Torsion Shear Stress Calculator

Calculator Inputs

Formula Used

For a circular shaft in elastic torsion, the shear stress varies linearly with radius:

• Shear stress: tau = (T · r) / J
• Solid shaft: J = (pi · d^4) / 32
• Hollow shaft: J = (pi · (do^4 − di^4)) / 32
• Twist angle: phi = (T · L) / (J · G)

Use the outer surface radius for maximum shear stress, especially for strength checks.

How to Use This Calculator

1. Select what you want to solve for, such as shear stress or required outer radius.
2. Choose the shaft type: solid, hollow, or custom J from test or CAD data.
3. Enter torque and geometry. Use consistent units or select conversion units here.
4. Pick the radius location for stress. Outer surface gives the maximum value.
5. Optionally enable twist to estimate angular deflection using L and G.
6. Click Calculate. Export the results using CSV or PDF buttons.

Example Data Table

Values are representative examples for verification and comparison only.

Professional Article

1. Why torsion shear stress matters

Torsional loading is common in drive shafts, spindles, couplings, and fasteners. When a shaft transmits torque, internal shear stress rises with radius and peaks at the outer surface. Designers often check this peak stress against allowable shear limits to prevent yielding or fatigue damage.

2. The stress distribution across the section

For elastic circular shafts, the shear stress varies linearly from zero at the centerline to a maximum at the surface. For hollow shafts, the material near the outer radius still carries most of the torque. This is why hollow sections can be weight-efficient at similar strength levels.

3. Polar moment of inertia as the key stiffness term

The polar moment J captures how the cross-section resists twisting. For a solid circular shaft, J scales with the fourth power of diameter. Doubling diameter increases J by sixteen times, which significantly reduces stress and twist for a fixed torque.

4. Typical engineering stress ranges

Many steel components use shear moduli near 75–82 GPa, while aluminum alloys are commonly 24–28 GPa. A mild steel shaft with yield strength around 250 MPa may use an allowable shear stress of roughly 80–120 MPa, depending on codes, safety factor, and loading type.

5. Sizing with allowable shear stress

When sizing a shaft, allowable shear stress is selected from material and design criteria, then an outer diameter or radius is computed. For hollow shafts, the diameter ratio k = di/do strongly affects capacity. For example, k = 0.6 reduces torsional strength compared with a solid shaft, but may reduce mass substantially.

6. Relating torque to power transmission

Torque often comes from power and speed, using T = P/omega. At 5 kW and 1500 rpm, the torque is about 31.8 N·m. Using accurate torque estimates prevents undersized designs and avoids unnecessary material use in low-load applications.

7. Twist angle and serviceability checks

Even if strength is acceptable, excessive twist can cause misalignment, backlash, or control issues. The twist angle phi depends on torque, length, J, and shear modulus. Longer shafts are more flexible, and increasing diameter is an effective way to reduce angular deflection.

8. Practical validation and reporting

Always verify input units, check whether stress is evaluated at the correct radius, and confirm hollow dimensions are realistic. For audits or client reporting, exporting results to CSV or PDF preserves assumptions and supports traceability. Use multiple scenarios to explore sensitivity to diameter, torque, and allowable stress.