1. MEF2 Homework 1 Problem 3.- The state of stress at a point in a structural component is specified by the components (all in MPa) Sigma[x] = -5, Sigma[y] = Sigma[z] = 1, Tau[xy] = -1 and Sigma[yz] = Sigma[zx] = 0. Determine the principal stresses, the principal stress deviations and the greatest shearing stress.

2. Formulation MPa  

3. Solutions were found by plugging in values for Sigma in the cubic equation from the formulation slide and then plotting the sum or the LHS of the cubic equation vs Sigma. When the line crossed zero it meant that there was a root to the cubic equation. Each root was a value for the principle stresses (Sigma 1, 2, or 3) Solution

4. Results

5. Mohr’s Circle Stress,  MPa   3 =1.14  1 = -5.16  abs  max =3.15  2 =1 Tau Shear (MPa) Not to Scale

6. Principle Stress Deviation