Practical non-linear modeling of RCC wall

1. Practical Nonlinear Modeling of Reinforced
Concrete Structural Walls
Kristijan Kolozvari, Ph.D., P.E., M.ASCE1
; and John W. Wallace, Ph.D., P.E., M.ASCE2
Abstract: Current engineering practice typically relies on the use of fiber-based modeling approaches with uncoupled axial-bending (P-M)
and shear (V) responses to simulate nonlinear behavior of reinforced concrete (RC) structural walls. However, more sophisticated numerical
models are available that incorporate coupled P-M-V behavior. The effect of using uncoupled and coupled modeling approaches and the
influence of various modeling assumptions, particularly modeling parameters related to wall shear behavior, on computed global and local
building responses are reported. A five-story archetype RC wall-frame building designed according to current U.S. code provisions is used for
the assessment. The results indicate that modeling parameters associated with wall shear behavior have a significant effect on computed
responses for uncoupled models; use of commonly recommended effective shear stiffness of 0.2EcAw to account for effects of concrete
cracking provides a reasonable estimate of roof displacement response. However, wall shear demands and interstory drift at stories where
wall yielding occurs tend to be overestimated and underestimated, respectively, in comparison with results obtained using coupled wall
models. DOI: 10.1061/(ASCE)ST.1943-541X.0001492. © 2016 American Society of Civil Engineers.
Author keywords: Analysis and computation.
Introduction and Background
Reinforced concrete (RC) structural walls are effective for resisting
lateral loads imposed by wind or earthquakes on building struc-
tures because they provide substantial lateral strength and stiff-
ness, in addition to deformation capacity, to meet the demands of
strong earthquake shaking. In general, it is not feasible to de-
sign a structural wall to remain elastic during a severe earthquake
[i.e., R-factors used in ASCE 7-10 (ASCE 2013) are typically 5
or 6]; therefore, inelastic wall deformations are expected, with
the distributions and magnitudes of the inelastic deformations de-
pending on the attributes of the structural system. Because struc-
tural walls are primary, and in some cases, the only lateral-force
resisting elements, it is essential that analytical tools capable of
capturing the hysteretic behavior of structural walls, in addition to
the interaction of walls with other structural members, are available
to researchers and engineers to investigate the design of new build-
ings and evaluation of existing buildings.
Current practice for design and evaluation of buildings where
nonlinear analysis procedures are used involves application of
fiber-based models with flexural response simulated using a series
of uniaxial elements (or macro-fibers) based on stress-strain/force-
deformation relations for concrete and steel, along with the plane
sections assumption, whereas shear behavior is typically accounted
for by using a horizontal spring with a specified force–deformation
(backbone) relation that is usually uncoupled from flexural behav-
ior. Fiber models have been implemented into various research-
oriented (e.g., OpenSees, McKenna et al. 2000) and commercially
available computer programs (e.g., PERFORM-3D) and have been
widely used to model RC walls. Studies that compare model and
experimental results (e.g., Orakcal and Wallace 2006; PEER and
ATC 2010) show that uncoupled fiber models provide reasonably
accurate predictions of flexure responses. However, the inability of
fiber models to account for interaction (coupling) between axial-
flexural and shear behavior is a significant drawback, as studies
have shown that uncoupled models tend to underestimate axial
compressive strains in wall boundaries even in relatively slender
RC walls controlled by flexure (Orakcal and Wallace 2006), and
overestimate the lateral load capacity in moderately slender walls
(Kolozvari 2013). In addition, when using an uncoupled model, a
shear force-deformation relation must be defined. Common ap-
proaches are to use a (1) linear relation with an effective shear
stiffness (e.g., GAeff¼ 0.2EcAw), (2) bilinear relation with an un-
cracked (i.e., GAuncracked¼ 0.4EcAw) and cracked region (e.g.,
GAeff¼ 0.2EcAw), and (3) trilinear relation that includes a bilinear
relation like (2) along with a postyield region. The approach used
will affect the obtained results; however, a systematic assessment of
the effects and implications has not been presented.
A number of analytical models have been proposed to cap-
ture the observed shear-flexure interaction (SFI) in RC walls
(e.g., Kolozvari et al. 2015a; Fischinger et al. 2012; Panagiotou
et al. 2011; Massone et al. 2006; Henry and Lu 2014; Dashti et
al. 2014; Belletti et al. 2013). An effective approach to capture
the SFI was proposed by Petrangeli et al. (1999) and Massone et al.
)
2006 ) and implemented this approach for monotonic analysis;
Kolozvari et al. (2015a) extended it to address reversed cyclic load-
ing. The model proposed by Kolozvari et al. addresses the issues
identified earlier for the uncoupled models, as coupling between
shear and flexural responses is captured at the model element
level. Therefore, the effect of shear behavior on concrete compres-
sive strain is directly incorporated, and shear stiffness evolves ac-
cording to computed responses and assumed material behavior
(versus use of a backbone relation); for example, Kolozvari (2013)
showed that the wall shear stiffness depends on wall shear demand,
wall axial load, the ratio of Mu=Vulw, and the extent of nonlinear
flexural deformations. In addition, the model has been shown to be
1
Assistant Professor, Dept. of Civil and Environmental Engineering,
California State Univ., Fullerton, CA 92831 (corresponding author).
E-mail: kkolozvari@fullerton.edu
2
Professor, Dept. of Civil and Environmental Engineering, Univ. of
California, Los Angeles, CA 90095-1593. E-mail: wallacej@ucla.edu
Note. This manuscript was submitted on April 6, 2015; approved on
December 10, 2015; published online on February 25, 2016. Discussion
period open until July 25, 2016; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Structural En-
gineering, © ASCE, ISSN 0733-9445.
© ASCE G4016001-1 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

2. an effective tool for the analytical modeling of nonlinear behavior
of RC walls, capable of successfully describing global and local
wall responses under cyclic loading (Kolozvari et al. 2015b).
Objectives and Scope
Fiber-based modeling approaches, with uncoupled axial-flexural
(P-M) and shear (V) behavior, are used widely for the seismic
design of new buildings and evaluation and retrofit of existing
buildings. The recent development, validation, and implementation
of a coupled P-M-V model that captures the interaction between
shear and flexural behavior under cyclic loading into the nonlinear
range for RC walls (e.g., Kolozvari et al. 2015a, b) provides an
opportunity to conduct novel systematic studies to assess the effects
of the various modeling approaches and assumptions on computed
global and local responses of RC structural walls. In this study,
comparative analytical studies are conducted using a fiber-based
wall model with uncoupled shear and flexural responses (Taucer
et al. 1991) and a model with coupled flexural and shear behavior
(Kolozvari et al. 2015a), both implemented in the widely used com-
putational platform OpenSees (McKenna et al. 2000). Particular
emphasis is placed on the effect of modeling assumptions related
to wall shear behavior (e.g., effective shear stiffness, linear versus
bilinear relationship) on computed responses by identifying ap-
proaches and/or assumptions that produce unreliable or inconsis-
tent results, in addition to providing recommendations for practical
applications for the nonlinear modeling of RC walls for design
and assessment. To provide context to the comparative studies pre-
sented, the modeling approaches selected are used to analyze the
behavior of an archetype five-story RC wall-frame building de-
signed according to current U.S. practice [i.e., ACI 318-11 (ACI
2011) and ASCE 7 standards] under a single ground motion and
a suite of seven ground motions.
Nonlinear Modeling Studies
The following sections provide information on archetype building
geometry, design approach, and member proportioning and detail-
ing, as well as descriptions of the analytical models.
Archetype Building
Building Geometry
Plan and elevation/section views of the archetype building
are shown in Fig. 1. The building footprint is 42.7 × 18.3 m
(140 × 60 ft), with 6.1 m (20 ft) long spans. An analysis is
conducted for shaking in the transverse direction only, in which
the lateral-force-resisting elements include two identical one-bay
frames located at the building perimeter (axis 1 and 8) and two
identical walls located near the center of the building (axis 4 and
5), as shown in Fig. 1. An iterative design procedure, outlined in the
following section, resulted in cross section dimensions of walls,
beams, and columns of 0.30×6.10 m (12×240 in:), 0.46 × 0.81 m
(18 × 32 in:, width × depth), and 0.71 × 0.71 m (28 × 28 in:),
respectively.
