Given the frame shown in figure a$,$ assume the frame is pin$-$connected at A and has a roller support at $D.$ The reactions at A and $D$ are provided in the figure.

a$.$ For frame member $AB,$ identify the unknown internal loadings at end $B.$ Draw the free body diagram $($FBD$)$ for $AB$ and explain how to choose the coordinates when writing

the equations of equilibrium to solve for the unknown loadings at end B$.(10$ pts$)$

b$.$ Using the provided FBD $($see fig. b$)$ for member BC$,$ write the equations of equilibrium needed to solve for the unknown internal loadings $($i$.$e$.$ loads at end C of frame

member BC$).(10$ pts$)$

c$.$ Assuming you have written the equations of equilibrium $($given below$)$ in order to solve internal moment at mid$-$point of member $AB,$ solve the equations for the shear $V$

and moment $M$ at mid$-$section of $AB.(5$ pts$)$

${\displaystyle \underset{?}{\overset{?}{}}}{M}_s=0$;$-6(3)-8\mathrm{.}71(4)+5(2\mathrm{.}5)+M=0$

uarr${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0$;$6(\frac{3}{5})+8\mathrm{.}71(\frac{4}{5})-5-V=0$

$($a$)$

$($b$)$

${\displaystyle \underset{?}{\overset{?}{}}}{M}_s=0$;$-6(3)-8\mathrm{.}71(4)+5(2\mathrm{.}5)+M=0$

uarr${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0$;$6(\frac{3}{5})+8\mathrm{.}71(\frac{4}{5})-5-V=0$