-
sole158
el pstigs. Rll pmnaselumofSPSret th
2014 Elsevier Ltd. All rights reserved.
s are oavailabame wd devshowpariso
forcednt resis
te that most of the ex-rmed on SPSWs in the
Journal of Constructional Steel Research 99 (2014) 7284
Contents lists available at ScienceDirect
Journal of Constructiomore recent studies have worked on new
types of SPSW systems, past, particularly before the existence of
codied design requirementsfor SPSWs, dealt with systems not meeting
the capacity design require-ments and therefore not necessarily
having a desirable mode of failure.shear panels as dampers [1012],
as alternatives to conventionalSPSWs to improve the dissipation
capacity of the system. However,
design level earthquakes will be satised [21]. Noperimental and
analytical research studies perfoload resisting framing.With these
advantages, this systemhas attractedmany research activities
throughout the world. Many researchers havefocused their research
on the discovery of the behavior of SPSWs[15], while others have
proposed the use of light-gauge [6] or lowyield point (LYP) SPSWs
[7,8], SPSWs with slits [9] or special metal
pendence of the angle of the tension elds on the cross-sectional
prop-erties of the surroundingmembers and the inll plate
thickness), resultsof recent research have shown that if the SPSWs
are designed accordingto the code recommendations, the desired
sequence of yielding will beachieved [20] and maximum interstory
drift requirements considering Corresponding author. Tel.: +98 171
444 1002; fax:E-mail addresses: [email protected] (S.A.A.
Ho
(M. Tehranizadeh).1 Tel.: +98 21 6454 3030; fax: +98 21 6454
3037.
http://dx.doi.org/10.1016/j.jcsr.2014.04.0040143-974X/ 2014
Elsevier Ltd. All rights reserved.ting frames, SPSWs havete fast
construction, andfor fewer bays of lateral
resulting from both tension eld yielding of the inll plates and
exuralyielding of the HBE ends. Although, the suggested design
procedurescan be an iterative and time-consuming process (due in
part to the de-fewer costly detailing requirements, facilitahave
high strength and ductility that allow1. Introduction
Steel plate shearwall (SPSW) systemlateral load resisting
systems currentlyThe SPSW system comprises a steel frthat are
allowed to buckle in shear anunder lateral loading. Past studies
haveexemplary seismic performance. In comeral load resisting
systems, such as reinious types of braced frames and momene of
themost promisingle to structural engineers.ith thin steel inll
plateselop tension eld actionn that SPSWs can exhibitn with
conventional lat-concrete shear walls, var-
such as semi-supported [13,14] and self-centering [15] steel
shearwalls, to further increase the efciency of the system.
Design clauses for design of SPSWs were provided rst in
CAN/CSA16-01 [16] and then in FEMA 450 [17], AISC 341 [18] and AISC
DesignGuide 20 [19]. To ensure a ductile and desirable behavior,
the currentcodes require capacity design of SPSWs. Capacity design
implies thatthe horizontal boundary elements (HBEs)must be designed
to resist de-mands resulting from tension eld yielding of the inll
plates, and thevertical boundary elements (VBEs) must be designed
to resist demandsBehavioral characteristics of code designed
S.A.A. Hosseinzadeh a,, Mohsen Tehranizadeh b,1
a Department of Civil Engineering, Faculty of Engineering,
Golestan University, Al-Ghadir Ave, Gb Department of Civil
Engineering, Amirkabir University of Technology, 424 Hafez Ave,
Tehran
a b s t r a c ta r t i c l e i n f o
Article history:Received 10 June 2013Accepted 2 April
2014Available online 4 May 2014
Keywords:Shear wallsWallframe
contributionInteractionStrengthDuctilityStiffness
A series of code designed stenumerically analyzed to invethe
wall/frame contributionfew of lower stories and in80% of the
compressive columore effective in resisting bshear force of the
frame coSPSWs due to early bucklingboundary frames of differentof
the current design procedutility of SPSWs having almos+98 171 444
1003.sseinzadeh), [email protected] plate shear wall systems
stan 49188-88369, Iran75-4413, Iran
late shear walls (SPSWs) with different aspect ratios and number
of stories areate different aspects of the behavior of such SPSWs,
particularly with regard toesults show that frames contribute
effectively in resisting story shear only at alates absorb
substantial part of story shear at the remaining stories. About
70axial force comes from plate tension elds. The tensile column is
found to beshear than the compressive one and it contributes about
5595% of the totaln bases at the ultimate state. Up to 32%
reduction in the overall stiffness oftheir inll plates is observed.
The rst yield points in the inll walls and in theWs occur at about
2545% and 7085% of their strength, respectively. As a resultthat
neglects the boundary framemoment resisting action, the stiffness
and duc-e same design lateral loads but different aspect ratios can
be quite different.
nal Steel ResearchHence, the ndings from those studies, although
valuable, are not nec-essarily valid for all SPSW systems,
especially for those designed per de-sign code.
In general, for a given panel geometry, inll plate thickness
andma-terial properties, the behavior of a SPSW system depending on
the
-
cross-sectional properties of its boundarymembers can be
controlled bytwo general types of failure mechanisms, namely
brittle and ductile. Alist of possible failure mechanisms of
typical SPSWs in the order oftheir desirability was provided by
Astaneh-Asl [5]. It is generally accept-ed that the tension
yielding in the inll plate, occurring under the actionof story
shear, should be considered as the primarymode of energy
dis-sipation of SPSWs. Again, for the full-tension yielding of the
inll plates,the boundary frame members should have adequate
strength and stiff-ness. However, if the frame member sections are
selected from weakerproles, the system behavior is primarily
governed by an undesirable orless desirable failuremode rather than
a ductile or desirable one and thefull-tension yielding of inll
plates would not be realized even at theultimate state. Several
experimental investigations have conrmed theabove discussion
[3,2224]. In some of those tests excessive deforma-tion, premature
yielding and/or buckling of boundary elements limitedthe strength
and ductility of the SPSW systems.
The overall behavior of a SPSW comprises the contributions of
theinll wall and boundary frame actions. Hence, separation of the
contri-butions of inll wall tension eld action and boundary frame
momentresisting action to the overall behavior, in addition to
studying the over-all behavior of the system, provides a better
insight into the systembehavior. It is to be noted that there is an
interaction effect betweenthe inll wall and the boundary frame,
which is too complicated to bedened by a closed form solution.
