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.