The Frame That Wobbled: Aluminum Extrusion Sizing, Not a Defect
A 40×40 aluminum extrusion frame for a machine. It wobbled under load. The customer thought the extrusion was defective. The wall thickness was 2 mm (light duty). The frame was 2 m long, supporting a 50 kg axis. It was undersized. This is about extrusion sizing, not about the material.
The extrusion series
| Series | Profile | Wall | Use for |
|---|---|---|---|
| 20 Series | 20×20 mm | 1.5 mm | Guards, small panels |
| 30 Series | 30×30 mm | 2.0 mm | Light frames, fixtures |
| 40 Series | 40×40 mm | 2.0 mm | Standard machine frames |
| 40 Series heavy | 40×40 mm | 3.0 mm | Load-bearing, long spans |
| 50/60 Series | 50×50, 60×60 mm | 3.0 mm | Heavy frames, bridges |
| 80/90 Series | 80×80, 90×90 mm | 4.0 mm | Very heavy, long spans |
What we found
The frame was a 40×40, 2 mm wall, 2 m span. The deflection at the center (50 kg load) was 3 mm. The customer needed 0.5 mm. The extrusion was too small for the span. We upsized to 40×40 heavy wall (3 mm). The deflection dropped to 0.8 mm. Then we added a diagonal brace. The deflection dropped to 0.3 mm.
The deflection rule
For a simply supported beam (extrusion frame), deflection is:
δ = (F · L³) / (48 · E · I)
For a 40×40 extrusion, I (moment of inertia) is about 7.7 cm⁴. For a 2 m span and 50 kg (500 N): δ = (500 × 2000³) / (48 × 70000 × 7.7e4) = 3.1 mm. That matches. For a 40×40 heavy wall, I is 13 cm⁴. δ = 1.8 mm. Still too much. With a diagonal brace (triangulation), the effective span halves. δ drops by 8x. We got 0.3 mm.
What we did
1. Heavy-wall extrusion. Upgraded from 2 mm to 3 mm wall. Stiffer for the same outside dimension.
2. Diagonal brace. Added a diagonal strut (40×40) between the posts. The frame can’t rack (twist). The wobble disappeared.
3. Cross-bracing. For a 2 m span, we added a middle support post. The span dropped from 2 m to 1 m. Deflection dropped by 8x (span³).
The frame rule: Size the extrusion for the span and load. Use the deflection formula. For spans over 1.5 m, add diagonal bracing. A 40×40 2 mm wall wobbles under load; a 40×40 3 mm with braces doesn’t. The frame that wobbled wasn’t defective — it was undersized for the span.
