Problem $1$

Use the same loading $($i$.$e$.$ shear$/$moment diagram$)$ as Problem $1$ from $\backslash (\backslash$mathrm$\{$HW$\}\backslash$# $4\backslash )($see solution for the correct shear$/$moment diagram$),$ as well as the following given information: The cross$-$section height is $\backslash (36^\{\backslash$prime $\backslash$prime$\}\backslash )$ and the width is $\backslash (14^\{\backslash$prime $\backslash$prime$\}\backslash ),$ and the concrete is normal$-$weight concrete and f $\text{'}\backslash (=6\backslash$mathrm$\{$ksi$\}\backslash ).$ The longitudinal reinforcement are $\backslash$# $6$ bars and all bars are $\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$y$\}\}=60\backslash$mathrm$\{$ksi$\}\backslash )$ Use the appropriate cover for the beam $($not exposed to earth$)$ in order to determine $"$d$".$

a$)$ Design the shear reinforcement $($using $\backslash (\backslash$# $4\backslash )$ stimps with $2$ legs$)$ in the beam. Draw the beam elevation $($like shown below$)$ and label what portions of the beam i$)$ require stirrups for strength, ii$)$ require just minimum stirrups, or iii$)$ require no stirrups at all.

b$)$ If stirrups are required for strength, determine the spacing required. If minimal reinforcement is needed, determine the necessary spacing of the stirrups per the tip below. If no stirrups are required, simply designate those areas and show the check you made to determine that. You need not check general spacing requirements.

Tip: if you find you only need minimal shear reinforcement, you can check the spacing requirement using the $\backslash (\backslash$mathrm$\{$A$\}\_\{$v$,\backslash$text $\{$ min $\}\}\backslash )$ equation where $\backslash (\backslash$mathrm$\{$A$\}\_\{$v$,\backslash$min $\}\backslash )$ is set equal to $\backslash (0\mathrm{.}4\backslash$mathrm$\{$in$\}^\{2\}\backslash )($for $2$ legs of a $\backslash (\backslash$# $4\backslash$mathrm$\{$bar$\}\backslash )).$ Then solve for the spacing required.