Nevertheless, in order to accuratelypredict the overall behavior of
the SPSWbased on the discrete behaviorsof the inll wall and the
frame, or to separate the wall and frame
interstory drift ratios for different SPSWs. The results show
that in all
73S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284responses from the
overall response of the SPSW, the effect of the inter-action must
be taken into account somehow.
The purpose of this research is to investigate different aspects
of thebehavior of code designed SPSWs, particularly with regard to
the rela-tive or respective contributions of their inll walls and
boundary framesto the overall behavior. To accomplish this, a
series of SPSWswith differ-ent aspect ratios and number of stories,
designed per design code [18,19], are analyzed using the nite
element method and the obtained re-sults are utilized to
investigate: (a) wallframe contribution shares ofstory shears, (b)
wallframe contribution shares of the VBE axial forces,(c)
comparison of the VBE axial and shear forces, (d) overall
stiffnessand ductility, and the contributions from inll walls and
frames,(e) base shear levels associated with the rst yielding of
walls andFig. 1. Typical plan and considered SPSW.designs, the
maximum interstory drifts are relatively low (lower than0.01 h).
This indicates that all designs are governed by strength andframes,
and (f) inuence of the SPSW aspect ratio and number ofstory on the
above.
2. Method of the study
2.1. Design of models
A number of SPSW systems having different aspect ratios and
num-ber of stories are considered for this research. SPSWs are
designed for atypical building plan (Fig. 1). The buildings
considered are 1, 2, 4, 6, 8,10, 12 and 15 stories tall and have
uniform story heights of 3.40 m.SPSWs are designed according to the
recommendations given in AISCSeismic Provisions [18] and AISC
Design Guide 20 [19]. The perimetergravity frames without shear
walls are assumed to have pinned beamto column connections and
therefore, they are not incorporated in de-sign and analysis.
However, gravity loads transmitted by perimeterframe beams to SPSW
beamcolumn connections, are considered inthe design and
analysis.
All models have beam-to-column connection details that include
re-duced beam sections (RBS) at each end, as recommended by the
AISCDesign Guide 20 [19], to ensure inelastic beam action at the
desired lo-cations. Also, the use of the RBS is reasonable
considering the followingtwo properties. First, the exural force in
the VBE due to HBE hinging istypically greater than that due to
plate tension. In such cases, the exureaway from the connection
does not govern the design of the VBE. Sec-ond, the required HBE
exural strength is governed by exure in themid-span due to plate
tension (in combinationwith gravity load effects,if any), not at
the ends. Based on these two properties, it is convenient touse a
RBS in the HBE to limit the required exural strength of the
VBE.Moreover, the RBS reduces the demand on the VBE when applying
thestrong columnweak beam requirement. However, special concernmust
be paid to the design of HBEs, particularly for intermediate
oneshaving RBS connections, since recent research [25] has shown
that thecurrent design approach does not necessarily lead to a
HBEwith the ex-pected performance. To reliably achieve capacity
design, analyticalmodels for estimating the design forces for
intermediate HBEs havebeen proposed by researchers [26].
A dead load of 4.6 kPa is used for each oor and 3.2 kPa for the
roof.Live loads are taken equal to 2.4 kPa for each oor and 0.96
kPa for theroof. According to the code-compliant range of aspect
ratios, the baywidths (L), measured from center to center of VBEs,
are assumed tovary from 2.9 to 8.5 m (i.e. L/h = 0.85, 1.4, 2 and
2.5). Inll plate thick-nesses are designed to resist the entire
story shear per [18]. Plate thick-nesses are selected from those
available in ASTM A36 steel [19]. Duringthe design, the minimum
practical inll plate thickness requiredfor handling and welding
considerations is considered to be 3.18 mm(1/8 in.). Note that the
inll plate, however, will often have someoverstrength (i.e. the
specied plate thickness will be thicker than re-quired by design)
not only due to the consideration of the minimumpractical plate
thickness but also due the fact that steel plates are avail-able in
discrete thicknesses on the market. The boundary frame mem-bers are
designed using the capacity design principles to resist theforces
from inll plate yielding. The resulting plate thicknesses andmember
sizes are shown in Table 1. Table 2 presents the RBS
connectiondimensions (see Fig. 2) for different HBE proles per AISC
358-05 [27].Throughout the article, each model will be identied by
the value ofSPSW aspect ratio (L/h) and number of story (n).
Finally, in order to check that drift requirements are met, the
de-signed SPSW systems in Table 1 are numerically analyzed under
the de-sign level earthquake forces as determined by ASCE 7-05
[28]. Table 3presents the design base shears and the corresponding
maximumnot by drift limitations. However, as can be inferred from
the results
-
Table 1Inll plate thicknesses and frame member sizes of
different SPSW models at different stories.
