Least-Weight Frameworks for Loads Across Span

Least-weight (minimum volume) layouts for plane frameworks supporting bridge (beam) type loading are presented and some of the practical implications of these results considered. Discrete or continuous loads, or both, acting vertically between a pair of supports are considered for half-plane fully-fixed, half-plane simply-supported, and corresponding full-plane situations. Generally, pin-jointed frameworks are obtained, but where possible continuous solutions are found. The optimal layouts presented are all of the arch and hanger type (e.g., funicular arch) and are lighter than any previously reported structures for this common form of loading. The linear programming approach for finding the lightest framework on a grid of fixed-position joints, and a method of optimizing the volume of an elastic framework with variable joint positions developed by the writer, and reported briefly, are then employed to obtain possible Michell structures for the loading considered.