Cantilever beam with a load in the middle
Moving the load away from the free end and into the middle of a cantilever makes the structure noticeably stiffer. The half of the beam beyond the load no longer bends on its own: it just follows the slope reached at the loading point.
This is a common real situation — a bracket loaded by a bolt somewhere along its length, a handrail post loaded by a fitting, or a machine arm carrying a tool at mid travel. The calculator below is pre-set to this exact case.
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/cantilever-mid-load#v1-AQEAAHpEAACgQZQBAQIAAAAAAADIQgAAAAA
How the beam is modelled
- The left end is rigidly fixed.
- The right end is free.
- A vertical point load acts at midspan, halfway along the beam, pointing down.
- The beam is a solid steel rod, 20 mm in diameter and 1000 mm long.
How to read the results
The load point sinks, and the section beyond it continues as a straight line tangent to the deflected shape, so the free end still shows the largest displacement even though the load is not there.
Compared with the same load applied at the free end, the midspan case deflects much less and puts a much smaller moment into the fixed end. Compare it directly with the end-loaded cantilever to see the difference.
The reactions at the fixed support are unchanged: the support still carries the full load and the full moment arm, which now ends at the loading point.
Formulas
| Formula | What it gives |
|---|---|
a = L / 2 | Distance from the fixed end to the load. |
delta_load = F * a^3 / (3 * E * I) | Deflection at the point where the load is applied. |
delta_max = F * a^2 * (3 * L - a) / (6 * E * I) | Deflection at the free end, which is the largest one. |
M_max = F * a | Bending moment at the fixed end. |
FAQ
Why is a cantilever loaded in the middle stiffer than one loaded at the tip?
Because only the loaded part of the beam stores bending energy. The span beyond the load stays straight and simply follows the slope, so the effective flexural length is the distance from the support to the load rather than the full beam length.
Where is the maximum deflection of this beam?
At the free end, not at the loading point. The deflected shape keeps curving up to the load and then continues as a straight tangent line, so the largest displacement is at the tip.
Can I move the load to any position?
Yes. Set the load type to a side-anchored load in the calculator and use the offset to place it anywhere along the beam; the formula above works for any distance a from the fixed end.
Does the result include self weight?
No. Only the loads you define are analysed, so add the beam weight as an extra load if it matters for your structure.
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.
- Steel pipe as a cantilever A clamped steel pipe loaded at its free end: deflection and reactions for a hollow circular section.
- 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.