Case # of stories,n
Bay width, L(m)
Aspect ratio,L/h
Plate thickness, tw (mm) HBE size VBE size
Intermediate Top
1 1 2.9 0.85 3.18 (1st) W14 132 W14 2112 1 4.8 1.4 3.18 (1st)
W14 233 W14 3113 1 6.8 2.0 3.18 (1st) W27 194 W14 3984 1 8.5 2.5
3.18 (1st) W40 211 W36 3305 2 2.9 0.85 4.76 (1st), 3.18 (2nd) W14
132 W14 132 W14 3116 2 4.8 1.4 3.18 (1st, 2nd) W14 132 W14 233 W14
3117 2 6.8 2.0 3.18 (1st, 2nd) W14 132 W27 194 W14 3988 2 8.5 2.5
3.18 (1st, 2nd) W14 132 W40 211 W36 3309 4 2.9 0.85 4.76 (1st,
2nd), 3.18 (3rd, 4th) W14 132 W14 132 W14 37010 4 4.8 1.4 3.18
(1st4th) W14 132 W14 233 W14 31111 4 6.8 2.0 3.18 (1st4th) W14 132
W27 194 W14 39812 4 8.5 2.5 3.18 (1st4th) W14 132 W40 211 W36 33013
6 2.9 0.85 7.94 (1st, 2nd), 6.35 (3rd, 4th), 4.76 (5th), 3.18 (6th)
W14 132 W14 132 W14 605 (1st4th), W14 311 (5th, 6th)14 6 4.8 1.4
4.76 (1st4th), 3.18 (5th, 6th) W14 132 W14 233 W14 500 (1st4th),
W14 311 (5th, 6th)15 6 6.8 2.0 3.42 (1st, 2nd), 3.18 (3rd6th) W14
176 W27 194 W14 500 (1st4th), W14 398 (5th, 6th)16 6 8.5 2.5 3.18
(1st6th) W14 132 W40 211 W36 361 (1st4th), W36 330 (5th, 6th)17 8
2.9 0.85 12.7 (1st, 2nd), 11.1 (3rd), 9.53 (4th), 7.94 (5th), 6.35
(6th), 4.76 (7th), 3.18 (8th) W14 132 W14 132 BUILT UP1a (1st4th),
W14 455 (5th8th)18 8 4.8 1.4 6.35 (1st4th), 4.76 (5th, 6th), 3.18
(7th, 8th) W14 132 W14 233 W14 730 (1st4th), W14 398 (5th8th)19 8
6.8 2.0 4.76 (1st4th), 3.18 (5th8th) W14 176 W27 194 W14 730
(1st4th), W14 398 (5th8th)20 8 8.5 2.5 4.76 (1st4th), 3.18 (5th8th)
W14 233 W40 211 W36 652 (1st4th), W36 330 (5th8th)21 10 2.9 0.85
12.7 + 3.18 (1st3rd), 12.7 (4th, 5th), 11.1 (6th), 9.53 (7th), 7.94
(8th), 4.76 (9th), 3.18 (10th) W14 176 W14 176 BUILT UP2b (1st5th),
W14 730 (6th10th)22 10 4.8 1.4 9.53 (1st, 2nd), 7.94 (3rd5th), 6.35
(6th, 7th), 4.76 (8th), 3.18 (9th, 10th) W14 132 W14 233 W36 800
(1st5th), W36 487 (6th10th)23 10 6.8 2.0 7.94 (1st, 2nd), 6.35
(3rd6th), 4.76 (7th, 8th), 3.18 (9th, 10th) W14 176 W27 194 W36 800
(1st5th), W36 487 (6th10th)24 10 8.5 2.5 6.35 (1st4th), 4.76
(5th7th), 3.18 (8th10th) W14 233 W40 211 W36 652 (1st5th), W36 487
(6th10th)25 12 4.8 1.4 11.1 (1st4th), 9.53 (5th, 6th), 7.94 (7th,
8th), 6.35 (9th), 4.76 (10th), 3.42 (11th), 3.18 (12th) W14 132 W14
233 BUILT UP3c (1st6th), W36 652 (7th12th)26 12 6.8 2.0 7.94
(1st5th), 6.35 (6th8th), 4.76 (9th, 10th), 3.18 (11th, 12th) W14
176 W27 194 BUILT UP4d (1st6th), W36 652 (7th12th)27 15 4.8 1.4
12.7 + 1.59 (1st5th), 12.7 (6th, 7th), 11.1 (8th, 9th), 9.53 (10th,
11th), 7.94 (12th), 6.35 (13th),
4.76 (14th), 3.18 (15th)W14 132 W14 233 BUILT UP5e (1st8th), W36
800 (9th15th)
28 15 6.8 2.0 11.1 (1st4th), 9.53 (5th7th), 7.94 (8th10th), 6.35
(11th), 4.76 (12th, 13th), 3.18 (14th, 15th) W14 176 W27 194 BUILT
UP6f (1st8th), W36 652 (9th15th)
a BUILT UP1: section depth = 550 mm, ange width = 500 mm, ange
thickness = 160 mm, web thickness = 100 mm.b BUILT UP2: section
depth = 650 mm, ange width = 600 mm, ange thickness = 180 mm, web
thickness = 120 mm.c BUILT UP3: section depth = 1150 mm, ange width
= 550 mm, ange thickness = 140 mm, web thickness = 80 mm.d BUILT
UP4: section depth = 1150 mm, ange width = 500 mm, ange thickness =
120 mm, web thickness = 70 mm.e BUILT UP5: section depth = 1150 mm,
ange width = 700 mm, ange thickness = 180 mm, web thickness = 100
mm.f BUILT UP6: section depth = 1150 mm, ange width = 600 mm, ange
thickness = 160 mm, web thickness = 90 mm.
74S.A.A.H
osseinzadeh,M.Tehranizadeh
/JournalofConstructionalSteelResearch99
(2014)7284
-
in Table 3, for taller (over 15-story) SPSWs, especially for
those havinglow aspect ratios, the drift may control the
design.
2.2. Description of nite element models
Using a detailed FE modeling approach similar to that used by
theauthors in the previous work [29], SPSWs are modeled and
analyzed.The FEmodeling approach's adequacy for representing the
pushover re-sponse of SPSWs has already been veried through
comparisons withexperimental results [29] and thus, is not repeated
here. However, forcompleteness and for convenience, a brief
description of the nite ele-ment modeling is presented herein.
The ASTM-A36 and ASTM-A572 conventional structural steel
stan-dards are, respectively, selected for inll wall and
framemember mate-rials. In order to study the nonlinear behaviors
of inll walls and frame
Table 2RBS connection dimensions for different HBE proles per
AISC 358-05.
RBSdimensions
W14 132 W14 176 W14 233 W27 194 W40 211
a (mm) 200 200 220 200 150b (mm) 300 300 330 600 800c (mm) 90 95
100 85 70
75S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284members, respective
stressstrain diagrams are adapted from [20].The nite element
program ABAQUS/Standard [30] is utilized for all
eigen-value and incremental nonlinear pushover analyses. All
framemembers and inll plates are modeled with a reasonably ne
meshusing the four-noded S4R element, a general purpose shell
elementwith reduced integration. The element size is selected from
a mesh re-nement study. The geometric nonlinearity phenomenon is
includedas a result of large displacements with small strains. An
isotropic hard-ening model is used for all nonlinear pushover
analyses.
The inll plates are considered to be connected directly to
theboundary members. The rst-story inll panel is assumed to be
an-chored to the ground rather than to an anchor beam at that level
andits nodes at the base are xed in displacement. Similarly, to
simulatethe x support conditions at the VBE bases, the bottom nodes
of bothFig. 2. Typical SPSW system.VBEanges andwebs are restrained
fromdisplacement in all directions.In order to replicate the
effects of the concrete slab of the oors, all HBEwebs are also
restrained against movement in the out-of-planedirection.
Initial imperfections need to be considered in the nite
elementmodels. To ensure satisfactory results, using imperfections
based onthe rst eigenmode together with the maximum anticipated
amplitudevalue based on the consideration of fabrication procedures
was recom-mended by some FE codes [31]. However, in the case of
typical slenderplates, the choice of imperfection amplitude and
shape does not inu-ence signicantly the overall behavior of the
system [32,33]. Based onthe above discussion, an initial
imperfection pattern corresponding tothe rst buckling mode of each
inll plate with peak magnitude of 1mm is applied in themodels.
