Least‐Weight Design of Steel Frameworks Accounting for P‐Δ Effects

Abstract

The paper addresses the problem of efficiently sizing steel frameworks to account for nonlinear load‐displacement (P‐Δ) effects. The design objective is to produce a minimum weight structure while simultaneously ensuring acceptable levels of combined first‐order and second‐order displacements and stresses in accordance with the governing steel design code. Conventional fabrication conditions are imposed and members are sized using commercially available standard sections. The design method involves coordinated use of second‐order elastic analysis, sensitivity analysis and optimization techniques within an iterative synthesis process. For a given trial design of the structure, second‐order elastic analysis and first‐order sensitivity analysis are together employed to approximate the performance constraints on displacements and stresses as explicit linear functions of the member‐sizing variables. Optimization techniques are then applied to find an improved (lower weight) design for the structure, which satisfies all performance constraints. The formulation of the design problem is updated for the new design and the synthesis process is repeated until convergence to the least‐weight structure occurs. The synthesis process is implemented in a comprehensive computer system developed for the least‐weight design of steel frameworks. The designs of two building frames are considered from a variety of viewpoints to illustrate both the features of the design method and some underlying issues related to second‐order design.