Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)
ISSN: 2311-9020; ISBN: 978-972-752-165-4
Nonlinear analysis of reinforced concrete shear wall using fiber elements
Dae-Han, Jun1
Department of Architectural Eng., Faculty of Civil&Architectural Engineering, Donseo University,
Jurye-ro 47, Sasang-gu, Busan, Korea
email: [email protected]
1
ABSTRACT: Reinforced concrete shear walls are effective for resisting lateral loads imposed by wind or earthquakes. Observed
damages of the shear wall in recent earthquakes in Chile(2010) and New Zealand(2011) exceeded expectations. Various
analytical models have been proposed in order to incorporate such response features in predicting the inelastic response of RC
shear walls. However, the model has not been implemented into widely available computer programs, and has not been
sufficiently calibrated with and validated against extensive experimental data at both local and global response levels.
This study investigates the effectiveness of a wall fiber element in predicting the flexural nonlinear response of reinforced
concrete shear walls. Model results are compared with experimental results for reinforced concrete shear walls with rectangular
cross sections subjected to high axial load. The analytical model is calibrated and the test measurements are processed to allow
for a direct comparison of the predicted and measured flexural responses. Response results are compared at top displacements
on the walls. Results obtained in the analytical model for rectangular wall cross sections compared favorably with
experimentally responses for flexural capacity, stiffness, and deformability.
KEY WORDS: Reinforced concrete shear walls; Fiber element; Nonlinear response; Plastic hinge.
1
BACKGROUND OF THE STUDY
Reinforced concrete shear wall is widely used as a structural
element as it has excellent resistance to lateral force due to
seismic excitation or wind load and it reduces lateral
displacement by increasing horizontal stiffness of high-rise
buildings. However, it is recently reported that structural
damages of shear wall occur more than expected in recent
earthquakes even in the buildings that are engineered by
relatively good seismic design1). Accordingly, interest in
seismic safety of high-rise apartments with shear walls widely
constructed in Korea and social demand toward an accurate
evaluation of seismic performance are increasing 2).
Reinforced concrete shear wall structure is a structural
system usually applied to high-rise apartments and hotels of
which space is partitioned in a certain area, and it is designed
so that the wall can resist shear force following a horizontal
load. In high-rise buildings, high axial load is applied to shear
walls. Stiffness and capacity evaluation of shear wall under
high axial load are important structural design factors. To
evaluate the nonlinear behavior of reinforced concrete shear
walls to the lateral load, a number of experimental and
analytical studies have been performed worldwide, and
recently, various nonlinear analysis models that can represent
the nonlinear behavior of reinforced concrete shear walls have
been suggested.2),3),4)
The representative analysis model to predict the nonlinear
behavior of reinforced concrete shear walls can be classified
into microscopic modeling and macroscopic modeling. Finite
element method is used in the microscopic modeling, and
bending moment and shear force on the reinforced concrete
shear wall can be accurately described in this method. In
particular, when the behavior of a squat shear wall is predicted
using a microscopic modeling, it is known that the local
behavior appearing on the actual shear walls can be
considered in a relatively accurate way compared to the
macroscopic modeling. Therefore, as this method can
accurately present the nonlinear behavior of reinforced
concrete shear walls, a precise nonlinear analysis is possible
in isolated walls on which bending-compression and shear
behavior occur in complex. However, when various structural
elements such as coupling beam and slab are used in complex
in a building structure, large number of finite elements are
required to be used to perform a nonlinear analysis. In that
case, running time becomes long and stability problems occur
in the numerical analysis, thus the microscopic modeling is
not appropriate as an analytical model.
The macroscopic modeling can be easily applied compared
to the finite element analysis when the structure is a high-rise
building or the plan is complicated. Its drawback is that the
analysis result is valid only in limited conditions.2) To
overcome this limitation, many researchers have suggested
various macroscopic models of reinforced concrete walls.
However, accurate prediction is hard as the behavior of the
wall differs greatly depending on the modeling approaches.
