Question

derivation for energy stored in a deformed body.​

Answer 1

Answer:

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. ... Regarding young's modulus E, the strain energy formula is given as, U = σ2 / 2E × V.

Answer 2

The stored energy is $\dfrac{1}{2}\times F\times\Delta L$

Explanation:

Strain energy :

Stored energy is defined strain energy in deformed body.

Strain energy is equal to the work done on the body to deformed it.

We know that,

Young's modulus is

$Y=\dfrac{FL}{Al}$

$F=\dfrac{YAl}{L}$

Where, F = force

A = area of cross section

l = stretched length

L = length

We need to calculate the store energy

Using formula of work done

$\int_{0}^{W}{dw}=\int_{0}^{\Delta L}{F\cdot dl}}$

Put the value in the equation

$\int_{0}^{W}{dw}=\int_{0}^{\Delta L}{\dfrac{YAl dl}{L}}$

On integrating

$W=\dfrac{YA}{L}(\dfrac{l^2}{2})_{0}^{\Delta L}$

$W=\dfrac{1}{2}\times F\times\Delta L$

Hence, The stored energy is $\dfrac{1}{2}\times F\times\Delta L$

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Topic : strain energy

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