The design of a transmission shaft is governed by two primary specifications: the power it transmits and its rotational speed. These parameters guide the selection of the shaft's material and cross-sectional dimensions, ensuring that the material's maximum shearing stress remains within the elastic limit while transmitting the desired power at the given speed. The system's power is intrinsically linked to the applied torque. The torque applied to the shaft can be calculated by reconfiguring the terms.

This calculation considers both the power requirements and the shaft's rotational speed. Once the torque and maximum allowable stress are calculated, they are incorporated into the elastic torsion formula. This process yields the minimum permissible value for the shaft radius. In the case of a solid circular shaft, the ratio of the polar moment of inertia to the shaft radius varies as the cube of the shaft radius. The minimum required value for the shaft radius is computed by substituting this value.

For a hollow cylinder shaft, the computations render the minimum permissible value for the outer radius of the shaft. As a result, the design process for a transmission shaft is a careful balance of power, speed, stress limits, and physical dimensions.