Torsional Stiffness of a Shaft
Torsional Stiffness of a Shaft
Torsional stiffness sets how much a shaft twists under torque — critical for precision drives and torsional vibration.
The torsional stiffness is k = G·J/L. where G is the shear modulus, J the polar second moment of area and L the length.
Inputs
G := 80 GPa=80000 MPa
J := 1.0e-6 m^4=1e-06 m^4
L := 1.5 m=1.5 m
Stiffness rises with G and J and falls with length.
k := G·J/L=53333.33 Nm
Results
A higher stiffness means less twist per unit torque and a higher torsional natural frequency. Shortening the shaft or increasing its diameter both stiffen it.
Assumptions & limitations
- Solid or hollow circular section.
- Linear-elastic material.
- Uniform section along the length.