For the beam shown in Figure $($a$)$:

a$)$ draw the shear force and bending moment diagrams. $(25$ points$)$

b$)$ Select the most economical $W$ shape for the beam with an allowable bending stress of $30$ ksi $.(10$ points$)$ Answer:

c$)$ determine the maximum tensile $($Answer: $q,$ and compressive bending stresses $($Answer: $q,$ at any location along the beam if the section shown in Figure $($b$)$ is used instead of the W shape section selected in Part b$.$ Would the beam be safe now? $(30$ points$)$

Answer: $q,$

$B$ is a pin support, $D$ and $F$ are roller supports and $E$ is an internal pin.

$3$