Question

derive the formula of strain energy

Answer 1

STRAIN ENERGY FORMULA

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape. It is usually denoted by U.

The strain energy formula is given as,

U = Fδ / 2

Where,

δ = compression,

F = force applied.

When stress σ is proportional to strain ϵ, the strain energy formula is given by,

U = 1 / 2 V σ ϵ

Where,

σ = stress,

ϵ = strain,

V = volume of body

Regarding young’s modulus E, the strain energy formula is given as,

U = σ2 / 2E × V.

Where,

σ = stress,

E = young’s modulus,

V = volume of body.

Example 1

When a force of 1000 N is applied on a body, it gets compressed by 1.2 mm. Determine the strain energy.

Solution:

Given:

Force F = 1000 N,

Compression δ = 1.2 mm

Strain energy formula is given by,

U = Fδ / 2

   = 1000 ×1.2×10−3 / 2

Therefore, U = 0.6 J.

Example 2

A rod of area 90 mm2 has a length of 3 m. Determine the strain energy if a stress of 300 MPa is applied when stretched. Young’s modulus is given as 200 GPa.

Solution:

Given:

Area A = 90 mm2,

Length l = 3m,

Stress σ = 300 MPa,

Young’s modulus E = 200 GPa.

Volume V is given by the formula,

V = AL

  = (90 × 10−6) × 3

V = 27 x10−6 m3

The strain energy formula is given as,

U = σ2 / 2E× V

  = (300×106)2 / 2 x 200×109 x 27 x 10-6

Therefore, U = 12.15 J.

Therefore, the strain energy of rod is 12.15 J.

 

 

Answer 2

U=8/2....have a good day