Design Approach
Structural design is performed for a residential building character-
ized with an importance factor of I ¼ 1.0, risk category I, and
design category D, according to ASCE 7-10 (ASCE 2013; S11.5
and S11.6). The frame was designed to resist 25% of the earthquake
lateral load, which classifies the building structural system as a
dual system according to ASCE 7-10 (ASCE 2013). Concrete com-
pressive strength of f0
c ¼ 34.47 MPa (5,000 psi) and reinforcing
steel (longitudinal and transversal) with yield strength of fy ¼
413.69 MPa (60,000 psi) were used. A uniformly distributed dead
load of 7.18 kN=m2 (150 psf) and live load of 1.91 kN=m2 (40 psf)
per ASCE 7-10 (ASCE 2013; Table 4-1, Residential Building) were
used for the design, whereas load combinations were adopted ac-
cording to ASCE 7-10 (ASCE 2013; S2.3). Because only one bay
of seismic-resisting perimeter frame on each side of the structure is
used, which resists less than 35% of the seismic force, the redun-
dancy factor [ASCE 7-10 (ASCE 2013; S12.3.4)] was taken as
ρ ¼ 1.3.
Seismic lateral loads on the building were calculated using the
equivalent lateral force procedure (ELFP) according to ASCE 7-10
(ASCE 2013; S12.8), based on the code prescribed spectrum char-
acterized with mapped short period and 1-s period accelerations
of SS ¼ 1.5 and S1 ¼ 0.6 g, respectively, assuming Site Class B
(Fa ¼ 1.0, FV ¼ 1.5) and design spectral acceleration parameters
of SDS ¼ 1.0 g and SD1 ¼ 0.6 g, which yielded T0 ¼ 0.12 s and
TS ¼ 0.60 s. Based on the fundamental period of the building
computed according to ASCE 7-10 (ASCE 2013; S12.8.2)
(T ¼ 0.60 s), the base shear of V ¼ CSW ¼ 0.19W ¼ 5,338 kN
(1,200 kips) was obtained, in which the total effective seismic
weight of the building was W ¼ 28,024 kN (6,300 kips). Axial
demands resulting from gravity loads on walls and columns are
computed based on prescribed dead and live loads [reduced in line
with ASCE 7-10 (ASCE 2013; S4.7)] according to tributary areas
for the considered load combinations, whereas axial load resulting
from seismic actions (horizontal and vertical) were computed ac-
cording to ASCE 7-10 (ASCE 2013; S12.14.3).
Instead of using linear analysis, a simple (and approximate)
collapse mechanism approach was used to determine the design
(a) (b) (c)
Fig. 1. Archetype building: (a) plan view; (b) frame elevation; (c) wall elevation
© ASCE G4016001-2 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

3. strength requirements for walls, beams, and columns using the
vertical distribution of seismic lateral forces [ASCE 7-10 (ASCE
2013; S12.8.3)]. The assumed collapse mechanism of the structural
system included wall and column yielding at the base, and the beam
yielding at each level [negative beam nominal moment capacity
was assumed to be one-half of the positive beam nominal capacity
in accordance with ACI 318-11 (ACI 2011; S21.5.2.2)], and the
strong-column weak-beam condition at each joint, determined the
flexural demands of MuW ¼37,638 kN·mð27;760 kips·ftÞ, MuB ¼
1,082 kN·mð798 kips·ftÞ, MuW ¼ 649 kN · m ð479 kips · ftÞ for a
wall, beams and columns, respectively.
A detailed assessment of the building lateral load resisting sys-
tem was conducted according to ASCE 7-10 (ASCE 2013) and ACI
318-11 (ACI 2011) provisions. A 6.10 m (20 ft) long and 0.30 m
(12 in.) thick structural wall, with 16 #11 bars [db ¼ 35.81 mm
(1.410 in.)] located at each boundary [Fig. 2(a)], satisfied P-M
strength requirements (ϕMnW ¼ 41,081 kN · m > MuW) and the
“stress-based” approach [ACI 318-11 (ACI 2011; S21.9.6.3)]
was used to determine that special boundary elements satisfying
S21.9.6.4 [ACI 318-11 (ACI 2011)] were required [Fig. 2(a)].
Axial load at the base of the wall of 3,839 kN (863 kips) resulted
in axial load ratio of Pu=ðAgf0
cÞ ¼ 3,839,000 N=ð6,100 mm ×
300 mm × 34.47 MPaÞ ¼ 0.06. Horizontal and vertical web rein-
forcement consisting of two layers of #5 bars [db ¼ 15.875 mm
(0.625 in.)] spaced at 457 mm (18 in.) satisfied the minimum hori-
zontal web reinforcing ratio according to ACI 318-11 (ACI 2011)
(ρl ¼ ρt ¼ 0.00284 > ρt;min ¼ 0.0025, S21.9.2.1) and provided
wall shear strength of ϕVn ¼ 3,011 kN (677 kips) according to
ACI 318-11 [ACI 2015; S21.9.4; Eqs. (21)–(7)], which was suffi-
cient to resist wall shear demand corresponding to 100% of seismic
force (Vu ¼ 5,338=2 ¼ 2,669 kN). Alternative design procedures
(e.g., capacity design approach) could lead to larger wall shear
capacity than the one obtained using the ACI code; however, the
primary objective and conclusions of the study depend on the me-
chanics of the modeling approaches used to assess nonlinear RC
wall behavior (i.e., uncoupled versus coupled models) and are
not sensitive to the adopted design methodology.
A one-bay, five-story frame [Fig. 1(b)] was designed to resist
25% of the lateral seismic demand obtained using ELFP. Based
on axial and flexural demands, a 0.71 × 0.71 m (28 × 28 in:) col-
umn with 12 #11 bars [db ¼ 35.81 mm (1.410 in.)] was adopted
along the height of the building [Fig. 2(b)]; the column P-M
strengths satisfy ACI 318-11 (ACI 2011; S10.3) requirements. The
beam design was characterized by a 0.46 × 0.81 m (18 × 32 in:)
cross section, with seven #9 bars [db ¼ 28.65 mm (1.128 in.)] at
the top and five #8 bars [db ¼ 25.4 mm (1.0 in.)] at the bottom of
the beam [Fig. 2(c)], which was sufficient to resist the beam flexu-
ral demand and satisfy the requirements of ACI 318-11 (ACI 2011;
S10.5 and S21.5.2). The strong column–weak beam provision of
ACI 318-11 (ACI 2011; S21.6.2) was checked at all floor levels.
Beams and columns were assumed to satisfy the shear strength
requirements of ACI 318-11 (ACI 2011; S21.5.4 and S21.6.5), re-
spectively, and the detailing requirements of S21.5.3 and S21.6.4,
respectively. The design of beam-column joints was performed ac-
cording to ACI 318-11 (ACI 2011; S21.7) for an exterior connec-
tion, assuming that beams that frame into beam-column joints yield
before the columns. Finally, building lateral displacements com-
puted according to ASCE 7-10 (ASCE 2013; S12.8.6) yielded
inter-story drifts of 0.0035, 0.0091, 0.0126, 0.0144, and 0.0151,
which were less than the allowable inter-story drift of 0.02hsx=ðρ ¼
1.3Þ ¼ 0.0154hsx [ASCE 7-10 (ASCE 2013; Table 12.12-1)].
