Steel pipe as a cantilever
Steel pipe is a very efficient cantilever material. A hollow circular section resists bending in every direction equally well, is easy to clamp, and carries far more load per kilogram than a solid bar of the same weight.
Typical examples are handrail posts, sensor arms, exhaust hangers, rack outriggers and scaffolding tubes. The calculator below is set to a DN32 pipe — 42.4 mm outer diameter with a 3.2 mm wall — clamped over a 1.5 m cantilever and loaded at the tip.
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/pipe-cantilever-end-load#v1-AREAgLtEmpkpQgAAEEKUAQEBAAAAAAAAFkMAAAAA
How the beam is modelled
- The left end is rigidly fixed, as if the pipe were clamped in a socket or welded to a frame.
- The right end is free.
- A vertical point load acts at the free end, pointing down.
- The section is a hollow round tube: 42.4 mm outer diameter, 36 mm inner diameter, so the wall is 3.2 mm.
How to read the results
For a pipe, the whole game is the wall thickness. The moment of inertia of a hollow circle grows with the fourth power of the outer diameter, but only with the first power of the wall, so a slightly larger pipe with a thin wall beats a smaller thick one by a wide margin.
Watch the wall thickness when you change the dimensions: if it becomes half the outer diameter or more, the section stops being a tube and the model is rejected.
The reported reactions are the shear force and the bending moment the clamp has to resist. In practice the clamp and its fasteners, not the pipe itself, are usually what limits a cantilever like this.
Formulas
| Formula | What it gives |
|---|---|
I = pi * (D^4 - d^4) / 64 | Bending moment of inertia of a hollow circular section. D is the outer and d the inner diameter. |
delta_max = F * L^3 / (3 * E * I) | Deflection at the free end. |
M_max = F * L | Bending moment at the clamped end. |
FAQ
How do I model a pipe that is welded instead of clamped?
Use the same fixed support. A full-penetration weld into a stiff frame behaves almost like a clamp; if the weld sits on a thin plate, the real structure will be more flexible than the model, so treat the result as an upper bound on stiffness.
Why is the pipe so much lighter than a solid rod of the same stiffness?
Because bending stresses are largest at the outside of the section. Material near the neutral axis contributes very little to the moment of inertia, so removing it saves weight with almost no loss of stiffness.
Does this work for other pipe standards?
Yes. Enter the actual outer diameter and wall thickness of your pipe; nominal diameters such as DN32 or 1 1/4 inch are only labels and differ between standards.
Can I check a horizontal pipe loaded sideways?
Yes. The angle parameter rotates the load; for a pipe lying horizontally and pushed sideways, the section is equally stiff in every direction, so only the load component perpendicular to the pipe matters for deflection.
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.
- Aluminium cantilever arm An aluminium rod fixed at one end and loaded at the other: why aluminium arms sag, and how to size one that does not.