A circular solid shaft of span $$L=5m$$ is fixed at one end and free at the other end. A twisting moment $$T=100$$ $$kN$$-$$m$$ is applied at the free end. The torsional rigidity $$GJ$$ per unit angular twist is $$50000$$ $$kN$$-$${m^2}/rad.$$ Following statements are made for this shaft:

$$1.$$ The maximum rotation is $$0.01$$ radius
$$2.$$ The torsional strain energy is $$1$$ $$kN$$-$$m.$$

With reference to the above statements, which of the following applies?

$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the same bar due to combined action of $${P_1}$$ and $${P_2}$$ will be

For the linear elastic beam shown in the figure, the flexural rigidity, $$EI$$ is $$781250\,\,kN$$ - $${m^2}.$$ When $$w=10$$ $$kN/m,$$ the vertical reaction $${R_A}$$ at $$A$$ is $$50$$ $$kN.$$ The value of $${R_A}$$ for $$w = 100\,kN/m$$ is

For the plane frame with an overhang as shown below, assuming negligible axial deformation, the degree of static indeterminacy, $$d,$$ and the degree of kinematic indeterminacy, $$k,$$ are