Preliminary analyses veried the sufcien-cy of the considered value.
Gravity loads are applied to SPSW beamcolumn connections in order
to include P-delta effects, although P-delta effects are not
important for SPSWs that are stiff enough to meetthe code drift
limit [34]. Lateral loads, as shown in Fig. 2, are equally ap-plied
to the exterior nodes of panel zones on either side of each
storybeam and are gradually increased from zero to a magnitude
beyondthe system's capacity. The ultimate state of SPSWs, per ASCE
7-05 [28],is considered to occur when the drift ratio at least at
one of the storiesof the system reaches a value of 2.5%.
3. Discussion of results
3.1. General behavior
In this section, characteristics of the general behavior of
SPSWs arediscussed. As such, SPSWs are classied into two groups,
namelylow-rise and high-rise, according to the behaviors of their
inllwalls and frames. Only SPSWs having practical dimensions (i.e.
1 b L/h 2) are considered here. However, such classication, in
general,depends on both the SPSW aspect ratio and height.
Typical and idealized behaviors of low-rise (1- or 2-story) and
high-rise (10-story or taller) SPSWs are depicted in Fig. 3. The
behavior of amedium-rise SPSW may be closer to a low-rise SPSW or a
high-riseSPSW, depending on the number of story and aspect ratio,
and thus isnot discussed here separately. In Fig. 3(a) and (b), the
absorbed baseshears by the inll wall and frame columnswere
individually calculatedby summation of the reaction forces at the
base nodes of each one in thein-plane direction. In thisway, the
effect of thewallframe interaction isimplicitly considered in the
behaviors of the inll wall and the frameand therefore, the overall
base sheardisplacement curve of the systemis equal to the summation
of the inll wall and frame base sheardisplacement curves (that is,
the principle of superposition applies). InFig. 3(c) and (d), it
was assumed that the idealized behaviors of the inllwall and the
frame are elasticperfectly plastic and that the principle
ofsuperposition is applicable.
Fig. 3(c) shows that in a low-rise SPSW, the inll wall has a
relativelyhigher stiffness than the frame in the early stages of
loading and absorbsa higher portion of story shear. As the inll
wall reaches its yieldedstrength (point (yw, Pw)), system stiffness
and additional strength areonly provided by moment frame action.
Thereafter, at = yf, theframe reaches its yielded strength (Pf). At
this point, the frame losesits stiffness and does not absorb any
additional shear force up to theultimate state. Eventually, the
frame exhibits greater strength than theinll wall at the ultimate
state. Comparing Fig. 3(c) and (d), it is ob-served that the frame
of a high-rise SPSW acts like the inll wall of alow-rise SPSW and
vice versa. This can be attributed to the increasedbending effects
in a high-rise SPSW, which in turn affect the effective-ness of the
inll wall and cause signicant yielding of the inll wall tohappen
after signicant yielding of the frame (i.e. yw N yf). On the
con-trary, in a low-rise SPSW where shear deformations are
dominant, sig-nicant yielding of the inll wall occurs prior to
signicant yielding of
the frame (i.e. yw b yf). From the results in Fig. 3(d), it is
also noted
-
that in a high-rise SPSW, the inll wall and the frame contribute
almostequally to the overall strength at the ultimate state.
3.2. Wallframe contribution shares of story shear
An effective method to better understand the behavior of SPSWs
isto measure the portion of the total shear force contribution
providedby the inll plates at different levels. It has been shown
from the push-over analyses of single-story SPSWs that the inll
plate is very effectivein the initial stages of loading and it
absorbs substantial part of storyshear (at the base level) before
development of diagonal yield zones
[20]. However, according to the work by the authors [35], in a
typicalsingle-story SPSW, the inll plate is less effective in
resisting lateralloads at the lower level than at upper levels in
the initial stages of load-ing. Once yielding occurs across the
inll plate, the percentage contribu-tion from the inll plate at
different levels becomes similar and after theframe reaches its
yielded strength, it remains almost constant up to theultimate
state (see Fig. 4).
Table 4 presents the percentage base shear contribution provided
byinll walls in different SPSWs at the ultimate state. As shown,
the per-centage strength provided by the inll wall increases
slightly with theheight of the system and generally varies between
32 and 55% of the
Table 3Design base shears and the corresponding maximum
interstory drift ratios for different SPSWs.
# of stories(n)
SPSW aspect ratio
L/h = 0.85 L/h = 1.4 L/h = 2.0 L/h = 2.5
Design baseshear, (KN)
Maximum interstorydrift, (%)
Design baseshear, (KN)
Maximum interstorydrift, (%)
Design baseshear, (KN)
Maximum interstorydrift, (%)
Design baseshear, (KN)
Maximum interstorydrift, (%)
1 770a 0.11 1360a 0.12 1945a 0.12 2320a 0.082 1125a 0.16 1360a
0.12 1945a 0.12 2320a 0.094 1125 0.19 1360 0.15 1945 0.15 2320a
0.136 1810 0.30 2000 0.19 2085 0.17 2320 0.158 2830 0.40 2620 0.26
2865 0.21 3440 0.1910 3410 0.56 3450 0.40 4383 0.30 4590 0.2712
3935 0.46 4365 0.33 15 5010 0.68 6030 0.48
a The design base shears for these cases are modied for the
overstrength due to the consideration of the minimum practical
plate thickness.
76 S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284Fig. 3.Typical and
idealizedbehaviors of low-rise andhigh-rise SPSWs: (a) typical
shear forcedrise SPSW, (c) idealized behavior of a low-rise SPSW,
and (d) idealized behavior of a high-riseisplacement curve of a
low-rise SPSW, (b) typical shear forcedisplacement curveof a
high-SPSW.
-
l sin
77S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284overall strength. Table
5, on the other hand, compares the percentageshear forces resisted
by inll plates at different stories of typical four-
Fig. 4. Percentage share of story shear by the inll walls at
different levels of typicat = 3.18 mm, (c) L/h = 2.0, t = 3.18 mm,
and (d) L/h = 2.5, t = 3.18 mm.and six-story SPSWs having various
aspect ratios at the ultimate state.Fairly similar results are
obtained for other multi-story SPSWs, andthus will not be presented
for brevity. It is also to be noted that the re-sults in Table 5
may be somewhat affected by the fact that in the designphase, as
can be seen in Table 1 and as mentioned in Section 2.1,
somethicknesses were homogenized due to the availability of steel
platesand/or the consideration of the minimum practical plate
thickness. Infact, the additional stiffness and overstrength
provided by the use ofthe thicker inll plate (relative to the
demand) would increase theplate contribution to the story shear to
some extent.
