Strength of Materials

Q1: The stress induced in a body, when suddenly loaded, is __________ the stress induced when the same load is applied gradually.

A equal to

B one-half

C four times

D twice

ANS:C - twice

Strain energy stored in the body = Work done by the load in deforming the body.
Strain energy stored in the body = Area of the load-extension curve.
Strain energy stored in the body = P. x.
U = P. x.

As we know that maximum strain energy stored in the body U will be provided by the following expression as mentioned here.
U=(σ^2/2E)*V.
U=(σ^2/2E)*A*L.
P*x=(σ^2/2E)*A*L.

Now we will secure the value of extension x in terms of Stress, Length of the body and Young's modulus of the body by using the concept of Hook's Law.
According to Hook's Law.

Within elastic limit, stress applied over an elastic material will be directionally proportional to the strain produced due to external loading and mathematically we can write above the law as mentioned here.

Stress = E. Strain
Where E is Young's Modulus of elasticity of the material.

σ = E. ε.
σ = E. (x/L).
x = σ. L/ E.

Let use the value of the extension or deformation "x" in the above equation and we will have
P*(σ/E)*L=[(σ^2)/(2*E)]*A*L.
P=σ*A/2.
σ=2(P/A).

Therefore, we can say here that maximum stress induced in the body due to suddenly applied load will be twice the stress induced in the body with the same value of load applied gradually.



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