Static and Dynamic Analysis of a Concrete Shear-Wall
Jaegyun Park1), Chul-Hun Chung1), Chang Hun Hyun2), Yong Lak Paek2), Kang Ryong Choi2)
1) Professor, Dankook University
2) Researcher, Korea Institute of Nuclear Safety
ABSTRACT
Many structures built under the earthquake resistant design were severely damaged in Loma Prieta(1989), Northridge(1994), and Kobe(1995) earthquakes. Current design trend is to limit the maximum displacement under the load. To evaluate the effectiveness of the displacement control under the near-field ground motion due to earthquake, IAEA initiated CRP program. In this paper, we try to regenerate the test results of the CRP program using ABAQUS, a general purpose nonlinear FE program, and compare the result with previous calculations. The model of the concrete shear wall came from the previous report KINS/GR317. A dynamic analysis on this model resulted in the 3 initial modes of the structure, which are similar to the modes of beam-stick model in that report. To describe the response of the concrete structure more precisely, more calibrations are necessary.
INTRRODUCTION
Many structures built under the earthquake resistant design were severely damaged in Loma Prieta(1989), Northridge(1994), and Kobe(1995) earthquakes. Therefore, more efficient analysis technique and design codes are required thesedays. Current design trend is to limit the maximum displacement under the load. To evaluate the effectiveness of the displacement control under the near-field ground motion due to earthquake, IAEA initiated CRP program. As a first step, they performed an analysis of a shear wall and compared the result with the shaking table test results. In this paper, we try to regenerate the test results using ABAQUS, a general purpose nonlinear FE program, and compare the analysis result with previous calculations and experiments.
TEST SETUP
The model of the concrete shear wall came from the previous report KINS/GR317 (Hyun et. al., 2005) by Korea Institute of Nuclear Safety(KINS). Fig. 1 describes the original shear wall for the real test and Fig. 2 presents the two dimensional (2D) model of the shear wall with rotational and translational springs on support.
Fig. 2 Two-Dim. Model
Fig. 3 2D Mesh for the FE analysis
Table 1. Material Properties of the Shear Wall
Concrete Steel Rebar
Strength(MPa) 35 500
Young’s
Modulus(MPa) 28000 200000
Poisson’s ratio 0.15 0.3
Fig 4. Rebar Configurations in Shear Wall
Table 2. Amounts of Rebar in Level 1 to Level 6
Lateral Rebar Central Rebar
Level
f (mm) No. As(mm2) Ratio(%) f (mm) No. As(mm2) Ratio(%)
Level 6 4.5 1 15.90 0.016 - 0 - -
Level 5 4.5 1 15.90 0.016 5.0 4 78.54 0.077 Level 4 6.0 1 28.27 0.028 5.0 4 78.54 0.077 6.0 1 28.27 0.028 5.0 4 78.54 0.077 8.0 1 50.27 0.049 4.5 2 31.81 0.031
4.5 1 15.90 0.016 - - - -
Level 3
S 94.44 0.093 S 110.35 0.108
6.0 2 56.55 0.055 5.0 4 78.54 0.077 8.0 2 100.53 0.099 4.5 2 31.81 0.031 4.5 2 31.81 0.031 6.0 1 28.27 0.028 Level 2
S 188.89 0.185 S 138.62 0.136
8.0 4 201.06 0.197 5.0 4 78.54 0.077 6.0 2 56.55 0.055 4.5 2 31.81 0.031 4.5 2 31.81 0.031 6.0 1 28.27 0.028 Level 1
The material model for concrete is ‘Concrete Damage Plasticity Model’ in ABAQUS which could describe the plastic behavior of uni-axial compression test very well(Kang, 2006). This model was originally proposed in Lubliner et al.(1989) and further developed in Lee and Fenves(1998). The concrete damaged plasticity model uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete. It is defined by using the *CONCRETE DAMAGED PLASTICITY, *CONCRETE TENSION STIFFENING, and *CONCRETE COMPRESSION HARDENING options, and, optionally, the *CONCRETE TENSION DAMAGE and *CONCRETE COMPRESSION DAMAGE options.
