Reliability Analysis for Eccentrically Loaded Columns

ACI Structural Journal, Sep/Oct 2005 by Szerszen, Maria M, Szwed, Aleksander, Nowak, Andrzej S

FINDINGS

The reliability index is sensitive to the compressive strength of concrete and even more to the reinforcement ratio. In ACI 318-05,1 the strength reduction factor is presented as a function of the extreme steel tensile strain in the cross section. This relationship for rectangular columns is presented in Fig. 7. Based on the reliability analysis presented in this paper, two different models for strength reduction factors can be proposed for eccentrically loaded columns. Proposed values differ depending on the reinforcement ratio. Results of the presented analysis show that the length of transition zone is longer than that presented in the ACI 318-05 Code. In the ACI 318-05 Code, this length is limited by tension strains (0.002 ≤ ε^sub t^ ≤ 0.005) in the more tensioned reinforcement. The findings in this study show that this length limit is even higher. The length of the transition zone is also dependent on the reinforcement ratio. The transition zone limits can be expressed as a function of the extreme tensile strain in steel, or normalized eccentricity of the load. For consistency with the code, a resistance reduction factor is proposed as a function of the tensile strain in steel, as shown in Fig. 20. The proposed values of φ factor are based on the assumption of the target reliability index equal to 4.0.

CONCLUSIONS

The reliability-based calibration was performed for eccentrically loaded RC columns, using the new statistical data for compressive concrete strength and yield strength of reinforcing steel. The objective was to calculate resistance factors for the design of concrete structures corresponding to loads and load combination factors specified by the ASCE 7-02 Standard.4 Sensitivity analysis showed that reliability index depends on: failure mode (compression control failure, balanced failure, or tension control failure), compressive strength of concrete, and reinforcement ratio. Closed-form resistance equations were used in the reliability analysis. For each design case, with regard to constituent materials, cross section size, and reinforcement ratio, the balanced failure point and the end of transition zone were determined. This information was used to find the length of the transition zone, from the balanced failure point to the end point defined by the extreme tensile strain in steel.

As a result of the presented research, a new model for strength reduction factor is proposed, separately for the sections with reinforcement ratio ρ lower than 2%, and those with ρ equal to or greater than 2%. Transition zones are described using linear equations.

ACKNOWLEDGMENTS

The research reported in this paper (PCA R&D Serial No. 2811) was conducted by the authors with the sponsorship of the Portland Cement Association represented by B. Rabbat and D. Bilow (PCA Project Index No. 99-10) and the Precast/Prestressed Concrete Institute represented by P. Johal, which is gratefully acknowledged.

REFERENCES

1. ACI Committee 318, "Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05)," American Concrete Institute, Farmington Hills, Mich., 2005, 430 pp.