Aluminium cantilever arm
Aluminium is attractive for cantilevers because it is light and easy to machine, but it is roughly three times less stiff than steel. The elastic modulus of common aluminium alloys is around 69 000 MPa, against about 200 000 MPa for steel, and strength does not compensate for that: an aluminium arm will usually bend visibly long before it breaks.
That is why aluminium cantilevers are normally sized by stiffness, not by strength. The calculator below is pre-set to a 16 mm aluminium rod over an 800 mm cantilever carrying 50 N at the tip — change the numbers to match your part.
Calculator
This calculator is already set up for the problem above. Change the length, the load, the profile or the material and it recalculates immediately; the address bar keeps a shareable link to your exact configuration.
Input data:
Beam:
Material: Construction steel (Generic)
Profile:
| Ax: 78.54mm2 | Jxx: 981.75mm4 |
| Asy: 78.54mm2 | Iyy 490.87mm4 |
| Asz: 78.54mm2 | Izz: 490.87mm4 |
Simulation results:
Displacements (mm):
| # | x | y | zz |
|---|
Reactions (newtons):
| # | x | y | zz |
|---|
Direct link to this setup: https://beamcalc.net/en/solve/aluminium-cantilever-end-load#v1-AQEAAEhEAACAQYYBAQEAAAAAAABIQgAAAAA
How the beam is modelled
- The left end is rigidly fixed.
- The right end is free.
- A vertical point load of 50 N acts at the free end, pointing down.
- The beam is a solid aluminium rod, 16 mm in diameter and 800 mm long.
How to read the results
Compare this setup with a steel rod of the same diameter: the aluminium arm deflects close to three times more, because deflection is inversely proportional to the elastic modulus.
To bring the aluminium arm back to the steel deflection you need a stiffer section — roughly three times the moment of inertia, which for a solid rod means about 32 percent more diameter.
The reaction values also give you the support moment, which is what the clamp or weld has to carry. For aluminium, check that the bearing stress under the clamp is acceptable, since aluminium creeps under sustained load.
Formulas
| Formula | What it gives |
|---|---|
I = pi * d^4 / 64 | Moment of inertia of a solid circular section. |
delta_max = F * L^3 / (3 * E * I) | Deflection at the free end. E is the elastic modulus of the aluminium alloy. |
delta_aluminium / delta_steel = E_steel / E_aluminium | For identical geometry, deflection scales inversely with stiffness. |
FAQ
Is aluminium really three times more flexible than steel?
For the same geometry, yes: deflection is inversely proportional to the elastic modulus, and common aluminium alloys have an elastic modulus of about 69 000 MPa against roughly 200 000 MPa for steel.
Why not simply use a higher-strength aluminium alloy?
Because elastic modulus is a property of the base metal, not of the temper. Heat treatment and alloying change the strength substantially, but the stiffness of aluminium stays almost the same.
How much thicker does an aluminium arm need to be?
For a solid round rod, to match a steel deflection you need about 32 percent more diameter, since the moment of inertia of a circle grows with the fourth power of the diameter.
Should I worry about creep?
For a short-term load, no. Under a sustained load at room temperature aluminium can slowly deform, so keep service stresses low and avoid long thin arms that work close to their deflection limit all the time.
More beam examples
- Cantilever beam with a load at the free end A beam fixed at one end and loaded at the free end: deflection, slope and reactions, solved online.
- Cantilever beam with a load in the middle A beam fixed at one end and loaded at midspan: where the load sits changes the deflection, and this page shows by how much.
- Steel pipe as a cantilever A clamped steel pipe loaded at its free end: deflection and reactions for a hollow circular section.