Analytical Modeling
Model Description
Analytical models of the archetype building lateral-load-resisting
system are generated in OpenSees (McKenna et al. 2000) according
to adopted geometry, cross sections, and material properties of
the structural elements. For the purposes of this study, a two-
dimensional model is used; therefore, torsion is neglected and
symmetry is used such that the model consists of one frame and one
wall [Fig. 3(a)]. Given that the primary objective of this study is to
compare two conceptually different modeling approaches for RC
walls, these simplifications in the building’s nonlinear model are
(a)
(b) (c)
Fig. 2. Structural element cross sections: (a) wall; (b) column; (c) beam
© ASCE G4016001-3 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

4. appropriate and will not affect the overall conclusions. The gravity
system is not included in the model based on ASCE 7-10 (ASCE
2013) requirements, and the assumption of a rigid diaphragm is
implemented within each story level. Tributary mass is assigned
at the element nodes at each story level along axes of the wall
and columns, whereas gravity load (dead and live) was assigned
according to the corresponding tributary areas as either nodal load
at wall-element nodes of each story or uniformly distributed load
along the beams of the frame.
RC frame elements (i.e., beams and columns) are modeled using
elastic beam-column elements by assuming the location of plastic
hinges at the faces of beam-column joints [Fig. 3(b)], the behavior
of which was simulated using the moment-rotation hysteretic
model (Lignos and Krawinkler 2011), with modeling parameters
adopted according to beam and column flexural capacities and the
ASCE 41 backbone relationships [Fig. 3(b)]. Stiffness modifiers for
elastic portions of beam and column elements were adopted accord-
ing to ASCE 41 [Table 6.5, ASCE 41-13 (ASCE 2014)] to account
for cracking. Given the objectives of the study, the behavior of RC
walls was simulated using two conceptually different modeling
approaches: (1) SFI wall model (Kolozvari et al. 2015a) that in-
corporates interaction between axial-flexural and shear behavior
under cyclic loading condition; and (2) nonlinear beam-column
element [B-C or fiber model (Taucer et al. 1991)] with uncoupled
axial/flexural and shear behavior, both briefly described in fur-
ther text.
Wall Models
The analytical model proposed by Kolozvari et al. (2015a)
[Fig. 4(a)], called the SFI-MVLEM, incorporates biaxial con-
stitutive RC panel behavior (Ulugtekin 2010), described with the
fixed-strut angle approach, into a two-dimensional macroscopic
fiber-based model formulation of the multiple-vertical-line-element
model (MVLEM, Orakcal et al. 2004); axial-shear coupling is
achieved at the panel (macro-fiber) level, which further allows cou-
pling of axial/flexural and shear responses at the SFI-MVLEM
element level. Biaxial behavior of concrete within each RC panel
element is described using a uniaxial stress-strain relationship for
concrete (Chang and Mander 1994), applied along fixed compres-
sion struts and parameters representing compression softening
(Vecchio and Collins 1993), and also incorporates hysteretic biax-
ial damage (Mansour et al. 2002) and tension stiffening effects
(Belarbi and Hsu 1994). The implemented uniaxial constitutive
relationship for reinforcing steel is the nonlinear hysteretic model
of Menegotto and Pinto (1973). In addition, the RC panel model
incorporates shear aggregate interlock effects along concrete cracks
b (%)
0.20
0.23
0.23
0.23
0.23
EIeff/EIg Mn (kN-m) a (%)
Element
Beams
Col. L1
0.20
0.55
0.42
Col. L2
Col. L3 0.34
Col. L4,5 0.30
106top/62bot
106
106
106
106
0.23
0.27
0.27
0.27
0.27
RC Wall RC Frame
Rigid
diaphragms
SFI-MVLEM or
Fiber Element
Beam Hinges
Column
Hinges
Elastic
Beam/Column
Rigid
Beam
Detail A
Column
Hinge
Beam
Hinge
Node
Rigid
Chord Rotation, θ
M/M
n
a b
1.0
EIeff
0.2
Detail A
(a) (b)
Fig. 3. Analytical model of archetype building: (a) wall-frame system; (b) plastic hinges
(a) (b)
Fig. 4. RC wall modeling approaches: (a) SFI-MVLEM; (b) beam-column element
© ASCE G4016001-4 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

5. and reinforcement dowel action (Kolozvari 2013; Kolozvari et al.
2015a).
In the nonlinear beam-column (B-C) element (Taucer et al.
1991), the flexural response is simulated by a series of uniaxial
elements (or macro-fibers) representing the wall cross section and
vertical reinforcement along with the assumption that plane sec-
tions remain plane after loading [Fig. 4(b)]. The stiffness properties
and force-displacement relationships of the fibers are defined ac-
cording to uniaxial stress-strain relations for concrete and steel,
evaluated at integration points along the each uniaxial fiber and
corresponding areas of the materials in the RC wall cross section.
In this study, the uniaxial material model proposed by Chang and
Mander (1994) is used to simulate the behavior of concrete,
whereas the uniaxial stress-strain law developed by Menegotto
and Pinto (1973) is used to describe the behavior of reinforcing
steel. Shear behavior is uncoupled from the axial/flexural behavior,
and is simulated using a horizontal spring with a specified shear
force–deformation (backbone) relation. The modeling parameters
governing the shear behavior, including hysteretic shape (e.g., lin-
ear, bilinear), stiffness and capacity, are typically adopted based on
available experimental data, and can vary significantly based on the
wall characteristics such as wall aspect ratio, amount of shear and
flexural reinforcement, and level of axial load. Therefore, the shear
force-deformation relationships that are commonly used in practice
are typically ad hoc.
As shown in Fig. 3(a), the RC wall is modeled using 10 equal-
length elements along the building height (i.e., two elements per
story height) for both considered wall models. Wall discretization
in the horizontal direction was performed using six macro-fibers to
represent the wall cross section, where two outer macro-fibers were
used to represent the confined wall boundaries and the remaining
four represented the unconfined wall web. In addition, parameters
of the material models for concrete and reinforcement are the same
for both modeling approaches to allow direct comparison of the
results, as described in the following section.
Material Calibration
Reinforcing Steel. The reinforcing steel stress-strain relationship
described by the Menegotto and Pinto (1973) model was calibrated
to represent the typical properties of Grade 60 reinforcing bars
using a yield strength of 413.69 MPa (60,000 psi) and strain hard-
ening ratio of 0.02. The parameters describing the cyclic stiffness
degradation characteristics of the reinforcing bars were calibrated
as R0 ¼ 20, a1 ¼ 18.5, and a2 ¼ 0.15, as proposed by Menegotto
and Pinto (1973).
Concrete. The monotonic envelope of the stress-strain model
for unconfined concrete in compression proposed by Chang and
Mander was calibrated to agree with the monotonic envelope pro-
posed by Saatcioglu and Razvi (1992) by matching the compres-
sive strength f0
c, the strain at compressive strength ε0
c, initial tangent
modulus Ec, and the parameter r defining the shape of the mon-
otonic stress-strain curve (Tsai 1988). The stress-strain envelopes
for confined concrete in compression were obtained by computing
the peak stress of confined concrete (f0
cc) and the strain at peak
stress (ε0
cc) based on the area, configuration, spacing, and yield
stress of the transverse reinforcement, using the confinement model
by Mander et al. (1988), whereas the initial tangent modulus for
confined concrete (Ecc) and corresponding shape parameter (rc)
are obtained based on the peak stress of confined concrete (f0
cc)
using empirical relations proposed by Chang and Mander (1994)
and Orakcal and Wallace (2006). The tensile strength of concrete
was determined from the relationship ft ¼ 0.31
ffiffiffiffiffi
f0
c
p
ðMPaÞ, and a
value of 0.00008 was selected for the strain at the peak monotonic
tensile stress εt, as suggested by Belarbi and Hsu (1994). The shape
of the monotonic tension envelope of the Chang and Mander
(1994) model was calibrated using the parameter r to reasonably
represent the average postcrack stress-strain relation proposed by
Belarbi and Hsu (1994), which represents the tension stiffening
effects on concrete. The parameters used for calibrating the constit-
utive models for concrete are presented in Table 1.