From the results in Table 5, it is shown that, generally, the
effective-ness of inll plates in resisting story shear increases at
upper stories.This is related to the decreased moment to story
shear ratio at higherlevels of the system, which tends to dominate
the shear-type behaviorat those levels compared to exural
deformation. Based on the resultsgiven in Table 5, inll plates
absorb substantial part of story shear atlevels above the second
oor. This implies that VBEs are effective in
Table 4Percentage ultimate base shear strength provided by inll
walls in different SPSWs.
# of stories (n) SPSW aspect ratio (L/h)
0.85 1.4 2.0 2.5
1 37 40 41 322 41 41 42 364 42 48 50 416 46 49 50 468 49 52 52
4710 49 51 51 5512 46 50 15 48 52 resisting story shear only at a
few of lower stories and they do not con-tribute much in resisting
story shear at the remaining stories. It is also
gle-story SPSWs, adapted from [35]: (a) L/h = 0.85, t = 3.18 mm,
(b) L/h = 1.4,observed from the results in Table 5 that at some
upper stories (espe-cially at the top), the shear forces in the
inll plates are greater thanstory shear. The reason for this
observation, as illustrated in Fig. 5 (themoments at the end of
columns are not shown in the gure for clarity),is that the total
shear force of the two VBEs due to inll plate tensionforces (i.e.
VLwall VRwall ), that acts in the direction of story shear,
isgreater than the total shear force of the two VBEs due to the
frame ac-tion (i.e. VLframe VRframe ), that acts in the opposite
direction of storyshear. Thus, the shear force of the inll plate
should be greater thanstory shear to satisfy the equilibrium
condition in the horizontal direc-tion. This is discussed further
below.
Consider two facts. First, on account of the small shear
contributionof the frame and limited story drift at upper stories,
the total shearforce of the VBEs due tomoment frame sway is
relatively small. Second,the upper story inll plates, which are
usually thicker than required bydesign, do not yield completely
even at the ultimate state (yield zones,
Table 5Percentage shear forces resisted by inll plates at
different stories of typical four- and six-story SPSWs having
various aspect ratios at the ultimate state.
Four-story SPSWs (n = 4) Six-story SPSWs (n = 6)
Story SPSW aspect ratio (L/h) Story SPSW aspect ratio (L/h)
0.85 1.4 2.0 2.5 0.85 1.4 2.0 2.5
1 42 48 50 41 1 46 46 50 462 58 65 67 54 2 64 79 83 743 59 98 99
81 3 64 85 96 914 122 163 176 158 4 87 96 98 99
5 99 105 108 1166 115 165 154 174
-
as shown in Fig. 5, develop only in one side of the inll plates
between inuential. As a result, the total shear force of the two
VBEs acts in the
Fig. 5.Mises stress distribution of a typical four-story SPSW at
the ultimate state and the illustration of frame reaction forces
for a partially yielded inll plate.
78 S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284the compressive (right)
columns and the lower beams),while the stresslevel in other areas
(i.e. near the tensile (left) columns and the topbeams) remains
low. These cause the shear force of the compressiveVBE due to plate
tension forces, that acts in the direction of storyshear, in
comparison to the shear force of the tensile VBE due to
platetension forces, that acts in the opposite direction of story
shear, to beFig. 6. Illustration of wall/frame contributidirection
of story shear.
3.3. Wallframe contribution shares of the VBE axial forces
Axial forces in the VBEs come from two sources: plate tension
eldsand moment frame sway (see Fig. 6). Plate tension elds impose
axialons to the VBE axial and shear forces.
-
forces on the VBEs in two ways. First, the vertical components
of platetension forces on interfaces with the VBEs produce tensile
PL
Fig. 7(a), it is also noted that in single-story SPSWs, and to
some extentin two-story SPSWs, the system aspect ratio does affect
the contribu-
Fig. 7. Percentage contribution of inll wall tension elds to the
VBE axial forces at the base of different SPSWs at the ultimate
state: (a) tensile and (b) compressive VBEs.
79S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284wall 1 and compressive
PRwall 1 axial forces in the left and right VBEs, respec-tively,
when the lateral loads act from left to right on the SPSW.
Second,the vertical components of plate tension forces on
interfaces with theHBEs indirectly cause axial forces in the VBEs
(PLwall 2 and PRwall 2 ).These axial forces are normally
compressive. This is mainly due to thefact that the net vertical
components of plate tension elds on HBEs atstory levels where plate
transitions occur and especially at the top,where the inll plate is
present on only one side of theHBE, act in down-ward direction
(note that the net vertical forces acting on HBEs thathave equal
thickness plates above and below are negligible). The axialforces
of the left and right VBEs due to moment frame sway (i.e.
PLframeand PRframe ) are respectively tensile and compressive, when
the lateralloads act from left to right on the SPSW.
Fig. 7 compares the percentage contribution of inll plate
tensionelds to the tensile and compressive VBE axial forces at the
base of dif-ferent SPSWs at the ultimate state. The curves in Fig.
7(a) show a sharpdifference between the percentage contribution of
plate tension eldsto the tensile (left) VBE axial force in
single-story SPSWs and in multi-story ones. Whereas the tensile VBE
axial forces in single-story SPSWs(especially those having high
aspect ratios) are governed by momentframe actions rather than by
plate tension eld actions, a high percent-age of the tensile VBE
axial forces inmulti-story SPSWs (especially thosewith n 4) comes
from plate tension elds. From the results inFig. 8. Typical
percentage contributions of the inll wall and frame actions to the
VBEtions of plate tension elds to the tensile VBE axial forces.
However, intaller SPSWs (n 4), the system aspect ratio does not
play an importantrole in the contribution of plate tension elds to
the tensile VBE axialforces (about 15% difference between curves
for different aspect ratios).Notably, the axial force of the left
(so-called tensile) VBE of a single-story SPSW due to plate tension
elds can be compressive if the SPSWlength is adequately greater
than its height (i.e. the case with n = 1and L/h = 2.5). This is
because of the greater compressive force of thetop beam on the left
VBE due to plate tension elds compared tothe tension from plate
tension forces along the height of the left VBE(i.e. PLwall 2
NPLwall 1 ).
