula for the natural
period of the SDOF osci1ator. The design base shear at maximum response, Vb' is then
detennined as a product of ke and âcl.
Defining the design displacement appropriate for the Iimit state considered (e.g.
serviceability limit state, damage conttollimit state), is one of the critical elements for the
application of this design procedure. Priestley (1998) points out that in many cases the
design displacement will be dictated by code drift limits.
Within the context of performance-based design, SEAOC (1995) provides a number of drift
indices corresponding to desired performance levels of the structural system in response to
earthquake with specified probability of e.'"<:ceedence. The performance level is described in
part by overall damage which is related to a pennissible drift. For a "life-safe" performance
leve~ moderate damage is expected and total pennissible drift is 2 percent (1.5°/0 ttansient
drift+0.5D/o permanent drift). Drift less than 0.5 percent is admissible for an "operational"
leve~ associated with moderate damage to nonstructural elements and light damage to
structural elements has occurred etc. The overall drift limit of 2 percent of the height
prescribed by NBCC could he, by analogy, associated with ''Iife-safe'' performance leveI.
Results of the non-linear analyses compiled within the present study for code-based EBFs
were examined with the objective of determining the appropriate design displacements that
could be used in the displacement-based method for EBF seismic design. In view of the two
limit states previously discussed, attention was directed to: (i) the inter-storey drift at first
yield of any link in the frame, and (u) the inter-storey drift corresponding to the first link
reaching the inelastic rotation design Iimit of0.09rad.
Table 6.26 snmmarizes results obtained for (i) and (u) for an duee frame heights responding
to the selected histoncal acceleration records. For each record, the link that yielded first was
identified, and the associated inter-storey drift was found. The same was done for the 1ink
6-31
6. STUDY OF EBF'S SE/SMIC BEHAV/OUR
that first developed inelastic rotation of 0.09rad. The results obtained were not dependent on
the a/v record group, 50 aIl the records were considered when deterrnjning Mean and
standard deviation. Final values of inter-storey drifts (i) and (u) are expressed in tenns of
Mean minus one standard deviation and given as a percentage of the typical storey height.
Variation of structural period resulted in small variation in observed inter-story drift (i). The
first Iink in the four- and eight-storey frames yielded at a drift of 0.3%, and in the fourteen
storey frame at 0.25%• Slighdy higher variation was observed in Înter-storey drift (U), which
attained values of 1.4, 1.3 and 1.2% for frames in increasing order ofheight. The rigid-plastic
mechanism anaIogy for geometric configurations considered herein yields limiting inter
storey drifts betweeo 0.9 and 1 % 11•
Hence, for the structures studied, the foUowing values of inter-storey drifts could be used in
determining design displacements for chevron-type EBF: (i) 0.25-0.3% to insure elastic
response of links, and (u) 1.2% (conservatively) to insure link inelastic rotations within
experimentally detennined bounds ta ensure stable hysteretic behaviour (O.09rad).
6.5.4 Snmmary
The relationship between the inelastic inter-storey drift, ~ and inelastic link rotation, y, was
examined in this section. For all frames studied, the two parameters showed very sttong
positive correlation. Approximation of the relationship between y to â from rigid-plastic
mechanism seems appropriate for design purposes. The use of the force reduction factor to
find inelastic displacements from their elastic values was examined and found inadequate. A
more direct approach was therefore adopted, where the pennissible inter-storey drifts,
associated with desired perfoanance of the links, were estabüshed based 00 the results from
non-linear analysis. The inter-storey drifts obtained could be further used to determine
design dispIacements in the context of displacement-based design method
11 For four and eight-storey frame L/e=10, thus fory=O.09rad D/hs=O.09*L/e=O.9For fourteen-storey frame LIe=l1.2S thus D /hs=O.09*LIe=1.01
6-32
Table 6.1 Four storey frame: Summary of selected sections (Design A)
Storey (a) Beams a (b)Braces Cc) Columns Mass (kg)
4 W130X28 1.49 127X127X8W250X33
3 W250X67 1.18 178X178X8
2 W360X79 1.17 203X203XI05783
1 W460X89 1.19 203X203X13W360XI01
Table 6.2 Four-storey frame, Design A: Predicted values ofy and A
Storey(a) Inelastic link rotation, y (rad) (b) Inelastic inter-storey drift, A (mm)
DesignA Design B Design C DesignA Design B Design C
4 0.070 0.049 0.044 34.64 36.35 32.20
3 0.064 0.050 0.035 31.73 36.68 26.01
2 0.050 0.045 0.038 24.64 33.25 28.20
1 0.041 0.031 0.029 24.62 28.03 25.84
Table 6.3 Four-storey frame, Design A: Maximum normalized link shear forces and inelastic
Fig. 6.10 Eight-storcy frame: Lateral force distribution obtaincd from modal analysis using rcsponsc spcctrum derivcdfor histoncal records ~ntcnncdiatca/v group)
C\1
U1\0
e
~~
(a) Low a/v records
1 ~------12-1--~~--~~--.
