Stochastic finite element method for the reliability analysis of nonlinear frames with PR connections.

Abstract

A nonlinear stochastic finite element-based procedure is developed for reliability analyses of structures. The procedure is based on the First Order Reliability Method. The failure criteria of structures are expressed in terms of the ultimate and serviceability state functions. The adjoint variable method is used to formulate the computation of the gradient vector. The assumed stress-based finite element method is used to compute nonlinear structural responses and the corresponding response gradients for steel frames. Nonlinearities due to geometry, material and partially restrained connections are considered in the procedure. A computational model based on the Richard model is developed to address the uncertain properties of partially restrained connections. The material properties, geometric properties, connections parameters and external loads are considered as random variables. Several observations with design implications are made from numerical examples. Frames designed considering strength may not be acceptable when serviceability is considered. The presence of partially restrained connections changes the stress distribution in frames and makes frames more flexible so that serviceability could become the governing limit state. It is essential to properly consider the presence of partially restrained connections in the analysis and design of frames. The proposed method can be used as an alternative to the currently available methods to design a structure and evaluate the corresponding reliability. As an extended study, an efficient finite element-based procedure is also developed for estimating nonlinear responses of complex two or three dimensional steel frames with partially restrained connections under dynamic and seismic excitations. The hysteretic behavior of partially restrained connections are modeled by using the Masing rule combined with the Richard model to describe the loading, unloading and reverse loading paths for connections. Numerical examples show that this procedure is accurate and efficient compared with other existing nonlinear methods.