Optimal Designs of I‐Beams against Lateral Buckling

Abstract

This paper concerns the optimal distribution of a given volume of material in I‐beams so as to maximize the elastic flexural‐torsional buckling capacities. The material distribution has been restricted to different top‐to‐bottom flange‐width ratios, linear tapering of flange width, or linear tapering of web depth. Based on the Rayleigh‐Timoshenko energy method, a canonical form of the Ray‐leigh quotient is derived for the three types of design considered. For the maximum buckling capacity, the quotient is first minimized with respect to the displacement function and then maximized with respect to the design parameter. To avoid inelastic behavior and a small cross‐sectional area in the optimal beam designs, a maximum permissible normal‐stress constraint is imposed. Optimal designs of simply supported I‐beams under general moment gradient are presented. A comparison study is made to determine which of the three design types is the most effective way of distributing material for maximum buckling capacities.