$(50$ pts $)$ A $2"x"$ ASTM A$36$ steel bar is loaded as shown below. Determine the maximum deflection at the end of the cantilever beam in inches using the following deflection methods:

A$.(25$ pts$)$ Superposition $($Formula$)$ method.

R$.(25$ pts$)$ Moment$-$Area Method.

NOTE: Both deflection method solutions will be the same. When doing the moment$-$area method you must add $4\text{'}$ to the $x-$bar of the triangular moment diagram.

Neglect the weight of the beam.

X bar for the triangle is the base length $x\frac{2}{3}.$