Problem $1$:

An overhanging A$-36$ steel beam is under the action of a distributed load $w_0=6ki\frac{p}{f}t,$ and a concentrated load $P=10$kip applied at point $E.$ The distance $a$ in Figure $1$ is equal to $3$ ft $.$

$($a$)$ Determine the value of the reactions at the supports and create the shear foree diagram and bending moment diagram for this beam.

$($b$)$ Select the most economical wide flanged shape for the beam knowing that the yield stress is $36$ ksi and a fictor of safety equal to $1\mathrm{.}8$ is enforeed.

$($c$)$ For the shape selected, find the maximum bending stress.

$($d$)$

Determine the beam vertical displacement at point $E,$ steel modulus of elasticity

$E=29000$ksi.

Figure $1$: Overhanging beam