Design three rectangular beam sections $($i$.$e$.,$ select $b$ and $d$ and the tension steel area $A_s)$ to resist a factored design moment, $M_u=260k-$ft$.$ For all three cases, select a section with $b0\mathrm{.}5d$ and use $f_c^{\text{'}}=4000$ and $f_y=60$ksi.

a$.$ Start your design by assuming that ${}_t=0\mathrm{.}0075($as was done in Section $5-3).$

b$.$ Start your design by assuming that ${}_t=0\mathrm{.}005.$

c$.$ Start your design by assuming that ${}_t=0\mathrm{.}0035.$ You will probably need to add compression reinforcement to make this a tension$-$controlled section.

d$.$ Compare and discuss your three section designs.