Finite Element Modeling of Reinforced

Earthquake Resistant Engineering Structures XI 35
FINITE ELEMENT MODELING OF REINFORCED

CONCRETE STRUCTURAL WALLS FOR
PERFORMANCE-BASED SEISMIC DESIGN
KRISTIJAN KOLOZVARI1, ROSS MILLER1 & KUTAY ORAKCAL2
1
Department of Civil and Environmental Engineering, California State University, USA
2
Department of Civil Engineering, Bogazici University, Turkey
ABSTRACT
A novel finite element modeling approach for nonlinear analysis of reinforced concrete (RC)
structural walls is developed and implemented in OpenSees, which is an open-source computational
platform widely used in earthquake engineering. The proposed analytical model incorporates a two-
dimensional RC constitutive panel behavior described with the fixed-strut angle model into a four-
node isoparametric quadrilateral finite element model formulation. The modeling approach is used to
simulate the responses of two medium-rise RC wall specimens (aspect ratios of 1.5 and 2.0) with
predominant shear-flexure interaction responses. Based on detailed comparison of experimental and
analytical wall responses, the model is found to be capable of predicting accurately the
experimentally-measured response attributes of the cyclic nonlinear wall behavior including lateral
strength, stiffness, stiffness degradation, as well as their hysteretic response characteristics. The
model also captures interaction between flexural and shear behavior, and provides accurate estimates
of the relative contribution of nonlinear flexural and shear deformations to wall lateral displacements
and their distributions over the wall height. Finally, the proposed modeling approach describes
reasonably well local response characteristics including magnitudes and distributions of strain and
stress fields, as well as cracking patterns. Based on the response comparisons presented, model
capabilities are assessed and possible model improvements are identified.
Keywords: reinforced concrete, structural walls, finite element modeling, performance-based design.
1 INTRODUCTION
Reinforced concrete (RC) structural walls are the most commonly used structural elements
in buildings to resist lateral loads imposed by earthquakes. They are designed and detailed
to provide adequate stiffness, strength and deformation capacity to achieve favorable
structural performance under moderate and severe seismic demands. Use of nonlinear
building models subjected to ground acceleration time-histories generally allows for a more
reliable assessment of system and element demands (e.g., lateral story drift, wall shear
demand, local strains or rotations), which are then compared with limits to judge if
acceptable performance is expected. This design methodology, called Performance-Based
Seismic Design (PBSD), has become very common in regions where moderate-to-strong
earthquake shaking is anticipated, and it greatly relies on accuracy of nonlinear analysis
approaches used to assess the expected performance of existing buildings (e.g., using
ASCE 41-13 [1]) or to design new buildings (e.g., using Los Angeles Tall Buildings [2]).
Because RC walls are the primary, and often the only lateral load resisting structural
elements in building structures, the availability of analytical models that are capable of
predicting important behavioral characteristics of their nonlinear seismic behavior is
essential for reliable implementation of PBSD.
Over the past decade, a great number of numerical approaches with various levels of
sophistication were introduced to simulate the nonlinear behavior of RC walls. The
majority of proposed models that are widely used in engineering practice are macroscopic,
based on a beam-column element formulation, where wall cross-section is discretized using
WIT Transactions on The Built Environment, Vol 172, © 2017 WIT Press
www.witpress.com, ISSN 1746-4498 (on-line)
doi:10.2495/ERES170041
36 Earthquake Resistant Engineering Structures XI
a number of concrete and steel longitudinal fibers. These so-called fiber models have
shown to be capable of predicting the nonlinear behavior of slender (flexure-controlled) RC
walls reasonably well in terms of global wall responses (i.e., load-deformation behavior),
whereas local responses (e.g., strains, rotations) are generally not predicted accurately due
to simplifying assumptions used in model development, such as commonly used plane
sections remain plane assumption. Furthermore, most of the models used in practice are not
capable capturing the experimentally observed interaction between flexural and shear
responses typically pronounced for structural walls with moderate aspect ratios (between
1.0 and 3.0). Experimental studies revealed that for such walls both flexural yielding and
nonlinear shear deformations occur simultaneously, where shear deformations can
constitute up to 30% to 50% of lateral wall displacements (e.g., Tran and Wallace [3]), and
could lead to reduced wall strength, stiffness and deformation capacity. Fiber-based
modeling methodologies commonly used in practice for PBSD of buildings typically
consider uncoupled shear and flexural response components, where shear strength and
stiffness are calculated according to code provisions and entered as an ad-hoc input
parameter in the model. This relatively crude approximation of shear behavior does not
capture accurately the mechanics of wall behavior under lateral loading (e.g., effect of axial
load to shear strength and stiffness is not considered), which leads to underestimation of
