$(2$ points$)$ Consider a beam $($problem $5\mathrm{.}34$ from textbook$)$ with the following:

The bar is made from $6061-$T$6$ Aluminum with $E=9,990$ksi and $G=3,770$ksi.

The bar has a rectangular cross$-$section $(k=1\mathrm{.}2)$ with height $h=4$ in and width

$w=2$ in$,$ resulting in area $A=8i{n}^2$ and moment of Inertia $I_x=10\mathrm{.}667i{n}^4.$

The bar has length $L=5ft$

The distributed load increases linearly from $0$ at each end to a peak value of

$W_{\text{m}\text{a}\text{x}}=180l\frac{b}{f}t$ in the middle.

Determine the deflection at the center of the beam $($in$)$

a$.$ Including transverse shear $(1$ point$)$

b$.$ Neglecting transverse shear $(1$ point$)$