G = Shear Modulus of Rigidity - or Modulus of Rigidity (Pa, psf) The angular deflection of a torsion shaft can be expressed as Polar Moment of Inertia of a circular hollow shaft can be expressed asĭ = shaft inside diameter (m, ft) Diameter of a Solid Shaftĭiameter of a solid shaft can calculated by the formulaĭ = 1.72 ( T max / τ max ) 1/3 (4) Torsional Deflection of Shaft Polar Moment of Inertia of a circular solid shaft can be expressed as T max = (π / 16) τ max (D 4 - d 4) / D (2c) Circular Shaft and Polar Moment of Inertia Τ max = maximum shear stress (Pa, lb f/ft 2)Ĭombining (2) and (3b) for a hollow shaft T max = maximum twisting torque (Nm, lb f ft) Maximum moment in a circular shaft can be expressed as: ' Area Moment of Inertia' - a property of shape that is used to predict deflection, bending and stress in beamsĬircular Shaft and Maximum Moment or Torque.

' Polar Moment of Inertia' - a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque.' Polar Moment of Inertia of an Area' is also called ' Polar Moment of Inertia', ' Second Moment of Area', ' Area Moment of Inertia', ' Polar Moment of Area' or ' Second Area Moment'. It is analogous to the ' Area Moment of Inertia' - which characterizes a beam's ability to resist bending - required to predict deflection and stress in a beam. The ' Polar Moment of Inertia' is defined with respect to an axis perpendicular to the area considered. the ' Polar Moment of Inertia of an Area' is a measure of a shaft's ability to resist torsion.J = Polar Moment of Inertia of Area (m 4, ft 4) R = distance from center to stressed surface in the given position (m, ft) The shear stress in a solid circular shaft in a given position can be expressed as: The shear stress varies from zero in the axis to a maximum at the outside surface of the shaft. When a shaft is subjected to a torque or twisting a shearing stress is produced in the shaft.

Polar moment of inertia circle equation