compressive strains even in relatively slender RC walls controlled by flexure (Orakcal and
Wallace [4]), and overestimation of the lateral load capacity of RC walls with moderate
aspect ratios (Kolozvari [5]) and low aspect ratios (Massone et al. [ 6 ] ) . G i v e n
m e n t i o n e d shortcomings of analytical approaches currently used in engineering practice
for implementation PBSD, there is a need for relatively simple modeling approaches for RC
walls that consider interaction (coupling) between axial, flexural, and shear responses, and
capture important global and local hysteretic response features for a wide range of wall
geometries and reinforcing details.
A relatively simple yet accurate finite element modeling methodology based on a fixed-
crack angle constitutive panel behavior was recently developed and implemented in
OpenSees (McKenna et al. [7]), which is an open-source computational platform widely-
used in earthquake engineering worldwide, for improved predictions of hysteretic nonlinear
behavior of RC walls. This paper presents the results of validation studies of the proposed
model formulation against experimental results obtained for two RC wall specimens (Tran
and Wallace [3]) that experienced significant flexural yielding and nonlinear shear
deformations. Model predictions were compared with the experimentally-measured wall
responses at various response levels and location to provide comprehensive assessment of
model capabilities and propose future model improvements.
2 ANALYTICAL MODEL DESCRIPTION
2.1 Finite element model formulation
The finite element model formulation presented in this study is an extension of the
modeling approach adopted by Gullu and Orakcal [8]. A four-node bilinear iso-parametric
quadrilateral element formulation (Cook et al. [9]) is used herein, for simulating the
behavior of RC structural wall model elements. The model element formulation is
characterized with two degrees of freedom (DOFs) per node (displacements in horizontal
and vertical directions) and four Gauss integration points (Fig. 1). A two-dimensional strain
field corresponding to plane-stress condition is obtained at each integration points based on
displacements at element DOFs using bilinear interpolation functions. Material constitutive
models that represent the behavior of concrete and reinforcing steel (described in the
following section) are used at each integration point to obtain corresponding stress and
stiffness properties. These quantities are then integrated over the element to obtain element
nodal forces and stiffness values.
2.2 Reinforced concrete panel behavior
A plane-stress constitutive model called the Fixed Strut Angle Model (FSAM, Fig. 2;
Orakcal et al. [10]) is used to define strain-stress behavior at each integration point within
the implemented finite element formulation.
FSAM is an in-plane, reversed-cyclic constitutive model based on the fixed-crack angle
modeling approach and assumption of perfect bond between concrete and reinforcing steel
bars, i.e., no slip between concrete and steel reinforcement. The reinforcing bars develop
uniaxial stresses under uniaxial strains in their longitudinal directions (Fig. 2(d)), whereas
concrete behavior is based on uniaxial stress–strain relationships applied in biaxial
directions, with orientations determined by the state of concrete cracking (Fig. 2(b)).
Figure 1: Four-node iso-parametric quadrilateral element. (a) Actual element; (b) Parent
element; and (c) 2-D constitutive material model FSAM.
Figure 2: Behavior and modeling parameters of the constitutive RC panel model FSAM.
(a) Strain-stress field; (b) Concrete biaxial behavior; (c) Concrete shear aggregate
interlock; (d) Steel behavior; and (e) Dowel action on reinforcement.
Concrete behavior is characterized by three consecutive stages: (a) uncracked concrete, (b)
after formation of the first crack, and (c) after formation of the second crack, as described
by Orakcal et al. [10]. Although the concrete stress–strain relationship is fundamentally
uniaxial in nature, it also incorporates biaxial softening effects including compression
softening (Vecchio and Collins [11]) and hysteretic biaxial damage (Mansour et al. [12]).
In this study, the uniaxial constitutive model for concrete by Yassin [13] and the stress-
strain relationship for steel proposed by Menegotto and Pinto [14] are used in the FSAM
formulation. In addition, the shear resisting mechanisms along crack surfaces in the FSAM
are described using a friction-based shear aggregate interlock model (Orakcal et al [ 1 0 ] ,
Fig. 2(c)) and a linear-elastic model (Kolozvari et al. [15]) to account for dowel action on
reinforcing steel bars (Fig. 2(e)).
3 EXPERIMENTAL PROGRAM
Experimental data obtained from two well-instrumented RC wall specimens tested by Tran
and Wallace [3] were used to validate the proposed analytical model. Specimens were
tested to failure under constant axial load and a reversed-cyclic displacement history
applied at the wall top. Wall specimens considered in this study were characterized with
aspect ratios of 1.5 and 2.0 (moderately-slender walls), moderate and high shear stress
ratios, and significant contributions of shear deformations to total lateral displacement.
Major specimen characteristics are presented in Table 1, whereas detailed descriptions of
the experimental study and test results are presented by Tran and Wallace [3].
4 ANALYTICAL MODELING STUDIES