The results in Fig. 7(b) demonstrate that neither the system
aspectratio nor the system height has any effect on the
contribution of platetension elds to the compressive (right) VBE
axial force at the baselevel. Based on the results, about 7080% of
the ultimate axial force ofthe compressive VBE base is resulted
from plate tension elds, regard-less of the SPSW aspect ratio and
height.
Fig. 8 is used to illustrate the percentage contribution shares
of theinll wall and frame actions on the VBE axial forces during
the loadinghistory of typical low-rise and high-rise SPSWs. The
gures show thatsimilarly, a high percentage (more than 80%) of the
tensile and com-pressive VBE axial forces at the early stage of
loading is due to inllwall tension forces in different SPSWs. In a
low-rise SPSW, with theaxial forces during the loading history of
(a) low-rise and (b) high-rise SPSWs.
-
The ratios of the compressive (right) to the tensile (left) VBE
axial
Fig. 9. Ratios of the compressive to the tensile VBE axial
forces at the base of differentSPSWs at the ultimate state.
80 S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284forces (i.e. PR/PL) at
the base level of different SPSWs at the ultimatestate are
presented in Fig. 9. Generally, the amount of the tensionforce
resisted by the inll wall (i.e. Pp) relative to the total
tensionforce in the system (i.e. PL + Pp), which is resisted by
both the inllwall and the left VBE, tends to become smaller as the
system aspectratio decreases or the height increases. Therefore,
the difference be-tween the tensile and compressive VBE axial
forces generally decreasesas the systemaspect ratio decreases or
the height increases; however, inincrease of lateral displacement,
the percentage contribution of inllwall tension forces to the
tensile VBE axial force decreases, while thepercentage contribution
of inll wall tension forces to the compressiveVBE axial force
remains nearly constant. In a high-rise SPSW, however,the
percentage contributions of inll wall tension forces to the
tensileand compressive VBE axial forces are nearly the same and
remainalmost constant during the loading history of the system.
3.4. The tensile and compressive VBE axial and shear forces
Asmentioned before, the forces from inll plate tension elds on
theHBEs reduce the tension in the VBE. Said in another way, at each
level ofthe SPSW, the total tension force in the system is resisted
by both theinll wall and the tensile VBE, while the total
compression force, dueto the plate high slenderness ratio, is
resisted essentially by the com-pressive VBE. Thus, the axial force
in the compressive VBE is greaterthan that in the tensile VBE and
the difference between the axial forcesof the two VBEs at each
level is equal to the amount of the vertical com-ponent of the
total tension force resisted by the inll wall at that level.Fig.
10. Percentage frame base shear intakes by the tensile VBEs of
different SPSWs at theultimate state.taller SPSWs, regardless of
the aspect ratio, the ratios of the compressiveto the tensile VBE
axial forces are very close to unity.
The components of the VBE shear forces at the base of a
typicalsingle-story SPSW regarding the inll wall tension eld action
and theboundary frame moment resisting action are illustrated in
Fig. 6. Asshown, whereas the shear forces of the tensile, VLframe ,
and compressive,VRframe , VBEs due tomoment frame sway similarly
act against story shearand are therefore additive, the shear forces
of the tensile,VLwall, and com-pressive, VRwall , VBEs due to plate
tension elds oppose each other (theshear force of the tensile VBE,
VLwall , acts against story shear and that ofthe compressive VBE,
VRwall , acts in the direction of story shear, whenthe lateral
loads act from left to right on the SPSW). Therefore, in a typ-ical
SPSW system, the shear force in the tensile VBE base would
begreater than that in the compressive VBE base.
Fig. 10 presents the percentage of frame base shears resisted
bythe tensile (left) VBEs of different SPSWs at the ultimate state
(i.e. [VL/(VL + VR) 100]). Note that the VBEs at the lower levels,
especially atthe base, would be more active in resisting story
shear than at upperlevels, as mentioned before. Fig. 10 shows that
generally, the contribu-tion of the tensile VBE to the frame base
shear resistance increaseswith the height of the system, while it
decreases with the aspect ratio.As shown, the tensile VBEs
especially in taller SPSWswith low aspect ra-tios contribute
signicantly to the frame base shear resistance.
Typical variation of the percentage frame base shear resisted
byeither the tensile or compressive VBE during the loading history
oflow-rise and high-rise SPSWs is drawn in Fig. 11. As noted, in
bothlow-rise and high-rise SPSWs, each of the tensile and
compressiveVBEs absorbs approximately half the frame base shear at
the earlystage of loading. In the case of a low-rise SPSW, the
contribution curvefor the tensile VBE rises with increasing lateral
displacement until theformation of full yield lines across the inll
wall. Afterwards, the contri-bution curve for the tensile VBE
declines until the frame reaches itsyielded strength and then
becomes almost constant up to the ultimatestate. In the case of a
high-rise SPSW, however, due to the increasedbending effects that
tend to delay the full-tension yielding of the inllwall, the
percentage shear contribution from the tensile VBE always
in-creases with an almost constant slope with increasing
lateraldisplacement.
3.5. SPSW ductility and stiffness
The measured ductility () of different SPSWs is presented
inTable 6. The ductility was calculated as the ratio of the maximum
dis-placement to the yield displacement (i.e. = max/y). The
maximumdisplacement (max) was dened as the top story displacement
at adrift ratio of 2.5% at least at one of the stories of the
system. The yielddisplacement (y) was measured through the concept
of equal plasticenergy, so that the area enclosed by the idealized
elasto-plastic curvewas equal to that of the actual pushover curve,
as depicted in Fig. 12.For comparison purposes, the ductility
ratios of the inll wall and theboundary frame calculated from the
respective shear forceroof dis-placement curves using the procedure
stated above are also presentedin Table 6. It is observed from the
results that generally, the ductilityvalues of inll walls, frames
and consequently SPSWs decrease as theheight of the systems
increases. In shorter SPSWs, inll walls are signif-icantlymore
ductile than frames. As the height of the systems increases,exural
deformations dominate over the shear deformations; with thiseffect
the effectiveness of inll walls decreases with the height of
thesystems and frames behave in a more ductile manner than inll
walls.The results also show that although the ductility of shorter
SPSWs isnot sensitive to the system aspect ratio, the ductility of
taller ones issomewhat dependent on the system aspect ratio; that
is, the greaterthe aspect ratio, the higher the ductility.
