Effect of shape on loading and stresses

Abstract

Having said in the previous chapter that the strength flow occasionally changes its nature along its path, we must add that the force intensity involved may also vary considerably. The longitudinal tensions in the upright columns of a press frame (Fig. 158) give rise to compressive and tensile stresses in the yoke at the top which may be many times that of the tensile stress in the columns. Anyone dealing regularly with strength of materials problems will be well aware of these relationships, and even in extreme cases they should not come as a surprise. It is important here, however, to note that this increase and decrease in the density of the lines of force is very largely dependent upon the shape of the parts in question, and that the designer himself is in a position to decide how large the variations in strength flow are going to be. Let us compare three ways of transmitting forces, seen in Fig. 159: a straight bar as at I, a kind of chain link II, and a crescent-shaped beam III. All of them carry the same maximum stress, so that the extravagant use of materials in III is striking; it can only be due to an increase in the strength flow in the curved beam.