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 $a=100cm,G=27$GPa, and $=2\frac{\%}{m},$ find the

magnitude and locations of maximum shear stress.

$=-G[\frac{1}{2}(x^2+y^2)+\frac{1}{2a}(x^3-3x{y}^2)-\frac{2}{27}{a}^2]$