Q$3.$ The plan shown is for a one$-$way slab. The slab is solid with a thickness of $20cm.$ The ultimate load including self$-$weight $Wu=2\frac{t}{m^2}.$ Where needed, double $10$ stirrups are used. Assume $20$ longitudinal bars are used where flexure and torsion act together, and $10$ longitudinal bars for torsion acting alone. All beams have $b=50cm$ and $h=80cm.$ In all strength calculations, use $d=dt=74cm.$

a$.(10$ points$)$ Draw the Tu diagram for the end span of beam B$1.$

b$.(5$ points$)$ Assuming that at a critical section of beam $B1,Vu=40t$ and $Tu=15$ t$.$m$,$ determine if torsion may be ignored, and show that the section is adequate.

c$.(10$ points$)$ Assuming torsion may not be ignored and the section is adequate, determine the required stirrup spacing for $Vu=40t$ and $Tu=15$ t$.$m$.$ Also, determine the required longitudinal reinforcement $"A{l}_1"$ to resist torsion.

d$.(10$ points$)$ Given $"$As$"$ required for flexure $=40c{m}^2,$ and $"A{l}_1"$ required for torsion $=15c{m}^2,$ provide a design sketch of the $x-$section showing the stirrups and the longitudinal reinforcement.Q$3.$ Une$-$way solid slab.

All columns are $70cm40cm$ All beams have $b=50cm$ and $h=80cm$