X4"r----~-~__~~\-~~~n- ~1 . 3-'-;;»--- _ NI.l1lA
1 l ,.t--, -----
~9
CI';
(b) Intermc:diate a/v records
-~. _.-- --.- _._---------------'--..
e
-600 -400 ·200 o 200 ..00 600 .(100 -t(H) ·200 o 200 400 600
Lateral force (kN) Lateral force (kN)
Fig. 6.11 Fourtecn-storey frame: Lateral force distributions (maxilnum positive and maximum negative force)
e e
(a) Low a/v recol'ds (b) Intermediate a/v reoords
500400300
._--- ._-_.._---,--_.,
200
-1'- NBC~
~------- NOCe lm..
NLlllA
~---------------_._--
100
..........-----}--~------_ .._--_._- ..._..-
~~. ---i
2
0·1 i , , i 1
o
1)
Il .\- ----~-~-,·------rr~
10 .-.. '-- ..-------.,,4
12
14
13
~ 8o 7..
(1) 6
5 f- --------~
..3
soo400300
,-----_..--~----_ ... _-
200
-M-- NUee:",.,..~ --=-"-~-···-Niië.(:'~:·----
------- NL11 lA .-----
100
1 • ~-------
+- If--é- --.~.-----
12-1-----·
14
13j~---,
::l-Jt-t 8'
S 7
Cf'
1
(1)6
S 5
4
3
2'
1
0
0
Lateral force (kN) Lateral force (kN)
Fig. 6.12 Fourtccn-storey frame: Lateral force distributions (absolutc maximum force)
e e
14 _....
13 ,-.--. ----------.---. '~--'
12 f----··_---------------~---".....' '---
1
-----
7' .------~
J'
----------- 1
-_._----.~-------~
-------=~.~=_ ....._.....__ .... ._. ._. .... -1
9 -f--------.-~--~-
JI 1------~-~-------
10 ---------------J-
~ 8
Y'
g 7fi}
0\
6
-5
1of
3
2
1
0
Lateral force
Fig. 6.13 Fourtccn-storey frame: Suggestcd lateral force profile
..••.,
••••..••~....
u
>
6-62
<1
(a) Four«orey frame
· 1·rrrst y =O.09rad ··~ - ··
" First link yield ·· 1
/ • j·V · 1·
1 3.0
:: 2.5
~ 2.0
.gI! 1.5
= 1.0~'ë 0.5CIIIIca 0.0
0.0 0.5 1.0 1.5 2.0 2S
Roof drift index (0.10)
(b) Eight«orey frame
1)3.0u
1~ ·z
> ., - ·-~
i"~ 2.0
oS.-
1-- -! 1.5
~ 1..1.0Il
/ 1Col..c:: 1III 0.5
/CIIIIIl 0.0= 0.0 0.5 1.0 1.5 20 25
Roof drift index C%)
(c) Fourteen«orey frame
····~ ···
" ·1 1
/ ·1·7 ··
1 3.0
~ 2.5
"~ 20C-; 1.5..= 1.0~';l 0.5CIIIIca 0.0
0.0 0.5 1.0 1.S 20 25
Roof drift index (".10)
Fig. 6.15 Force-deformation relationships
6-63
e
1.2, R,H 'l,
e
9'~
/~lJ
"'-------------Note: n corresponds to RJ
......1
o---~-r
Period
Fig. 6.16 Typical qualitative rclationship betwecn RIJ and n (after Fischinger and Fajfar, 1994)
CANADIAN DESIGN REQUIREMENTSFOR SEISMIC DESIGN OF EBFs
Table 4.1.9.1.8.Force Modification Flclorsll)
Fonning Part of Sentence 4.1.9.1.(8)
4.1.9.1.
