19.7 : 圆轴中的应力集中

Recall the elastic torsion formula, applicable to a circular shaft with a uniform cross-section. Here, it is assumed that the shafts are loaded at their ends by rigid plates solidly attached to them.

However, torques are often applied to the shaft via flange couplings or gears connected by keys fitted into keyways.

This alters the stress distribution close to the torque application point, diverging from the distributions projected by the torsion formula.

Abrupt changes in diameter could also lead to non-uniform distribution of stress concentrations, especially near the joints.

These stresses can be reduced by implementing a fillet. The maximum value of the shearing stress at the fillet can be expressed in terms of the stress concentration factor.

The stress concentration factor, dependent on shaft diameter ratios and fillet size, can be precomputed and stored for practical use.

This analysis method remains valid as long as the maximum stress value does not exceed the material's elastic limit. If plastic deformations occur, they will result in lower maximum stress values.