Shape sensitivities in the reliability analysis of nonlinear frame structures

A unified and comprehensive treatment of shape sensitivity that includes variations in the nodal coordinates, member cross-section properties, and global shape parameters of inelastic frame structures is presented. A novelty is the consideration of geometric uncertainty in both the displacement- and force-based finite element formulations of nonlinear beam-column behavior. The shape sensitivity equations enable a comprehensive investigation of the relative influence of uncertain geometrical imperfections on structural reliability assessments. For this purpose, finite element reliability analyses are employed with sophisticated structural models, from which importance measures are available. The unified approach presented herein is based on the direct differentiation method and includes variations in the equilibrium and compatibility relationships of frame finite elements, as well as the member cross-section geometry, in order to obtain complete shape sensitivity equations. The analytical shape sensitivity equations are implemented in the OpenSees software framework. Numerical examples involving a steel structure and a reinforced concrete structure confirm that geometrical imperfections may have a significant impact on structural reliability assessments.