A steel flat of rectangular section of size $$70 \times 6\,\,mm$$ is connected to a gusset plate by three bolts each having a shear capacity of $$15$$ $$kN$$ in holes having diameter $$11.5$$ $$mm.$$ If the allowable tensile stress in the flat is $$150$$ $$MPa,$$ the maximum tension that can be applied to the flat is

The maximum and minimum shear stresses in a hollow circular shaft of outer diameter $$20$$ $$mm$$ and thickness $$2$$ $$mm,$$ subjected to a torque of $$92.7$$ $$N.m$$ will be

A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam has constant flexural rigidity.

The bending moment at the middle support is

A steel column, pinned at both ends, has a buckling load of $$200$$ $$kN.$$ If the column is restrained against lateral movement at its mid-height, its buckling load will be