SFEM-based reliability analysis of frames with uncertain support and connection conditions

Abstract

Modeling of rigidity of support and connection conditions in a structure and the uncertainties associated with the modeling are comprehensively addressed in this paper. The actual rigidity of supports and connections is generally unknown. In most cases, the idealized support conditions, i.e., pinned or rigid, do not represent in-place conditions. Furthermore, the parameters necessary to model the partial rigidity are highly uncertain, even when they are formulated to represent real conditions, e.g., using the concept of partial rigidity. A Stochastic Finite Element-based algorithm is proposed to address these problems. Issues related to the reliability evaluation of nonlinear steel structures are particularly addressed. The assumed stress-based finite element formulation is used to represent the structure. The four-parameter Richard model is used to formulate the partial rigidity of support and connection conditions. The First Order Reliability Method (FORM) is used to estimate the corresponding reliability. Both the strength and the serviceability failure criteria are used for reliability analysis. The algorithm is explained with the help of an example. If the uncertainties in the support and connection conditions are considered properly, both in terms of rigidity and the uncertainty in the parameters associated with the formulation of the rigidity, the serviceability criterion, instead of the strength criterion, may become the controlling limit state, and the frame may need to be redesigned. The uncertainty in modeling the supports and connections cannot be overlooked.