Problem $1(25$ points$)$:

In Figure $1,$ the spring has an unstretched length of $0\mathrm{.}2$ m $,$ and the uniform bars, $AB$ and $BC,$ each have a mass of $30$ kg $.$ The mass of the members is not ignorable in both questions below $($assume gravity $=10\frac{m}{s^2}$ for this problem$).$

$($a$)$ Determine the angle $$ for equilibrium. Note that you cannot use the method of virtual work for this problem. $(15\%)$

$($b$)$ Determine the normal force, shear force and bending moment at point $D.(10\%)$