Under plane stress (\sigma_3 = 0) with principal stresses \sigma_1 > 0 and \sigma_2 < 0, the Tresca maximum shear stress yield condition is given by:

(A) \sigma_1 - \sigma_2 = \sigma_y

(B) \sigma_1 = \sigma_y

(C) \sigma_2 = -\sigma_y

(D) \sigma_1 + \sigma_2 = \sigma_y

Answer Key:

A

### Solution: When \sigma_1 > 0 and \sigma_2 < 0, the three principal stresses are \sigma_1, 0, \sigma_2. The maximum shear stress is au_{max} = (\sigma_1 - \sigma_2)/2. Yielding occurs when au_{max} = \sigma_y / 2 ==> \sigma_1 - \sigma_2 = \sigma_y. Correct: A.

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