Suddenly Applied Loads:

If a load P is applied slowly to a bar to generate an extension δ, the load-extension graph will be as illustrated in Figure. However, if a load P′ is applied suddenly to the bar (by suddenly we mean that the value of P′ is attained instantaneously but not slowly as is the case with P) so as to develop the same extension δ, the load extension graph now looks as given in Figure

Figure

As the bar is strained to the similar extent in both of the cases, the strain energy must be the similar for the two cases. Though, strain energy is equal to the work done by the load.

∴          W = W ′

or         (½) × P δ= P′ δ or  P′ = P/2

It means that the suddenly applied load which is needed to generate a certain value of instantaneous strain is half the equivalent value of static load (steadily applied load) needed to generate the same strain. Vice-versa, one might say that the effect of a suddenly applied load is two times that attained when the load is applied gradually. Therefore, greater care should be exercised whereas designing structural elements that are susceptible to sudden loading conditions.