Consider the beam in problem $2,b=12in,d=17\mathrm{.}5in,f_c^{\text{'}}=3000,$ and $f_y=60000.$

Assume spiral transverse reinforcement.

a$.$ Determine ${}_{\text{m}\text{i}\text{n}}$ and ${}_b.$

$5$ points

b$.$ Create an Excel sheet to determine the value of $M_n$ and $$ for $20$ values of $$ ranging

between ${}_{\text{m}\text{i}\text{n}}$ and ${}_b.$

$15$ points

c$.$ Use this Excel sheet to plot $$ vs $,$ vs $M_n,$ and $$ vs $M_n,$ where ${}_{\text{m}\text{i}\text{n}}{}_b.$

$10$ points

d$.$ Discuss your observations from the three figures from part c$.$ Specifically, discuss the effect

of increasing $$ on $M_n.$

$10$ points