Problem $1-(3$ points$)$

The beam shown to the right has properties:

Elastic modulus $E=29,000$ksi

Shear modulus $G=11,500$ksi

Moment of inertia $I=120i{n}^4$

Effective shear area $\frac{A}{K}=12$ in ${?}^2$

Point $A$ is a fixed end, point $B$ is a hinge, and point $C$ is a roller.

Find the vertical displacement at point $D$ using the method of virtual work. Consider deformations due to moments and shear forces.