Problem $2-$ The simply supported RC beam is cast with $f_c^{\text{'}}=3,000$ psi concrete and reinforced with $Gr-60$ steels.

$0+3$ No$.10$

Fig. $1-$ Simply supported RC beam

$($a$)(6$ points$)$ Determine the bending capacity $(M_n)$ of the beam section as shown in Fig. $1($b$).$ You may assume the section to be a perfect$-$T section $($i$.$e$.,$ neglect the small triangular section between a flange and the web$).$ Also, determine the maximum service live load $(\frac{k}{f}t)$ allowed on the beam. The beam is simply$-$supported with a span of $20-$ft long, with a live load to dead load ratio is $2\mathrm{.}0.$

$($b$)(2$ points$)$ For the same beam section, determine the corresponding $A_{s\text{m}\text{i}\text{n}}$ and $A_{s\text{m}\text{a}\text{x}}$ for flexural design. For $A_{s\text{m}\text{a}\text{x}},$ use ${}_t={}_s=0\mathrm{.}005i\frac{n}{i}n,$ and $d=d_t={36}^{\text{'}\text{'}}.$

$($c$)(2$ points$)$ Determine the beam's shear capacity $(V_n)$ as shown. Also, what would be the maximum $V_n$ allowed for the section shown.

Problem $2-$ The simply supported RC beam is cast with $f_c^{\text{'}}=3,000$ psi concrete and reinforced with $Gr-60$ steels.

$0+3$ No$.10$

Fig. $1-$ Simply supported RC beam

$($a$)(6$ points$)$ Determine the bending capacity $(M_n)$ of the beam section as shown in Fig. $1($b$).$ You may assume the section to be a perfect$-$T section $($i$.$e$.,$ neglect the small triangular section between a flange and the web$).$ Also, determine the maximum service live load $(\frac{k}{f}t)$ allowed on the beam. The beam is simply$-$supported with a span of $20-$ft long, with a live load to dead load ratio is $2\mathrm{.}0.$

$($b$)(2$ points$)$ For the same beam section, determine the corresponding $A_{s\text{m}\text{i}\text{n}}$ and $A_{s\text{m}\text{a}\text{x}}$ for flexural design. For $A_{s\text{m}\text{a}\text{x}},$ use ${}_t={}_s=0\mathrm{.}005i\frac{n}{i}n,$ and $d=d_t={36}^{\text{'}\text{'}}.$

$($c$)(2$ points$)$ Determine the beam's shear capacity $(V_n)$ as shown. Also, what would be the maximum $V_n$ allowed for the section shown.