Beam Torsion Calculator

Model torque effects across common beam sections quickly. Estimate stress, twist, rigidity, and safety margins. Clear results help engineers verify rotating members with confidence.

Beam Torsion Inputs

Example Data Table

Case Section Torque Length G Main Dimensions Approx. Stress Approx. Twist
1 Solid Circular 2.5 kN·m 1.2 m 79 GPa Diameter = 60 mm 58.95 MPa 1.71 deg
2 Hollow Circular 3.2 kN·m 1.5 m 79 GPa Do = 80 mm, Di = 50 mm 37.56 MPa 1.02 deg
3 Rectangular 1.8 kN·m 1.0 m 26 GPa 100 mm × 50 mm 31.46 MPa 1.39 deg

Formula Used

This calculator works in consistent internal units of N·mm, mm, and MPa. It then reports engineering values in readable output units.

Solid circular section

J = πd4 / 32
τmax = Tc / J, where c = d / 2
θ = TL / JG

Hollow circular section

J = π( Do4 − Di4 ) / 32
τmax = T(Do / 2) / J
θ = TL / JG

Rectangular section

J ≈ ab3[ 1/3 − 0.21(b/a)(1 − b4 / 12a4) ]
τmax ≈ T / { ab2[ 1/3 − 0.21(b/a)(1 − b4 / 12a4) ] }
θ = TL / JG

Symbols: T = torque, L = member length, G = shear modulus, J = torsion constant, τ = shear stress, and θ = angle of twist.

How to Use This Calculator

Choose the section type first. Enter the applied torque, member length, shear modulus, and geometric dimensions using any supported units.

Provide allowable or yield shear stress if you want utilization and factor of safety. Leave your design notes if you want them included in exports.

Press Calculate Torsion. The page shows results above the form, places the graph below the form, and enables CSV and PDF exports.

Use the example data table as a quick validation reference. For rectangular sections, treat peak stress values as engineering approximations.

Frequently Asked Questions

1. What does this beam torsion calculator solve?

It calculates torsion constant, maximum shear stress, angle of twist, torsional stiffness, strain energy, shear strain, utilization, and factor of safety for common beam sections.

2. Which section types are supported?

The tool supports solid circular, hollow circular, and rectangular sections. Circular cases use standard closed-form equations, while the rectangular option uses a widely accepted approximation.

3. Why is shear modulus required?

Shear modulus controls angular deformation under torque. Without G, the calculator cannot estimate twist angle or torsional stiffness, even though stress can still be related to geometry and torque.

4. Why are rectangular results marked approximate?

Noncircular members warp when twisted. Because of that behavior, rectangular torsion uses approximation formulas for torsion constant and maximum shear stress rather than exact circular expressions.

5. What units can I use?

You can mix metric and imperial input units for torque, length, dimensions, and stress. The calculator converts everything internally into consistent engineering units before solving.

6. What does factor of safety mean here?

Factor of safety is the ratio between provided allowable or yield shear stress and calculated maximum shear stress. Larger values generally indicate more remaining torsional capacity.

7. Can I use this for shafts as well?

Yes. The same torsion relations are commonly applied to rotating shafts, drive members, and beam-like components carrying torque, as long as loading assumptions remain reasonable.

8. What should I check beyond this calculator?

You should still review fatigue, stress concentrations, combined loading, support conditions, dynamic effects, allowable twist limits, and code requirements before finalizing a design.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.