Problem $2(50pts)$ For the reinforced concrete beam cross$-$section shown below, compute the

design bending moment capacity $M_n.$ The beam is reinforced with $3$ No$.8$ bars. Use $f_c^{\text{'}}=5000$

psi and Grade $40$ bars $($i$.$e$.,f_y=40$ksi.$)[$Must check if it is tension$-$controlled or not$]$

For the calculation of As$,$ use the chart below.

Problem $3(50$ pts$)$ The beam cross$-$section used in Problem $1$ is used to build a simply$-$

supported beam, spanning $20$ ft$.$ The beam supports a superimposed uniform dead load $w_D$ of

$2\mathrm{.}0ki\frac{p}{f}t$ and a superimposed uniform live load $w_L$ of $1\mathrm{.}0ki\frac{p}{f}t.$ Check if the design bending

moment capacity $M_n$ is greater than the required bending moment $M_u$ or not.

Note: the self$-$weight must be computed and added to the dead load. Use the density of

reinforced concrete of $150l\frac{b}{f}{t}^3$ for self$-$weight calculation. Therefore, the self$-$weight

$w_{\text{s}\text{e}\text{l}\text{f}}=150\frac{lb}{f{t}^3}(12in\frac{1ft}{12in})(24in\frac{1ft}{12in})=300l\frac{b}{f}t=0\mathrm{.}3\frac{k}{f}t$

Therefore, the factored load, $w_u$ to be used for computing $M_u$ must be

$w_u=1\mathrm{.}2(w_D+w_{\text{s}\text{e}\text{l}\text{f}})+1\mathrm{.}6w_L$