Case Type of Lateral-Force-Resisting System RSteel Structures Cesigned and Detailed According to CAN/CSA-S16.1-M
1 ductile moment-resisting frame 4.02 ductile eccentrically braced frame 4.03 ductile steel plate shear wall 4.04 ductile braced frame 3.0·5 moment-resisting frame with nominat ductility 3.06 nominalJy ductile steel plate shear wall 3.07 braced frame with nominal duetirlty 2.08 ordinary steel plate shear wall 2.09 other lateral-force-resisting systems not defined in cases 1to 8 1.5
Reinforced Concrete Structures Designed and Detailed According ta CSA A23.310 ductile moment-resisting frame 4.011 ductile coupled wall 4.012 other ductile wall systems 3.513 moment-resisting frame with nominal duetility 2.014 wall with nominal ductility 2.015 other lateraJ-force-resisting systems not defined in Cases lOto 14 1.5
limber Structures Oesigned and Detailed According to CSA 086.116 nailed shear panel with plywood, waferboard or osa 3.017 concentrically braced heavy timber frame with ductile connections 2.018 moment-resisting wood frame with ductUe connections 2.019 other systems not included in Cases 16 ta 18 1.5
Masonry Structures Designed and Detailed According to CSA 8304.120 reinforced masonry wall with nominal ductility 2.021 reinforced masonry 1.522 unreinforced masonry 1.023 O1her Lateral-force-resistina SYStems not Defined in Cases 1to 22 1.0
Notes to Table 4.1.9.1.8.:(1) See Appendix A.
Table 4.1.9.1.C.Foundation Factors(1)
Forming Part of Sentence 4.1.9.1.(11)
Categories Type and Depth of Rock and Soil Measured from the Foundation or Pile Cap Levet F
1 Rock, dense and very dense coars&grained soUs, very stiff and hard fine-grained soilS; compact 1.0coarse-grained soifs and firm and stiff fine-grained soils from 0 to 15 mdeep
2 Compact coarse-grained soifs, finn and stiff fine-grained soifs with a depth greater than 15 m; very 1.310058 and 10058 coarse-grained soils and very soft and soft fine-grained soils from 0 to 15 mdeep
3 Very loose and loose coarse-grained soifs with depth greater than 15·m 1.5
4 Very soft and soft fine-grained soifs wi1h depth greater than .15 m 2.0
Notel to Tlble 4.1.9.1.C.:(1) see AppencfIX A.
9-1 f.
Umit Staw D6ign ofStH/ StruàUm
27.5.4The beam attached to chevron or V·braces shall be contfnuous between columns and fu top andbottom flanges shall be designed ta resist a f~teral load of 1.596 of the ffange yield force at thepoint of intersection with the braces.
27.5.5Whe" a beam is supported from below by chevron braces, it shall be a Class 1 section and shaJlhave adequate nominal mistance to support its tributary gravity loads without the supportprovided by the braces. The beam connections at the columns shall resist forces corresponding taplastic bending at the brace intersection point.
Braces in chevron braced frames in velocity related seismic zones 4 and higher shall confarm tothe requirements of Clause 27.4.3.1.
27.6 Ductile Eccentrically Braced FramesMembers in the braced bays of eccentrically braced frames shall be designed in accordance withthe following requirements.
27.6.1 Uak Beam
27.6.1.1The Iink beam in an eccentrically braced frame is a beam containing a segment (link) that isdesigned ta yield, either in flexure or in shear, prior to yield of other parts of the structure. A linkshall be provided at least at one end of each brace. The section used for a link beam shaU be Crass 1,and its yield strength, Fy, shall not exceed 3S0 MPa.
27.6.1.2Axial forces in fink beams due to forces from the braces and due ta transfer of seismic force ta theend of the frames shall be considered in the design.
27.6.2 Uak ResistanceThe shear resistance of the link shalf be taken as the lesser of V; and 2M; lewhere
V{ =Vr ", - (:A~,J and
M; =1.18.• Mp(, - A~) S • Mp
Vr is given in Clause 13.4.1.2Pf is the factored axial tensile or compres.sive force in the fink, ande is the length of the link.
When :~ S 0.15, the effect of Pf on the fink resistance may be negleeted.
