Two prismatic beams having the same flexural rigidity of $$1000\,kN$$-$${m^2}$$ are shown in the figures.

If the mid-span deflections of these beams are denoted by $${\delta _1}$$ and $${\delta _2}$$ (as indicated in the figures), the correct option is

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

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 ____________

While aligning a hill road with a ruling gradient of 6%, a horizontal curve of radius 50 m is encountered. The grade compensation (in percentage, up to two decimal places) to be provided for this case would be ______.