Therefore, to accomplish a precise seismic performance
evaluation of high-rise buildings or apartments with
reinforced concrete shear walls, a nonlinear analysis model
that can make accurate evaluation on reinforced concrete
shear walls having various systems such as isolated wall and
coupling wall, is needed.
In this paper, we will use the fiber element model that can
make more accurate analysis on nonlinear behavior of shear
walls and study the applicability of the analytical model based
on the existing experimental data.
To achieve a nonlinear analysis of reinforced concrete shear
walls, a large number of studies have been performed using
microscopic models and macroscopic models. However, since
each modeling method includes errors in analysis result, it is
hard to decide which nonlinear analysis model can make an
accurate evaluation. If the fiber element is used to compose a
nonlinear analysis model of shear walls, it can effectively
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
represent bending deformation of the element, by reflecting
the material nonlinearity of concrete and steel reinforcement,
while a precise prediction of the shear deformation is not
possible. To evaluate the seismic performance of a shear wall
structure with accuracy, a nonlinear spring element that can
represent the shear deformation should be added to the fiber
element model.
In this study, reinforced concrete shear walls were modeled
with fiber elements, which cross section and reinforcement
details of shear walls can be arranged freely, and nonlinear
analysis was performed by adding nonlinear shear spring
elements that can represent the shear deformation. This
analysis result will be compared with the existing experiment
results. To investigate the nonlinear behavior of reinforced
concrete shear walls, reinforced concrete rectangular section
single shear walls subjected to high axial loading were
selected.
2
FAILURE MODE OF SHEAR WALLS
Based on the experiments previously performed, ASCE41-06
defined the behavior of reinforced concrete shear walls by
classifying with shear span ratio6). Slender shear wall with
shear span ratio higher than 3.0 was defined to a show a
flexural behavior. A wall with a shear span ratio lower than
1.5(squat wall or short wall) was defined to show a shear
behavior. A reinforced concrete shear wall with shear span
ratio between 1.5 and 3.0 was classified to be affected by both
flexure and shear.
In Figure 2-1(a), the longitudinal reinforcement located at
the base of the walls on the tension side is gradually tended
and at the ultimate state, successive failures occur from the
steel reinforcement located on the boundary region, forming a
flexure failure. Figure 2-1(b) shows the shear failure mode.
An inclined failure occurs on shear walls due to the lack of
transverse reinforcement. When sufficient transverse
reinforcement is added on the wall, inclined failure can be
prevented and it can resist high shear force. Here, when the
compression stress increases on the compression strut and
exceeds the compression strength of the concrete, the
compression strut experiences a compression crushing, and
ultimately an inclined compression failure can occur. As
shown in Figure 2-1(c), in the case of shear walls on which
inclined failures and inclined compression failures are
prevented, a sliding shear failure can occur. Figure 2-1(d)
shows a web crushing failure of shear walls caused by a cyclic
load.
3
3.1
ANALYSIS MODEL OF SHEAR WALLS
Fiber element model
Figure 3-1 shows the common 3-dimensional structural
behavior of reinforced concrete shear walls. To represent the
3-dimensional behavior of reinforced concrete shear walls, the
cross section is divided into fiber slices as shown in Figure 32. These fiber elements can model steel slice and concrete
slice by assigning a stress-strain relation to each slice. Fiber
slice can express the axial force and the bending moment
behavior in the walls. W, C1, and C2 represent the shear
behavior of walls and the columns attached to the walls. W is
the spring that represents the in-plane shear stiffness of the
shear wall, and C1 and C2 are springs that represent Y
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direction shear stiffness of the attached columns. It is assumed
that the cross section of the shear walls maintains plane when
an in-plane wall deformation occurs. Following the plane
section remain plane assumption, strain of the fiber element in
the cross section is proportional to the distance from the
neutral axis. The stress of each slice is calculated using the
stress-strain relation from the strain of each fiber slice, and the
bending moment is calculated by summing the moments to the
center of the cross section.