Shear Force–Deformation Relationship. Two different force–
deformation relationships are used in this study to represent the
shear behavior of the beam-column model: (1) linear-elastic and
(2) bilinear backbone curves; conceptual relationships and the
modeling parameters are presented in Fig. 5. A relatively wide
range of effective shear stiffness can be found in current provisions
and recent research. For example, ASCE 41-13 (ASCE 2014) sug-
gests the use of bilinear or trilinear relationships with 1.0 G for
uncracked shear modulus; LATBSDC (2015) proposes the use
of 0.5 G as the effective shear modulus; and PEER/ATC 72 (PEER
and ATC 2010) provides 0.05 G (wall shear stress of 5
ffiffiffiffiffi
f0
c
p
) or
0.1 G (wall shear stress of 10
ffiffiffiffiffi
f0
c
p
) for the secant shear modulus
corresponding to flexural yielding. In addition, based on recent
tests results on moderately slender RC walls (Tran 2012), a shear
modulus of 0.25 G was found to be the most appropriate to re-
present the wall effective shear stiffness, whereas validation against
tests on slender RC walls (Gogus 2010) revealed that the effective
shear stiffness after concrete cracking of 0.025 G captures the tests
results the most appropriately. Based on a previous discussion,
three different values of shear stiffness are used (0.5, 0.2, and
0.1GAw) for two considered backbone relationships (linear and
Table 1. Concrete Material Modeling Parameters
Parameter Boundary (confined) Web (unconfined)
Compression
f0
c (MPa) 53.12 34.47
ε0
c 0.005 0.002
Ec (MPa) 34,494 27,789
xcr−
a
1.030 1.015
Rb
13 15
Tension
ft (MPa) 1.82 1.82
εt 0.00008 0.00008
Ec (MPa) 27,789 27,789
xcrþ
a
∞ ∞
rb
1.2 1.2
a
Parameter defining the normalized strain (relative to ε0
c=εt) where the
compression/tension envelope curve starts to follow a straight line until
zero stress is reached (Chang and Mander 1994).
b
Parameter defining the shape of the compression or tension envelope curve
(Tsai 1988).
Fig. 5. Considered force–deformation relations for shear behavior
© ASCE G4016001-5 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

6. bilinear), shown in Fig. 5; the shear yielding in the bilinear relation-
ship was adopted based on wall nominal shear capacity according
to ACI 318-11 (ACI 2011) (Vn;ACI). Although the actual wall shear
capacity could be larger than the capacity obtained from the ACI
code (Wallace 1996; Orakcal et al. 2009), a commonly used value
of Vn;ACI was adopted in this study to be consistent with the current
design and evaluation practice; using a larger value (e.g., 1.5Vn;ACI)
would not change the overall conclusions reported in this study.
Ground Motion Records
Nonlinear analysis of the archetype building was performed using
seven horizontal ground motions from sites located greater than
or equal to 10 km from fault rupture (soft rock/stiff soil, strike-
slip, and thrust mechanism); vertical earthquake components are
not considered important for evaluation. Ground motions in-
cluded in the set are selected from the PEER National Geospatial-
Intelligence Agency (NGA) database, and have peak ground
accelerations (PGAs), peak ground velocities (PGVs), and magni-
tudes greater than 0.20 g, 15 cm=s, and 6.5, respectively; records
were used on previous ATC 63 (ATC 2009) studies. Individual and
mean response spectra of the seven ground motion records used are
provided in Fig. 6 and compared with the adopted code design
spectrum; as observed from the figure, the mean of seven response
spectra match reasonably well the code design spectrum.
Analysis Results
Detailed comparisons of analytical results obtained for the arche-
type building are provided in the following sections, including
sensitivity studies of the B-C model results to the adopted shear
force–deformation relationship and their comparisons against the
results obtained using the SFI-MVLEM for a single ground motion,
in addition to a comparison of the average responses for seven
ground motions.
Sensitivity of Beam-Column Model to Shear
Force–Deformation Relationship
Sensitivity of analytical predictions obtained using the nonlinear
B-C model to shear force–deformation relationship is presented,
and the results are compared with the predictions obtained using
the SFI-MVLEM. Two force–deformation relationships are con-
sidered to represent the wall shear behavior in the B-C model:
(1) linear-elastic relation with effective shear stiffness (GAeff) equal
to 0.5, 0.2, and 0.1GAw; and (2) elasto-plastic relation with initial
effective stiffness of 0.5GAw and shear capacity equal to the wall
nominal shear capacity according to ACI 318-11 (ACI 2011)
(Vn;ACI). Comparisons of analytical results are conducted at both
global and local response levels. The sensitivity studies presented
are obtained for a single selected ground motion with a response
spectrum that matches reasonably the design spectrum (Fig. 6);
however, the same trends were observed for the remaining six
ground motions.
Building Fundamental Period
Variations of the initial fundamental building period (T1;start) that
were predicted by the B-C wall model for the range of effective
shear stiffness of 1.0, 0.5, 0.2, 0.1, and 0.05GAw are presented
in Table 2. The initial fundamental building period obtained using
the uncracked shear stiffness (i.e., GAeff ¼ 1.0GAw) is equal to
0.54 s, which is in agreement with the initial fundamental period
predicted by the SFI model that corresponds to uncracked RC panel
macro-fibers within the model elements. However, reduction of the
effective shear stiffness from 0.5 to 0.05GAw increases the initial
fundamental period from 0.57 to 0.98 s (by approximately 70%),
revealing considerable sensitivity of the fiber model to the adopted
value of effective shear stiffness, which could significantly affect
the reliability of analytical predictions obtained using fiber models,
given the relatively wide range of effective shear stiffness available
in current modeling recommendations. Table 2 also presents the
average of seven fundamental periods corresponding to end of the
time-history analyses (T1;end), which indicates that the fundamental
period shifts for approximately the same amount, of approximately
0.20 s, for all considered models.
Response Histories of Roof Displacement and Base Shear
Force
The comparison of wall roof displacement and base shear force
histories are presented in Fig. 7 for the wall models considered.
It can be observed from Figs. 7(a and b) that the roof displacement
and base shear force histories predicted using the fiber model with
linear-elastic shear relationship and effective stiffness of 0.5GAw
match reasonably well the responses predicted by the SFI model,
although approximately 30% larger maximum shear force at 5.5 s
was obtained using the fiber modeling approach. Figs. 7(a and b)
further reveal that the roof displacement and base shear force
histories predicted by the fiber model with elasto-plastic shear re-
lationship (Fig. 5) agree well with the responses predicted by the
SFI model up to approximately 5.0 s, when the base shear force in
the wall reached the adopted wall shear capacity Vn;ACI [4,017 kN
(903 kips)]. After the wall shear capacity is reached, the predicted
wall response becomes numerically unstable, suggesting shear fail-
ure within the first story, as the shear stiffness within the model
element reduced abruptly from the initial value to a post-yield value
(Fig. 5); the node located at the mid-height of the first story expe-
rienced unreasonably large displacements as a result of pure-shear
deformations. To avoid the described numerical instabilities, and to
Fig. 6. Ground motion record set response spectra and design spectrum
Table 2. Sensitivity of Beam-Column Model Fundamental Periods to
Shear Stiffness
Model GAeff=GAw T1;start (s) T1;end (s)
Beam-column 0.05 0.98 —
0.10 0.78 1.02
0.20 0.66 0.84
0.50 0.57 0.80
1.00 0.54 —
SFI —a
0.53 0.75
a
Shear stiffness degrades throughout the analysis.