27.6.3 LeDgth of LiDkWhen Pt IAFy > 0.1 S, the len9th of Iink shall not exceed:
for~ <! 0.3 ~, [1.1 S- 0.5 ~ ~t~~r)At" Vf 1.6Mr
for A < 0.3 Pt' v;-
9-2
\
CAN/CSA·S16.1-94
27.6.4 lJDk RotationThe rotation of the IInk segment relative ta the rest of the beam, ·at a total frame drift of O.SR timesthe drift determined for faetored loading, shan not exceed the following:(a) 0.09 radians for links having a cfear length of 1.6MrNr or less;(b) 0.03 radians for links having a clear length of 2.6MrNr or greater; and(c) a value obtained by IInear interpolation between the above limits for links having clear lengthsbetween the above Iimits.Note: Ris ddintd in aaus~ .,. 7.9 of th~National Buildrng Code ofCanada, 1995.
27.6.5 LiDk StiffeDers
27.6.5.1Full-depth web stiffeners shall be provided on bath sides of the be~m web at the brace end of theIink. The roffeners shan have a combined wfdth of not less than b - 2w and a thfckness of not lessthan O.75w or 10 mm.
27.6.5.2Intermediate Iink web rolfeners shaU be full depth and shall be provided as foflows:
(a) when e < l·~rMr stfffeners shall be spaced at intervals not exceeding (30w - O.2d) when the link
rotation angle is 0.09 radians, or (52w - 0.2d) when the rotation is 0.03 radians, or less. Unearinterpolation shall be used for values between 0.09 and 0.03.
(b) When 2.~~r < e < 5';:r ~tiffenersshall be placed at a distance of 1.Sb trom each end of the Iink.
(c) When 1.~~r < e < 2.~~r roffeners shall be provided as in (a) and (b).
(d) When e> Sv~r noInt~rmediate stiffeners are required.
27.6.5.3Full.depth intermediate web stiffeners are required on only one side of the web for link beams lessthan 650 mm in depth and on bath sides of the web for beams 650 mm or greater in depth. Thethickness of one.side stiffeners shall not be leu than w or 10 mm whichever fs larger, and thewidth shall not be less than O.Sb - w.
27.6.5.4Fillet welds connecting the stiffener to the beam web shall develop a stiffener force of AsFy. FiUetwelds connecting the stiffener ta the flanges shall develop a stiffener force of 0.25AsFy•
27.6.6 Lateral Support for LlDkLateral support shall be provided ta both top and bottom flanges at the ends of a link. Theselateral supports shall have a resistance at lean equal ta O.06btFy.
27.6.7 LiDk Beam-to-CoIIIIDD Coanec:tioa
27.6.7.1Unks conneaed ta columns shall not exceed a length of 1.6MrNr, unless it can be demonstratedthat the link·to·column connection Is adequate to undergo the required inelastic link rotation.
1·96 9-3
\
Umlt States Oaign ofStftl St11letuta
27.6.7.2Where a link is adjacent to the column, the following requirements shall be met:Ca> The beam flanges shall have complete joint penetration groove welds ta the column.
(b) The web connedion shaU be welded to develop the nominal axial, f1exuraJ and shear resistancesof the beam web.
Cc) The capacity of the co'umn ta resist the flange yield load shall be deterrnined from Clause21.2.4.3.
27.6.7.3Where the·link is connected to the column web, the beam tlanges shalf have complete Joint .penetration groove welds to the conneetion plates and the web conneetion shall be welded tadeve'op the factored axial, f1exural and shear resistance of the beam web. The rotation betweenthe IInk beam and the column shall not exceed 0.015 radians at O.SR times the drift due tafaetored loading.
27.6.7.4Unk beam connections to columns may be designed ta resist transve~e shear only if the link is notadjacent ta the column. Such connections must have capacity ta resist a torsional moment of0.015 btdlY.
27.6.8 Braœ-to-lJak Beam. CoDDectioDSBrace-ta-Iink beam connections shan develop the nominal resistance of the brace and transfer thisforce ta the beam web. If the brace Is designed to resist a portion of the link end momen~ fullend restraint shan be provided. No part of the brace-to-beam connection shall extend into theweb area of a Iink beam. The intersection of the brace and beam centre-Iines shall be at or withinthe link. The beam shall not be spJiced within or adjacent to the conneetian between beam andbrace.
