Problem 2. For the triangular section shown in figure below, it is found that the following stress function is valid. Assume z-direction is the length direction of the structure and Torque is applied counter-clockwise about z-axis.
Obtain shear stresses developed in the section. If $a = 100$ cm, $G = 27$ GPa, and $\theta = 2^\circ$/m, find the magnitude and locations of maximum shear stress.
$\phi = -G\theta \left[ \frac{1}{2} (x^2 + y^2) + \frac{1}{2a} (x^3 - 3xy^2) - \frac{2}{27} a^2 \right]$
