27.5:
Impact Loading
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.
27.5:
Impact Loading
Impact loading occurs when a moving object collides with a stationary structure, such as a rod with a uniform cross-sectional area fixed at one end. Under these conditions, the rod absorbs the kinetic energy from the striking object, leading to deformation and subsequent stress development. As the rod returns to its original position and reaches maximum stress, the absorbed energy, initially manifested as kinetic energy, transforms entirely into strain energy.
In cases of elastic deformation, where the material returns to its initial shape without permanent damage, the strain energy accumulated at the point of maximum deformation is equivalent to the kinetic energy of the moving object. This equivalence assumes that no energy is lost to heat or rebound, an idealization not typically found in practical environments. From this relationship, the maximum stress experienced by the rod based on the velocity and mass of the striking object and the rod's modulus of elasticity can be derived.
The assumptions made in this analysis lead to a conservative approach to engineering design, ensuring that structures can withstand unexpected forces. This approach often results in over-engineering, incorporating safety factors to account for energy losses and other dynamics not covered by the theoretical model.