3.2
Shear spring element
If a fiber element is used in the nonlinear analysis model of
reinforced concrete shear walls, material nonlinearity of
concrete and reinforcement is reflected and only flexure
behavior of the shear wall can be evaluated efficiently.
However, the shear deformation cannot be assigned only by
fiber element. To compensate this shortcoming, a nonlinear
shear spring element that can represent the shear deformation
should be added in the analytical model. Figure 3-3 shows the
force-displacement relation of the nonlinear shear spring
element.
To achieve an accurate prediction of nonlinear behavior of
reinforced concrete shear walls, accurate evaluation of initial
stiffness, cracking strength, shear yielding strength, and
yielding displacement of the nonlinear shear spring are
important. Various parameters that define the nonlinear shear
spring should be established depending on the failure mode of
the shear wall. Figure 3-4(a) shows the force-displacement
relation of reinforced concrete shear walls having a preemptive shear failure. In the figure, the shear yielding strength
is reached before the steel reinforcement on the tension side
reaches yielding and a shear failure occurs. Figure 3-4(b)
shows the force-displacement relation of a shear wall having
flexure-shear failure. First, yielding of flexure tension bar
occurs and it reaches to a shear failure of reinforced concrete
shear walls5). As shown in these figures, defining each
parameter of nonlinear shear spring considering the failure
mode of the shear wall can predict the nonlinear behavior of
reinforced concrete shear walls with accuracy.
3.3
Stress-strain of the material
As seen above, the fiber element model can idealize the steel
element and the concrete element by assigning a stress-strain
relation. Figure 3-5 shows the stress-strain relation of the steel
slice and the concrete slice, respectively.
4
ANALYTICAL SHEAR WALL MODEL
In this paper, a rectangular section single wall subjected to
high axial load as shown in Figure 4-1 was selected, and the
experiment result and the analysis result were compared.
As shown in Figure 4-1, height, length, and thickness of the
rectangular section single wall are 1750mm, 700mm, and
100mm, respectively. Shapes of the specimens are all same.
Strength of reinforcing bar and concrete strength of each
specimen are set differently by specimen. Horizontal load is
applied at 1500mm height from the bottom of the wall.
The nonlinear response analysis of reinforced concrete
shear wall was carried out using CANNY-2010 software7). In
a nonlinear static response analysis, the lateral force increased
until the base section of shear wall reached ultimate states.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
5
DISCUSSION OF ANALYSIS RESULT
In this study, a nonlinear analysis of reinforced concrete shear
wall was accomplished using a fiber element model described
in the section 3.1 to verify the validity of the analytical model.
The validity was confirmed by comparing the result of the
experimental research and the result obtained from the
nonlinear response analysis.
In the analytical model to examine the nonlinear behavior
of a rectangular section single wall subjected to high axial
load, the cross section of the shear wall is divided into
concrete slice and steel slice as shown in Figure 3-2, and for
the nonlinear shear spring, the shear strength-shear
deformation relation was set as shown in Figure 3-3. Various
equations have been suggested to estimate the shear strength
and the shear stiffness. The nonlinear shear spring parameters
were estimated by JBDPA code equations8). The calculated
parameters of the nonlinear shear spring used in this analysis
are shown in Table 5-1.
The analysis was implemented up to the yielding point and
the result before and after the yielding was compared based on
the yielding point. Here, the yielding point was set based on
the time when the longitudinal reinforcement yields on the
tension side of the wall. The flexure cracking strength was
defined as the time when the concrete cracks.
In a shear wall structure, the plastic hinges are concentrated
on the lowest floor when an ultimate load is applied.
Therefore, high curvature ductility is required to well absorb
the seismic energy. Depending on how to set the length of a
plastic hinge, the value of the plastic deformation angle and
wall displacement differs. Plastic deformation angle and
plastic hinge length can be used to determine the curvature of
the wall, and the curvature effects on the lateral displacement.
