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sample-prob-exam1 - 1 The principal stresses at a point are...

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1. The principal stresses at a point are 1 2 3 10 , 2 , 12 MPa MPa MPa σ σ σ = = = − . Without calculating their principal stresses, indicate which of the following stress tensors are NOT consistent with these principal stresses. [ ] [ ] [ ] [ ] 10 0 0 10 0 0 ( ) : 0 5 7 ( ) : 0 7 5 0 7 5 0 5 7 12 0 0 10 0 12 ( ) : 0 6 46 ( ) : 0 5 7 12 7 5 0 46 6 a b c d σ σ σ σ = = = = 2. The principal stresses at a point are 1 2 3 10 , 5 , 5 MPa MPa MPa σ σ σ = = = . The yield stress is 10MPa. Compare the safety factor using the Tresca, Von Mises, and Rankine criteria. It would help to change the principal stresses some for some of these criteria. 3. Why are there multiple stress tensors, and which one are we using in this course? 4. When do we have more than three principal directions (+ and – do not count)? 5. In the equations of equilibrium, why is it reasonable that we have derivatives of stresses but not of body forces?
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