Calculation History
| Date | Calculation | Summary |
|---|---|---|
| No saved calculations yet. | ||
Formula Used
Unit conversion raises each ordinary length ratio to six. This preserves the warping constant’s length-to-the-sixth dimension. Always convert the complete factor before multiplying the value.
Cw,target = Cw,source × (Lsource ÷ Ltarget)⁶ Doubly symmetric I-section relation: Cw = Iy × h₀² ÷ 4 Thin-walled open-section integration: Cw = ∫A (ω - a - bx - cy)² dA
How to Use
Select direct conversion for a known published property. Choose source units, target units, and your preferred notation. Review displayed steps before using results in design work.
Select a generated shape for a preliminary section estimate. Enter consistent centreline dimensions and positive wall thicknesses. Verify estimates against trusted section tables before final structural decisions.
Choose custom segments for unusual open thin-walled layouts. Enter connected segment endpoints with matching shared-node coordinates. Avoid closed loops because they need different torsion methods.
Example Data
| Example | Inputs | Operation | Expected use |
|---|---|---|---|
| Unit conversion | 1 in⁶ | Convert into mm⁶ | Compare imperial and metric tables |
| I-section relation | Iy = 26,666,666.67 mm⁴; h₀ = 290 mm | Cw = Iyh₀²/4 | Check a doubly symmetric section |
| Generated I-section | d = 300; b = 200; tf = 10; tw = 8 mm | Thin-wall integration | Preliminary open-section estimate |
| Custom section | Five connected segment lines | Sectorial-coordinate integration | Model branching built-up layouts |
Warping Constant and Torsional Constant
The warping constant measures resistance associated with restrained section warping. The torsional constant measures Saint-Venant twisting resistance instead. Both properties affect torsional behaviour but represent different mechanisms.
Open sections often develop important warping stresses under restraint. Closed sections usually require different sectorial and torsional treatment. Use section-specific standards for every final engineering assessment carefully.
Assumptions and Limitations
Generated models place material along idealised centreline segments. They neglect fillets, corner radii, tapers, and residual details. These omissions can affect precise catalogue or design values.
Custom modelling supports connected open graphs without geometric cycles. All coordinates and thicknesses must share one consistent unit. Independent engineering verification remains necessary for safety-critical structural applications.
Frequently Asked Questions
Why is the warping constant measured in length⁶?
Its definition combines area with squared sectorial coordinates. Area contributes length squared, while sectorial coordinates contribute length squared. Squaring both contributions produces the overall sixth-power length dimension.
Does the calculator raise Cw itself to six?
No, the value already carries sixth-power length dimensions. Only the ordinary unit conversion ratio receives exponent six. Raising Cw again would produce an incorrect physical quantity.
Can I enter scientific notation?
Yes, standard numeric scientific notation works in all value fields. An entry like 1.25e12 remains valid and precise. Choose scientific output for especially large or tiny results.
What does h₀ represent?
It represents the distance between flange centroids in I-sections. It differs slightly from the section’s complete overall depth. Use measured centroid spacing for the most reliable calculation.
Are generated section values exact?
They are thin-wall centreline estimates rather than catalogue values. Fillets and local geometry are intentionally excluded from models. Confirm important results using approved properties or specialised software.
Can custom segments form branches?
Yes, connected branches are supported by the segment solver. Shared endpoints must use exactly matching coordinate values. Every accepted model must remain cycle-free and fully connected.
Why are closed loops rejected?
Closed cells require additional torsion compatibility and circulation conditions. The current solver targets open thin-walled section graphs only. Use specialised closed-section analysis for tubes and box sections.
What is the difference between Cw and Iy?
Iy measures bending resistance about the section’s minor axis. Cw measures resistance connected with nonuniform torsion and warping. Their units and structural roles are therefore fundamentally different.
Can results replace a structural engineer?
No calculator can replace project-specific professional engineering judgement. Loads, restraints, standards, tolerances, and fabrication details still matter. Seek qualified review for every safety-critical structural design decision.