© ASCE G4016001-6 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

7. allow further investigation of the fiber model with elasto-plastic
shear relationship, an alternative analytical model of the building
with one wall model element per level was created. It can be
observed from Figs. 7(c and d) that this modification resulted in
stable roof displacement and base shear force responses that match
closely the responses obtained using the SFI model and fiber
model with a linear-elastic shear relationship of GAeff ¼ 0.5GAw
[Figs. 7(a and b)]. Furthermore, Figs. 7(b and d) reveal that the
trend of roof displacement time history obtained using the reduced
values of effective shear stiffness of 0.2 and 0.1GAw diverge from
the two previously considered cases; the reduction of effective
shear stiffness from 0.5 to 0.1GAw increases the maximum roof
displacement by approximately 40%, from 100 mm (3.9 in.) to
140 mm (5.5 in.). Finally, the comparisons of wall base shear force
histories show similar trends for the three cases of fiber models with
linear-elastic shear stiffness, although considerable sensitivity of
peak shear force can be observed relative to the adopted effective
shear stiffness; maximum base shear occurs at 5.5 s for all fiber
models and varies from approximately 6,200 kN (1,400 kips) for
the model with shear stiffness of 0.5w or 0.2GAw to 4,000 kN
(900 kips) for the model with 0.1GAw.
Vertical Profiles of Wall Deformation Characteristics
Vertical profiles of wall maximum drifts, lateral displacements,
and contributions of shear deformations to lateral displacements
are presented in Fig. 8. It can be observed from the figure that
profiles of interstory drifts [Fig. 8(a)] and lateral deformations
[Fig. 8(b)] predicted by the SFI wall model and fiber model with
effective shear stiffness of 0.5GAw (linear-elastic and elasto-plastic
shear relationship) are in good agreement over the building height,
except within the first level where the SFI model predicts approx-
imately 50% larger lateral displacements and interstory drifts.
Figs. 8(a and b) also show that a reduction in the effective shear
stiffness in the fiber (B-C) model from 0.5 to 0.1GAw resulted
in improved predictions of interstory drifts and lateral deformations
within the first level relative to the SFI model results. However,
deformations at levels 2–5 are now overestimated by approximately
50%. Furthermore, Fig. 8(c) illustrates that contributions of shear
Fig. 7. Time histories of wall responses: (a) top displacement and (b) base shear force for SFI model and beam-column model with linear elastic
(GAeff¼ 0.5GAw) and elasto-plastic (GAeff¼ 0.5GAw) shear behavior; and (c) top displacement and (d) base shear force for beam-column model
with linear elastic (GAeff ¼ 0.1 and 0.2GAw) and elasto-plastic (GAeff¼ 0.5GAw, one element per level) shear behavior
Fig. 8. Vertical profiles of maximum wall responses for selected ground motion: (a) interstory drifts; (b) lateral displacements; (c) contributions of
shear deformation
© ASCE G4016001-7 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

8. deformations to total lateral displacement over the wall height are
significant within the first level for all considered models. The SFI
model predicts the largest contribution of shear deformations of
73% within the bottom wall element, whereas the corresponding
contributions of shear deformations obtained from fiber model
with linear-elastic shear relationships are 23, 41, and 58% for ef-
fective shear stiffness values of 0.5, 0.2, and 0.1GAw, respectively.
Finally, the fiber model with elasto-plastic shear backbone curve
and initial effective shear stiffness of 0.5GAw predicts approxi-
mately two times larger contributions of shear deformations over
the first story, compared with the corresponding linear elastic
case (i.e., 43 versus 23%), but 40% smaller shear contributions
compared with the SFI model.
Wall Responses within the First Story
To investigate the predicted wall behavior in the region where
nonlinear deformations are expected, the force–deformation and
the moment–curvature responses over the first story height are pre-
sented in Fig. 9. It can be observed from the shear force versus first
story lateral displacement responses [Fig. 9(a)] that the B-C wall
models with linear-elastic shear behavior and effective shear stiff-
ness of 0.5 and 0.2GAw predict wall demands that exceed Vn;ACI by
approximately 50%, whereas the first story maximum shear force
of the B-C model with effective shear stiffness of 0.1GAw and the
SFI-MVLEM are in good agreement and approximately 10% larger
than Vn;ACI. It can be also observed from Fig. 9(a) that using
elasto-plastic shear backbone relation in the B-C model resulted
in hysteretic loops that are characterized with an abrupt change of
stiffness after the adopted shear capacity (Vn;ACI) is reached,
whereas the overall stiffness and lateral deformations are in reason-
ably good agreement with the SFI-MVLEM results. As expected,
the B-C model with an effective shear stiffness of 0.1GAw pro-
duced the largest first-story lateral displacements from the three
cases of linear-elastic shear stiffness [22 mm (0.87 in.)], which
are slightly smaller than the lateral deformations predicted by the
B-C model with elasto-plastic shear backbone relation [25 mm
(0.99 in.)] and the SFI model [28 mm (1.10 in.)].
Shear force versus shear deformation response [Fig. 9(b)]
further reveals that the total shear deformation predicted by the SFI-
MVLEM over the first story is 14 mm (0.55 in.) and 12 mm
(0.48 in.) in the positive and negative directions, respectively. Shear
deformation at shear yielding is approximately 2.0 mm (0.08 in.,
shear strain of 0.0006), which agrees well with the shear deforma-
tion corresponding to Vn;ACI predicted by the B-C wall model with
the effective shear stiffness of 0.5GAw. The occurrence of nonlinear
shear deformations in the SFI-MVLEM results does not necessarily
suggest shear failure, as the mechanics of the analytical model cap-
ture coupled nonlinear shear and flexural behavior. Furthermore,
the B-C models with effective shear stiffnesses of 0.2 and 0.1GAw
predict approximately 30 and 60% of the maximal shear deforma-
tions obtained using the SFI model, respectively, suggesting that
an even lower value of effective shear stiffness (e.g., 0.05GAw)
would be more appropriate to account for the nonlinear shear de-
formations obtained using the SFI model. Finally, the B-C model
with elasto-plastic shear backbone relation (with one element per
level) predicts the maximal nonlinear shear deformations that are
approximately 30% smaller than the shear deformations obtained
using the SFI-MVLEM, but captures cyclic shear stiffness degra-
dation, although the shape of the hysteretic loops could be im-
proved by calibration of material parameters used to represent the
cyclic shear behavior.
Moment versus curvature relations plotted in Fig. 9(c) reveal
that the moment yield capacity predicted by all considered
modeling approaches is the same and equal to approximately
50; 000 kN · m ð36; 900 kips · ftÞ, which is slightly larger than
the nominal moment capacity obtained using the section analysis
of 45; 284 kN · m ð33; 400 kips · ftÞ, whereas curvatures over the
first story are significantly different. Fiber models with linear-elastic
shear behavior predict the largest maximum curvature, whereas com-
puted curvature is approximately two times smaller when the fiber
model with elasto-plastic shear behavior is used as a result of pure-
shear deformations over the first level after the shear capacity is
reached [Fig. 9(b)]. The maximum curvature predicted by the SFI
model is in between the two extreme cases of fiber models (linear-
elastic and elasto-plastic shear behavior) as a result of coupled non-
linear shear and flexural deformations at the model element level.
Vertical Profiles of Shear Force and Bending Moment
Fig. 10 plots the distribution of maximum shear force and bending
moment over the height of the wall for selected ground motion
record obtained using the SFI and B-C wall models. It can be ob-
served from Fig. 10(a) that the B-C model with a linear elastic shear
stiffness of 0.5GAw predicts generally higher shear force demands
over the entire height of the wall compared with the SFI model, in
which a significant difference can be observed within the first level
where the predicted shear force is approximately 30% larger. It can
be also observed from Fig. 10(a) that the fiber model with a reduced
effective shear stiffness of 0.1GAw provides predictions of the shear
Fig. 9. First-level wall responses for selected ground motion: (a) shear force versus total lateral displacement; (b) shear force versus shear displace-
ment; (c) moment versus curvature
© ASCE G4016001-8 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

9. force over the wall height, including the first level, which is in very
good agreement with the shear force predicted by the SFI model.
Furthermore, Fig. 10(a) reveals that the shear force over the first
and the second levels predicted by the B-C model with elasto-
plastic shear relationship reached the prescribed wall shear capacity
of 4,017 kN (903 kips, Vn;ACI), whereas the B-C models with a
linear-elastic shear relationship and effective shear stiffness of 0.5
and 0.2GAw predicted shear force that exceeds 1.5Vn;ACI, a value
that is commonly considered to represent the mean shear strength
of shear-controlled walls (Wallace 1996; Orakcal et al. 2009).
