A new strain energy theorem and its use in the optimum design of continuous beams

The subject of this paper is the design of a continuous beam for optimum support geometry. The design variables are a preselected set of simple support locations and the objective function is the strain energy of the beam. It is shown that the design for minimum strain energy is close to the design for minimax bending moment A theorem is presented stating that the strain energy is minimized with respect to the location of simple supports if the slopes of the elastic curve of the beam at the supports are zero. Based on the theorem an efficient iterative procedure for the minimization of the energy is presented. A simple computer program implements the technique for a large class of problems. This program is very economical compared to any of the standard minimization packages.