A reinforced concrete beam of rectangular cross section of breadth $$230$$ $$mm$$ and effective depth $$400$$ $$mm$$ is subjected to maximum factored shear force of $$120$$ $$kN.$$ The grades of concrete, main steel and stirrup steel are $$M20,$$ $$Fe415$$ and $$Fe250$$ respectively. For the area of main steel provided, the design shear strength τc is per $$IS: 456$$-$$2000$$ is $$0.48$$ $$N/m{m^2}.$$ The beam is designed for collapse limit state.

In addition, the beam is subjected to a torque whose factored value is $$10.90$$ $$kN$$-$$m.$$ The stirrups have to be provided to carry a shear $$(kN)$$ equal to

A simply supported beam of a beam and slab system, rests on a support of width $$450$$ $$mm.$$ The clear span of the beam is $$10.0$$ $$m.$$ The thickness of the slab is $$120$$ $$mm.$$ The depth of the beam below the slab is $$480$$ $$mm$$ and the width of the beam is $$250$$ $$mm.$$ The beam is reinforced with one row of $$32$$ $$mm$$ diameter steel rods. The total load including the super imposed dead load, live load and its own weight is $$25.0$$ $$kN/m$$ at service stage. Compute the maximum nominal design shear stress in the concrete _______________