Steel pipe loaded in the middle
"Will a steel pipe bend if I hang something in the middle of it?" is one of the most common questions in everyday workshop engineering — for handrails, canopy frames, rack beams, tent structures or a simple improvised support.
The answer always depends on three things: the pipe diameter, the wall thickness and the span. Because the moment of inertia of a tube grows with the fourth power of the outer diameter, a modest increase in diameter helps far more than adding steel to the wall.
This page is pre-set to a DN32 pipe — 42.4 mm outer diameter with a 3.2 mm wall — spanning 2 m between two supports and loaded with 300 N at midspan. Adjust the three numbers to your own pipe.
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/steel-pipe-mid-load#v1-ARsAAPpEmpkpQgAAEEKUAQECAAAAAAAAlkMAAAAA
How the beam is modelled
- The left support is a pin, the right one a roller.
- A vertical point load of 300 N acts at midspan, pointing down.
- The beam is a hollow round tube: 42.4 mm outer diameter, 36 mm inner diameter, 3.2 mm wall.
- The span is 2000 mm and the material is construction steel.
How to read the results
The reported deflection is what you would measure at midspan with a ruler. In practice, for a handrail or a rack beam people usually want the deflection to stay below roughly one two hundredth of the span; compare your value against whatever limit applies to your structure.
The pipe bends about whichever axis the load acts in, and a circular section has the same moment of inertia in every direction, so a pipe never has a weak bending direction — unlike an I-beam or a rectangular tube.
The reactions tell you what the supports must carry, and the moment under the load tells you the largest bending stress in the pipe wall.
If the wall is too thin relative to the outer diameter, the section is no longer a valid tube and the model is rejected — a reminder that very thin tubes also fail by local buckling long before the material yields.
Formulas
| Formula | What it gives |
|---|---|
I = pi * (D^4 - d^4) / 64 | Moment of inertia of the pipe. D is the outer and d the inner diameter. |
delta_max = F * L^3 / (48 * E * I) | Deflection at midspan. |
M_max = F * L / 4 | Bending moment under the load. |
sigma = M_max * (D / 2) / I | Bending stress in the outer fibre of the pipe wall, in MPa when M is in N·mm and I in mm⁴. |
FAQ
How much does a steel pipe sag under its own weight?
The calculator only includes the loads you enter. Add the pipe mass as an extra load at midspan to include it; for long spans the self weight can be a significant share of the total.
Does a thicker wall make a big difference?
Less than you would expect. The moment of inertia depends on the fourth power of the diameter but only roughly on the first power of the wall, so up-sizing the diameter is the far more effective lever.
What is a good deflection limit for a pipe?
There is no single universal limit. Handrails and cosmetic structures are usually held to about L/200, machine components to much tighter values, while a temporary support can tolerate more. Always check the rule that applies to your application.
Can I check a pipe resting on three supports?
Not with this model. The calculator analyses a single span between two supports; a continuous multi-span beam behaves more stiffly because the intermediate supports also resist rotation.
More beam examples
- Simply supported beam with a load in the middle The classic pin-and-roller beam loaded at midspan: deflection, moment and reactions, solved online.
- Simply supported beam with an eccentric load A rectangular steel bar supported at both ends and loaded at the third point: where the load sits decides which support works harder.
- Simply supported beam with two point loads A steel tube on two supports carrying two equal loads: the middle section bends without shear, exactly like a four-point test.
- Simply supported beam with an inclined load A force pushing at an angle onto a supported beam: split it into bending and axial parts, and only the first one visibly bends the beam.