$($a$)$ Determine the maximum ultimate moment, $M_a-$

$($b$)$ Compute the flexural strength, Mk$,$ of the beam using internal couple method.

$($c$)$ Compute the flexural strength, $M_k,$ of the beam using ACI tables method $($Using flowchart and appendix tables$).$

$($d$)$ Is this beam sdequate for the design moment according to ACI Code?

$($e$)$ If it is over$-$designed, $M_k{M}_u,$ what would you suggest as Structural Enginecr to change in section$/$reinforcing to decrease it$?$ Explain why.

$($f$)$ Does it satisfy other requirements of ACI Code $($minimum required width of the beam to furnish rebsrs, min. reinforcement ratio$)?$

Other properties of the beam:

Concrete properties: $f_c=4000$ psi and density of $150$ pef.

Steel properties: grade $60$ steel rebars.

Beam is an internal member, Cover $=1\mathrm{.}5in$

Assume $$3$ stirrups are used.

Design of reinforcing for singly$-$reinforced conerete beams. Design a rectangular reinforeed concrete beam to resist a total design moment, $M_4$ of $140k-f($This includes the moment due to self$-$weight of beam$).$ Architectural considerations require that the width $($b$)$ be $12in.$ and the overall depth$($h$)$ be $18in.$ and clear cover is $1\mathrm{.}5$in$.$ Use $fe=3000p$ si and $fy=60,000$ psi. Sketch your design.

Free Beam Design. Design a rectangular heam for a $25-1$ simple span if a dead load of $1$ Eft $($not including the beam weight$)$ and a live load of $2\frac{k}{f}t$ are to be supported. Use fo$\text{'}-4000$ paind $y=60\mathrm{.}000.$ Sketch your design.