Statistical Evaluation of Response Modification Factors for Reinforced Concrete Structures

Keywords: Reinforced Concrete Structures, Soil Structure Interaction, Multivariate Nonlinear Regression Analysis, Response Modification Factor (R), Earthquake Resistant Design, Seismic Design Criteria, Building Codes, Frames, and Shear Walls.

Abstract: This report presents a statistical evaluation of the response modification factor for reinforced concrete structures. The response modification factor R is defined as the ratio of the absolute maximum linear elastic base shear to the absolute maximum nonlinear base shear of a structure subject to the same earthquake accelerogram. Twelve structural models with various dynamic characteristics are first constructed. Next, 90 synthetic earthquakes are generated from three power spectra representing different soil conditions. Then, the nonlinear and corresponding linear time history analyses are performed to produce structural response data. On the basis of these data, an empirical formula for the response modification factor is established from a multivariate nonlinear regression analysis. The empirical formula describing the mean value of R factor is a function of the maximum ductility ratio, the viscous damping ratio and the earthquake-structure period ratio. In addition, variation of R factor in terms of the maximum ductility ratio is also established from the multivariate nonlinear regression analysis. The empirical formula is demonstrated using two structures. In addition, comparison of the proposed formula with Newmark's formulas is also made. From the empirical formula, the response modification factors recommended for the design of reinforced concrete structures are also presented. The authors believe that most of the R factors specified in the current NEHRP provisions are too large and unconservative. Thus, the specification of more reasonable R factors in the seismic design provisions is warranted.