Initial stiffness of different SPSWs, calculated at very early
stages ofnonlinear pushover analyses, is presented in Table 7. For
comparison
purposes, the wall/frame contribution shares on the overall
stiffness
-
sults show that the reductions in the stiffness due to early
buckling ofinll plates can be considerable (up to 32%) especially
for shorter
ve V
81S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284are also presented in
Table 7. The respective contributions of the inllwall and the
moment frame to the overall stiffness were calculated bydividing
the absorbed base shear by each one by the roof displacement.From
the results in Table 7, it can be seen that for a given number
ofstories, the stiffness values of inll walls, frames and
consequentlySPSWs increase signicantly with the increase of the
aspect ratio, al-though all the SPSWs have been designed for the
same plan area andtherefore the same design lateral loads
(neglecting the difference inthe plan area or design forces
resulted fromdifferent SPSWbaywidths).Further, due to the increased
bending effects, the stiffness of SPSWs de-creases noticeably with
the height of the systems. According to the re-sults given in Table
7, for a given system height (i.e. number ofstories), the initial
stiffness of a SPSW with L/h = 2.5 is about 3 timesgreater than
that of a SPSW with L/h = 0.85, and for a given aspectratio, the
initial stiffness of a ten-story SPSW is about 10% of that of
asingle-story SPSW. The results also show that both inll walls and
mo-ment frames are effective in providing stiffness to the SPSWs.
As a gen-eral trend, however, it can be seen that the effectiveness
of inll wallsdecreases with the height of the systems so that in
taller SPSWs, framesbecome more effective than inll walls.
Typical SPSWs due to early buckling of their inll plates at very
early
Fig. 11. Percentage frame base shear intakes by the
tensile/compressistages of loading experience a signicant loss of
stiffness. However, thisis not the case for SPSWs with stiffened
large rectangular openings,where the inll plates are divided into
separate parts with relativelylower slenderness ratios by the
introduction of the openings and localboundary elements around the
openings [29]. In typical SPSWs, buck-ling of the inll plates due
to gravity or fabrication process occurseven before the application
of lateral loads. Therefore, a realistic esti-mate of the system
stiffness (termed effective stiffness here) is found
Table 6Ductility ratios of SPSWs and their inll walls and
boundary frames.
# of stories (n) SPSW aspect ratio
L/h = 0.85 L/h = 1.4
SPSW Wall Frame SPSW Wall F
1 7.4 9.7 6.0 7.5 10.4 52 7.2 8.4 6.4 7.7 10.0 54 4.5 4.7 4.4
5.7 6.5 56 3.2 2.7 3.5 4.4 4.6 48 2.5 2.2 2.7 3.5 3.5 310 2.0 1.4
2.4 2.9 1.9 312 2.6 1.6 315 2.2 1.3 2SPSWs with high aspect ratios,
and generally, the amount of the reduc-tions decreases with the
height of the systems. In fact, as the systemheight increases, the
contribution of the inll wall to the overall stiffnessand
consequently the effect of inll wall buckling on the overall
stiffnessdecreases.
3.6. Lateral load levels associated with the rst yielding of
walls and frames
According to recent research studies [20,29], the general
behavior ofa SPSW system can be divided by three stages (see Fig.
14). The rststage (OA) is considered from the onset of applying
shear load (pointO) to the occurrence of the rst yield point in the
inll plate (point A).by considering the effect of inll plate
buckling. Fig. 13 depicts typicalstiffnessdrift ratio curves of
four typical SPSW systems of differentnumber of stories and aspect
ratios, obtained from pushover analyses.As shown, a similar trend
is observed in the stiffness curves of differentSPSW systems. Table
8 is used to quantitatively demonstrate that effectfor SPSWs having
different number of stories and aspect ratios. The re-
BE versus lateral displacement, (a) low-rise and (b) high-rise
SPSWs.During this stage, the inll plate is geometrically nonlinear
but materi-ally elastic. Note that the inll plate after
installation is already in abuckled shape due to fabrication
tolerances, welding distortion andgravity. During the second stage
(AC), tension zones spread across theinll plate, while frame
members remain essentially elastic. Finally, inthe third stage
(CD), that is considered from the occurrence of therst yield point
in frame members (point C) to the ultimate state(point D), partial
or fully plastic hinges form in frame members.
L/h = 2.0 L/h = 2.5
rame SPSW Wall Frame SPSW Wall Frame
.4 7.6 11.5 4.8 7.9 12.2 5.8
.8 8.1 11.1 5.5 8.3 11.8 6.2
.0 6.8 8.2 5.4 7.3 8.8 6.1
.3 5.1 5.8 4.4 5.8 6.3 5.3
.6 4.7 5.0 4.3 5.4 5.3 5.4
.6 3.6 3.0 4.1 4.1 3.6 4.5
.3 3.3 2.8 3.7
.8 2.7 2.0 3.2
-
The contribution of plate tension elds to the tensile VBE axial
forcesis dependent on both the system aspect ratio and height;
however,
Fig. 12. Denition of a yield point, adapted from [29]. Fig. 13.
Stiffnessdrift ratio curves of typical SPSWs with n = 1, 4 and L/h
= 1.4, 2.
82 S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284The knowledge of the
load magnitude associated with each of theabove stages can be
useful not only in ensuring the efciency of designfor different
earthquake hazard levels but also in reducing post-earthquake
rehabilitation costs. From the seismic design point of view,minor
earthquake loads can be controlled by the system during therst
stage of the behavior. In moderate earthquakes, the inll plates
ex-perience extensive yielding, ensuring a relatively large global
energydissipation capability, while frame members remain
essentially elastic(i.e. the second stage of the behavior).
Consequently, if necessary, dam-aged inll plates due to earthquake
loading can be simply replacedwithoutmajor involvement of the
primary structure. Under severe seis-mic events, widespread
yielding of the inll plates and plastic hinging offramemembers
ensure an extremely large energy dissipation capabilityand also a
stable response (i.e. the third stage of the behavior).
