The criteria of failure under combined stresses

Abstract

If a ductile prismatic bar is directly loaded a load-extension curve similar to that shown in figure I is obtained. A twisted prismatic bar of the same material yields a torque-angle curve of the same type. A specially simple relation between these two curves exist, namely E=2C(I=m). However, the relation between a curve obtained from a similar material subjected to a complex loading system to any of the above curves may be very complicated. Attempts to extract simple generalisations from the very complex phenomena have been made by both engineers and mathematicians. The engineer have used specimens of specially simple from which they have subjected to external forces or distortions and they have found the effect on their test of varying physical conditions. The mathematicians have assumed and ideal material and have given it properties which may or may not be possessed by some real material. They have then analysed the theoretical distributions of stress and strain when this ideal material is subjected to given boundary conditions [...].