$(4$ pts$.)$ A pin in a knuckle joint carrying a tensile load F is shown in diagram $($a$)$ below. The actual loading on the pin from the joint is as shown in diagram $($b$).$ However, two different approximations are often used to model the loading on the pin and simplify the analysis. These approximations are shown in diagrams $($c$)$ and $($d$).$

Dimensions are as follows: $a=0\mathrm{.}5in,b=0\mathrm{.}75in,d=0\mathrm{.}5$ in and $F=1000lb.$

Draw the shear and bending moment diagrams for each approximation shown in $($c$)$ and $($d$).$ Then, calculate the maximum bending stress and the maximum transverse shear stress for each approximation and note how they compare.