Correct option is D
The strain energy stored in a prismatic bar due to an axial tensile force is proportional to the square of the applied load. When two forces,
P₁ and
P₂, act together, the total strain energy is greater than the sum of the individual strain energies due to the forces acting separately. This is because the strain energy is calculated as:
where
P is the applied load,
L is the length of the bar,
A is the cross-sectional area, and
E is the modulus of elasticity. When both forces act together, the total load is
P₁ + P₂, and the combined strain energy will be greater than the sum of the individual energies due to the square relationship with the forces. Therefore,
U > U₁ + U₂.
