Problem $2$: Shear$-$moment Diagram Review

A beam is subject to a distributed load and two point loads as shown below. Assume that the member

cross section is rectangular with dimensions $10$ inches by $3$ inches, oriented such that bending occurs in

the strong axis. The member has a modulus of elasticity of $29,000$ksi and is supported by a pin toward

one end and a roller toward the other end.

a$)$ Determine the reactions at the supports.

b$)$ Draw the shear and moment diagrams.

c$)$ Determine the maximum $($magnitude$)$ normal stress due to bending.

d$)$ Determine the maximum $($magnitude$)$ normal strain due to bending.

e$)$ Determine the maximum $($magnitude$)$ shear stress.

f$)$ Sketch the approximate deflected shape.