Uniform strength for large deflections of cantilever beams under end point load

Abstract

Analysis is conducted for slender beams with a varying cross-section under large non-linear elastic deformation. A thickness variation function is derived to achieve optimal - constant maximum bending stress distribution along the beam for inclined end load of arbitrary direction. Closed form solutions are derived for the large deflections that correspond to the various loading conditions. The analysis is repeated for a beam with optimally varying width (for arbitrary end force) and the width variation function is also determined.