# Calculate the deflection of aluminium profiles Quelle: > Calculate the deflection and bending stress of aluminium profiles free of charge: simply supported, cantilever or fixed, point or distributed load, with dead weight. How far does a profile bend under load? Choose the support, load and length; deflection, bending stress and rating appear instantly. Support Load **Material and safety** Modulus of elasticity of aluminium 70,000 N/mm². Standard: AlMgSi 0.5 F25 with Rp0.2 = 200 N/mm². **Good** The profile carries the load with little deflection. **Deflection f** **1.55 mm** L/644 · Good **Bending stress σ** **25.9 N/mm²** 19 % of 133 · Good **Maximum bending moment** 124.9 N·m **of which from dead weight** f 0.04 mm · 18.5 N Deflection line dashed, shown greatly exaggerated. Cut to L, in 0.5 mm steps. Add the bearing or clamping length if needed. [To the profile page](https://mvg-frankfurt.de/en/aluminium-profiles/nut-8/aluprofil-40x40-leicht) ## How the calculator works It is based on beam theory for slender beams with a constant cross-section. F is the load, L the length, E the modulus of elasticity (aluminium 70,000 N/mm²) and I the second moment of area about the bending axis. For a distributed load, q = F / L. | Support | Load | Deflection f | Moment M | |---|---|---|---| | Simply supported | Point load, middle | F·L³ / (48·E·I) | F·L / 4 | | distributed | 5·q·L⁴ / (384·E·I) | q·L² / 8 | | | Fixed at one end | Point load, end | F·L³ / (3·E·I) | F·L | | distributed | q·L⁴ / (8·E·I) | q·L² / 2 | | | Fixed at both ends | Point load, middle | F·L³ / (192·E·I) | F·L / 8 | | distributed | q·L⁴ / (384·E·I) | q·L² / 12 | | The dead weight acts as a distributed load with the same support and is added to the load. The bending stress is σ = M / W with the section modulus W. The permissible stress is σzul = Rp0.2 / safety factor. ### Rating - **Deflection:** up to L/500 good, up to L/300 borderline, above that too high. - **Stress:** up to 80 % of σzul good, up to 100 % borderline, above that overloaded. ### Limits of the calculation - Only elastic deformation under static load. Impacts, vibrations and fatigue strength are not included. - The flexibility of connectors, T-slot nuts and screw connections is not included. Real frames therefore deflect more; “fixed” is the most favourable limiting case. - Shear deformation, torsion and buckling are not considered. - The section values of the ProFix profiles are catalogue values of the nominal cross-section. Extrusion tolerances change them slightly. For profiles without catalogue values, choose “Other profile” and enter the values from the data sheet. - The result is an estimate to help you choose. It does not replace a structural calculation or check. ## Example: ProFix Profile 40 × 40 slot 8 Light with 50 kg A ProFix Profile 40 × 40 slot 8 Light rests on two supports 1,000 mm apart. A load of 50 kg hangs in the middle, i.e. F = 490.5 N. The profile has I = 96,200 mm⁴ and W = 4,830 mm³. - **Deflection from the load:** f = F·L³ / (48·E·I) = 490.5 · 1,000³ / (48 · 70,000 · 96,200) = 1.52 mm - **Dead weight:** 1.89 kg/m gives 18.5 N and an additional 0.04 mm. - **Total:** f = 1.55 mm, that is L/644. - **Bending stress:** σ = M / W = 25.9 N/mm², permissible 133.3 N/mm² (19 % utilised). Result: Deflection below L/500 and stress in the green range. The profile is sufficient for this case. Use the calculator above to check other lengths, loads and profiles. ## Frequently asked questions **How do I calculate the deflection of an aluminium profile?** You need the support, load, span L, the modulus of elasticity of aluminium (70,000 N/mm²) and the second moment of area I of the profile about the bending axis. For a simply supported beam with a point load in the middle, f = F·L³ / (48·E·I). The calculator above uses the catalogue values of the ProFix profiles and adds the dead weight. **Which deflection is permissible?** That depends on the application. For frames and cladding, L/300 is the usual limit; for workbenches and guides rather L/500 or less. With a 1000 mm span, that is 3.3 mm and 2 mm respectively. **How do I convert kg to newtons?** Mass in kg times gravitational acceleration 9.81 m/s². 10 kg is roughly 98 N. The calculator converts automatically when you choose the unit kg. **What does upright instead of flat achieve?** The second moment of area grows with the cube of the height in the load direction. A 40 × 80 profile mounted upright deflects about four to five times less than flat. **Why is a fixed beam so much stiffer?** Fixing the ends prevents rotation at the support. With a point load in the middle, deflection drops to a quarter, with a distributed load to a fifth compared with a simply supported beam. Real profile connections are never completely rigid, so the result lies between the two cases. Next: [Machine profiles and accessories](https://mvg-frankfurt.de/en/aluminium-profiles) · [Machine profiles slot 8](https://mvg-frankfurt.de/en/aluminium-profiles/nut-8) · [All calculators](https://mvg-frankfurt.de/en/calculators) · [Weight calculator](https://mvg-frankfurt.de/en/calculators/weight)