KEVOS® MAKEOS · Strength
Beam Sizing for Strength and Deflection
What section modulus and second moment of area does this beam need for its loads, span and deflection limit?
Required section properties for a beam carrying a uniform load and a point load together: maximum bending moment by superposition (sampled along a simple span, or at the critical sections of a cantilever or fixed-ended beam), the section modulus for the allowable stress, the second moment of area for a span-over deflection limit, and the utilisation of a chosen section.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Supports | choice | Support arrangement. |
| Span | mm | Span (or cantilever length). |
| Uniform load | N/mm | Uniformly distributed load including self-weight. |
| Point load | N | Concentrated load. |
| Point load position from the left support (or fixed end) | mm | Position of the point load (ignored for fixed ends, where it is taken at mid-span). |
| Allowable bending stress | MPa | Allowable bending stress for the material and code. |
| Elastic modulus | GPa | Elastic modulus of the beam material. |
| Deflection limit: span ÷ | Deflection limit as span divided by this number (360 for floors, 180–250 for many machine frames). | |
| Chosen section modulus (0 = none) | mm³ | Section modulus of a section you want to check. |
| Chosen second moment of area (0 = none) | mm⁴ | Second moment of area of that section. |
Method and formulas
- Simple span: M(x) = w x (L − x) ÷ 2 + point-load moment, maximum found along the span; deflection = 5wL⁴ ÷ 384EI + P b (L² − b²)^1.5 ÷ (9√3 L E I) (sum of the two maxima, conservative).
- Cantilever: M = wL² ÷ 2 + P a; tip deflection = wL⁴ ÷ 8EI + P a² (3L − a) ÷ 6EI.
- Fixed ends: M = wL² ÷ 12 + PL ÷ 8; deflection = wL⁴ ÷ 384EI + PL³ ÷ 192EI.
- Required Z = M ÷ allowable; required I from the deflection limit.
- Example: the default beam needs Z ≥ 79,545 mm³ and I ≥ 6,348,600 mm⁴; both checks governs the choice.
Limitations
- Elastic, laterally restrained beam; slender beams also need a lateral-torsional buckling check.
- Shear and local bearing at supports and loads are not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a steel or aluminium section for a frame member
- Check whether strength or stiffness governs
- Compare an available section against the loads
Who it is for
- Design engineers
- Mechanical engineers
- Engineering managers
What you get
- Maximum moment and its position
- Required section modulus and second moment of area
- Utilisation of the chosen section
Interpreting the result
- If stiffness governs, a deeper section is far more effective than a stronger material.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 258–275. Topic reference; no source tables or recommended settings are reproduced.
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