Consider a rod of uniform cross-sectional area fixed at one end. When another moving object hits the free end of the rod, the rod deforms, and stress is developed within it.  

As the rod reaches the maximum stress, it vibrates about the mean position. The stress that has built up disappears as it comes to rest. These events are known as impact loading.

Here, it is assumed that the striking body transfers its entire energy to the rod, meaning no heat dissipation occurs, and the striking body does not bounce off the rod.

So, the strain energy corresponding to the maximum stress equals the kinetic energy of the striking body.

In the elastic regime of the deformation, the strain energy can be rewritten in terms of the maximum stress and the modulus of elasticity.

Rearranging the terms, an expression for the maximum stress in terms of the velocity of the striking body is obtained.

The assumption used here results in a conservative design for the impact loading, as the assumptions are not valid in real systems.