Problem $2$:

a$)$ Show that $=C[(3{)}^{\frac{3}{2}}a(y^2+x^2)-2y^3+6y{x}^2+A]$

where $A,C,$ and a are constants, is a permissible Prandt$1$

stress function and evaluate C in lerms of G and $.$

b$)$ Show that $$ of part a$)$ is the stress function for the

equilateral triangle shown below. Find $A$ so that $$ satisfies

the boundary conditions.

c$)$ Using the resuits of parts a$)$ and b$),$ evaluate the stresses

and the torsional constant J for an equilateral triangle.