Test: Structural Analysis- 1 - GATE MCQ

Strain Energy in beams is basically equals to integration of square of Bending Moment over the length divided by EI.
For a given beam, higher the static indeterminacy lower the bending moment is developed in the cross-section, thus, resulting in lower strain energy.
Moreover, if the indeterminacy is same then, lower the number of supports, higher will be bending moment generated thus, leading to higher strain energy.
From above statements, we can conclude that cantilever has maximum strain energy.

If we consider the joint equilibrium at B, the force in member AB will be zero.

If we consider the joint equilibrium at b, the force in member BD will be 4 kN compressive.

Summation of forces and moments in all three directions need to be zero
Fx=0; Fy=0; Fz=0; Mx=0; My=0; Mz=0

A structure is statically determinate when the external reactions can be determined from force-equilibrium equations.
A structure is stable when the whole or part of the structure is prevented from large displacements on account of loading.
In (a), the structure is stable and there are three reaction components that can be determined from two force equilibrium conditions and one moment equilibrium condition.
But in case of (b), the structure is stable but statically indeterminate to the second degree and in case of (c), the structure has both reaction components coinciding with each other, so the moment equilibrium conditions will never be satisfied and the structure will not be under equilibrium.
In (d), the structure is simply unstable.

Therefore, the ratio of sway moments in columns AB and CD will be equal to 9/8.