Calculation
It ≈ (b1·t1³ + h·t2³ + b2·t3³)/3
For an open thin-walled section, wall thickness enters with the third power; a slit changes torsional behaviour fundamentally compared with a closed cell.
St.-Venant-Torsionskonstante eines offenen dünnwandigen Profils · It ≈ Σ bi·ti³/3
Calculate the Torsion Constant of an Open Thin-Walled Section
For an open thin-walled section, wall thickness enters with the third power; a slit changes torsional behaviour fundamentally compared with a closed cell.
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Result
Select a target and calculate.
Understand the inputs
- Saint-Venant torsion constant It — Geometric property of the open section in mm⁴; with free warping, G·It gives torsional rigidity. Do not confuse it with a second moment of area about a bending axis.
- First free flange length b1 — Midline length of the first straight open wall strip from the web; zero if absent.
- First flange thickness t1 — Uniform wall thickness of the first strip from drawing or measurement; small relative to its length.
- Web midline length h — Straight centreline length of the middle wall strip between flanges.
- Web thickness t2 — Uniform thickness of the middle strip; small relative to h.
- Second free flange length b2 — Midline length of the second straight open wall strip; zero for an L-section.
- Second flange thickness t3 — Uniform thickness of the second strip; when b2 = 0 it has no effect on the result.
Example
An open U-section with 50 mm + 100 mm + 50 mm of wall midline and 2 mm uniform thickness has It ≈ (50+100+50)·2³/3 = 533.3 mm⁴.
Assumptions and limits
Three straight thin open wall strips, each of uniform thickness, with negligible corner regions. Saint-Venant rigidity GIt applies to free warping; restrained warping adds normal stresses. Closed or multicell sections need another model. The calculation gives It only, not stress or twist angle.
Understand Torsion constant of open thin-walled sections
A thin open section often twists much more readily under torque than a closed one. This calculator finds its geometric Saint-Venant torsion constant from up to three straight wall strips.
What does this quantity describe?
Torsion constant It is the geometric part of torsional rigidity G·It, where G is material shear modulus. For a straight thin open wall strip of midline length bi and uniform thickness ti, its approximate contribution is bi·ti³/3. Here two free flanges of lengths b1 and b2 and a middle web of length h give It ≈ (b1t1³ + ht2³ + b2t3³)/3. The cubic thickness dependence explains the low torsional rigidity of thin open walls.
Formula and variables
It ≈ (b1·t1³ + h·t2³ + b2·t3³)/3
Per strip: It,i ≈ bi·ti³/3Three strips: It ≈ (b1t1³ + ht2³ + b2t3³)/3With free warping: torsional rigidity G·It
| Symbol / input | Meaning |
|---|---|
| Saint-Venant torsion constant It | Geometric property of the open section in mm⁴; with free warping, G·It gives torsional rigidity. Do not confuse it with a second moment of area about a bending axis. |
| First free flange length b1 | Midline length of the first straight open wall strip from the web; zero if absent. |
| First flange thickness t1 | Uniform wall thickness of the first strip from drawing or measurement; small relative to its length. |
| Web midline length h | Straight centreline length of the middle wall strip between flanges. |
| Web thickness t2 | Uniform thickness of the middle strip; small relative to h. |
| Second free flange length b2 | Midline length of the second straight open wall strip; zero for an L-section. |
| Second flange thickness t3 | Uniform thickness of the second strip; when b2 = 0 it has no effect on the result. |
Choose the inputs correctly
b1 and b2 are midline lengths of the free flanges from the section drawing; a missing flange may have zero length. h is positive web midline length. t1, t2 and t3 are uniform thicknesses of corresponding strips from drawing or measurement; they must be positive and much smaller than their strip lengths. It is torsion constant in mm⁴ for later twist calculations, not a second moment of area about a bending axis.
How to use the calculator
Check that the wall is open and not welded into a closed loop. Split the straight wall midlines into no more than three segments, enter lengths and thicknesses, and calculate It. Use b2 = 0 if there is no second flange. To find twist, also determine G, member length and torque in a suitable torsion model and check whether warping is free.
Worked example
An open U-section has b1 = b2 = 50 mm, h = 100 mm and thickness t = 2 mm throughout. Thus It ≈ (50·2³ + 100·2³ + 50·2³)/3 = 533.3 mm⁴. Doubling thickness alone multiplies It by eight while thin-wall assumptions remain valid.
Understand the result and units
Each strip contributes linearly with length but cubically with thickness. Open and closed sections of similar outside shape must therefore use different torsion models.
All lengths convert internally to metres and It to m⁴. The existing SI registry converts millimetres; mm·mm³ gives mm⁴. It and second moment of area share a unit but describe different properties.
Typical applications
Geometric pre-calculation for open U-, L- and similar thin-walled sections in torsional deflection with free warping.
Assumptions, limits and common mistakes
Open thin-walled sections of at most three straight strips, each of uniform thickness, with negligible corners. If warping is restrained, warping torsion can change rigidity and normal stresses substantially. Closed or multicell sections, thick walls and local connections are excluded; the result is not a strength verification.
Common mistake: Do not use the strip sum for a welded or otherwise closed perimeter. Assign each thickness to the correct strip; doubling it multiplies that contribution by eight. Do not read It as a bending second moment of area.
Frequently asked questions
What is “Torsion constant of an open thin-walled section” used for?
Geometric pre-calculation for open U-, L- and similar thin-walled sections in torsional deflection with free warping.
Where do the input values come from?
b1 and b2 are midline lengths of the free flanges from the section drawing; a missing flange may have zero length. h is positive web midline length. t1, t2 and t3 are uniform thicknesses of corresponding strips from drawing or measurement; they must be positive and much smaller than their strip lengths. It is torsion constant in mm⁴ for later twist calculations, not a second moment of area about a bending axis.
What does the result not cover?
Open thin-walled sections of at most three straight strips, each of uniform thickness, with negligible corners. If warping is restrained, warping torsion can change rigidity and normal stresses substantially. Closed or multicell sections, thick walls and local connections are excluded; the result is not a strength verification.