Strain energy is the internal energy that is stored in any material which is loaded within elastic limit.

  • SE is called as the work done by a loaded material.
  • It is also called as ‘ Resilience’.
  • Unit of SE is N-cm, N-cm, N-mm.
  • For strain energy to be stored material must deform within the elastic limit.
  • SE depends upon the applied load.
  • When the load is removed the material will regain its original shape.

Application:- Used in springs.

The load applied on a material can be :-

  • Gradually applied load.
  • Suddenly applied load.
  • Impact load [ load falling from height ]
Formula for strain energy:-

Strain energy (u) = ((σ)^2 × v)/2E (N-mm)


(σ) = stress in the material (N-mm^2)

E = young’s modulus

V = volume of material

Derivation of Strain Formulae:-

SE in an axially loaded member.

strain energy elongation
Fig. Stress stored in bar

Stress , (σ) = P/a

Area = ½ × p × dl

strain energy graph
Fig:- gradual applied load.

= ½ × σA ×dl

= ½ × σA × (pl/AE)

= ½ × σA × (σAL/AE)

= σ^2V/2E

  • The formula of SE is σ^2V/2E.
  • The formula for a suddenly applied load is 2P/A
  • The formula for impact loading
Strain Energy Calculation

Authored by:- Cdt. Nikhil Choudhary, TMI

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