Fig 5. The Concept of Concrete Damaged Plasticity Model
Table 3. Concrete Damaged Plasticity Model used for Analysis
Inelastic
strain Stress dc Elastic strain strain Total Plastic strain
0.000000 7.42 0.000 0.000307 0.000307 0.000000
0.000012 9.60 0.020 0.000397 0.000409 0.000004
0.000029 11.64 0.040 0.000481 0.000510 0.000009
0.000053 13.53 0.060 0.000559 0.000612 0.000017
0.000082 15.28 0.080 0.000631 0.000713 0.000027
0.000117 16.88 0.109 0.000698 0.000815 0.000032
0.000158 18.34 0.126 0.000758 0.000916 0.000048
0.000205 19.66 0.144 0.000812 0.001017 0.000068
0.000257 20.83 0.161 0.000861 0.001118 0.000091
0.000316 21.86 0.179 0.000903 0.001219 0.000119
0.000380 22.74 0.196 0.000940 0.001320 0.000151
0.000450 23.47 0.213 0.000970 0.001420 0.000187
0.000526 24.07 0.231 0.000995 0.001521 0.000228
0.000608 24.51 0.248 0.001013 0.001621 0.000274
0.000696 24.82 0.265 0.001026 0.001722 0.000325
0.000790 24.97 0.283 0.001032 0.001822 0.000383
0.000889 24.99 0.300 0.001033 0.001922 0.000446
STATIC ANALYSIS
Pushover analysis was performed to obtain the static response data. The lateral force F, with a triangular shape, was applied as follows:
- Level 6: F ´ 5/15 - Level 5: F ´ 4/15 - Level 4: F ´ 3/15 - Level 3: F ´ 2/15 - Level 2: F ´ 1/15
Displacement was measured at Level 6. The pushover analysis is carried out by incrementally applying the lateral loads to the structure. Fig. 6 shows the force-displacement plot of the current analysis. For comparison purpose, Fig. 7 (Hyun et al, 2005) presents the previous results from other countries, which reveals that the stiffness of current model is slightly above average.
0 20 40 60 80 100 120 140
0 10 20 30 40 50 60
displacement (mm)
L
o
a
d
(k
N
)
.
Fig. 6 Push over Test
DYNAMIC ANALYSIS
To investigate the modal characteristics of the shear wall, a modal analysis was done first. One major difference in the model between the dynamic analysis and static push over analysis is the existence of the lumped mass in the dynamic model.
Fig. 8 Mode 1: 8.94 Hz
Fig. 9 Mode 2: 40.43 Hz
Fig. 10 Mode 3: 43.20 Hz
RUN1-Top -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
6 8 10 12 14 16 18 20 22 24
Time (s ec)
A c c . (g )
Fig. 11 Top Acceleration Time History (Analysis Result)
EX P RUN1
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
6 8 10 12 14 16 18 20 22 24
Time (s ec)
A c c . (g )
Fig. 12 Top Acceleration Time History (Experiment Result)
This test was named ‘Run 1’ in Hyun et. al.(2005). As shown above, the difference in the result between the analysis and the experiment clearly exists. Because the elastic behavior can be well predicted relatively, the major difference comes from the plastic behavior of concrete model, which is the main target to be refined further.
CONCLUSION
Plasticity of concrete is different from that of metal. As expected, a result from all FE analysis can only estimate the real behavior approximately due to the intrinsic uncertainty in the FE model of concrete material. More refined and systematic approach is required to improve the performance of the concrete model.
REFERENCES
1. Hyun, C.H., Choi, S., Choi, K.R., Kim, M.S., Noh, M., Shin, H.M. and Park, J.H., IAEA Coordinated Research Program(CRP), Safety Significance of Near Field Earthquake/Assessment of Near Field Earthquake Effect, KINS, GR-317, 2005.
2. Kang, Un-Suk, “Analysis of concrete structures using plasticity theory,” MS thesis, Dankook University, Seoul, 2005. 3. Lubliner, J., Oliver, J., Oller, S., and Onate E., “A Plastic-Damage Model for Concrete,” Int. J. Solids Structures, Vol.
25, No. 3, pp.299-326, 1989