The distributions of bending moment over the height of the wall
presented in Fig. 10(b) illustrate that predicted moment demand is
significantly less sensitive to the choice of modeling approach than
the shear force demand. Absolute maximum moment at the base
of the wall of approximately 54; 000 kN · m ð39; 850 kips · ftÞ is
predicted by all considered modeling approaches, which is approx-
imately 15% larger than the nominal flexural capacity of the wall
obtained from section analysis, suggesting that flexural yielding
occurred for all models as shown in Fig. 9(c).
Wall Vertical Strains and Rotations
Fig. 11 illustrates the profiles of maximal tensile and compressive
vertical axial strains and maximum rotations computed over the
wall height. Fig. 11(a) shows that the tensile strains over the first
model element (i.e., bottom 1.82 m or 6.0 ft of the wall) are sig-
nificantly larger than strains in the second model element for all
considered models, indicating that the plastic hinge length of the
wall predicted by the adopted models is approximately lw=3. Using
more elements over the first story might slightly change the distri-
bution of strains over the height; however, the plastic hinge length
would still be within lw=2, which is typically considered as a plas-
tic hinge length for a wall with well-confined boundaries. The SFI
model predicts a maximum tensile strain of 1.0%, whereas the B-C
models with a linear-elastic shear relationship predict maximum
tensile strains of approximately 1.25% (25% larger) on average of
the three considered values of effective shear stiffness. Fig. 11(a)
also reveals that the maximum vertical tensile strain predicted by
the B-C model with elasto-plastic shear behavior and one element
over the story height is only 0.60%, which corresponds to the
Fig. 10. Vertical profiles of maximum wall responses for selected ground motion: (a) shear force; (b) overturning moment
Fig. 11. Vertical profiles of maximum wall responses for selected ground motion: (a) boundary compressive/tensile vertical strains; (b) rotations
© ASCE G4016001-9 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

10. average strain over the first level obtained from the corresponding
model with linear-elastic shear relationship, indicating that sparse
discretization might not capture appropriately the plastic hinge
length of the wall and could significantly underestimate the com-
puted strain demands. Maximum compressive strains are approx-
imately 0.15% for all models, and no significant variations are
observed in the presented results, likely because of the relatively
slender wall used; the effect of the modeling approach on concrete
compressive strain is expected to be more significant for lower
aspect ratio walls (Orakcal and Wallace 2006).
Similar trends can be observed for distributions of rotations over
the wall height [Fig. 11(b)]. Maximum and minimum rotations of
0.3 and −0.4% are predicted by the SFI model, whereas the B-C
models with linear-elastic shear behavior predict approximately
25% larger wall rotations in both positive and negative directions.
Although the B-C model with elasto-plastic shear relationship
predicts maximum wall rotations that match reasonably well the
rotations obtained using linear-elastic B-C models, the distribution
of rotations (i.e., plastic hinge length) is not accurately captured
because of sparse model discretization of one element per building
level.
Overall, the sensitivity studies presented in this section reveal
that global responses (e.g., roof displacement, interstory drifts,
shear force) predicted using the B-C wall model are considerably
sensitive to the adopted relationship used to represent wall shear
behavior, whereas the sensitivity of local responses (e.g., strains
and rotations) is not that significant. Reduction of effective shear
stiffness from 0.5 to 0.1GAw increased the computed interstory
drifts for approximately 50%, whereas the computed base shear
force varied by approximately 30%, depending on the adopted ef-
fective shear stiffness. In addition, the use of elasto-plastic shear
relation resulted in either unstable response at mid-level nodes
(using two wall elements per story) or underestimated shear force
and vertical strains (using one wall element per story). Finally, the
predicted wall responses within the plastic hinge region (i.e., first
building level) using the B-C model with an effective shear stiffness
of 0.1GAw are in good agreement with the predictions of SFI-
MVLEM in terms of lateral deformation profiles, interstory drifts,
base shear force, and bending moment, whereas the best match
among these responses at the remaining building levels are ob-
tained using the effective shear stiffness of 0.5GAw.
Comparison of Results for a Suite of Seven Ground
Motions
Comparisons of predicted wall behavior are further conducted for
the average responses obtained from the suite of seven ground
motions using the SFI model, B-C model with linear-elastic
(GAeff ¼ 0.5GAw) shear behavior, and B-C model with elasto-
plastic shear behavior (GAeff;initial ¼ 0.5GAw, Vy ¼ Vn;ACI) and
discretization of only one element per level.
Vertical profiles of maximum interstory drifts, lateral deforma-
tion profiles, and contributions of shear deformations are presented
in Fig. 12. Fig. 12(a) reveals that magnitudes of interstory drifts
predicted using the SFI-MVLEM and the B-C model are consid-
erably different within the first story, where the flexural yielding is
reported. Maximum average interstory drifts within the first level as
predicted by the SFI model are approximately 0.56%, whereas the
B-C model with linear-elastic shear behavior predicts the maximum
average interstory drifts of 0.34%, which is approximately 40% less
than the drifts obtained using the SFI model. In addition, interstory
drifts at the top story level predicted by the B-C model are approx-
imately 10% larger than the drifts obtained using the SFI model.
The maximum average interstory drifts within the first level ob-
tained using the B-C model with elasto-plastic shear behavior are
approximately 0.45%, which is larger than the drifts computed
using the linear-elastic B-C model, but still approximately 20%
smaller than the drifts predicted by the SFI model. The SFI wall
model generally predicts larger drifts (and smaller shear force de-
mands) within the plastic hinge region (i.e., at the location of wall
yielding) as a result of the interaction between nonlinear flexural
and shear deformations and cyclic degradation of shear stiffness, as
captured at the model element level (Fig. 9), as opposed to the fiber
modeling approach in which this interaction/degradation is not
captured. Fig. 12(b) plots the lateral deformation profiles for the
three modeling approaches, illustrating that larger lateral deforma-
tions over the first story are predicted using the SFI wall model,
which is consistent with the maximum lateral drift profiles
presented in Fig. 12(a), although the three profiles are generally
similar in shape and the amount of maximum lateral displacement
predicted at the roof level. Fig. 12(c) further reveals that the
nonlinear shear deformations predicted by the SFI-MVLEM
are significant within the first level, where nonlinear flexural
Fig. 12. Average vertical profiles of maximum wall responses: (a) interstory drifts; (b) lateral displacements; (c) contributions of shear deformation
© ASCE G4016001-10 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

11. deformations are reported, by contributing approximately 70% to
the total lateral deformation of the bottom wall element and approx-
imately 45% (on the average of two wall elements) over the first
level. This is in close agreement with the contributions of shear
deformations predicted by the B-C model with an elasto-plastic
shear backbone relation over the first story height, although this
model is not capable of producing refined responses because of
its sparse discretization. The B-C model with a linear-elastic shear
force-deformation relation predicts the contribution of shear defor-
mations of only 41% over the bottom wall element and approxi-
mately 20% over the first story level (average of two elements),
given the inability of the modeling approach to capture the nonlin-
ear shear deformations and shear stiffness degradation.
Distributions of average maximum shear force [Fig. 13(a)] and
bending moment [Fig. 13(b)] over the height of the wall obtained
using the three considered cases are further explained. It can be
observed from Fig. 13(a) that shear force distributions that are com-
puted using the three considered models are in good agreement
within the top three levels of the building, whereas significant
differences in predicted shear force demand exist within the first
level. The average shear force demand within the bottom level pre-
dicted using the B-C model with linear-elastic shear behavior
[5,811 kN (1,306 kips)] is 31% larger than the shear force obtained
using the SFI model [4,423 kN (994 kips)] and approximately 45%
larger than the maximum shear force developed in the B-C model
with a prescribed shear capacity of Vn;ACI [4,017 kN (903 kips)].
