Torsion of Solid and Hollow Shafts
This torsion calculator computes shear stress, angle of twist, polar moment of inertia (J),
and power transmitted by solid and hollow circular shafts based on classical torsion formulas.
Torsion of Solid and Hollow Shaft Calculator to calculate
maximum shear stress, angle of twist,
power requirement and polar moment of inertia
of a shaft under torsion. The calculator is only valid for sizing of
solid or hollow circular shafts.
A shaft is a rotating member, usually of cylindrical shape, used to
transmit torque, power and motion between elements such as electric or
combustion motors, gear sets, wheels, cams, flywheels, pulleys, turbines
and electric generators. Shafts can be solid or hollow. During power
transmission, shafts twist and stresses and deformations occur.
Torsion is the twisting of an object due to an applied torque.
When a shaft twists, one end rotates relative to the other and shear stresses
are produced on any cross section.
Shear stress is zero on the axis passing through the center of a shaft under torsion
and maximum at the outside surface. On an element where shear stress is maximum,
normal stress is zero. This element is oriented so that its faces are either
parallel or perpendicular to the shaft axis. To obtain stresses in other
orientations, plane-stress transformation is required, based on the shear
stresses found with this calculator.
Sign convention
-
Torque T:
Positive torque acts in the sense of shaft rotation and follows the
right-hand rule.
-
Shear stress τ:
Reported as a positive magnitude at the outer surface
(direction is implied by the torque sign).
-
Angle of twist θ:
Positive when the loaded end rotates in the same sense as the applied torque,
measured in radians (or converted to degrees).
-
Rotation speed ω:
Enter rotation speed as a positive value in rpm; the calculator converts it
internally to rad/s.
For typical shaft sizing, the magnitudes of τmax and θ are critical;
the direction is defined by the torque sense via the right-hand rule.
Torsion of shaft calculator
Solid circular shaft
Hollow circular shaft
Note: Use dot “.” as decimal separator.
Results
| Parameter |
Value |
| Maximum shear stress [τmax] |
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|
|
| Angle of twist [θ] |
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|
|
| Power requirement [P] |
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|
|
| Polar moment of inertia [J] |
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|
|
Definitions
Angle of twist:
Rotation of a cross-section from its original position when a torque is applied.
Dynamometer:
Device used to measure torque or power (eddy-current brake, magnetic powder brake,
hysteresis brake, etc.).
Modulus of rigidity (shear modulus G):
Rate of change of unit shear stress with respect to unit shear strain for pure shear
within the proportional limit.
Typical values: Aluminum 6061-T6 ≈ 24 GPa, structural steel ≈ 79.3 GPa.
Notch sensitivity:
A measure of how sensitive a material is to notches or geometric discontinuities.
Polar moment of inertia:
Geometric property of a cross-section; measure of its resistance to torsion.
Stress concentration factor:
Ratio of peak stress near a geometric discontinuity (holes, shoulders, fillets, cracks)
to the nominal average stress.
Torque meter:
Device for measuring torque on a rotating system.
Frequently Asked Questions (FAQ)
What is torsional shear stress in a shaft?
Torsional shear stress is the shear stress produced when a circular shaft is subjected to torque. It is zero at the center and maximum at the outer surface.
How do you calculate angle of twist?
The angle of twist is calculated using θ = TL / (GJ), where T is torque, L is length, G is shear modulus, and J is polar moment of inertia.
Is a hollow shaft stronger than a solid shaft?
For equal weight, a hollow shaft has higher torsional strength and stiffness because more material is distributed farther from the axis.
What units does the calculator support?
The calculator supports SI (N·m, mm, MPa, kW) and Imperial (lbf·in, ft, psi, hp) units through dropdown selections.
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