Optimum Properties for I-Shaped Beams

The bending strength and stiffness of both homogeneous and hybrid I-shaped beams vary with two geometric properties of the cross section: the web slenderness and the area ratio (ratio of web area to total area). Equations and charts defining the variation strength and stiffness with these two geometric properties are developed for beams with different combinations of flange and web steels. For both homogeneous and hybrid beams, the maximum bending strength and stiffness for a given cost are achieved by using the maximum permissible web slenderness (as limited by buckling or fabrication requirements) and an optimum area ratio is 1/2 for elastic strength and 2/3 for plastic strength. For hybrid beams, the optimum area ratios are higher, and increase as the web/flange yield-strength ratio decreases. For both homogeneous and hybrid beams, the optimum area ratio for stiffness is 3/4.