Problem $1$

Refer to the beam below, which has concentrated loads on it that are already factored per the $1\mathrm{.}2$D$+1\mathrm{.}6$L load combination. Draw the shear$/$moment diagram of the beam, making sure to include the self$-$weight of the beam $($determine the uniform self weight load based on the beam dimensions and make sure to factor the self$-$weight per the $1\mathrm{.}2$D$+1\mathrm{.}6$L load combination $-$ see explanation on next page$).$ The cross$-$section height is ${36}^{\text{'}\text{'}}$ and the width is $14",$ and the concrete is normal$-$weight concrete and f $\text{'}c=6$ksi. Use the appropriate cover for the beam $($not exposed to earth$)$ in order to determine $"d".$ You can assume that the stirrups are #$4$ bars.

a$)$ Draw the longitudinal reinforcement in the elevation view of the beam to show the extent of the reinforcement and whether it is needed at the top or bottom of the beam.

b$)$ Determine the number of #$6$ bars needed to have adequate flexural strength.

c$)$ Check that the selected design complies with $mi\frac{n}{m}ax$ requirements and spacing requirements.

Problem $1$

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

a$)$ Design the shear reinforcement $($using #$4$ stirrups with $2$ legs$)$ in the beam. Draw the beam elevation $($like shown below$)$ and label what portions of the beam i$)$ require stirups 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.

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Tip: if you find you only need minimal shear reinforcement, you can check the spacing requirement using the $A_{v,\text{m}\text{i}\text{n}}$ equation where $A_{v,\text{m}\text{i}\text{n}}$ is set equal to $0\mathrm{.}4i{n}^2($for $2$ legs of a #$\frac{4}{b}ar).$ Then solve for the spacing required.

Problem $2$

Using the same beam dimensions provided in Problem $1,$ determine the stirrup spacing required if you have a maximum shear demand of $165$ kips.

Solve Problem $1$ on the right with the information on the left