A beam of rectangular cross section has b $=22$ in$.$ and h $=15$ in$.$ It is to carry a total factored

load of $3600$ lb$/$ft uniformly distributed over its $26$ ft span, and in addition the beam will be

subjected to a uniformly distributed torsion of $1800$ ft$-$lb$/$ft at factored loads. Closed stirrup$-$ties

will be used to provide for flexural shear and torsion, placed with the stirrup steel centroid $1\mathrm{.}75$

in$.$ from each concrete face. The corresponding flexural effective depth will be approximately

$12\mathrm{.}5$ in$.$ Design the transverse reinforcement for this beam and calculate the increment of

longitudinal steel area needed to provide for torsion, using fc$=4000$ psi and fy $=60000$ psi.