Usually, the length of a plastic hinge is (1/2)lw of effective
depth of the wall.9),10)
Figure 5-1 shows the lateral load-lateral displacement
relation of the shear wall SW7. Overall behavior of the shear
wall based on the stiffness and the displacement was similar
in the experiment result and the analysis result. It was
confirmed that the initial stiffness and the yield strength of the
shear wall were almost same in the experimental result and
the analysis result. However, the yielding displacement of the
shear wall was higher in the experiment than the analysis. It is
considered that the stiffness degradation following the cyclic
loading causes this higher yielding displacement in the
experiment result.
Figure 5-2 shows the lateral load-lateral displacement
relation of SW8. Overall lateral load-lateral displacement
relation until reaching the yield point was similar in the
experiment result and the analysis result. However, the
analysis result showed some difference of the initial stiffness
and the ultimate strength of the wall. It is considered that
strain hardening effect of reinforcement causes this higher
ultimate strength in the experiment result.
Figure 5-3 shows the lateral load-lateral displacement
relation of the shear wall SW9. This shear wall was controlled
primarily by shear behavior in experiment. The analysis result
showed some difference behavior pattern to the behavior of
the wall in the experiment. Overall behavior of the shear wall
based on lateral load-lateral displacement relation was similar
in the experiment result and the analysis result. In this analysis
of shear wall, after nonlinear shear spring element was the
first to reach the yield state and the shear wall became
ultimate state. Assuming that the shear spring is elastic, the
yield strength of shear wall increased. Thus, the yield strength
of the shear wall was almost same in the experimental result
and the analysis result. However, the yielding displacement of
the shear wall was still higher in the experiment than the
analysis. This issue will be discussed in detail in the future
studies.
(a) Bending
failure
(b) Shear
failure
(c) Sliding
failure
(d)Web crushing
failure
Figure 2-1. Failure mode in shear walls10)
Figure 3-1 Structural behavior of shear walls
Figure 3-2 Fiber model for shear walls
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
(a) Steel stress-strain relations
Figure 3-3 Shear force-deformation relation of shear spring
(b) Idealized concrete stress-strain relations
Figure 3-5 Stress-strain relation of fiber slice
(a) Pre-emptive shear failure
(b) Flexure-shear failure
Figure 3-4 Force-displacement relation according to
failure mode of shear wall
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Figure 5-2 Lateral load-displacement relation of SW8
Figure 4-1 Geometry and reinforcement details of
rectangular wall specimens
Figure 5-3 Lateral load-displacement relation of SW9
Figure 5-1. Lateral load-displacement relation of SW7
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Table 4-1 Experimental parameters of rectangular wall specimens
SW7
SW8
SW9
Concrete compression strength fck(MPa)
29.7
32.0
35.4
Yield stress(MPa)
405
432
375
Reinforcement
4-ϕ14
(ϕ6@50)*
4-ϕ12
(ϕ6@50)*
4-ϕ20(ϕ6@75)*
Yield stress(MPa)
305
305
305
Size and space (mm)
ϕ8@150
ϕ8@150
ϕ8@150
Yield stress (MPa)
305
305
305(ϕ8), 366(ϕ6)
Size and space (mm)
ϕ8@100
ϕ8@100
ϕ8@75+ϕ6@150
499
784
595
Main flexural
reinforcement
Longitudinal
reinforcement
Horizontal
reinforcement
Axial load (kN)
Dimension of the specimen(mm):
Lengh×Thickness×Height
700×100×1500
Table 5-1 Shear force-deformation parameters in nonlinear shear spring
(These values correspond to parameters in shown figure 3-3)
Specimens
Initial elastic
stiffness
K0(kN/cm)
Cracked
stiffness ratio
A(%)
SW7
692708
16
SW8
694580
SW9
726031
Post-yielding
stiffness ratio
B(%)
Cracking
strength
Fc(kN)
Yielding
strength
Fy(kN)
0.1
146.5
251.8
16
0.1
156.5
261.8
16
0.1
153.3
258.6
ACKNOWLEDGMENTS
This research was supported by Basic Science Research
Program through the National Research Foundation of
Korea(NRF) funded by the Ministry of Education, Science
and Technology(No. 2012R1A1A4A01011211).
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