Failure of an axially compressed beam with uncertain initial deflection of bounded strain energy (Q1261673)

Energy-bound convex models are used to represent uncertainty in the initial deformation of a uniform beam. The main result is to relate these convex models of uncertainty to the maximum bending moment failure criterion for the axially loaded beam. Analytical relations are obtained which determine the maximum allowable, critical, initial deformation energy as a function of the applied load. This theoretical critical load is compared against and seems consistent with allowed engineering data.