KEVOS® MAKEOS · Strength
Special Section Beam Check (Section Properties, Beam Case, Stress, Deflection Limit)
For a beam made from a hexagon, ellipse, half-round, triangle or holed round bar, what are its section properties, and are the bending stress and deflection within limits for my supports and loads?
Check of a beam with an uncommon solid section: area, second moment of area and extreme fibre distance of an ellipse, hollow ellipse, half circle, hexagon, isosceles triangle, or round bar with a hexagonal or square hole (as the more section shapes tool), then the reactions, largest bending moment, bending stress and deflection for a fixed, guided, propped or simply supported case (as the more beam cases tool), against your allowable stress and span-to-deflection limit, with the mass per metre.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Section | choice | Shape of the cross-section, bent about its horizontal axis. |
| Dimension A | mm | First dimension of the section (see the shape list). |
| Dimension B | mm | Second dimension. |
| Dimension C | mm | Third dimension (hole or inner axis). |
| Dimension D | mm | Fourth dimension (inner axis of the hollow ellipse). |
| Beam | ||
| Beam case | choice | How the beam is supported and loaded. |
| Load (each point load, or total uniform load) | N | Each point load, or the total uniform load. |
| Span | mm | Span between supports. |
| Distance a | mm | Position of the load (see the beam case). |
| Modulus of elasticity | GPa | Modulus of elasticity of the material. |
| Allowable bending stress | MPa | Allowable bending stress. |
| Deflection limit (span ÷) | Largest deflection allowed as a fraction of the span (250 means span ÷ 250). | |
| Density | kg/m³ | Density for the mass per metre. |
Method and formulas
- Section area and I_x of the chosen shape; extreme fibre half the height, or the larger of the centroid distances for the half circle and triangle (as the more section shapes tool).
- Reactions, maximum moment and deflection for the beam case (as the more beam cases tool).
- Stress = M c ÷ I; deflection limit = span ÷ limit.
- Example: I = 779,420 mm⁴; 92.376 MPa and 6.7742 mm deflection against 8 mm allowed.
Limitations
- Bending about the horizontal axis only; unsymmetrical sections can also twist under load.
- Elastic, with rigid fixed ends where shown.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a hex bar or half-round used as a beam
- Check a guide rail or slide of odd section
- Compare sections for stiffness
Who it is for
- Design engineers
- Machine designers
- Toolmakers
What you get
- Section area, I and extreme fibre
- Reactions, moment, stress and deflection
- Against the stress and deflection limits
Interpreting the result
- For the same area, sections with more material far from the axis (hollow shapes) are much stiffer.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 234–246, 257–270. Topic reference; no source tables or recommended settings are reproduced.
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