Optimization of light-gage cold-formed steel shapes by parametric bandwidth constriction

Abstract

Optimization of structural shapes governed by the American Iron and Steel Institute Specification for the Design of Cold-Formed Steel Structural Members presents particular problems. Not only must a variety of buckling formulas be considered for flexural-torsional buckling of the shape as a whole as well as for buckling of the separate plate elements of the cross-section, but also the section properties used to evaluate buckling stress constraints are themselves stress dependent. A simplicial technique is detailed for forcing convergence to competitive designs in spite of the iterative computational oscillations caused by the nonlinear complexity and discontinuities that are present in the mathematical programming problem which must be solved. The set of constraints includes all applicable and unmodified design formulas appearing in the AISI specification. The technique is a two-phase process which gradually constricts the range limits of the design parameters as observed over a set number of iterations and adaptively relieves cyclic infeasibilities caused by the constriction. Convergence is also aided by the use of a character string manipulation language to generate machine readable expressions for the exact differentials of all nonlinear functions. The behavior of the convergence forcing technique is demonstrated for a lipped Z shape in flexure and for a two-channel lipped wide flange beam column.