Mechanical Engineering - Strength of Materials - Discussion

Gradually applied load is given as σ = (F/A) ------ (F is the gradually applied load)

Here, work done is given as (F δL) / 2 and strain energy stored = (σ2 / 2E) AL
Work done is equal to the strain energy stored.

(F δL) / 2 = (σ2 / 2E) AL

Therefore, σ = (F/A) ----------- (1)
- Suddenly applied load is given as σ = (2F/A), here work done = (F δL)

(F δL) = (σ2 / 2E) AL
Therefore, σ= (2F/A) ------------- (2)
From (1) and (2), it can be concluded that,
Hence, suddenly applied load is twice the gradually applied load.

The given answer is correct.

With gradual loading, it is half the stress produce than without gradual.
With sudden loading, it is twice the stress produce than without sudden.

Hence, strain energy for sudden loading will be 1/4th of gradual loading.

As stress is 2 times in case of sudden loading the strain energy.

U=(sigma^2/2E)*V,
And sigma = 2(p/A),

Therefore strain energy in case of sudden loading is 4 times than in the case of gradual loading.

We know U=strain energy, U= Pdl.
Take, Us = strain energy stored suddenly and Ug= strain energy stored gradually.

Us = Pdl, Ug=1/2Pdl.
Asked, Us=_____Ug?

Answer. Pdl = 1/2Pdl.
Therefore Us = 1/2 Ug.

Strain energy = .5 * W * dL = (.5*W^2*L)/AE.
Now, the load is twice wen it is sudden w.r.t gradually applied.
Strain energy for sudden applied load = [.5 * (2W)^2 * L]/AE = 4[.5 * W^2 * L]/AE.

Answer is D
U=1/2 * P * delta
Delta= P * V/E
So U= P * δ/2E
Put the value of p for gradually applied.
And The value of 2p for suddenly applied load.
So the answer is 4 times.

Strain energy for the suddenly applied load is 4 times the gradually applied load. And stress energy due to suddenly applied load is twice the gradually applied load.

U = (stress square*Volume)/2.
For sudden loading Stress = 2W /A so put the value and you find U2= 4 times of U1.

It depends on the elongation too. For the same deltaL, U2 is twice U1.

strain energy is directly proportional to stress^2.