Problems

In the following problems, unless noted otherwise, use normal weight concrete with a unit weight of $150$ pcf$,1\mathrm{.}5$ in$.$ for beam clear concrete cover, and $0\mathrm{.}75$ in$.$ for slab clear concrete cover.

$2\mathrm{.}1$ Consider a section with a width $(b)$ of $14$ in$.$ and reinforced with $4$ #$9$ bars in a single layer. $f_c^{\text{'}}=4,000,$ and $f_y=60,000$ psi. Determine the moment capacity of the section, $M_R,$ using Method I or II$,$ for the following cases:

$($a$)d=28$ in$.$

$($b$)d=32$ in$.$

$($c$)d=36$ in$.$

$($d$)d=40$ in$.$

Show the changes in $M_R$ with respect to the section$\text{'}$s effective depth. Calculate the percentages of increase in $M_R$ versus $d.$

Please write it out on paper if you can