Detailed comparisons between experimentally measured and analytically predicted global
and local wall responses for specimens SP2 (aspect ratio = 2.0) and SP4 (aspect ratio = 1.5)
are presented; including lateral load versus total, flexural, and shear displacements at the
top of the walls, shear and flexural deformation profiles along wall height, and distribution
of vertical (flexural) strains at the wall base.
4.1 Finite element model generation
Experimentally applied cyclic top displacement histories for each specimen, which
consisted of three cycles for each drift level, were applied to the analytical model to
replicate each test. A constant axial load value of approximately 663 kN was applied at the
top of the wall model for both specimens to replicate the average resultant of vertical forces
applied by actuators during testing. Concrete and steel material models were calibrated
Table 1: Properties of test specimens.
( 2) Web Boundary
Test Specimen hw h
w
Pax Reinforcement (3) Reinf.(3) V @ M n V @ M n
No. (1) code (mm) l Ag f 'c t=l b Vn A f'
w configuration conf. cv c
(%) (%)
RW-A20-
SP2 2440 2.0 0.073 0.61 2#3@152 mm 7.11 8#6 0.91 6.1
P10-S63
RW-A15- 4#6
SP4 1830 1.5 0.064 0.73 2#3@127 mm 6.06 0.85 7.0
P10-S78 +4#5
(1) Used in further text when referring to test specimens
(2) l = 1220 mm, t = 152 mm for both specimens
w w
(3) US bar sizes called out
using the procedure described by Orakcal and Wallace [4] to match corresponding
specimen material properties obtained from uniaxial material tests. Geometry of the
specimens in horizontal direction was discretized using ten model elements in the
horizontal direction, where two elements were used to model each boundary element
(confined concrete) and six elements were used in the web (unconfined concrete), as
illustrated in Fig. 3b. Along the specimen height, sixteen and twelve model elements were
used for specimen SP2 and SP4, respectively, where model element height was selected so
the aspect ratio of each element is approximately equal to 1.0 (Fig. 3a). Reinforcing steel
was distributed uniformly throughout each boundary and web element in both vertical and
horizontal directions, where the reinforcing ratios used is calculated based on the
reinforcement configuration reported by Tran and Wallace [3].
4.2 Lateral load versus top displacement responses
The comparisons of lateral load versus top wall displacement responses for specimens SP2
and SP4 obtained from the experiments and the analyses are presented in Fig. 4. It can be
observed from the figure that major hysteretic characteristics of the load-deformation
response are well predicted by the analytical model, including wall yield and ultimate
lateral load capacity, stiffness, cyclic degradation of unloading/reloading stiffness, and
overall shape of the hysteretic loops (pinching characteristics and plastic displacements at
zero lateral load). Wall stiffness at lateral drift levels lower than 0.5% is slightly
overestimated, which is very common in analysis of structural walls because the majority of
analytical models do not account for effects of micro-cracking in concrete and strain
penetration effects. Furthermore, the model captures the initiation of lateral strength
degradation of specimen SP4 (see Section 4.4.3) during the loading cycle to a lateral drift
ratio of 3.0%, suggesting that the model is capable of predicting the wall lateral drift
capacity reasonably well. However, significant strength loss observed during the
experiments, initiated by concrete crushing and rebar buckling at wall boundaries followed
by lateral instability of the wall compression zone for Specimen SP2 and shear sliding
Figure 3: Wall discretization for specimen SP4. (a) Elevation with OpenSees material
assignment and (b) Cross-section.
Figure 4: Lateral load versus wall top displacement. (a) SP2; and (b) SP4.
adjacent to the wall-pedestal interface for Specimen SP4, was not captured in analysis
results because bar buckling, sliding shear, and lateral instability failure mechanisms are
not implemented in the current modeling approach.
4.3 Flexural and shear deformation components
As mentioned earlier, contribution of shear deformations to total lateral displacements for

