Torsional Deflection of Shaft

Strength Mechanics of Materials


Torsion Rigidity

Torsional Deflection of Cylinder

The angular deflection of a cylinder with torsion loading applied:

θ = L T / (G Io

Open Torsional Deflection of Shaft Calculator


θ = angular shaft deflection (radians)
T = torque (N-mm, in-lb)
L = length of shaft (mm, in)
G = shear modulus of rigidity (Mpa, psi)
Io = second moment of inertia (mm4, in4)

The angular deflection of a torsion solid shaft

θ = 32 L T / (G π D4)

Open Angular Deflection of a Torsion Solid Shaft Calculator


D = outside diameter (mm, in.)

The angular deflection of  hollow shaft

θ = 32 L T / (G π (D4- d4))

Open Angular Deflection of Hollow Shaft Calculator   

The angle in degrees can be achieved by multiplying the angle θ in radians with 180/π 

Solid shaft (π substituted)

   θdegrees ≈ 584 L T / (G D4)


D = outside diameter (mm, in.)
d = inside diameter (mm, in.)

Hollow shaft (π sustituted)

   θdegrees ≈ 584 L T / (G (D4- d4)       

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