Sensitivity Analysis of Thin‐Walled I‐Beams Resting on Elastic Foundation

Abstract

Thin‐walled I‐beams resting on a Winkler‐type elastic foundation and subjected to axial and torsional loadings are considered. The first‐order variations of an arbitrary internal force, a reaction, or a displacment due to a variation of the design variables are derived using the adjoint method. The cross‐section dimensions, except for the web height, the beam material constants, and the foundation torsional stiffness, are assumed to be the design variables. The coefficients of the design variable variations determining the sensitivity of the bimoment and the angle of the cross‐section rotation at the midspan of a simply supported beam are presented. An accuracy of the approximation by using the first‐order variations is also discussed.