Analytical finite element meshes, maximum shear strengths, failure modes, load-deflection curves and cracking patterns are shown in Figs. 5.9, 5.10 and 5.11 from representative analytical results of beams, panels and shear walls, respectively.
S P M I M U S tor u t l r t i t
.' it hi A* ill a) Finite Element Idealization
-!*. Ar-
Experimental result Shioharas model Naganuma's model
Uchida.s model-1 Uchida's model-2
shear strength 730kN 684kN 655 kN 427kN 607kN
Failure mode Flexural yielding Flexural compression failure
Shear compression failure Shear compression failure(edge) b)Comparisons of Analytical Results with Test Results of Beam PB4
B 00 700
100
c) Load-Displacement Relationships
E x x r i M n U l r e s u l t - S h j o h a r a ' s oodcl
- K a i a n u u ' t Bodel Uchida's sodel -1 Uchida's oodcl-2 10.0 IS.O Displacement (mm)
P3-U
d) Crack Pattern (PB-4 at Maximum Strength)
Fig. 5.9. Finite element idealization and analytical results of New RC beam, P B 4 tested by F. Watanabe.
5.4.3.1. Analysis of Beam Test Specimens
In the analysis of four specimens in the beam test, PB series, and six specimens in the beam test, B series using high strength concrete in the New RC project, the analytical stiffness corresponds to the test results as shown by an example in Fig. 5.9. The analytical strength is generally lower than the test results.
Higher values of tested strength are attributed to the details of specimens, e.g. the spacing of shear reinforcement is 50 mm and relatively dense with high confinement on the core concrete. High confinement on the core concrete is also given by heavy longitudinal reinforcement. The analytical reduction factor of the compressive strength of cracked concrete is based on the previous panel test, but the strength does not seem to decrease in beams or columns with a relatively large width as compared to the thin panels. As for the shear transfer mechanism through a crack plane, the Al-Mahaidi equation based on the deep beam test is often used. But it is considered that the contribution of the dowel action of reinforcement is relatively large in the case of these specimens with large amount of longitudinal reinforcement and shear reinforcement. The shear transfer characteristics denned by a function of crack width or strain normal to the crack direction like the Al-Mahaidi equation may underestimate the strength.
5.4.3.2. Analysis of Panel Specimens
Eleven panel specimens with high strength concrete were analyzed. Analytical results were compared with each other as well as with experimental results in terms of shear stress-shear strain curves. Figure 5.10 shows an example of comparison of a test with analyses by Noguchi, Shirai, Naganuma, Sumi and Takagi. There is not a large difference in general, though there is some differ- ence between the models in the behavior right after the initial cracking. There is scattering in the maximum shear strength by each analysis, and the strength was evaluated generally high.
In the case of failure mode where yielding of reinforcement takes place prior to compressive failure of concrete, the effect of modeling of stress-strain curve of reinforcement appears quite clearly in the analytical results. This is particularly true in case of a simple stress condition like a panel. Therefore, when the stress-strain curve of high strength reinforcement is different from the ordinary strength steel, a model considering the steel test result is preferred over simple models such as a bilinear model.
A panel is idealized as a single eleacnt.
a) Finite Element Idealization
b)Comparisons ol Analytical Results with Test Results of Panel 8-8-8
Experimental result Noguchi's model
Shirai's model-1 Shirai's model-2 Shirai's model-3 Shirai's model-4 Shirai's model 5 Naganuma's model-1
Sumi's modet-1 Sumi's model-2 Takagi's model
Shear strength 9.62MPa 9.37MPa 10.2MPa I0.2MPa 10.2MPa 11.2MPa 10.2MPa 11.0MPa 10.4MPa 10.4MPa 9.02MPa
Failure mode Cut off reinforcement Cut off reinforcement
Yielding of reinforcement Cut off reinforcement Cut off reinforcement
CO
I— cfl CD - C W
1.0 2.0 Shear Strain (%) c) Shear Stress-Shear Strain
Fig. 5.10. Finite element idealization and analytical results of New RC panel by K. Sumi of Hazama Corporation.
8-8-8 tested
In the case of failure mode where concrete compressive failure occurs before steel yielding, there is a scatter among analyses using different evaluation of compressive reduction factor. From the comparison between the analytical and test results of specimens with concrete strength of 100 MPa and 70 MPa, the analytical results using the modified equation of Stevens (Ref. 5.16) con- sidering concrete strength, shown as Shirai's model-1 in Fig. 5.10, gave a better agreement with the test results than the analysis using the original equation of Stevens where the compressive reduction factor was given only as the function of tensile principal strain.
In the case of specimens with different reinforcement ratios between longitudinal and lateral re-bars, there is difference in the analytical results using different modeling of the shear transfer characteristics of crack planes.
In the Stevens model, the maximum shear strength was overestimated, and there is high possibility that the shear transfer effects of the crack planes were overestimated in his model.
5.4.3.3. Analysis of Shear Walls
Two specimens were analyzed for ordinary strength concrete and fourteen specimens were analyzed for high strength concrete. In the NW series includ- ing both ordinary strength concrete and high strength concrete, the maxi- mum shear strength was grasped well by each analysis as shown in Fig. 5.11.
Although the stiffness tended to be higher, the load-displacement curves were well simulated up to the ultimate stage. The analytical initial stiffness of the specimens Nos. 1 to 8 gave a good agreement with the test results, but the stiffness after cracking and the maximum strength were overestimated as com- pared with the test results. The pattern of the load-deflection curves could simulate the test results. Considering that the experimental failure mode was flexural compressive failure, it is inferred that the input value of the concrete compressive strength was too high.
5.4.3.4. Conclusions
RC structural members using high strength material were analyzed by FEM, and the comparison and verification of the material constitutive law were
carried out. The comparison between the test results and analytical results
revealed that few analytical cases gave a perfect agreement of stiffness and maximum strength. There is also a scatter among analytical results due to
( M i l i u m
.7S i : — i - < >
r A\-VT
~7\7
a) Shirai's model d) Crack Pattern (NW-1 at Maximum Strength) b)Comparisons of Analytical Results with Test Results of Shear Wall NW-1
Experimental results Noguchi's model
Shirai's model-3 Naganuma's model-1
Takagi's model
Shear strength 1063KN 1113KN 1013KN 1016KN 999KN
Failure mode Flexural failure
Flexural yielding failure
.
Compressive failure at the bottom of compression columns after flexural yielding
Compressive failure at shear wall after column flexural yealding 1500
500
Experimental result Noguchi' 5 sodel
— Shirai's model-3 Naganuaa' s Bodel-I Tafcagi" s node]
0.0 20.0 40.0 60.0
WSPLACEMEMT (mm)
c) Load-Displacement Relationships
Fig. 5.11. Finite element idealization a n d analytical results of New R C shear wall, N W - 1 tested by T . Kabeyasawa.
the different material constitutive laws, and no material constitutive laws were found to be definitely applicable. But there are some analyses that gave good agreement with the test results for the load-deflection curves and the maximum strength. Therefore, it is expected that a more reliable simulation of RC members using high strength materials can be achieved by the accumulation of research on the material constitutive laws.