Material and shape selection for stiff beams under non-uniform flexure

A shape and material selection model has been previously introduced to characterize the structural efficiency of a slender beam under pure bending. The method is extended here and applied to the case of a beam undergoing non-uniform flexure. In the first part of this paper, the strain energy density is used to formulate the beam stiffness in terms of strain energies due to both transverse shear forces and bending moments. Shape transformers are defined to capture the shear deformation that shapes of alternative cross-section exhibit with respect to beam slenderness. In the second part, the expressions of the shape properties are plotted on selection charts that assist co-selecting the best material, shape and slenderness of a lightweight stiff beam under non-uniform bending. Numeric results from finite element analysis validate the model for concept design.