27.6 : 悬臂梁上的冲击载荷

Consider a cantilever beam fixed at one end, having a circular cross-section.

If an object is dropped on the free end of the cantilever from a height h, then the potential energy of the mass is converted into kinetic energy. This kinetic energy is then transferred to the cantilever due to impact loading.

The maximum strain energy at the fixed end is expressed in terms of the bending moment, where the bending moment at a distance x from the free end is written as a negative product of the weight of the object and distance x.

Integrating the strain energy equation and rearranging the terms expresses the maximum load.

The maximum stress occurring is proportional to the maximum load and inversely proportional to the moment of inertia of the cantilever.

Substituting the value of the maximum load in terms of strain energy and rewriting the moment of inertia in terms of the volume of the cantilever gives the expression for maximum stress in terms of the modulus of elasticity and the strain energy developed in the cantilever.