大尺寸钢筋混凝土无腹筋梁的有限元分析

Abstract： The behaviors of reinforced concrete beams such as cracking shear strength and the ultimate shear strength， crack propagation and load deflection response were examined. And the size effect phenomenon of the specimens was observed. The study used the finite element analysis program VecTor2 for numerical analysis of the models. The results are viewed to compare with experimental data.

Key Words：Size effect；Reinforced Concrete Beams；Finite element Analysis；Stirrup；crack propagation

1.Finite Element Modeling

The model used for depicting the behavior of crack in concrete in VecTor2 is the DSFM/MCFT model. Modified compression field theory is used for predicting load-deformation response in reinforced concrete when subjected to normal stresses and shear. The equilibrium relationship stresses are related with compatibility relationship strains by constitutive models， for concrete in compression principal compressive stress fc2 and the principal compressive strain εc2 are related by the constitutive relationship.

Here the Hongenstad parabolic relationship is used as the numerator and the value of ε0 is the concrete cylinder strain related to the peak compressive stress， fc’.

2.Modeling of the Specimen

According to the objectives of the thesis the cross-sectional height， longitudinal reinforcement ratio and stirrup configuration were taken into account when designing the specimens. Seven series of shear-critical reinforced concrete beams were modeled， namely， B5N， B6N， B8N， B10N， B12N， B6L and B10L， similar to the experiments done by Yu Lei. The beams differ in height from 500mm to 1200mm.

The B6L and the B10L beams have less reinforcement ratio than the BN series. Load is applied to the beam at the mid point of the beams.

3.Finite Element Analysis Results Discussion

3.1Comparison of Cracking Shear Strength and Ultimate Shear Strength

3.1.1 Effect of Depth

From the Fig. ?3.1， the change in vcr due to the change in height can be seen. The value of the cracking shear strength is continuously decreasing with the increase of the cross-sectional height. From the graphs we can see that the value of ultimate shear strength for the beam B5N is 1.7 times higher than the value of B12N.

The results for the cracking shear strength and ultimate shear strength from the finite element analysis are given in Fig. ?3.1.

From the ratio of average of the cracking shear strength and the ultimate shear strength vu/vcr， we can deduct that the value for the BN series is higher than the value for BL. For the BN series the average value for vcr is 0.82 where as for BN series it is 0.59， the value of vu for the BN series is 1.22 and for 0.88 this shows there is a significant decrease in strength as the longitudinal reinforcement ratio decreases.

3.1.2 Effect of Longitudinal Reinforcement

The Fig. ?3.1 shows the effect of longitudinal reinforcement on the values of cracking shear strength and ultimate shear strength for the analysis results. When comparing the results， it is easily visible that the value of both cracking shear strength and ultimate shear strength the BN series is considerably higher than the value for the BL series. The reinforcement ratio for the BN series is higher than the values for the BL series of specimens. When we compare the values of B10L and B10N the value of B10L is 80% for the ultimate shear strength and 78% for the cracking shear strength.

3.2 Comparison of Load-Deflection Curves

For the purpose of comparing the experimental results Fig. ?4.3 is plotted from data from the paper from Yu Lei’s doctoral dissertation compared with the data from the FEA.

For specimens B5N， B6N and B8N values of mid-span deflection from FEM analysis and experiments do not show a big difference. When compared with FEA results there is a visible difference where B10N curve in FEA results shows its deflection took a larger loading than experimental results. The results in the experiment show for specimen B10N deflection curve has lower force applied than the rest of the specimen.

4.Conclusion

The amount of longitudinal reinforcement from the FEM analysis showed that there is a large difference in load bearing capacity of beams with similar depth. For the case of 600mm specimen namely B6N and B6L， the analysis results show that there is a 31% decrease in the ultimate shear strength of the beams. And for the case of 1m specimens， B10N and B10L there is a decrease of 20% in cracking shear strength. The difference in the results from the analysis and experimental program suggest that there is still much to be improved in the finite element analysis program

References

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2.M. P. Collins D. Kuchma. How Safe Are Our Large， Lightly Reinforced Concrete Beams， Slabs， and Footings？ [J] Structural Journal. 1999.

3.Z. P. Bazant， S. Sener， and J.-K. Kim. Effect of cracking on drying permeability and diffusivity of concrete [J].ACI Materials Journal.1987.