Abstract
Abstract Beams with uniform strength subjected only to bending have the same maximum flexural stress at any cross section. The shapes, deflections, and weights are given for cantilever, simple, and fixed beams of uniform strength and appreciable weight subjected to uniformly distributed loadings. Explicit solutions are given for beams having rectangular cross sections and constant height. Solutions in integral form are provided for rectangular beams of constant width. This method is also applicable to beams with constant ratio of height to width, as well as beams with circular cross sections. Examples illustrate the large material savings over uniform cross-section beams which may be achieved.
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