$(40$ points$)$ Design a beam for the span and loading shown below.

a$.$ The deadload is $1\mathrm{.}5ki\frac{p}{f}t$

b$.$ The live load is the three point loads shown.

i$.$ Draw the unfactored shear and moment diagrams for the live load.

c$.$ Design the beam for the maximum factored moment $(M_u)$ and sketch the final design in

the space below.

i$.$ Calculate $M_u$

ii$.$ Determine the required section with reinforcing.

iii. Compare $M_u$ to $M_n$

iv$.$ Report the strain in the steel at the nominal moment $(M_n).$

v$.$ Check the spacing.

Given:

$f_c^{\text{'}}=4,000,E_c=3,600,000,w_c=150\frac{lb}{f{t}^3}$

$f_y=60,000,E_s=29,000,000$

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