$,$ A prestressed concrete beam with width $b=300mm$ and depth $h=600mm$ is simply supported

over a span of $10m.$ The prestress force $P_0=200kN($after transfer$)$ acts at constant eccentricity

of $100mm.$ Area of prestressing steel is Aps $=154m{m}^2.$ Self$-$weight of beam is $0\mathrm{.}7k\frac{N}{m}.$ Live

load on the beam is $7k\frac{N}{m}.$ Es$/$Ec$=6,Ec=30k\frac{N}{m}{m}^2,f_{cr}=4\frac{N}{m}{m}^2.$

a$)$ Determine the cracking moment and corresponding cracking load.

b$)$ Determine the maximum immediate deflection at $1\mathrm{.}5$ times the working load.