Now that the principal stresses are known in terms of the load P, the failure criteria can be applied. For the maximum distortion energy criteria, the following relationship must be meet,
Substituting the principal stresses and yield stress (do not forget the factor of safety), gives
(174.88P)^{2} + (30.00P)^{2}
 (174.88P)(30.00P) = (36,000/2)^{2}
Solving for P, gives
P = 93.91 lb
The final principal stresses are
σ_{1} = 174.88 P = 16.42 ksi
σ_{2} = 30.00 P = 2.82 ksi
These principal normal stresses can be normalized with the design stress, 18 ksi, to give
σ_{1}/σ_{design} = 16.42/18 = 0.9122
σ_{2}/σ_{design} = 2.82/18 = 0.1567
This point are plotted on the failure envelop diagram at the left.