27.6.9 LiDk Beam. Resistance
27.6.9.1The beam outside the Iink shall have nominal axial, bending, and shear resistance which equals orexceeds the forces corresponding to 1.5 times the controlfing resistance of the Hnk.
27.6.9.2The.beam outside of the link shall be provided with sufficient lateral support_to maintain stabilityof the beam under farces corresponding to 1.5 times the cantrolling resistance of the link. Lateralbracing shall be provided ta both top and bottom f1anges and shan have a resistance at least equalta 0.015 btF}t.
27.6.10 Diago~BracesEach diagonal brace shall have a nominal resistance to support axial force and momentcorresponding ta 1.5 times the controlling resistance of the link beam (Clause 21.6.2). Sectionsshall be Class 1 or 2.
27.6.11 ColaDIDSMoments and axial laads introduced into a column at the cannection with a Iink or brace shall notbe less than those generated by 1.25 tfmes the controlling resistance of the linle.
1-97
9-4
\
CANICSA-Sf 6. f -94
27.6.12 RoofLiDk Be8mAIink beam is not required in roof beams of frames over flve storeys ln height.
27.6.13 Coaceatric Drace iD CombfaatioaThe tint storey of 1 frame over five storeys ln height may be concentrically braced if this $lorey canbe shown to have a resistance of at leut 1.5 times the loading associated with yielding of anyother storey of the structure. .
27.7 Special ~rudDgSystems
2-7.7.1 Steel Plate Sheu WallsSteel plate shear walls shall meet the requirements of Appendix M.
27.7.2 Other FnmdDg SystemsOther framing systems and frames that incorporate special bracing, base isolation, or otherenergy.absorbing devices shall be designed on the basis of published research mults, observedperformance in past earthquakes, or special investigation.
28. Fabrication
28.1 GeneralUnless otherwise specified, the provisions of Cause 28 shall apply ta bath shop and field fabrication.
28.2 Straigbmess ofMaterialPrior to layout or fabrication, rolled material shall be straight within established rolling mill .toleranclS. If straightening is necessary, ft shall be done by means that will not injure the material.When heat is applied locally, the temperature of the heated area shall not !Xceed the limits givenin CSA Standard W59. Sharp kinks and bends stiall be cause for rejection.
28.3 Gas CuttingGas cutting shall be done by machine where praeticable. Gas-cut edges shall confonn ta CSAStandard W59. Re.entrant corners shall be free trom notches and shall have the largest praeticalradii, with a minimum radius of 14 mm.
28.4 Shearecl or Gas-Cut Edge FiDish
28.4.1Planing or finishing of sheared or gas-cut edges of plates or shapes shall not be required, unlessspecificaUy noted on the drawings or included in a stipulated edge preparation for weJding.
28.4.2The use of sheared edges in the tension area shall be avoided in locations subjeet to plastic hingerotation at factored loading. If used, such edges shall be finished smooth by grinding, chipping, orplaning. These requirements shall be noted on design drawings and shop details where applicable.
28.4.3Burrs shall be removed<a> as required in Clause 23.3.3;(b) when required for proper fit-up for welding; and(c) when they create a huard during or after construction.
