Free T-Slot Aluminum Extrusion Deflection Calculator
Calculate structural beam deflection, center sag, and bending stress for 2020, 3030, 4040, and 80/20 aluminum extrusion frames.
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Engineering Deflection of T-Slot Extrusions
Modular extruded aluminum profiles (T-slot and V-slot) are the foundation of modern CNC routers, 3D printers, laser cutters, and industrial robotics workstations. When designing a long horizontal beam, keeping sag under control is essential to prevent binding linear rails and print layer distortion.
1. Beam Deflection Governing Equations
- Simply Supported Center Load:
δ = (F × L³) / [48 × E × I] - Simply Supported Uniform Load:
δ = (5 × W × L³) / [384 × E × I] - Fixed Ends Center Load: Clamping both beam ends rigidly into heavy uprights cuts center deflection by 75%:
δ = (F × L³) / [192 × E × I] - Cantilever Load:
δ = (F × L³) / [3 × E × I]
2. Deflection Limits by Application
- High-Precision CNC Milling Gantry: Sag must not exceed L / 1,000 or 0.002" (50 µm) to maintain milling flatness.
- 3D Printer CoreXY Gantry: Sag under L / 500 or 0.005" (125 µm) is required to ensure consistent first-layer squish.
- Workbenches & Enclosures: Sag up to L / 250 (e.g. 0.14" over a 36" table span) is completely acceptable structurally.
Frequently Asked Questions
Why is steel stiffer than aluminum even if they weigh the same?
Stiffness depends on the Elastic Modulus (E). Structural steel has an elastic modulus of ~30 Mpsi (200 GPa), which is 3x higher than aluminum (10 Mpsi / 69 GPa). To match steel's rigidity, an aluminum profile must have a larger outer dimension to increase its second moment of inertia.
What is the difference between 6063-T6 and 6005-T5 aluminum extrusions?
6063-T6 is the standard architectural and hobbyist extrusion alloy (clean surface finish, yield strength ~31,000 psi). Heavy-duty industrial profiles (like genuine 80/20) use 6005-T5, which offers higher yield strength (~35,000 psi) and superior T-slot flange pull-out resistance.
How does tightening corner brackets affect beam deflection?
Using heavy cast-aluminum corner gussets or steel internal blind joints partially clamps the beam ends, shifting behavior from simply supported toward fixed ends and reducing mid-span deflection by 30% to 50%.
What is the "strong axis" vs "weak axis" on 2040 and 4080 extrusions?
When an extrusion is oriented vertically like a floor joist (tall side vertical), bending forces act against the strong axis (high Ix). Rotating it flat puts bending forces against the weak axis (low Iy), resulting in 3x to 4x greater sag under the same load.