KEVOS® MAKEOS · Strength
Section Properties: Ellipse, Hexagon, Triangle, Z and Cross
What are the area, second moments and section moduli of this section?
Area, centroid, second moments of area, section moduli, radii of gyration and polar moment of elliptical, hollow elliptical, half-round, hexagonal, triangular, round-with-hexagon-hole, round-with-square-hole, Z and cross (X) sections.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Section | choice | Section type; the option text names each dimension. |
| Dimension A | mm | First dimension as described. |
| Dimension B | mm | Second dimension where needed. |
| Dimension C | mm | Third dimension where needed. |
| Dimension D | mm | Fourth dimension where needed. |
Method and formulas
- Ellipse: I = πab³/4 about the major axis (a, b semi-axes); hollow ellipse subtracts the inner ellipse.
- Half circle: centroid 4r/3π; Ix = (π/8 − 8/9π) r⁴. Hexagon (side s): I = 5√3 s⁴/16 about any centroidal axis. Triangle: Ix = bh³/36.
- Round with a hole: subtract the hole’s properties. Z and cross sections: sum of rectangles with the parallel axis theorem; principal moments for the Z.
- Example: a 30 mm across-flats hexagon has A = 779.42 mm² and I = 48,714 mm⁴.
Limitations
- Sharp corners; rolled and drawn sections have radii that change the properties slightly.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find properties of bars, extrusions and fabricated sections
- Check torsion and bending of hex and special bars
- Replace handbook section tables
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Area and centroid
- Ix and Iy about centroidal axes
- Section moduli and radii of gyration
- Polar moment where meaningful
Interpreting the result
- For torsion of non-circular sections, use the torsion tools rather than the polar moment.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 234–246. Topic reference; no source tables or recommended settings are reproduced.
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Open the Section Properties: Ellipse, Hexagon, Triangle, Z and Cross calculator
