Design Optimization of Single Span Fixed-Feet Portal Frame Using Generalised Reduced Gradient Method

Abstract

The design of single span fixed-feet portal frames was optimized using MSExcel solver, a multi-disciplinary optimizing ad-in in MSExcel spreadsheet formulated using Generalised Reduced Gradient (GRG2) method of optimization. Portal frames of different geometries with two sets of different loading arrangements were designed using structural design software - PROKON (version W2.0.11) and the resulting design sections were mass-optimized based on the area of member cross section, using Excel solver. In the optimization exercise, the objective function (area of cross section) was minimized subject to the satisfaction of the constraints in accordance with the relevant British Standard. After the optimization process, the portal frame structural members (two vertical members and one horizontal member) for the first set of loading were 21.86%, 19.65% and 27.22% lighter than their initial sections thereby giving an average of 22.91% lighter section, and the second set of loading results show that the optimized sections were 30.31%, 31.27% and 30.29% lighter than their initial sections giving an average of 30.62% lighter section.

Keywords: optimization, excel solver, generalised reduced gradient, portal frame.