Strong and weak shapes

Abstract

When designs involve a high level of mechanical stress, the way in which the material is arranged is of immense importance. If a bar is intended to take only a tensile load, it can equally well be of round, square, or oblong section—all, provided they are of equivalent cross-sectional area, offer the same strength. If, however, the tension is replaced by compression, the shape of the cross-section is immediately of importance; a bar may buckle under compression, and the closer the material is to the centroid of the cross-section, the easier it is for this to happen. Buckling is a form of bending in which the decisive factor is the second moment of area (sometimes called ‘moment of inertia’) and, depending on the length of the bar and the load to be carried, there is a given value below which this quantity must not be allowed to fall. Since the buckling may occur in any of the planes, the second moment of area should ideally be the same for all cross-sectional axes. This condition is met by a round tube, as well as by a square box girder. The further outwards the cross-sectional area is located, the greater the saving in material (Fig. 127).