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 which
have only subjected the materials to 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 it is these complicated systems ofdetermining allowable working stresses so that failure will not occur. Thus the function of the
theories of elastic failure is to predict from the behaviour of materials in a simple tensile test
when elastic failure will occur under any condition of applied stress.

A number of theoretical criteria have been proposed each seeking to obtain adequate
correlation between estimated component life and that actually achieved under service load
conditions for both brittle and ductile material applications. The five main theories are:

(a) Maximum principal stress theory (Rankine).
(b) Maximum shear stress theory (Guest-Tresca).
(c) Maximum principal strain (Saint-Venant).
(d) Total strain energy per unit volume (Haigh).
(e) Shear strain energy per unit volume (Maxwell-Huber-von Mises)