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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 Mt L / G ( do4 - di4 )

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


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



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