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Angle of Twist Shaft Subjected to Torque Formula and Calculator

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Angle of Twist - Shaft Subjected to Torque Formula and Calculator

This calculator will determine the angle of twist due to the applied torque on a shaft - results given in radians or and degrees

Eq. 1
Modulus of Elasticity

G = E / ( 2 ( 1 + ν ) )

Eq. 2
Polar Moment of Inertia

J = π ( D_o⁴ - D_i⁴ ) / 32

Eq. 3
Angle of Twist

θ = T L / ( G J )

rad to deg conversion
( 1 rad ) x ( 57.2957795 deg / rad) = 57.2957795 radians

Where:

E = Modulus of Elasticity (psi, Pa)
ν = Poisson Ratio (dimensionless)
D_o = Shaft Outer Diameter (ft, m)
D_i = Shaft Inner Diameter (ft, m)
T = Torque applied (ft-lbf, N-m)
L = Length of Section (ft, m)
G = Modulus of Rigidity (psi, Pa)
J = Polar Moment of Inertia (ft⁴, m⁴)
θ =Shaft Angle of Twist (rad)

Source:

Reference: Reference: Samuel. E Robello. 501 Solved Problems and Calculations for Drilling Operations. Sigma Quadrant. 2015. Houston, Texas, Page: 369.

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