Abstract: In this paper, a total criterion on elastic and fatigue failure in complex stress, that is. octahedral stress strength theory on dynamic and static states on the basis of studying modern and classic strength theories. At the same time, an analysis of an independent and fairly comprehensive theoretical system is set up. It gives generalized failure factor by 36 materials and computative theory of the 11 states of complex stresses on a point, and derives the operator equation on generalized allowable strength and a computative method for a total equation can be applied to dynamic and static states. It is illustrated that the method has a good exactness through computation of eight examples of engineering. Therefore, the author suggests applying it to engineering widely.

Key words: the strength theory on octahedral stresses, the generalized failure factor of materials, tension-compression ratio, yield-strength ratio, the factor of engineering design, the operator [σ_τ] for generalized allowable strength of materials