An equivalent linear method for structural system reliability with nonlinear safety margins

In Ref. [1 (Comput. Struct.42, 255-262, 1992)], the authors presented the numerical integration method in M space for computing structural system reliability with linear safety margins of the structural system failure modes. It has two advantages over the integration method in the space constructed by the basic variables of the structural system in that: (1) the integral domain is very simple and the integral grid can easily be generated; (2) the computer run time is short. In this paper, an equivalent linear method of the nonlinear safety margins is presented and the integration method in M space is employed in solving the equivalent linear system. Furthermore, for decreasing the computer run time or increasing the computational accuracy, the Gaussian numerical integration method is used for computing the two- and three-order joint failure probabilities of structural failure modes. Several examples illustrate the effectiveness of the method.