BIZOMAT MAKEOS · Strength
Section Properties: I, T, Channel and Angle
What are the area, centroid, second moments and section moduli of this I, T, channel or angle section?
Area, mass per metre, centroid, second moments of area, principal axes, section moduli and radii of gyration of built-up or rolled I, T, channel and angle sections made from rectangles.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Shape | choice | Section type; root radii are ignored. |
| Overall depth (vertical leg) | mm | Overall depth (for angles, the vertical leg length). |
| Overall width (flange or horizontal leg) | mm | Overall width (for angles, the horizontal leg length). |
| Flange thickness | mm | Flange thickness (for angles, the horizontal leg thickness). |
| Web thickness | mm | Web thickness (for angles, the vertical leg thickness). |
| Density | kg/m³ | Material density for mass per metre. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Shape
- What it is
- The type of section built from rectangles: a symmetrical I or H, a T, a channel or an angle.
- Units and format
- Choose one of 4 options from the list: I or H section (symmetrical); T section; Channel; Angle.
- Example
- The form opens with “I or H section (symmetrical)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Root and toe radii are ignored, so rolled-section values will differ slightly from maker’s tables.
What this means: Overall depth (vertical leg)
- What it is
- The overall depth of the section from bottom face to top face; for an angle, the length of the vertical leg.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Overall width (flange or horizontal leg)
- What it is
- The overall width across the flanges; for a channel, the flange width including the web; for an angle, the length of the horizontal leg.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Flange thickness
- What it is
- The thickness of the flange plates measured vertically; for an angle, the thickness of the horizontal leg.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For an I or channel, two flanges must fit inside the overall depth, so twice this must be less than the depth.
What this means: Web thickness
- What it is
- The thickness of the web plate measured horizontally; for an angle, the thickness of the vertical leg.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not mix up flange and web thickness; the web is the vertical plate.
What this means: Density
- What it is
- The density of the section material, used only to work out the mass per metre of length.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 50000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass per metre rises in proportion; the geometric properties do not change.
- Get it right
- Enter kilograms per cubic metre, not grams per cubic centimetre.
Method and formulas
- The section is split into rectangles; A = Σ aᵢ, centroid = Σ aᵢ cᵢ ÷ A (from the bottom-left corner).
- I about centroidal axes by the parallel axis theorem: I = Σ (Iᵢ + aᵢ dᵢ²); Ixy = Σ aᵢ dxᵢ dyᵢ.
- Principal moments = (Ix + Iy)/2 ± √(((Ix − Iy)/2)² + Ixy²); Z = I ÷ extreme fibre distance; r = √(I/A).
- Example: a 200 × 100 I-section with 10 mm flanges and a 6 mm web has Ix = 20.983 × 10⁶ mm⁴ and Zx = 209.83 × 10³ mm³.
Limitations
- Root and toe radii of rolled sections are ignored, so tabulated values differ slightly; use the maker’s tables for rolled sections.
- Thin-walled torsion and warping properties are not given.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find properties of fabricated sections
- Check a rolled section approximately
- Feed beam and column calculations
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Area and mass per metre
- Centroid position
- Ix, Iy and principal moments
- Section moduli and radii of gyration
Interpreting the result
- For angles, bending about the principal axes governs unless the angle is restrained.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 234–246. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Slenderness and the shape of the section
What it covers: Why the radius of gyration, not the area, decides how well a section resists buckling: tubes, angles, channels, bars and flats of the same mass compared, and the least axis that governs.
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Open the Section Properties: I, T, Channel and Angle calculator