Calculator inputs
Plotly graph
The chart shows how the warping constant changes when one entered dimension scales from 80% to 120%, while the remaining dimensions stay fixed.
Formula used
For the symmetric I-section model, the calculator uses these expressions:
Clear web depth: h = D - 2tf
Flange centroid spacing: h0 = D - tf
Minor-axis inertia: Iy = [h·tw3 + 2tfB3] / 12
Torsional constant: J = [2B·tf3 + h·tw3] / 3
Warping constant: Cw = Iy·h02 / 4
Warping rigidity: E·Cw
The final warping constant has dimensions of length6. Keep all section dimensions in one unit system for valid results.
How to use this calculator
- Select the section length unit.
- Choose a material preset or keep custom values.
- Enter overall depth, flange width, flange thickness, and web thickness.
- Click the calculate button.
- Read the result panel above the form for Cw, Iy, J, and E·Cw.
- Review the sensitivity graph to see which dimension most changes warping behavior.
- Export the current result as CSV or PDF when needed.
Example data table
| Case | D (mm) | B (mm) | tf (mm) | tw (mm) | h0 (mm) | Iy (mm4) | J (mm4) | Cw (mm6) |
|---|---|---|---|---|---|---|---|---|
| Example 1 | 300 | 150 | 15 | 8 | 285 | 8.449020e+6 | 3.835800e+5 | 1.715679e+11 |
| Example 2 | 450 | 200 | 20 | 10 | 430 | 2.670083e+7 | 1.203333e+6 | 1.234246e+12 |
| Example 3 | 600 | 250 | 25 | 12 | 575 | 6.518337e+7 | 2.920967e+6 | 5.387813e+12 |
FAQs
1. What does the warping constant represent?
It measures how strongly a section resists restrained warping during torsion. Larger values usually mean greater resistance to nonuniform twisting effects.
2. Which sections suit this calculator?
It is intended for doubly symmetric I-sections with equal flanges. It is not a full solver for channels, tees, asymmetric I-shapes, boxes, or arbitrary thin-walled sections.
3. Why is the result unit length to the sixth power?
The equation multiplies a second moment of area, with length to the fourth power, by a squared distance. That produces length to the sixth power.
4. Why does flange width change Cw so much?
Minor-axis inertia includes flange width cubed. Because Cw depends on Iy, wider flanges often increase the warping constant rapidly.
5. What is the difference between J and Cw?
J describes Saint-Venant torsion for uniform twist. Cw describes resistance related to restrained warping in nonuniform torsion. Both can matter in open sections.
6. Does material affect the warping constant?
The geometric warping constant depends only on the section shape. Material changes the warping rigidity E·Cw, which is why Young’s modulus is included.
7. Are fillets and corner radii included?
No. This version uses an idealized plate model. Rolled-shape fillets and detailed geometry can shift section properties slightly.
8. When should I use a more advanced tool?
Use a more advanced tool for asymmetric sections, welded built-up members, tapered shapes, code checks, and cases where exact manufacturer properties are required.