Circular-Shaft Torsional Shear Stress
Find the shear stress magnitude at a specified radius in an elastic circular shaft.
Try this formula
Calculate torsional shear stress magnitude or choose another supported quantity.
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Try this formula
Calculate torsional shear stress magnitude or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Torsional shear stress magnitude
Enter the known values to see the result.
Use small strains and a homogeneous, linearly elastic material. Loads are static or slowly applied; remain below the proportional limit. Use a solid or concentric hollow circular shaft under Saint-Venant torsion. Evaluate at a radius within the material; use the outer radius for maximum stress. J is a geometric area moment in m⁴, not rotational mass inertia.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Torsion — Shear Stress. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Shear stress increases linearly with radius in an elastic circular shaft. At the outer surface the stress is largest, while a larger polar area moment reduces the stress produced by the same torque.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Torsional shear stress magnitude | ||
| Applied torque magnitude | ||
| Distance from the shaft axis | ||
| Polar second moment of area |
Real-World Applications
Drive shafts
Estimate outer-surface torsional stress.
Shaft comparison
Compare circular sections under the same torque.
Worked Example
Problem
A circular shaft carries 500 N·m. At radius 0.02 m, J = 0.00000025 m⁴. Find the shear stress magnitude.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Torsion — Shear Stress. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use small strains and a homogeneous, linearly elastic material.
- • Loads are static or slowly applied; remain below the proportional limit.
- • Use a solid or concentric hollow circular shaft under Saint-Venant torsion.
- • Evaluate at a radius within the material; use the outer radius for maximum stress.
- • J is a geometric area moment in m⁴, not rotational mass inertia.
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