19.7:
Stress Concentrations in Circular Shafts
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.
19.7:
Stress Concentrations in Circular Shafts
Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions predicted by the torsion formula. Additionally, sudden shifts in the diameter can also cause an irregular distribution of stress concentrations, particularly around the joint areas.
These stresses can be mitigated by incorporating a fillet. The stress concentration factor can represent the highest value of the shearing stress at the fillet. This factor, which relies on the ratios of the shaft diameter and the size of the fillet, can be calculated in advance and saved for future reference and practical application. This analysis method remains effective if the maximum stress value stays within the material's elastic limit. If plastic deformations happen, they will lead to lower peak stress values, emphasizing that understanding these factors and their impact on stress distribution is crucial for accurate and practical applications of the elastic torsion formula.