the wall specimens considered was significant, suggesting that behavior of the wall
specimens was influenced by shear-flexural interaction (SFI). In order to investigate the
capability of the proposed modeling approach to capture this interaction, magnitudes and
distributions of analytically obtained flexural and shear deformations are compared with
experimentally measured responses in terms of load-deformation behavior and vertical
profiles. Experimental shear and flexural deformation values were obtained from vertical
and diagonal LVDT’s during wall specimen testing using procedure described by Massone
and Wallace [16]. Analytical shear deformations for each horizontal row of wall elements
are calculated by integrating average shear strain (for the horizontal row of elements),
whereas flexural deformations are obtained from by subtracting analytical shear
deformations from the total lateral deformation.
4.3.1 Load-deformation responses

A representative comparison of experimentally measured and analytically predicted load
versus flexural and load versus shear deformation responses for specimen SP4 is presented
in Fig. 5, which indicates that analytical model is capable of capturing the presence of
nonlinear shear deformations, as well as their coupling with nonlinear flexural
deformations, through the entire cyclic loading history. Simultaneous occurrence of
nonlinear shear and flexural deformations (at the same level of lateral load) reveals that SFI
behavior is reflected in both analytical and experimental results. Furthermore, the relative
magnitudes of the contributions of shear and flexural deformations are reasonably well
predicted by the model for all of the loading cycles, where both experimental and analytical
results suggest that contribution of shear deformations to the total lateral displacement of
the wall is approximately 30% to 40%. Analytical results diverge from the experimentally
measured shear deformations only during the last loading cycle, as the model was unable to
capture the sliding shear deformations observed along the base of both wall specimens near
the end of the tests. This sliding deformation was not concentrated at the wall-foundation
interface, but occurred over the highly damaged region near the wall base. Finally, the
overall hysteretic shape of the shear and flexural load-deformation loops is well predicted
by the model, where shear behavior is characterized with highly pinched hysteretic
response, whereas no pinching is observed in the flexural hysteresis.
4.3.2 Vertical deformation profiles

Experimentally measured and analytically predicted vertical profiles of shear and flexural
deformations (along wall specimen height) generated at selected peak top displacements
corresponding to first loading cycles in positive and negative loading directions for
specimen SP2, are presented in Fig. 6. It can be observed from Fig. 6(a) that in both
experimental and analytical results, nonlinear flexural deformations (rotations) develop
mostly within the bottom region of the wall along a height of 600 mm, whereas the flexural
displacement profiles are almost linear above this height, indicating that flexural
deformations are relatively small in the upper regions of the wall. The magnitudes of
flexural displacements along wall height are well predicted by the analytical model, with
approximately 5% deviation between model and test results. Furthermore, the comparisons
shown in Fig. 6b indicate that the shape of the measured and predicted shear deformation
profiles for both specimens agree reasonably well, demonstrating that the model captures
the experimentally observed concentration of shear deformations along the bottom 600 mm
of the wall where nonlinear flexural deformations are measured. Therefore, the analytical
Figure 5: Lateral load versus top displacement components for specimen SP4. a) Shear;
and b) Flexure.
Figure 6: Deformation distribution along height of SP2. (a) Flexure; and (b) Shear.
model is capable of predicting nonlinear shear deformations developing even for a wall that
yields in flexure, which has been also been observed in the current and previously
conducted experimental studies (e.g., Tran and Wallace [3]; Massone and Wallace [16];
Oesterle et al. [17]), and provides another proof of capability of the model to capture
experimentally observed SFI. The model reasonably predicts the magnitude of shear
displacements along wall height at low and moderate drift levels in the positive loading
direction for wall specimen SP2.
4.4 Local wall responses
Evaluation of the analytical model is further conducted by assessing local wall responses
(i.e., strains and stresses) at various wall locations and by comparing them to the measured
experimental data obtained for specimen SP4.
4.4.1 Vertical deformation profiles

