(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the expressions for principal stresses in both plane strain and plane stress conditions

sigma(x) = (K/(sqrt(2*pi*r)))*cos(theta/2)*(1-sin(theta/2)*sin(3*theta/2))

sigma(y) = (K/(sqrt(2*pi*r)))*cos(theta/2)*(1+sin(theta/2)*sin(3*theta/2))

T(xy) = (K/(sqrt(2*pi*r)))*cos(theta/2)*sin(theta/2)*cos(3*theta/2))

Since the problem asks for expressions, no variables are given values.

2. Relevant equations

Mohrs Circle for Principal Stress

Principal Strain

3. The attempt at a solution

Should I take derivatives of (x), (y), and (xy) and then use that to solve for the angle theta? All I know is I'm supposed to look for sigmas x, y, and xy (not sure if my teacher meant x', y' and xy') and then sigmas 1 and 2. Ideas?

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# Principal Stress and Strain on a Fracture

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