The angular deflection of a torsion hollow shaft can be expressed as The angular deflection of a torsion solid shaft can be expressed as 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.
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