Various analytically obtained and experimentally observed local wall responses for
specimen SP4 are presented in Fig. 7 in order to describe overall characteristics of local
response predictions obtained using the proposed modeling approach. Fig. 7a compares the
experimentally-observed crack pattern recorded during testing at a drift ratio of 3.0% (grey
lines) and the crack orientations predicted by the analytical model (red lines). Crack
orientations (directions perpendicular to the cracks) in the model formulation represent the
directions along which the principal tensile strains first exceed the cracking strain of
concrete within each model element. It can be observed from the figure that the analytically
predicted orientation and distribution of cracks on the wall are in reasonable agreement
with the experimentally observed crack pattern, suggesting that the cracking criteria and the
orthogonal crack assumption of the model are both reasonable. The orientation of the
cracks is more horizontal at the wall boundaries where flexural (vertical) strains
predominate over shear strains, whereas the cracks are more inclined towards the middle of
the wall web where shear (diagonal tension) strains are more dominant. As well, since
flexural effects decrease along the wall height, orientation of the cracks at wall boundaries
becomes more inclined towards the top of the wall.
Fig. 7b and Fig. 7c further show analytically obtained field of vertical normal strains (y)
and shear stresses (xy) in the wall, respectively, corresponding to 3.0% lateral drift in the
positive loading direction. As it can be observed in Fig. 7a, the distribution of vertical
strains predicted by the model are reasonable, where tensile strains decrease over the height
of the wall since the moment demand is decreasing linearly and the axial load is constant.
As well, the predicted plastic hinge of the wall, where most of the nonlinear behavior is
concentrated, is located approximately along the height of the bottom two elements (300
mm ≈ lw/4, commonly used plastic hinge length for walls with well-detailed boundaries),
which is in agreement with the experimental observations by Tran and Wallace [3].
Furthermore, results presented in Fig. 7c show that shear stresses along the wall height
develop mainly along the main diagonal compression strut, and that shear stresses are
generally resisted by model elements that are subjected to axial compression (Fig. 7b),
whereas elements subjected to tension resist zero (or very small) shear stress. This
correlation between axial strains and shear stresses shown in Fig. 7b and Fig. 7c reveal the
capability of the model to capture axial/flexural and shear interaction at section (local)
response level in RC walls in addition to SFI that has been observed earlier from global
analytical responses. It should be also mentioned that the level of shear stress in individual
model elements reaches approximately 40√f’c (Fig. 7c), which is significantly higher than
the average (over the entire cross-section) shear stress of 7.0√f’c (Table 1) that would be
obtained with models that do not capture shear-flexural interaction and are currently used in
engineering practice for performance-based seismic design. Therefore, the proposed
modeling approach provides improved analytical capabilities for capturing migration of
local stress demands within the cross-section of structural wall subjected to lateral loads.
4.4.2 Strain profiles along the wall base and vertical growth
Fig. 8a presents a representative comparison between analytically and experimentally
obtained vertical normal strain profiles along the wall base for specimen SP4, at selected
drift levels. The experimental strains are measured over a vertical gauge length of 335 mm
(14 in.) whereas the analytical results are obtained from the bottom 300 mm (12 in.),
Figure 7: Strain and stress responses for specimen SP4 at 3.0% drift. (a) Cracking pattern;
(b) Vertical strain field; and (c) Shear stress field.
corresponding to the total height of two bottom wall elements. Overall, the model provides
reasonably accurate predictions of both compressive and tensile strains, as well as the
location of the neutral axis on the wall cross section. Although relaxation of tensile strains
at the wall boundary in tension is not predicted by the model, which leads to modest
overestimation of tensile strains at large drift levels, the presented finite element modeling
approach is capable of predicting the overall nonlinear distribution of strains along the wall
base, which is not possible with macro-modeling approaches (which assume plane sections
remain plane) typically used in engineering practice. This allows overall better prediction of
wall strains, especially the compressive strains in concrete.
Comparison of analytical and experimental results for the relationship between vertical
growth and lateral deformation at the top of wall specimen SP2 is shown in Fig. 8b.
Vertical growth of the wall specimen during testing was caused by plastic (permanent)
deformation of the boundary steel reinforcement. Analytical model results indicate an
approximately constant vertical growth of the wall throughout the loading history and are in
good correlation with experimentally measured data at both maximum applied lateral
displacement and zero lateral displacement (i.e., residual vertical growth). Therefore, the
proposed modeling approach and the constitutive material model adopted for steel describe
the cyclic behavior of the boundary reinforcement within the plastic hinge region
reasonably well.
4.4.3 Strength loss prediction
Tran and Wallace [3] reported that initiation of failure in specimen SP4 occurred due to
crushing along diagonal strut (Fig. 9a), followed by crushing and rebar buckling in the wall
boundaries (Fig. 9b), which led to sliding shear failure along the wall-pedestal interface of
the wall. To illustrate the source of strength degradation in the model results, Fig. 9c shows
the analytical stress-strain behavior of concrete along the diagonal strut (parallel to the
crack) in the boundary model element, which clearly suggests degradation in the stress-
strain relationship of concrete at this location. However, the complete failure mechanism
observed during tests is not captured by the analytical model, due to the inability of the
model to predict failure mechanisms associated with buckling of reinforcement and shear
sliding.
Figure 8: Local responses. (a) Vertical strain profiles along wall base specimen SP4; and
(b) Vertical growth versus lateral top displacement for specimen SP2.
Figure 9: Predicted and observed wall boundary responses for specimen SP4 at 3.0%
drift. (a) Wall damage; (b) Boundary damage; (c) Predicted concrete behavior in
principal direction.
5 SUMMARY AND CONCLUSIONS

