Static and dynamic reliability analysis of frame and shear wall structural systems

Abstract

Effective and accurate algorithms are developed to evaluate the reliability of frame and shear wall structural system subjected to both static and dynamic loadings. The basic deterministic finite element algorithm is based on the assumed stress-based finite element method in which the tangent stiffness can be expressed in explicit form and fewer elements are required to realistically capture the structural behavior. These features are desirable for developing an efficient reliability analysis algorithm for both static and dynamic cases. The presence of shear walls is represented by plate elements. The stiffness matrix for the combined system is then developed. To verify the accuracy of the deterministic algorithm, a 2-bay 2-story building consisting of five similar frames is considered. Only one frame is assumed to have shear walls. The responses of the frame with shear walls subjected to static and dynamic loadings are evaluated. The responses of the same structural system are also evaluated using a commercially available computer program. The results match very well, implying that the deterministic algorithm developed in this study is accurate. The deterministic algorithm is then extended to consider the uncertainty in the random variables. For the static case, a stochastic finite element-based approach consisting of the reliability approach, the first-order reliability analysis procedure and the finite element method is proposed. For the dynamic case, a hybrid approach consisting of the response surface method, the finite element method, the first-order reliability method and the linear iterative scheme is used. The unique feature of this algorithm is that the earthquake loading can be applied in the time domain. The material and cross-sectional properties, the damping and the magnification factors of earthquake time histories are considered to be random variables in this study. The reliability of a frame without and with shear walls is evaluated for the strength and serviceability performance functions. The results are verified using the Monte Carlo simulation technique.