Consider the following states of biaxial stress: (1) s1 = 30, s2 = 0, (2) s1 = 30,s2 =

Chapter 6, Problem 6.22

(choose chapter or problem)

Consider the following states of biaxial stress: (1) \(\sigma_1 = 30, \sigma_2 = 0\), (2) \(\sigma_1 = 30, \sigma_2 = -15\), (3) \(\sigma_1 = 30, \sigma_2 = -30\), (4) \(\sigma_1 = 30, \sigma_2 = 15\), (5) pure shear, \(\tau = 30\). With the aid of a s1–s2 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 \(S_y = 80 \ \mathrm{psi}\) for the plot and calculate safety factors for each failure theory and stress state.