A new finite element modeling approach for simulation of the nonlinear behavior of RC
structural walls is described in this paper. The model incorporates a plane stress constitutive
RC panel behavior described with a fixed-crack angle approach into a four-node
quadrilateral finite element model formulation. The analytical model is implemented in the
widely-used computational platform OpenSees.
Calibration and validation of the presented modeling approach is conducted using
detailed experimental data recorded for two medium-rise RC wall specimens with aspect
ratios of 1.5 and 2.0 tested under reversed-cyclic loading conditions. The behavior of the
specimens was characterized with significant nonlinear shear deformations
and pronounced shear-flexural interaction. Comparison between analytically obtained and
experimentally measured wall responses was conducted at both global and local response
levels, including load versus total, flexural and shear deformation responses, profiles of
shear and flexural deformations at various drift levels along wall height, as well as local
strain and stress distributions. Based on assessment of the model results, it can be
concluded that the proposed modelling approach is capable of accurately simulating the
cyclic global load-deformation behavior including strength, stiffness, and pinching of
the walls investigated. The proposed model also successfully captures the experimentally
measured magnitudes and distributions of flexural and shear deformations and shear-
flexural interaction. Unlike in fiber models, plane sections do not necessarily remain plane
in the proposed finite element model formulation, which is more consistent with the
experimentally-measured strain profiles and provides better predictions for the compressive
strains in concrete, compared to fiber model formulations. Hence, both tensile and
compressive strains are in good correlation with experimental data within the wall plastic
hinge region, and the overall distribution of strains and stresses is reasonable.
Overall, the novel finite element modeling approach presented in this paper represents a
promising approach for simulation of the nonlinear behavior of RC walls subjected to
seismic actions. Future studies will involve extensive validation of the modeling approach
against specimens with a wide range of wall characteristics, particularly aspect ratios, to
assess model capabilities to accurately simulate the behavior of squat (shear-controlled) and
slender (flexure-controlled) walls. The model is currently being extended to three-
dimensional problems with the objective to simulate the behavior of walls with various
nonrectangular cross-sections (C-shaped, T-shaped, core walls) under earthquake loading.
Development of user manuals, OpenSees Wiki pages, and examples is underway, and it is
expected that the models will become publicly available by the end of 2018.
ACKNOWLEDGEMENT
This work was supported by the National Science Foundation, Award No. CMMI-1563577.
Any opinions, findings, and conclusions expressed herein are those of the authors and do
not necessarily reflect those of the sponsors.
REFERENCES
[1] ASCE 41-13, Seismic Evaluation and Retrofit of Existing Buildings, American
Society of Civil Engineers, Reston, Virginia.
[2] LA Tall Buildings Structural Design Council, An Alternative Procedure for Seismic
