Elastic Versus Plastic Optimal Strength Design

The aim of this note is to extend the Prager-Shield cost-gradient method from optimal plastic design to optimal elastic permissible stress design. It is shown in the context of beams having a constrained depth that, in general, optimal elastic strength designs are not.fully stressed. if hinges are not permitted. However, the minimum cost solution may be obtained if: for fully stressed segments, the usual Prager-Shield cost-gradient condition is used; and for understressed segments, a criterion proposed originally in the context of elastic beams with a deflection constraint, by Barnett and Shield and Prager is used. This foregoing results appear logical if it is realized that kinematic boundary conditions can be expressed as deflection constraints, and optimal elastic structures without hinges must use their understressed segments for rectifying the kinematic inadmissibility of the fully stressed design.