All three considered models predicted almost identical average mo-
ment distributions over the wall height [Fig. 13(b)], with the wall
maximum moment at the base of 49;258 kN·mð36;330 kips·ftÞ,
which is approximately 10% larger than the wall nominal flexural
capacity of 45; 284 kN · m ð33; 400 kips · ftÞ as a result of strain
hardening.
Comparisons of the average maximum vertical strains and the
wall rotations over the building height are presented in Fig. 14. The
distribution of vertical strains [Fig. 14(a)] predicted by the SFI
and fiber modeling approach are similar in terms of distribution
Fig. 13. Average vertical profiles of maximum wall responses: (a) shear force; (b) overturning moment
Fig. 14. Average vertical profiles of maximum wall responses: (a) boundary compressive/tensile vertical strains; (b) rotations
© ASCE G4016001-11 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

12. of strains over the height, whereas the fiber model predicts approx-
imately 10% larger tensile and compressive vertical strains. The
corresponding wall rotations [Fig. 14(b)] obtained from the vertical
strains at the wall boundaries follow similar trends as the vertical
strains, with rotations predicted by the fiber model that are approx-
imately 10% larger than the rotations predicted by the SFI model at
the base of the wall. Based on results presented in Fig. 14, the an-
alyzed wall experienced moderate (average) strain/rotation ductility
demands of approximately 5.5 under the suite of seven selected
ground motions. Although using stronger ground motions could
lead to generally larger ductility demands in the wall, the overall
conclusions of this study would not change as they are primarily
based on the mechanics of the modeling approaches used, and not
by the severity of the ground motions.
Analytically predicted wall responses over the first level ob-
tained using the B-C model with a linear-elastic shear stiffness
of 0.5GAw and SFI-MVLEM are summarized in Table 3. The most
significant discrepancies among the results computed by the un-
coupled and coupled wall models can be observed for interstory
drifts and shear force. The average maximum interstory drift pre-
dicted by the B-C model is approximately 60% of the interstory
drift predicted by the SFI model, suggesting that the use of un-
coupled approaches might significantly underestimate the level of
damage in structural elements of a lateral-load-resisting (or gravity)
system within the plastic hinge region in comparison with the SFI
model. In contrast, the uncoupled wall model imposes approxi-
mately 30% higher shear force demand on the wall than the SFI
model, which could result in differences in distribution of total
shear force within the elements of the lateral-load-resisting system.
Furthermore, tensile or compressive strains and rotations obtained
using the B-C model are generally 10% larger than the responses
predicted by SFI-MVLEM, whereas predictions of the moment at
the wall base using the two modeling approaches are very similar.
Table 3 further reveals that the largest variation in predicted wall
responses are obtained for interstory drifts, tensile strains and ro-
tation, where the coefficient of variation (COV) is approximately
50%, moderate variation is observed for the shear force (COV ¼
12%), whereas the least variation of responses for both models
can be observed for the compressive strains and bending moment
(COV < 10%).
Summary and Conclusions
This paper presents the results of a detailed assessment of analyti-
cally predicted RC wall behavior of an archetype building obtained
using two conceptually different RC wall modeling approaches
available in OpenSees: (1) SFI-MVLEM, which captures the
interaction among axial/flexural and shear responses and nonlin-
ear shear deformations (coupled model); and (2) a nonlinear
beam-column model (fiber model) with uncoupled axial/flexural
and shear behavior. Shear behavior in the fiber-based modeling
approach was represented with either a linear-elastic relationship
with effective shear stiffness of 0.5, 0.2, and 0.1GAw or elasto-
plastic (bilinear) shear backbone relationship with effective shear
stiffness of 0.5GAw and shear capacity calculated according to
ACI 318-11 (ACI 2011) (Vn;ACI). A five-story archetype RC build-
ing with a lateral-force-resisting system consisted of RC walls and
special moment frames that resisted 25% of the seismic load
(i.e., dual system) was designed to satisfy the current U.S. code
provisions [i.e., ACI 318-11 (ACI 2011) and ASCE 7-10 (ASCE
2013)]; the wall shear strength corresponding to the minimum
reinforcing ratio according to ACI 318-11 (ACI 2011) was suffi-
cient to resist the shear force demand corresponding to 100% of
seismic code-level force. Nonlinear response-history analyses were
performed using a set of seven far-field ground motion records
from soft rock/stiff soil sites with peak ground accelerations larger
than 0.25 g. The main conclusions of the paper are direct conse-
quences of conceptually different formulations of coupled and un-
coupled modeling approaches, and are not affected by the design
approach used (e.g., displacement-based, capacity-based) and/or
severity of ground motions.
The sensitivity of analytical responses to variations of effective
shear stiffness used for the nonlinear beam-column model revealed
that both global and local responses are considerably sensitive to
the adopted relationship used to represent wall shear behavior.
It has been observed that, with a reduction of effective shear stiff-
ness from 0.5 to 0.1GAw, the initial building period increased
approximately 37% (from 0.57 to 0.78 s), the predicted lateral dis-
placements increased approximately 40%, and the interstory drifts
increased approximately 50%. In addition, the nonlinear beam-
column model with elasto-plastic shear force-deformation rela-
tionship was shown to be numerically unstable during OpenSees
analyses at nodes that are not connected to beams of the special
moment frame. The instability resulted after the prescribed wall
shear capacity defined by the backbone relation was reached, re-
sulting from the pure-shear deformation of the wall elements,
which led to unreasonable analytical predictions of building re-
sponses. Therefore, only one element over the story height for the
bilinear shear relation was considered. The results further revealed
that the predicted wall responses using the beam-column model
with effective shear stiffness of 0.5GAw (linear and bilinear shear
behavior with one element per story) are in good agreement with
the predictions obtained with SFI-MVLEM in terms of vertical pro-
files of maximum interstory drift, lateral deformation, and shear
force, except within the plastic hinge region (i.e., first level), where
the best match among first level responses are obtained using the
effective shear stiffness of 0.1GAw.
A comparison of maximum average responses obtained for a
set of seven ground motions revealed that the beam-column wall
Table 3. Comparisons of Absolute Maximum Wall Responses
Response
SFI-MVLEM Beam-column model
μBC=μSFI
Mean (μ)
Standard deviation
(σ)
COV ¼ μ=σ
(%) Mean (μ)
Standard deviation
(σ)
COV ¼ μ=σ
(%)
Max drift (%) 0.56 0.30 53 0.34 0.30 49 0.61
Shear force (kN) 4,423 541 12 5,811 944 16 1.31
Moment (kN · m) 48,408 3,579 7 50,109 4,238 9 1.04
Min strain (%) −0.07 0.01 9 −0.08 0.01 8 1.11
Max strain (%) 1.00 0.48 48 1.10 0.60 55 1.10
Rotation (%) 0.29 0.16 55 0.33 0.19 59 1.11
© ASCE G4016001-12 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

13. model with an effective shear stiffness of 0.5GAw (typically used in
practice) generally predicts the maximum shear force within the
plastic hinge region of the wall (i.e., within the first story), which
is approximately 30% larger than the maximum shear force pre-
dicted by the SFI modeling approach. In contrast, the interstory
drift and contributions of the shear deformation within the first level
predicted by the uncoupled model are approximately 40% lower in
comparison with the coupled modeling approach. The analyzed
wall experienced a moderate (average) strain ductility demand of
5.5 according to all considered modeling approaches, whereas the
beam-column model predicted tensile vertical strains and rota-
tions that were generally 10% larger than the responses predicted
using the SFI-MVLEM. The results for both the single ground
motion and the suite of seven ground motions suggest strongly
that the use of a single model to determine the responses to evalu-
ate local and global force and deformation demands is biased,
based on the assumed wall shear stiffness in the uncoupled modeling
approaches.
