Consider the elevation view of an interior beam shown below. The beam has a rectangular cross$-$

section. It frames into $18$ by $18$ in$.$ columns at both ends and is continuous at both ends.

Assume:

Center$-$to$-$center length not $\{$:$l_n)=30ft$

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Calculate the design moments, $M_u,$ at midspan and at a support using ACI moment

coefficients. Assume the beam will be rectangular.

Design an efficient rectangular singly$-$reinforced beam section for mid$-$span. Iterate until

the design strength, $M_n,$ is within approximately $20\%$ of $M_u.$ Provide a drawing of the

section design that clearly shows the location of the longitudinal reinforcement $($you can

assume No$.4$ stirrups are used$).$ Be sure to show the section complies with all relevant

Code requirements $(A_{s,\text{m}\text{i}\text{n}},$ bar spacing, clear cover, ${}_{t,\text{m}\text{i}\text{n}},$ etc.$).$

Design an efficient rectangular doubly$-$reinforced beam section for the face of a support.

Iterate until the design strength, $M_n,$ is within approximately $20\%$ of $M_u.$ Provide a

drawing of the section design that clearly shows the location of the longitudinal

reinforcement $($you can assume No$.4$ stirrups are used$).$ Be sure to show the section

complies with all relevant Code requirements $(A_{s,\text{m}\text{i}\text{n}},$ bar spacing, clear cover, ${}_{t,\text{m}\text{i}\text{n}},$ etc.$).$

Are the section dimensions selected for $(2)$ and $(3)$ the same? If not, how would you modify

your design so the same dimensions are used throughout the span $($no need to redesign$)?$