Problem $2$: For a given concrete floor system supported by series of parallel beams, which a simplysupported beam. The span of the simply$-$supported beam is $36$ ft $.$ The spacing between beams is $6$ ft $.$ The floor slab thickness is $5$ in $.$ The distance between the centers of the bottom reinforced steel to the bottom of concrete beam is $2\mathrm{.}5$ in $.$ The midspan moment of each beam due to dead load $($including self$-$weight$)Md=41500lbs-ft,$ and the midspan moment of each beam due to live load $M_l=56850lbs-ft.$ The reinforce steel yield strength is fy$=60,000$psi. The concrete strength $f_c^{\text{'}}=4000$ psi.

For the given beam section shown below, determine the effective width of flange for the beam midspan section, $b($or $b_f)(4$ points$).$

Determine the design moment and the required nominal moment capacity of the beam at the mid span $(4$points$).$

Estimate and finally determine the required reinforced steel at the beam midspan section to resist the given moment $($i$.$e$.,$ determine the number of the rebar and size of the rebar needed as you did for your design project $)(4$ points$).$

Determine the strength reduction factor, $,$ for the design moment capacity of the beam midspan section $(4$ points$).$

Compare the design flexural $($moment$)$ strength, $M_u,$ with design moment, $M_n,$ at the beam midspan section to determine if the selected reinforcement is sufficient $(4$ points$).$

Section $A-A$

$4$