Optimum Choice of Determinate Methods Under Multiple Loads

An algorithm for choosing the least-weight statically determined configuration of a given truss under two loading conditions is presented. The procedure is based on modifying the optimal truss, under the same conditions. This latter truss is, in general, indeterminate statically and can be easily obtained, using a decomposition method briefly reviewed in the paper. At every cycle of the procedure one bar (or more) is eliminated, thus yielding an optimal truss with a lower degree of indeterminacy, until the final solution is reached. The relationship between this method and an interactive fully-stressed design procedure is examined, and an example is given. The topology of the problem is covered in an appendix. Extension to more than two loading conditions is suggested. Besides the merits of statically determinate trusses in certain structures and conditions, the least-weight truss and least-weight determinate truss provide useful bounds on the truss weight and can be used as criteria for efficient design.