FAILURE OF AN AXIALLY COMPRESSED BEAM WITH UNCERTAIN INITIAL DEFLECTION OF BOUNDED STRAIN-ENERGY

Energy-bound convex models are used to represent uncertainty in the in itial deformation of a uniform beam. The main result is to relate thes e convex models of uncertainty to the maximum bending moment failure c riterion for the axially loaded beam. While the maximum-moment concept is a local failure criterion, it is governed by global energetic cons iderations. The initial deformation energy specifies the degree of unc ertainty in the initial beam shape, as well as the greatest bending mo ment which can be attained in the loaded beam. Analytical relations ar e obtained which determine the maximum allowable, critical, initial de formation energy as a function of the applied load. This theoretical c ritical load is compared against and seems consistent with allowed eng ineering data. Considerable simplification is attained by exploiting a single physical parameter-the deformation energy-for specifying both the shape uncertainty and the failure criterion. The ability of the in itial deformation energy to serve as a failure criterion, equivalent t o the maximum bending moment criterion, is given a physical interpreta tion.