An algorithm for grouping members in a structure

An automated method for grouping discrete structural members is presented in this paper. The number of groups is specified by the user, and members are grouped according to their mass per unit length. The method first optimizes a structure assuming that every member can have a different section. This is done using the Virtual Work Optimization (VWO) method, but any method can be used. The initial solution is the lightest possible, but the number of sections required makes it impractical and uneconomical to construct. Next, an exhaustive search of all possible grouping permutations is carried out. The mass of the structure is predicted for each permutation. The permutation which results in the lightest structure is selected. The structure is passed through the optimization process one last time. The solution produced satisfies all strength and deflection criteria. A method for reducing computational cost is proposed to address very large structures. Four case studies are presented to demonstrate the effectiveness of the grouping algorithm. A stepped cantilever, a 15 storey frame, a truss and a warehouse are investigated. As an example of results, the 195 members of the 15 storey frame are placed into 25 groups to produce a structure only 2.4% heavier than the ungrouped solution. The configuration computed is 5.9% lighter than grouping the structure using the method found in the literature.