Abstract
The purpose of this paper is to present a theory and procedure for the optimization of unstiffened hybrid and homogeneous I-beams considering shear and moment at the same time. Using a correction factor in the web contribution to the section modulus, a simple unreduced flange stress can be used without iterating with respect to the ratio of web area versus flange area. The end result consists of a uniform I-beam, with all the dimensions uniquely determined, fully stressed in bending and shear, also achieving minimum cost in materials. Applications of the theory are presented and several examples showing the savings are included.

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