Design of Doubly$-$Reinforced Rectangular Beams

Problem $1(5$ pts$)$

Complete Problem $4\mathrm{.}2($b$)$ from the Hassoun text, with the following modifications$/$additions:

Assume #$4$ Gr$.60$ stirrups, with $1\mathrm{.}5^(\text{'}\text{'})$ clear cover

Assume $3//4^($n$)$ max. aggregate size

Check that your selected reinforcement meets the minimum spacing requirements of ACl $25\mathrm{.}2$

You are required to arrange your tension reinforcement in two even layers $($i$.$e$.$ same number of bars in

each layer$),$ separated by the minimum vertical spacing from the ACI code.

Note that in this scenario, d$!=$d$.$ You must consider how this affects your use of the design

formulas and tables in the appendix of your textbook. You may assume that d$=$d$\_($t$)$ for

preliminary design purposes, but you must take the actual value of d$\_($t$)$ into account in your final

verification of your design.

Hint$/$question: is it conservative to assume that d$\_($t$)=$d $?$

Use the provided $"$d$"$ and $"$ d$"$ values as preliminary values for your design. Once you have designed

your reinforcement, select a height $($ h $)$ of the beam that is rounded to the nearest $0\mathrm{.}50^($@$).$ Then,

calculate the actual values of d$,$d$\_($L$),$ and d$\text{'}$ based on clear cover and bar diameters. Show that your

design with the updated values of d$,$d$\_("$t$,")$ and d$^(\text{'})$ still meet code requirements.

Provide an engineering sketch of your designed cross$-$section, showing the relevant geometry,

reinforcement $($tension steel and stirrups$),$ and material properties.

Do not provide a value of d or d$^(\text{'}),$ nor the distance from the extreme compression fiber to the

center of any reinforcement on the drawing; rather, provide enough information $($cover

distance, stirrup size, tension bar size$)$ so that d and d$\text{'}$ could be calculated

Hassoun $4\mathrm{.}2$ b:

Based on the information given in the following table and for each assigned problem, design a rectangular section with compression reinforcement to resist the factored moments shown. Use f$\text{'}$c $=4$ ksi, fy $=60$ ksi, and d$\text{'}=2\mathrm{.}5$ inches. Draw detailed sections. Mu $=790$ k$*$ft$,$ b $=16$ inches, d $=24\mathrm{.}5$ inches