Future studies could focus on extensive investigation of wall
responses for a large set of ground motion records to verify the
trends observed in this study, and conduct further reliability studies
using the considered modeling approaches. Future work could also
focus on the investigation of wall responses for a range of building
heights (e.g., 3, 8, 12, 15 stories) and different relative strengths of
walls and frames (e.g., frames that resists 10 and 50% of seismic
load), to investigate the sensitivity of the analytical predictions over
a wider range of building configurations for uncoupled and coupled
wall modeling approaches. Comparison studies could also be per-
formed for coupled wall systems with various coupling beam
strengths and configurations, and for tall buildings (e.g., 40 stories)
in which the discrepancies among the model predictions could be
more significant as a result of a larger contribution of higher modes
to building seismic behavior.
References
ACI (American Concrete Institute). (2011). “Building code requirements
for structural concrete.” ACI 318-11. Farmington Hills, MI.
ASCE. (2013). “Minimum design loads for buildings and other structures.”
ASCE 7-10, Reston, VA.
ASCE. (2014). “Seismic evaluation and retrofit of existing buildings.”
ASCE 41-13, Reston, VA.
ATC (Applied Technology Council). (2009). “Quantification of build-
ing seismic performance factors.” Rep. No. ATC-63, Redwood
City, CA.
Belarbi, A., and Hsu, T. C. (1994). “Constitutive laws of concrete in tension
and reinforcing bars stiffened by concrete.” ACI Struct. J., 91(4),
465–474.
Belletti, B., Damoni, C., and Gasperi, A. (2013). “Modeling approaches
suitable for pushover analyses of RC structural wall buildings.”
Eng. Struct., 57, 327–338.
Chang, G. A., and Mander, J. B. (1994). “Seismic energy based fatigue
damage analysis of bridge columns. Part I: Evaluation of seismic
capacity.” NCEER Technical Rep. No. NCEER-94-0006, State Univ.
of New York, Buffalo, NY.
Dashti, F., Dhakal, R. P., and Pampanini, S. (2014). “Simulation of out-
of-plane instability in rectangular RC structural walls.” 2nd Euro-
pean Conf. on Earthquake Engineering and Seismology, Istanbul,
Turkey.
Fischinger, M., Rejec, K., and Isaković, T. (2012). “Modeling inelastic
shear response of RC walls.” Proc., 15th World Conf. on Earthquake
Engineering, Lisbon, Portugal.
Gogus, A. (2010). “Structural wall systems—Nonlinear modeling and
collapse assessment of shear walls and slab-column frames.” Ph.D.
dissertation, Univ. of California, Los Angeles.
Henry, R. S., and Lu, Y. (2014). “Research to address the performance of
lightly reinforced concrete walls during the 2010/2011 Canterbury
earthquakes.” 2nd European Conf. on Earthquake Engineering and
Seismology, Istanbul, Turkey.
Kolozvari, K. (2013). “Analytical modeling of cyclic shear-flexure interac-
tion in reinforced concrete structural walls.” Ph.D. dissertation, Univ. of
California, Los Angeles.
Kolozvari, K., Orakcal, K., and Wallace, J. W. (2015a). “Modeling of cyclic
shear-flexure interaction in reinforced concrete structural walls. Part I:
Theory.” J. Struct. Eng., 10.1061/(ASCE)ST.1943-541X.0001059,
04014135.
Kolozvari, K., Tran, T., Orakcal, K., and Wallace, J. W. (2015b). “Modeling
of cyclic shear-flexure interaction in reinforced concrete structural
walls. Part II: Experimental validation.” J. Struct. Eng., 10.1061/
(ASCE)ST.1943-541X.0001083, 04014136.
LATBSDC (Los Angeles Tall buildings Structural Design Council).
(2015). “An alternative procedure for seismic analysis and design
of tall buildings located in the Los Angeles region.” Los Angeles.
Lignos, D. G., and Krawinkler, H. (2011). “Deterioration modeling of steel
components in support of collapse prediction of steel moment frames
under earthquake loading.” J. Struct. Eng., 10.1061/(ASCE)ST.1943
-541X.0000376, 1291–1302.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress-
strain model for confined concrete.” J. Struct. Eng., 10.1061/(ASCE)
0733-9445(1988)114:8(1804), 1804–1826.
Mansour, M. Y., Hsu, T. C., and Lee, J. Y. (2002). “Pinching effect in
hysteretic loops of R/C shear elements.” ACI, 205, 293–321.
Massone, L. M., Orakcal, K., and Wallace, J. W. (2006). “Shear–flexure
interaction for structural walls.” ACI SP-236-07, ACI (American
Concrete Institute), Farmington Hills, MI.
McKenna, F., Fenves, G. L., Scott, M. H., and Jeremic, B. (2000). “Open
system for earthquake engineering simulation (OpenSees).” Pacific
Earthquake Engineering Research Center, Univ. of California, Berkeley,
CA.
Menegotto, M., and Pinto, E. (1973). “Method of analysis for cyclically
loaded reinforced concrete plane frames including changes in geometry
and non-elastic behavior of elements under combined normal force and
bending.” Proc., IABSE Symp. on Resistance and Ultimate Deformabil-
ity of Structures Acted on by Well-Defined Repeated Loads, Lisbon,
Portugal.
Orakcal, K., Conte, J. P., and Wallace, J. W. (2004). “Flexural modeling of
reinforced concrete structural walls—Model attributes.” ACI Struct. J.,
101(5), 688–698.
Orakcal, K., Massone, L. M., and Wallace, J. W. (2009). “Shear strength
of lightly reinforced wall piers and spandrels.” ACI Struct. J., 106(5),
455–465.
Orakcal, K., and Wallace, J. W. (2006). “Flexural modeling of reinforced
concrete walls—Experimental verification.” ACI Struct. J., 103(2),
196–206.
Panagiotou, M., Restrepo, J., Schoettler, M., and Geonwoo, K. (2011).
“Nonlinear cyclic model for reinforced concrete walls.” ACI Struct.
Mater. J., 109(2), 205–214.
PEER (Pacific Earthquake Engineering Research Center) and ATC
(Applied Technology Council). (2010). “Modeling and acceptance
criteria for seismic design and analysis of tall buildings.” PEER/ATC
72-1), Richmond, CA.
PERFORM 3D [Computer software]. Computers and Structures, Walnut
Creek, CA.
Petrangeli, M., Pinto, P. E., and Ciampi, V. (1999). “Fiber element for
cyclic bending and shear of RC structures. I: Theory.” J. Eng. Mech.,
10.1061/(ASCE)0733-9399(1999)125:9(994), 994–1001.
Saatcioglu, M., and Razvi, S. R. (1992). “Strength and ductility of con-
fined concrete.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1992)118:
6(1590), 1590–1607.
Taucer, F. F., Spacone, E., and Filippou, F. C. (1991). “A fiber beam-
column element for seismic response analysis of reinforced concrete
structures.” Rep. No. UCB/EERC-91/17, Earthquake Engineering
Research Center, College of Engineering, Univ. of California,
Berkeley, CA.
© ASCE G4016001-13 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.

14. Tran, T. A. (2012). “Experimental and analytical studies of moderate
aspect ratio reinforced concrete structural walls.” Ph.D. dissertation,
Dept. of Civil and Environmental Engineering, Univ. of California,
Los Angeles.
Tsai, W. T. (1988). “Uniaxial compressional stress-strain relation of
concrete.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1988)114:9(2133),
2133–2136.
Ulugtekin, D. (2010). “Analytical modeling of reinforced concrete panel
elements under reversed cyclic loadings.” M.S. thesis, Dept. of Civil
Engineering, Bogazici Univ., Istanbul, Turkey.
Vecchio, F. J., and Collins, M. P. (1993). “Compression response of cracked
reinforced concrete.” J. Struct. Eng., 83(2), 219–231.
Wallace, J. W. (1996). “Evaluation of UBC-94 provisions for seismic
design of RC structural walls.” Earthquake Spectra, 12(2), 327–348.
© ASCE G4016001-14 J. Struct. Eng.
J. Struct. Eng., 2016, 142(12): G4016001
Downloaded
from
ascelibrary.org
by
Anna
University
Chennai
on
08/05/21.
Copyright
ASCE.
For
personal
use
only;
all
rights
reserved.