Shafts Torsion
Calculator for shear stress, angular deflection, and diameter of solid and hollow circular shafts subjected to torsion
Shear Stress in Circular Shafts
When a shaft is subjected to torque, shearing stress is produced. The shear stress varies from zero at the axis to maximum at the outer surface.
Formula: τ = T × r / J
Where:
- τ = shear stress (Pa)
- T = twisting moment (Nm)
- r = distance from center (m)
- J = Polar Moment of Inertia (m⁴)
Torsional Deflection of Shaft
The angular deflection of a shaft under torsion:
Solid Shaft: α = 32 L T / (G π D⁴)
Hollow Shaft: α = 32 L T / (G π (D⁴ - d⁴))
Where:
- α = angular deflection (radians)
- L = length of shaft (m)
- G = Shear Modulus of Rigidity (Pa)
- D = outer diameter (m)
- d = inner diameter (m)
Polar Moment of Inertia
Measure of shaft's ability to resist torsion:
Solid Shaft: J = π D⁴ / 32
Hollow Shaft: J = π (D⁴ - d⁴) / 32
Where:
- D = outer diameter (m)
- d = inner diameter (m)