b$)$

$7\mathrm{.}3.$ The beam shown in cross section in Fig. P$7\mathrm{.}3$ is a typical interior member of a continuous building frame, with span $30$ ft between support faces. At factored loads it will carry a uniformly distributed vertical load of $3500l\frac{b}{f}t,$ acting simultaneously with a uniformly distributed torsion of $3000ft-l\frac{b}{f}t.$ Transverse reinforcement for shear and torsion will consist of No$.4$ stirrup$-$ties, as shown, with $1\mathrm{.}5$ in $.$ clear to all concrete faces. The effective depth to flexural steel is taken equal to $22\mathrm{.}5$ in $.$ for both negative and positive bending regions. Design the transverse reinforcement for shear and torsion, and calculate the longitudinal steel to be added to the flexural requirements to provide for torsion. Torsional reinforcement will be provided only in the web, not in the flanges. Material strengths are $f_c^{\text{'}}=4,000$ psi and $f_y=60,000.$Design for critical location only