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Circular Shaft Torsional Stiffness Calculator — result sheet
Estimate the torsional stiffness, twist torque, and outer-fiber shear stress of a circular shaft from material rigidity and geometry.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a circular shaft J = π(do⁴−di⁴)/32; torsional stiffness k = GJ/L; torque T = kφ; outer-fiber shear stress τ = T(do/2)/J.
This page treats a circular shaft as a linear torsional spring. It calculates the polar second moment from outer and inner diameters, applies the shear modulus and length, and then converts a chosen twist angle into torque and outer-fiber shear stress. It is a first-pass elastic relation, not a shaft-sizing approval: keyways, stress concentrations, fatigue, yielding, buckling, joints, speed, temperature, and noncircular sections need additional analysis.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Shear modulus — GPa; minimum 1.0E-6; maximum 1000000
- Outer diameter — mm; minimum 1.0E-6; maximum 1000000
- Inner diameter — mm; minimum 0; maximum 1000000
- Shaft length — m; minimum 1.0E-6; maximum 1000000
- Twist angle — °; minimum 1.0E-6; maximum 180
Worked example
| Input | Value |
|---|---|
| Shear modulus | 79.3 |
| Outer diameter | 20 |
| Inner diameter | 0 |
| Shaft length | 1 |
| Twist angle | 1 |
A 20 mm solid, 1 m shaft with G = 79.3 GPa has J about 1.5708e−8 m⁴, stiffness about 1,245 N·m/rad, and torque about 21.73 N·m at 1° twist.
Assumptions and limits
- The shaft is circular, prismatic, and homogeneous with a constant shear modulus.
- The inner diameter is nonnegative and strictly smaller than the outer diameter.
- The material remains in the small-twist linear elastic range represented by T = kφ.
- Diameters are converted from millimetres to metres and the twist angle is converted to radians.
- The stress output is the elastic Saint-Venant outer-fiber value for the ideal circular section.
- Loads, keyways, shoulders, threads, stress concentrations, fatigue, plasticity, dynamics, and safety factors are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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