Mechanical Engineering - Strength of Materials - Discussion

strain energy is directly proportional to stress^2.

The right answer is twice.

According to me, the correct answer is B.

What is the formula for this?

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.

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.

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.

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.

Answer is twice.

Stress : - twice.

Strain energy :- four times.