Warping Constant Calculator

Calculator

Section type

Pick the approach that matches your data source.

Output unit for Cw

Warping constant has length⁶ units.

I/H input method

Dimensions mode uses a common sharp-corner approximation.

Length unit for dimensions

Overall depth, d

Flange width, bf

Flange thickness, tf

Web thickness, tw

Iy (minor-axis second moment)

Iy unit

h0 (distance between flange centroids)

h0 unit

Warping constant, Cw

Cw unit

Built-in checks

Requires positive inputs and realistic thickness relationships.
Highlights that closed thin-walled sections often use Cw ≈ 0.
Shows alternate units to help spot conversion mistakes.

Good to know

Warping constant is used with torsion and lateral-torsional buckling models for open sections. If you have a section table value, prefer manual entry.

Example data table

Section	Inputs	Computed result
I/H (dimensions)	d=300 mm, bf=150 mm, tf=12 mm, tw=8 mm	Cw ≈ 1.402e+11 mm⁶
I/H (Iy & h0)	Iy=1.50e+8 mm⁴, h0=288 mm	Cw ≈ 3.110e+12 mm⁶
Closed thin-walled tube	Typical design assumption	Cw ≈ 0

Examples are illustrative and use simplified geometry assumptions.

Formula used

Warping constant for symmetric I/H

A commonly used practical expression is:

Cw = (Iy · h0²) / 4

Cw is the warping constant (length⁶).
Iy is the minor-axis second moment of area (length⁴).
h0 is the distance between flange centroids (length).

Iy from dimensions (sharp-corner approximation)

For a symmetric I/H shape (ignoring fillets):

Iy = 2 · (tf · bf³ / 12) + ( (d - 2tf) · tw³ / 12 )

h0 = d - tf

How to use this calculator

Select the section type that matches your member.
For I/H, choose Dimensions or Known properties.
Enter values carefully and pick the correct units.
Click Calculate to see the result above the form.
Use Download CSV for spreadsheets or Download PDF for reports.

Warping constant guide

1) What the warping constant represents

The warping constant Cw describes how an open section resists non-uniform torsion. When a beam twists, flanges and webs do not stay perfectly planar, so the cross‑section “warps.” A larger Cw means the section can better develop warping restraint effects in analysis.

2) Where it appears in calculations

Cw is used with torsion and lateral‑torsional buckling models for open shapes, especially I/H sections. It is commonly combined with stiffness terms such as E·Cw and depends on boundary restraint. If ends are free to warp, warping effects reduce; if restrained, warping stresses can increase.

3) Units and scaling behavior

Cw has length⁶ units (mm⁶, in⁶, m⁶). Because of the sixth‑power scaling, small changes in flange spacing can strongly change Cw. Doubling a characteristic length can increase Cw by about 64×, so unit consistency is critical.

4) Open versus closed sections

Closed thin‑walled tubes and boxes mainly resist torsion through St. Venant shear flow, so many design workflows treat Cw as approximately zero. Open thin‑walled sections, such as I‑beams, channels, and angles, can develop significant warping and therefore have non‑zero Cw values.

5) The I/H section shortcut used here

For a doubly symmetric I/H section, a common practical relation is Cw = (Iy·h0²)/4, where Iy is the minor‑axis second moment and h0 is the distance between flange centroids. In dimension mode, Iy is estimated from simple rectangles and ignores fillets.

6) Data to enter for reliable results

Use real section dimensions from drawings or catalogs, including flange and web thickness. For rolled shapes, fillets slightly change Iy, so catalog values can be more accurate than purely geometric estimates. If you already have Iy and h0, select the known‑properties mode to reduce assumptions.

7) Interpreting results and spotting mistakes

Compare the computed Cw with a reference example or table value. For many rolled I‑beams, Cw often falls around 10¹⁰–10¹³ mm⁶, depending on size and flange spacing. If the number seems off by 10⁶ or 10¹², it is usually a unit mismatch (mm vs m) or an input typed in the wrong unit. This tool also shows mm⁶ and m⁶ simultaneously.

8) Practical workflow tip

When you are checking lateral‑torsional buckling, start with catalog section properties, verify the chosen h0 definition matches your reference, then export a CSV or PDF record. Saving the inputs and the computed Cw helps keep calculations auditable during design reviews and revisions.

FAQs

1) Is Cw the same as the torsional constant J?

No. J relates to St. Venant torsion (uniform twist). Cw relates to warping resistance (non‑uniform torsion) and is mainly important for open sections and buckling models.

2) Why does Cw have mm⁶ units?

Warping effects depend on a second moment (length⁴) times a squared spacing term (length²). Multiplying them produces length⁶, which is why output units are mm⁶, in⁶, or m⁶.

3) Should I use the closed‑section option for solid shafts?

Solid circular shafts are closed sections and typically use J for torsion. For many workflows, Cw is not required and can be taken as nearly zero compared with open sections.

4) What is h0 and how do I estimate it?

h0 is the distance between the centroids of the two flanges. For a symmetric I‑section with flange thickness tf and overall depth d, a common estimate is h0 ≈ d − tf.

5) Does the dimension method include fillets or tapers?

No. It uses a sharp‑corner rectangle approximation for Iy. If your shape has large fillets, tapered flanges, or non‑standard geometry, prefer catalog properties or manual entry.

6) What if my section is not symmetric?

This calculator targets symmetric I/H sections for the built‑in formula. For unsymmetric shapes, Cw requires more detailed section analysis. Use a section‑property program and enter the known Cw manually.

7) How can I quickly validate the output?

Run the same section in known‑properties mode using catalog Iy and your h0 value. If both approaches match within a few percent, your units and geometry assumptions are likely consistent.