The strain energy of a structure due to bending is given by

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This question was previously asked in

BPSC AE Paper 5 (Civil) 11 Nov 2022 Official Paper

Answer 1

Concepts:

The strain energy is the energy stored in a body due to its elastic deformation.

The most general formula for strain energy is:

\(U = {\frac{1}{2}} \times F \times \delta \)

Where, F is the applied force and δ is deformation

However, When stress σ is proportional to strain, ϵ, the strain energy formula is:

\(U = {\frac{1}{2}} \times V \times \sigma \times \epsilon\); V is the volume of material.

Based on the above formals, the strain energy stored in the material due to different types of forces/moments is given as:

1. Strain energy due to bending is:

\(U = \int\frac{M^{2}}{2EI}dx\)

2. Strain energy due to Torsion is :

\(U = \int\frac{T^2L}{2GJ}dx\)