The sizing of a rectangular aluminum tube is based on geometric and mechanical parameters that online tools oversimplify. Here, we propose a structured approach, focused on the truly discriminating checks for an extruded profile in alloy 6000 subjected to structural loads.
Fatigue of 6xxx alloys: the parameter that static calculation ignores
A properly sized rectangular aluminum tube 6060-T5 or 6082-T6 under static bending can fail prematurely under cyclic loads. The S-N curves specific to 6xxx alloys show a notable decrease in allowable strength after one million cycles. Vibrating structures, machine supports, frames subjected to wind: high cycle fatigue imposes safety factors much higher than those used for quasi-static loads.
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The Aluminum Design Manual (2020 edition, errata 2023) formalizes this requirement. We recommend systematically checking whether the structure experiences repeated stress variations before settling for a purely static calculation of a rectangular tube’s strength. A profile that passes all checks in bending and compression can fail in fatigue if the alternating stress range exceeds the allowable threshold for the chosen alloy.
In practice, this means applying a reduction to the allowable stress as soon as the structure is subjected to more than a few hundred thousand cycles over its lifetime. This point is rarely covered by online calculators.
Further reading : How to Easily Estimate the Strength of an Aluminum Tube for Your Structures
Section properties of the rectangular tube: moment of inertia, elastic modulus, and plastic modulus
The mechanical behavior of a rectangular tube directly depends on its geometric section characteristics. Three quantities drive the bending sizing.
Bending moment of inertia
The moment of inertia (I) quantifies the profile’s stiffness against deformation. For a hollow rectangular tube with outer dimensions B x H and thickness t, the calculation is performed by the difference between the full outer rectangle and the empty inner rectangle, according to each axis (y-y and z-z).
The further the material is from the neutral axis, the greater the moment of inertia increases: a tube with a large height H but a small width B will be stiff in bending according to y-y, but much less so according to z-z.
Elastic modulus and plastic modulus
The elastic bending modulus (W_el = I / v, where v is the distance to the extreme edge) determines the maximum stress in service under elastic assumption. The plastic modulus (W_pl) comes into play when partial plasticization of the section is allowed, which is common for ductile alloys like 6082-T6.
Confusing elastic modulus and plastic modulus skews the utilization ratio by a significant factor. In design according to Eurocode 9 (calculating aluminum structures), the choice between the two depends on the section class of the profile.
Strength checks according to aluminum design standards
The complete sizing of a rectangular aluminum tube is not limited to bending. Four checks must be performed simultaneously.
- Bending check in both axes: comparison of the applied moment to the resisting moment, calculated from the section modulus and the yield strength of the chosen alloy.
- Shear check: verification that the shear force in each web of the tube does not exceed the shear strength of the net section.
- Compression check (buckling): a rectangular tube subjected to axial compression must be checked for overall buckling (Euler’s formula corrected by buckling curves) and local buckling of thin walls.
- Tensile check: relevant for bracing bars or tensioned members, taking into account the net sections at the locations of holes.
The standards used in practice are Eurocode 9 (EN 1999-1-1), ADM 2020 (North America), and CSA S157-17 (Canada). Each standard applies different partial safety factors, which alters the required tube section for the same load.
Local buckling of thin walls: the trap of low-thickness tubes
On a rectangular tube, the ratio between the width of each flat wall and the thickness (b/t ratio) conditions the sensitivity to local buckling. A large-section tube with reduced thickness can locally buckle well before reaching the yield strength of the material.
Local buckling of a wall reduces the actual load-bearing capacity of the profile compared to the theoretical strength calculated on the gross section. Eurocode 9 classifies sections into four categories (1 to 4) based on the b/t ratio. Class 4 sections, common with thin-walled aluminum tubes, require a calculation on a reduced effective section.
We observe that this point is often overlooked in common sizing. A rectangular aluminum tube with a generous section but insufficient thickness may offer lower strength than a more compact tube with thicker walls.
Influence of the alloy and heat treatment on the tube’s strength
The choice of aluminum grade directly modifies the yield strength used in each check. Common grades for extruded rectangular tubes are 6060-T5, 6060-T66, and 6082-T6, with increasing yield strengths.
The transport and demountable structures industry increasingly uses 7000 series alloys with very high yield strength to reduce thickness for equal strength. The mass gain is real, but welding these grades imposes stricter controls and a more significant reduction in strength in the heat-affected zone (HAZ) compared to 6xxx.
A welded tube loses a fraction of its strength near the weld. On a 6082-T6, the strength in the HAZ drops significantly compared to the base metal. This parameter must be integrated from the choice of section, not treated as a post-correction.
The sizing of a rectangular aluminum tube for a structure is not limited to a bending formula. The combination of section class, mode of loading, potential fatigue, and metallurgical state at the welds determines the actual reliability of the frame. Each omitted check is a weak link in the safety chain.