$(20)$ Given a fixed support timber beam with a rectangular cross$-$section shown below, subjected to bending due to a $625lb$ load at the cantilevered end with a maximum moment of $30,000lb-$in$.,$ and an allowable $($not to exceed$)$ bending stress of $250$ksi.

a$.$ Draw the complete free body diagram of the system.

b$.$ Will a beam ABC with the same cross$-$sectional dimensions throughout of $25$ inches $(b=2$ in$.$ and $h=5$ in$.)$ be suitable? Show your work.

c$.$ What is the normal $($axial strain$)$ between the $1ft$ section $AB$ assuming the timber is Red Pine with an elastic modulus of $1630$ksi $?$