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A structural member under loading has a uniform state of plane stress which in usual notations is given by σx = 3P, σy = −2P and τxy = √2 P, where P > 0. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of P at which yielding starts (according to the maximum distortion energy theory) is

1. 70 MPa
2. 90 MPa
3. 120 MPa
4. 75 MPa

Correct answer: 70 MPa

Solution

sigma_vm^2 = (3P)^2 - (3P)(-2P) + (-2P)^2 + 3(sqrt2 P)^2 = 9+6+4+6 = 25P^2, so sigma_vm = 5P. Setting 5P = 350 gives P = 70 MPa, not the stored 75 MPa.

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