Reliability of Geometrically Nonlinear PR Frames

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Abstract
An efficient stochastic finite element method is proposed for the reliability analysis of nonlinear frame structures using the first-order second-moment reliability method. The assumed stress-field approach is used in computing nonlinear structural responses and the corresponding response gradients. Both geometric and material nonlinearities of structures are considered. The flexibility of a connection is represented by its moment-relative rotation relationship. Emphasis is placed on the comparison of the reliability indexes of linear structures, nonlinear structures, and nonlinear structures with flexible connections. Both the strength (combined axial compression and bending) and serviceability (deflection) limit states are considered. For stability-related structures, nonlinearity has a considerable influence on the structural reliability, and the reliability will be very different when the flexible connections are taken into consideration. The method is verified using the Monte Carlo simulation technique. The applicability, accuracy, efficiency, and robustness of the method are verified with the help of an example.