A rectangular beam carries uniformly distributed service $($unfactored$)$ dead load of $2\mathrm{.}3$ kip$/$ ft$.,$

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 $15$ in$.,$ and it has a total depth of $30$ in$.$ It has $5-$ #$10$ bars in one

layer. Use f$$c $=6,000$ psi and f y $=60,000$ psi. Hint: Calculate the bending moment capacity, the

maximum factored bending moment, and then compare for ensuring safety.