Torsional Deflection of Shaft

Strength Mechanics of Materials
Mechanics of Machine Design, Equations and Calculators

Angular Deflection of Solid Cylinder or Shaft with Torsion Applied

Torsional Deflection of Cylinder

The angular deflection of a solid cylinder with torsion loading applied:

θ = L T / (G J )

Open Torsional Deflection of Shaft Calculator

Where:

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

#2 Equation and Calcuator for Angular Deflection of Solid Cylinder or Shaft with Torsion Applied

Torsional Deflection of Cylinder

θ = 32 L T / (G π D⁴)

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

Solid shaft (π substituted)

θ_degrees ≈ 584 L T / (G D⁴)

Open Angular Deflection of a Torsion Solid Shaft Calculator

Where:

D = outside diameter (mm, in.)
T = torque (N-mm, in-lb)
L = length of shaft (mm, in)
G = modulus of rigidity (Mpa, psi)

Angular Deflection of Hollow Shaft or Cylinder Equation and Calculator

Torsion Rigidity

Open Angular Deflection of Hollow Shaft Calculator

The angular deflection of hollow shaft

θ = 32 L T / (G π (D⁴- d⁴))

Where:

D = outside diameter (mm, in.)
d = inside diameter (mm, in.)
G = modulus of rigidity (Mpa, psi)
T = torque (N-mm, in-lb)
L = length of shaft (mm, in)

Hollow shaft (π substituted)

θ_degrees ≈ 584 L T / (G (D⁴- d⁴)

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