A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and inner diameter of $$50mm.$$ If the allowable shear stress is $$125$$ $$MPa$$, the maximum torque (in $$kN$$-$$m$$) that the shaft can resist is ___________

In a material under a state of plane strain, a 10×10 mm square centered at a point gets deformed as shown in the figure. If the shear strain $$\gamma_{xy}$$ at this point is expressed as 0.001k (in rad), the value of k is

Consider the portal frame shown in the figure and assume the modulus of elasticity, $$E = \,2.5 \times {10^4}\,\,MPa$$ and the moment of inertia, $${\rm I} = 8 \times {10^8}\,\,m{m^4}$$ for all the members of the frame.

The rotation (in degrees, up to decimal place) at the rigid joint $$Q$$ would be ____________

Consider the frame shown in the figure.

If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to