Explain with a sketch the method which is used to compute the stress ratio.

Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 220 psi in size. (a) Determine the stresses Ox, Oy, and the magnitude of Txy and show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). Answer: (a) ox= i Oy = Txy = i i (b) Op1 = i op2 = i max in-plane y i C psi psi psi X psi psi psi σ

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1. Derive the six second-order and three fourth-order compatibility equations based on the six strain-displacement equations.