BIZOMAT MAKEOS · Engineering
Section Properties
What area and bending properties follow from this section?
Calculate area, centroidal second moments, elastic section moduli and radii of gyration for four ideal section shapes.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Ideal section shape | choice | Select the ideal geometry; commercial sections can have corner radii and tolerances. |
| Width or outside diameter | mm | Outside horizontal width for rectangles or outside diameter for circles. |
| Outside height (rectangles only) | mm | Outside vertical height; ignored for circles. Leave a valid positive value when unused. |
| Wall thickness (tubes only) | mm | Uniform wall; ignored for solid sections. Leave a valid positive value when unused. |
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: Ideal section shape
- What it is
- The idealised cross-section of the bar or tube: solid rectangle, sharp-cornered rectangular tube, solid round bar or round tube. It decides which formulas are used and which dimensions apply.
- Units and format
- Choose one of 4 options from the list: Solid rectangle; Rectangular tube, sharp corners; Solid circle; Circular tube.
- Example
- The form opens with “Solid rectangle” selected as a worked example. Choose the option that matches your case.
- Get it right
- Commercial hollow sections have corner radii; the sharp-cornered model gives slightly higher values than real stock.
What this means: Width or outside diameter
- What it is
- For rectangles, the outside horizontal width of the section across the X direction. For circles and round tubes, the outside diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Iy rises with the cube of width for rectangles; for solid circles both I values rise with the fourth power of diameter.
- Get it right
- For round sections, enter the full diameter, not the radius.
What this means: Outside height (rectangles only)
- What it is
- The outside vertical depth of a rectangular section, measured in the direction of bending about the horizontal X axis. It is not used for circular shapes.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Ix rises with the cube of height, so a deeper section is much stiffer about X.
- Get it right
- Leave a positive value in place when a circle is selected; it is ignored but the form still checks it.
What this means: Wall thickness (tubes only)
- What it is
- The uniform thickness of the tube wall, from outside surface to inside surface. It is used only for the two tube shapes.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker wall increases area and second moment of area.
- Get it right
- It must be less than half the smallest outside dimension; it is ignored for solid shapes.
Method and formulas
- Rectangle: A = bh, Iₓ = bh³/12, Iᵧ = hb³/12. Circle: A = πD²/4, Iₓ = Iᵧ = πD⁴/64.
- For tubes subtract the centred inner shape. Section modulus Z = I divided by the corresponding extreme-fibre distance; gyration radius = √(I/A).
- Example: a 40 × 80 mm rectangle gives A = 3200 mm², Iₓ = 1,706,666.667 mm⁴, Iᵧ = 426,666.667 mm⁴ and Zₓ = 42,666.667 mm³.
Limitations
- Hollow rectangles have sharp corners. Use certified catalogue or CAD properties for rounded stock.
- Area second moments are not mass moments. Iₓ + Iᵧ is not the torsion constant of a rectangle.
- No stress, allowable load, buckling resistance or structural-code compliance is determined.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- second moment of area
- section modulus
- rectangular tube
Who it is for
- Mechanical designers
- CAD users
- Fabricators
What you get
- Area and centroid from lower-left bounding corner
- Centroidal horizontal Iₓ and vertical Iᵧ
- Elastic section moduli and gyration radii
Interpreting the result
- Match the bending axis when transferring I or Z to another calculation.
- Centroid coordinates use the lower-left outside bounding corner; moments are about centroidal axes.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 236–244. Topic reference; implementation and examples are original, and no source tables 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
Bound the answer by hand before you mesh
In Design Simulation by the Numbers
What it covers: Use beam theory, section properties, mass and a one-mass frequency estimate to predict each result, reject a weak design early and catch unit errors.
Method explained here · BIZOMAT original book
Rings, stiffeners and flanges
What it covers: Roll a 75 × 75 × 6 angle into a ring on its centroid, not its back: length, toe and heel strains, toe-out against toe-in, splices, bolt circles on the outlet flange, and a ring cut 132 mm short.
Useful alongside · 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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