Analysis and Design of Tall Buildings Located in the Los Angeles Region, 2014.
[3] Tran, T.A. & Wallace, J.W., Cyclic Testing of Moderate-Aspect-Ratio Reinforced
Concrete Structural Walls. ACI Structural Journal, 112(6), pp. 653–665, 2015.
[4] Orakcal, K. & Wallace, J.W., Flexural modeling of reinforced concrete walls – model
calibration. ACI Structural Journal, 103(2), pp. 196–206, 2006.
[5] Kolozvari, K., Analytical Modeling of Cyclic Shear-Flexural Interaction in
Reinforced Concrete Structural Walls. PhD issertation, UC Los Angeles, 2013.
[6] Massone, L.M., Orakcal, K. & Wallace, J.W., Modeling of squat structural walls
controlled by shear. ACI Structural Journal, 106(5), pp. 646–655, 2006.
[7] McKenna, F., Fenves, G.L., Scott, M.H. & Jeremic, B., Open System for Earthquake
Engineering Simulation (OpenSees), Pacific Earthquake Engineering Research
Center, University of California, Berkeley, CA, 2000.
[8] Gullu, M.F. & Orakcal, K., Nonlinear Finite Element Modeling of Reinforced
Concrete Structural Walls. Proceedings, 16th World Conference on Earthquake
Engineering, Santiago, Chile, 2017.
[9] Cook, D.R., Malkus, S.D., Plesha, E.M. & Witt, J.R., Concepts and Applications of
Finite Element Analysis, John Wiley & Sons, 2001.
[10] Orakcal, K., Massone, L.M. & Ulugtekin, D., Constitutive Modeling of Reinforced
Concrete Panel Behavior under Cyclic Loading. Proceedings, 15th World
Conference on Earthquake Engineering, Lisbon, Portugal, 2012.
[11] Vecchio, F.J. & Collins, M.P., Compression response of cracked reinforced concrete.
ASCE Journal of Structural Engineering, 83(2), pp. 219–231, 1993.
[12] Mansour, M.Y., Hsu, T.C. & Lee, J.Y., Pinching effect in hysteretic loops of R/C
shear elements. ACI Structural Journal, 205, pp. 293–321, 2002.
[13] Yassin, M.H.M., Nonlinear Analysis of Prestressed Concrete Structures Under
Monotonic and Cyclic Loads. PhD dissertation, UC Berkeley, 1994.
[14] Menegotto, M. & Pinto, E., 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. Proceedings, IABSE
Symposium, Lisbon, Portugal, 1973.
[15] Kolozvari, K., Orakcal, K. & Wallace, J.W., Modeling of Cyclic Shear-Flexure
Interaction in Reinforced Concrete Structural Walls. I: Theory. ASCE Journal of
Structural Engineering, 141(5), 04014135, 2015.
[16] Massone, L.M. & Wallace, J.W., Load – deformation responses of slender reinforced
concrete walls. ACI Structural Journal, 101(1), pp. 103–113, 2004.
[17] Oesterle, R., Aristizabal-Ochoa J., Fiorato A., Russel H., and Corley W., Earthquake
Resistant Structural Walls-Tests of Isolated Walls: Phase II. Portland Cement
Association, Skokie, IL, 327, 1979.

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Earthquake Resistant Engineering Structures XI 35

FINITE ELEMENT MODELING OF REINFORCED

2 ANALYTICAL MODEL DESCRIPTION

2.1 Finite element model formulation

2.2 Reinforced concrete panel behavior

4 ANALYTICAL MODELING STUDIES

4.1 Finite element model generation

Table 1: Properties of test specimens.

4.3 Flexural and shear deformation components

As mentioned earlier, contribution of shear deformations to total lateral displacements for

4.3.1 Load-deformation responses

4.3.2 Vertical deformation profiles

4.4 Local wall responses

4.4.1 Vertical deformation profiles

5 SUMMARY AND CONCLUSIONS

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