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Shaft Torsional Deflection and Rigidity Formulae and Calculator

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Shaft Torsional Deflection and Rigidity Formulas and Calculator

Shaft Torsional Deflection Rigidity is based on the permissible angle of twist. The amount of twist permissible depends on the particular application, and varies about 0.8 deg. per foot for machine shafts to about 1.0 deg per foot for line shafting.

For a Hollow Circular Shaft Eq. 1
θ = 584 M_t L / G ( d_o⁴ - d_i⁴ )

For a Solid Circular Shaft Eq. 2
θ = 584 M_t L / ( G d⁴ )

Where:

θ = angle of twist, deg.
M_t = torsional moment, in-lb
d_o = diameter outside hollow shaft, in
d_i = diameter inside hollow shaft, in
L = length of shaft, in
d = diameter solid shaft, in
G = torsional modulus of elasticity, psi

Related:

• Power Transmission Shaft Design Formulas and Calculator
• Cross Shaft Torsional Deflection, Stress Equation and Calculator
• Strength and Mechanics of Materials
• ASME Shaft Design Allowable Stress and Diameter equations and calculators
• Torsional Stiffness Solid Shaft Equations and Calculator
• Torsion Spring Force Calculator and Formula
• Truck and Car Universal Joint Design and Engineering Equation
• Combined Loading Circular Shaft in Direct Compression and Torsion Equations and Calculator

References:

• Schaum's Outline Theory and Problems of Machine Design -
  • McGraw Hill (1968),
  • Allen S. Hall, Alfred R. Holowenko,
  • Herman G. Laughlin