Problem $1-$ Beams $(25$ marks$)$

The cantilever beam with a span length of $10ft$ is a W$10$x$77$ of A$992$ steel with $F,=50$ksi and

$E=29,000$ksi. There is no lateral support other than at the fixed end. Use an unbraced length equal

to the span length. The beam is subjected to a uniform dead load $150l\frac{b}{f}t$ including the beam

weight and the concentrated live load $90$ kips as shown in Figure. Check if the beam is adequate with

the following steps:

$($a$)$ Determine the nominal shear strength for the beam $(5$ marks$).$

$($b$)$ Determine the nominal flexural strength using $C_b=1\mathrm{.}0(10$ marks$).$

$($c$)$ Using $($a$)$ and $($b$),$ check if the beam is adequate to support the service loads by using shear

and bending moment diagrams $(10$ marks$).$