The shaft is made in steel with modulus of rigidity 79 GPa (79 10 9 Pa). (π / 16) τ max ((2 R) 4 - (2 r) 4) / (2 R)Įxample - Shear Stress and Angular Deflection in a Solid CylinderĪ moment of 1000 Nm is acting on a solid cylinder shaft with diameter 50 mm (0.05 m) and length 1 m. Α degrees ≈ 584 L T / (G (D 4- d 4) (6b) Torsion Resisting Moments from Shafts of Various Cross Sections The angle in degrees can be achieved by multiplying the angle θ in radians with 180 / π. 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: