Topological Optimization of Beams in a Steel Floor

摘要

Optimization of floor girders is a complex nonlinear problem for which a simple computational procedure has been suggested. The Generalized Reduced Gradient (GRG). Nonlinear algorithm available in Excel Solver were utilized to optimize the design of plate girder for minimum weight and maximum allowable distance between secondary beams, given the span and grade of the material of the girder. Optimizing a girder for bending moment is achieved by moving material away from the neutral axis of the beam, in other words, by making the web more slender. When lateral supports are used to prevent from lateral torsional buckling, all the forms of the compressed flange instability will become the critical failure mechanism. Due to high slenderness values, the deflection of the beam is not a gouverning condition. In this paper, the maximum spacing between lateral supports against lateral-torsional buckling were maximized meanwhile respecting the provisions of the norm SR EN 1993-1-1. Results of the numerical computations considering various lengths of beams and girders are presented herein. Girders are considered to be efficiently designed with respect of the presented technique of optimization.