A rectangular prestressed concrete section, $200mm$ wide and $450mm$ deep, is subject to a shear force of $300kN$ at the support of a simply supported beam. The distribution of compressive prestress is such that $4$MPa is applied at the centroid on the section. The characteristic cube strength of concrete is $40$MPa and the yield strength of steel is $415$MPa. Effective cover to centre of reinforcement is $50mm.$ Assume any other data required suitably

$($a$)$ Determine the shear resistance of at the support section of the simply supported beam and provide shear reinforcement required as per IS $1343$: $2012(10$ marks$)$

$($b$)$ If the same rectangular cross$-$section is used for a continuous beam, where the ultimate moment and ultimate shear force acting at support are $2000kNm$ and $350kN$ respectively, determine the flexure$-$shear resistance of the section

For part $($b$),$ Area of steel in the section $=1500m{m}^2,$ Tensile strength of tendons $f_p=1600$MPa, Effective stress in tendons after all losses $f_{pe}=700$MPa. Effective stress at the extreme tensile face of the beam $=15$MPa $(10$ marks$)$