1-989-5
\
Deœtrrber f994
APPENDIXB
FLOW CHARTS, FORMATS OFINPUT AND OUTPUT FILES
/0. APPENDIXB
READ FILEN.TlME.T:NCAS.NELTOT.BMS.SME.BMDES,BRB.BRE,BRDES,CLB,CLE.CLDES FROM TItIEH
DESIGN MODULE
PROGRAM RES~EXE
FLOWCHART
STEP = TIMEIT+1NR=NELTOT
SUBROTINES:
CD INPUT~ PROP@ RATIO@ SELECT@ STASEL
INITIAlIZE R (NR.5)
SUBROUTINE INPUTPREPARES DATAFUSING INFORMATIONPROVIDED IN DATA.USR
NO
YES
YES
REAC FROM DATAF:NE.FLR.W8R.TR,C'f,CRX,CR'f,MP,ONEMU.CEX,F'f,ZA,SEC.SECIND
ZA=AXlAREACALlPROPCALCULATE MR USING MRRCALCULATE MRS USING MRRMOMMAX = MAX (MOMI,MOMJ)MOSMAX = MAX (ELMOMI,ELMOMJ)CALL RAno (...AX,MOMI,MOMJ,-CLA,RA,RB.RC)CALL RAno (-ELAX,ELMOMI,ELMOMJ,"CLB,RSA,RSB,RSC)CLTOT = MAX (CLA,CLB)CALL SHEAR (WBR,WT.D,F'f.ELVEL,ELVIEL,RATSHE,RATSHI)RMAX = MAX (RA,RB,RC,RSA,RSB,RSC.RATSt-IE,RATSHI)
NO
YES POSSEC (1) = SNAMERMAX (1) = RMAX
( END )~ -.J
10-11
JO. APPENDIXB
INPUT FILES
(i) DESIGN MODULE
TIMEH
- NAME OF TIME HISTORY FILE (ENCLOSE IN ' ')- TOTAL DURATION OF EARTHQUAKE RECORD- TIME STEP FOR rvŒMBER FORCES OUTPUT- CASE: 1 - BEAMS ELASnC, BRACES ANn COLUMNS ELASTIC
2 - BEAMS INEUSnC, BRACES AND COLUMNS EL\STIC- TOTAL NUMBER OF ELEMENTS TO RESPOND ELASTICALLY- FIRST BEM.-f ELE~[ENT, LAST BEAM ELEMENT, BRACE SECTIONS
DATABASE- FIRST BRACE ELE~ŒNT, LAST BRACE ELEMENT, BRACE SECTIONS
DATABASE- FIRST COLU~fN ELE~ŒNT, LAST COLU1fN ELEJ\fENT, COLU~fN SECTIONS
Ibis file follows the format of file DATA.USR. Forces produced by goveming load
combinatians are obtained from elastic analysis for each element group and specified as
follows:
- ~XIAL FORCE (CO~IPRESSION- positive), MOMENT AT END l, MOMENT ATEND J (same sign for double curvature), ELASTIC SHEAR FORCE, INEL\STICSHEAR fORCE (for all elements other than beams, inelastic shear force is set ta zero)
NOTE: Resistances are calculated using resistance factor f equal to J. O. This has to hetaldng into accounl when definingforcesfor file STAT (i.e., divide magnitude offorces by0.9)
The file contains as many lines as there are e1ements other than links.Following data is
provided:
- NUMBER OF ELEMENT, bit, h/w, Tet Cy, Ca' C~., Mp, ~~ (00=1.0), Ca' Fy, ZxlA,FIRST LErrER OF SECTION DESIGNATION, SECTION DESIGNATION
(ü) DATA MODIFICATION MODULE
- In addition to DATA.USR and DATAF, following input file is needed to calculate braceinclination angles, in order to update beam and brace end eccentricities:
ANGLE
OUTER BEAIvI SPAN, STOREY HEIGHT (starting with first storey)
EXAMPLE: (for four storey frame)
36004500360036003600360036003600
10-14
NOTE Ta USERS
Page (5) not included in the original manuscript isunavailable trom the author or university. The
manuscript was microfilmed as received.
Pg 10-15 in Chapter 10
This reproduction is the best copy available.
DATA MODIFICATION MODULE
PROGRAM MODFF.EXEFLOWCHART
TRANSFORMTEMPLATEINPUT FILE DATA.TSTINTO DIRECT ACCESS FILE
ID. APPENDIXB
REAC DATA FROM CONTROLUNES TO DETERMINE LOCATIONOF DATA TO MOQIFY
READ DATA FROM CONTROLUNES TO DETERMINE LOCATIONOF DATA TO MOOIFY
flEAD DATA FROM FILE DATAF jTO DETERMINE RIGID OFFSETSAT BEAM-TO-BRACE CONNECTIO
Jo
CALCULATE RIGID OFFSETSAT BEAM-TO·BRACE CONNECTIONAND STORE IN MATRIX ECC
•UPDATE STIFFNESS AND YIELOINGSURFACES FOR COLUMN ELEMENTS(ACCOUNT FOR THE CLASS OF THE seCTION)
•UPDATE STlFFNESS AND YIELDINGSURFACES FOR BEAM AND L1NK ELEMENTSALSO UPDATE RIGID OFFSETS
~
UPDATE STIFFNESS AND YIELOINGSURFACES FOR BRACe ELEMENTS(ACCOUNT FOR THE CLASS OF THE SECTION)AlSO UPDATE RIGID OFFSerS
