The width and effective depth of a reinforced concrete beam is $$250$$ $$mm$$ and $$440$$ $$mm$$ respectively. The beam is provided with $$4$$ number of $$20$$ $$mm$$ bars in the tension zone. The beam is subjected to a shear force of $$150$$ $$kN$$ (Factored). Check the requirement of shear reinforcement and provide if required. Grade of concrete is $$M20$$ and that of steel is $$Fe415.$$ The shear strength of concrete for different percentage of tensile steel are as below $$8$$ $$mm$$ diameter vertical stirrups are available.
$$\left[ {{V_{us}} = 0.87\,\,{f_y}{A_{sv}}\,\,d/{S_v}} \right.$$ and $${\left( {{A_{sv}}/{S_v}} \right) \ge 0.4b/{f_y}}$$ with the terms having usual meaning $$\left. \, \right]$$

Maximum strain at the level of compression steel for a rectangular section having effective cover to compression steel as $$d'$$ and neutral axis depth from compression face $${X_u}$$ is

The minimum area of tension reinforcement in a beam shall be greater than

Two wheels, placed at a distance of $$2.5$$ $$m$$ apart, with a load of $$200\,\,kN$$ on each of them are moving on a simply supported girder ($${\rm I}$$-section) of span $$6.0$$ $$m.$$ The top and bottom flanges of the $${\rm I}$$-section are of $$200 \times 20\,\,mm$$ and the size of web plate is $$800 \times 6\,\,mm$$. If the allowable and average stresses are $$110\,MPa,$$ $$165$$ $$MPa$$ and $$100$$ $$MPa$$ respectively, check the adequacy of the section against bending and shear stress (self-weight of the girder, may be neglected)