$2.)$ For the beam shown with $a=10\mathrm{.}2ft,b=7\mathrm{.}6ft,w_a=3\mathrm{.}6$kip$\frac{s}{f}t,$ and $w_b=11\mathrm{.}5$kip$\frac{s}{f}t$ :

a$.)$ Derive equations for the shear force V and the bending moment M for any location in the beam.

b$.)$ Use the equations you derived in part $A$ to determine the shear stress and bending moment at $x=$

$5\mathrm{.}2$ ft and $x=16\mathrm{.}8ft$

$[$at $5\mathrm{.}2ft,V=26\mathrm{.}1$kips and $M=185$kipft, at $x=16\mathrm{.}8ft,V=-67\mathrm{.}8$kips,$M=73\mathrm{.}5$kipft $]$

c$.)$ Use the derived functions to plot the shear$-$force and bending$-$moment diagrams for the beam.

d$.)$ Determine the bending moment with the largest $($absolute$)$ value $M_{\text{m}\text{a}\text{x}}$ and its location $x_{\text{m}\text{a}\text{x}}[M_{\text{m}\text{a}\text{x}}$

$[$:$=273$kipft,$x_{\text{m}\text{a}\text{x}}=10\mathrm{.}9ft$