Chapter 15 - Theories of Elastic Failure

Abstract

When dealing with the design of structures or components the physical properties of the constituent materials are usually found from the results of laboratory experiments that are subjected to the materials of the simplest stress conditions. The most usual test is the simple tensile test in which the value of the stress at yield or at fracture, whichever occurs first, is easily determined. The strengths of materials under complex stress systems are not generally known except in a few particular cases. In practice, these complicated systems of stress are more often encountered, and therefore, it is necessary to have some basis for determining allowable working stresses so that failure will not occur. Thus, the function of the theories of elastic failure is to predict from the behavior of materials in a simple tensile test when elastic failure will occur under any condition of applied stress. This chapter primarily focuses on five theories: maximum principal stress theory (Rankine), maximum shear stress theory (Guest-Tresca), maximum principal strain (Saint-Venant), total strain energy per unit volume (Haigh), and shear strain energy per unit volume.