The relative base shears (normalized by the ultimate base
shearstrength) associated with the rst yielding of inll walls and
boundaryframes for different SPSWs are presented in Fig. 15. For
comparison pur-poses, the normalized design base shears for
different SPSWs are alsopresented in the gure. As shown, the
normalized base shears associat-ed with the rst yielding of inll
walls and frames increase slightly withthe height of systems. Based
on the result, the rst yield points in theinll walls and in the
frame members of different SPSWs occur at baseshear levels of about
2545% and 7085% of the ultimate strength, re-spectively. In
addition, the design base shears for the different systemslie
between about 20 and 30% of their ultimate strength. This
indicatesthat the current design approach, which assumes that 100%
of storyshear is resisted by each inll panel, can lead to a SPSW
system withan overstrength factor of between about 3 and 5 (based
on the obtainedresults), although ASCE 7-05 [28] suggests an
overstrength factor of 2.5for SPSWs. From the results in Fig. 15,
it can also be implied that unlikethe assumption in design codes
(i.e. uniform yielding of inll plates onall stories under design
level earthquake forces), no signicant yieldingwould occur in the
inll wall of a code designed SPSW under designlevel earthquake
forces. This is mainly due to the fact that theTable 7Initial
stiffness of different SPSWs and contribution shares of their inll
walls and frames.
# of stories (n) SPSW aspect ratio
L/h = 0.85 L/h = 1.4
SPSW Wall Frame SPSW Wall F
1 273 130 143 461 263 12 188 87 102 267 150 14 75 31 44 117 646
53 20 33 93 428 41 17 24 68 3210 33 11 22 50 1612 45 1315 30
9contribution of the boundary frame in resisting story shear, which
canbe considerable especially at the lower stories as mentioned
before, isnot considered by design codes.
4. Conclusions
A series of code designed SPSWswith different aspect ratios
(L/h=0.85, 1.4, 2 and 2.5) and number of stories (n = 1, 2, 4, 6,
8, 10, 12 and15) were numerically analyzed using the nite element
method andthe obtained results were utilized to investigate
characteristics of thebehavior of code designed SPSWs and to
evaluate the effectiveness oftheir inll walls and boundary frames.
The following can be concludedfrom this study:
- In a low-rise SPSWwhere the behavior is shear-type, the
signicantyielding of the inll wall occurs prior to the signicant
yielding of theframe, while in a high-rise SPSW the increased
bending effects delaythe full-tension yielding of the inll
plates.
- VBEs are found to be effective in resisting story shear only
at a few oflower stories where the exural deformations are
dominant, andinll walls absorb substantial part of story shear at
the remainingstories where the behavior mode is mainly
shear-type.
- At upper stories,where the plate thicknesses are usually
thicker thanrequired by design and drifts are limited, inll plates
do not yieldcompletely. As a result, the total shear force of the
VBEs will act inthe direction of story shear and the shear force of
the inll platewill be therefore greater than story shear to satisfy
the equilibriumcondition in the horizontal direction.
- Regardless of the system aspect ratio and height, about 7080%
ofthe compressive VBE axial forces come from plate tension elds.L/h
= 2.0 L/h = 2.5
rame SPSW Wall Frame SPSW Wall Frame
98 666 415 252 1084 562 52217 389 240 149 554 290 26452 189 116
73 256 135 12251 120 69 51 147 74 7336 99 54 45 135 62 7334 82 34
48 100 48 5232 64 24 40 21 53 19 33
-
Table 8Effective stiffness and loss of stiffness due to early
buckling of inll plates for different SPSWs.
# of stories (n) Effective stiffness (KN/mm)
L/h = 0.85 L/h = 1.4 L/h = 2.0 L/h =
1 187 317 456 7352 140 190 271 3844 63 89 141 1866 51 77 95 1148
40 59 83 10910 33 48 72 8412 45 57 15 30 49
d (b
83S.A.A. Hosseinzadeh, M. Tehranizadeh / Journal of
Constructional Steel Research 99 (2014) 7284Fig. 14. (a) Typical
lateral loaddisplacement anin taller SPSWs (i.e. with n 4),
regardless of the system aspect ratioand height, about 6080% of the
tensile VBE axial forces at the ulti-mate state come from plate
tension elds.
- In a typical SPSW, the inll wall has a contribution in
resisting thetotal tension in the system, but a small or no
contribution in resistingthe total compression. Therefore, the
axial force in the tensile VBE issmaller than that in the
compressive one. Generally, the ratio of thetension force resisted
by the inll wall to the total tension force inthe SPSW and
consequently the difference in the axial forces of thetwo VBEs tend
to become smaller as the system aspect ratio de-creases or the
height increases.
- The shear forces of the tensile VBE base due to moment frame
swayand due to inll panel tension elds act in the same direction,
whilethose of the compressive one act in opposite directions. As a
result,the tensile VBE is more effective in absorbing base shear
than the
Fig. 15. Normalized base shears associatedwith different stages
of the behavior of SPSWs.Loss of stiffness due to inll buckling
(%)
2.5 L/h = 0.85 L/h = 1.4 L/h = 2.0 L/h = 2.5
31 31 32 3226 29 30 3116 23 26 275 17 21 232 13 16 190 4 12 16 0
11 0 6
) stiffnessdrift ratio curves, adapted from [29].compressive
one. Based on the results obtained, the tensile VBEs ab-sorb about
5595% of the total base shear in the frame columns atthe ultimate
state.
- As a result of the current design procedures that neglect the
contri-bution from the boundary frames, the stiffness and ductility
ofSPSWs that are designed for the same plan and consequently
thesame design lateral loads can vary signicantly depending on the
as-pect ratio; that is, the greater the aspect ratio, the higher
the stiffnessand the ductility. In turn, these variations are not
only due to thechange in the stiffness and ductility of frames, but
also due to thechange in the stiffness and ductility of inll
walls.
- Typical SPSWs experience a signicant loss of stiffness at the
earlystage of loading due to buckling of their inll plates (up to
32% re-duction). The percentage reduction in the stiffness
generally in-creases with the system aspect ratio, while it
decreases with theheight.
- The rst yield points in the inll walls and in the boundary
framemembers of different SPSWs occur at base shear levels of
about2545% and 7085% of the ultimate strength, respectively.
- Unlike the assumption in design codes (i.e. uniform yielding
of inllplates on all stories under design lateral loads), no
signicant yield-ingwould occur in the inll wall of a code designed
SPSW under de-sign level earthquake forces. This is mainly due to
the fact that thecontribution of the boundary frame in resisting
story shear, whichcan be considerable especially at lower stories,
is not considered bydesign codes.
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Behavioral characteristics of code designed steel plate shear
wall systems1. Introduction2. Method of the study2.1. Design of
models2.2. Description of finite element models
3. Discussion of results3.1. General behavior3.2. Wallframe
contribution shares of story shear3.3. Wallframe contribution
shares of the VBE axial forces3.4. The tensile and compressive VBE
axial and shear forces3.5. SPSW ductility and stiffness3.6. Lateral
load levels associated with the first yielding of walls and
frames
4. ConclusionsReferences