Consider the following states of biaxial stress: (1) .-30, 2=0, (2) .-30, 2=-15, (3) : 30, 2

Consider the following states of biaxial stress: (1) σ.-30, σ2=0, (2) σ.-30, σ2=-15, (3) ơ": 30, ơ2 -30, (4) ơi 30, ơ2-15, (5) pure shear,--30. with the aid of a ơi-c2 plot, list these stress states in order of increasing likelihood of causing failure according to (a) the maximum-normal-stress theory, (b) the maximum-shear-stress theory, and (c) the maximum-distortion-energy theory. Assume an arbitrary value of Sy=80 psi for the plot and calculate safety factors for each failure theory and stress state.