Problem $1$: $(30$ Points$)$ A cross section through a railroad bed is shown. The rails are supported by ties that are made of wood, and the ties rest on ballast, which is crushed stone. Assume the ballast applies a uniformly distributed load to the ties, as shown in the detail below. Determine $($a$)$ the value of this uniformly distributed $($rectangular$)$ load, in kip$/$inch$.$ Then determine the value of $($b$)$ the shear force and $($c$)$ the bending moment, at the center of the tie $($point $\backslash ($ C $\backslash )).$