A rectangular beam carries uniformly distributed service $($unfactored$)$ dead load of $2\mathrm{.}3ki\frac{p}{f}t.,$ excluding its own self$-$weight $($for lightweight concrete$)$ and $1\mathrm{.}7$kip$/$ft$.$ service $($unfactored$)$ live loads. Factored concentrated loads of $10$ kip each are placed as shown on the span in addition to the given distributed loads. Calculate the beam's bending moment capacity and check if it is safe for bending. The beam width is $15in.,$ and it has a total depth of $30in.$ It has $5-$ # $10$ bars in one layer. Use $f_c^{\text{'}}=6,000$ psi and $f_y=60,000$ psi. Hint: Calculate the bending moment capacity, the maximum factored bending moment, and then compare for ensuring safety.