Problem $1$:

The simply supported beam shown has a span of $22$ ft $,$ and dimensions $h=20in,b=12$ in and $d=17in.$ The beam is subjected to a uniformly distributed dead load of $1\mathrm{.}2ki\frac{p}{f}t($including its own weight$)$ and a uniform live load of $1\mathrm{.}3ki\frac{p}{f}t.$ Material properties are $f_{c^{\text{'}}}^{\text{'}}=4000$ and $f_y=40,000($stirrups$).$

a$)$ Determine the maximum shear force $V_u$ at the critical location.

b$)$ Determine the concrete shear strength $V_c.$

c$)$ Using #$3$ stirrups determine the required spacing, $"s",$ so that the design strength in shear is greater than $V_u$