A singly reinforced, rectangular section is to be used for $2-$span beam and loading shown. The

beam weight is NOT included in the dead load shown, and all the loads shown are unfactored.

Design the beam using $f_c^{\text{'}}=5,000,$ grade $80$ reinforcement, and interior exposure.

a$.$ Determine the maximum positive moment in each span and the maximum negative

moment on each side of the center support using the ACI Moment Coefficients. Note that

the discontinuous ends of this beam are unrestrained.

b$.$ Design the beam using the maximum negative moment by establishing an acceptable $b,$

h $,$ and $A_5.$ Sketch of the cross$-$section showing bar sizes, arrangement, spacing, and cover.

Target a reinforcement ratio of $$~$=\frac{0\mathrm{.}18f_c^{\text{'}}}{f_y}$ and a depth to width ratio of $\frac{d}{b}$~$=1\mathrm{.}5.$

c$.$ Determine $A_5$ for the positive moment section of the beam using the beam dimensions

selected in part b$.$ Sketch of the cross$-$section showing bar sizes, arrangement, spacing,

and cover.

d$.$ If the depth of the beam cannot exceed $15$ in$,$ determine an acceptable $b$ and $A_s$ using the

maximum negative moment targeting a reinforcement ratio of $$~~$\frac{0\mathrm{.}23f_c^{\text{'}}}{f_y},$ Sketch of the

cross$-$section showing bar sizes, arrangement, spacing, and cover.

Bonus

e$.$ Determine the maximum positive moment in each span and on each side of the center

support using structural analysis. You may use the Moment$-$Distribution method or the

Force Method for your analysis, and you can assume that EI is constant for the entire

beam. Three live load cases are required to establish the maximum positive and

maximum negative moments in this beam.