Optimum Hole Shapes in Beams under Pure Bending

An effective method of weight reduction for a beam in pure bending is to remove material near the neutral axis, often in the form of holes. Minimizing the stress concentration around these holes is an important consideration in engineering design. One of the methods to minimize the stress concentration is to change the hole shape itself until the optimized shape with minimum stress concentration factor (s.c.f.) is reached within specified geometric constraints and loading condition. In the present note, using conformal transformation technique, centrally located quasi‐square holes in isotropic beams under pure bending are analyzed. It is well‐known that for circular hole with $d/W⩽0.45$ there will be no stress concentration and hence the hole does not weaken the beams. The present study shows that with the optimized quasi‐square hole shapes, holes as large as $d/W=0.6$ can be introduced without producing any stress concentration.