Cantilever Beam Multiple Loads Calculator
Calculate fixed-end moment and shear, tip deflection, tip rotation and bending stress for a cantilever beam carrying several point loads at different distances plus an optional uniform load. Enter one load per line.
Input
Meters, from the fixed support to the free end.
One per line as “distance from fixed end (m), load (kN)”. Use a distance equal to L for a load at the free end.
kN/m over the full length. Leave blank for none.
Section & material
mm⁴ about the bending axis.
mm, from the neutral axis to the outer face.
Output
| Metric | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/cantilever-beam-multiple-loads-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"span": "3",
"pointLoads": "1, 5\n2.5, 8",
"udl": "",
"momentOfInertia": "8360000",
"extremeFiberDistance": "150",
"material": "structural-steel",
"elasticModulus": ""
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `cantilever-beam-multiple-loads-calculator` tool (Cantilever Beam Multiple Loads Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
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<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
What this tool does
Most cantilever calculators accept a single load at the tip. Real cantilevers — balconies, brackets, signs, canopies — usually carry several loads at different distances. This calculator takes any number of point loads plus an optional uniform load and uses superposition to find:
- the fixed-end shear (reaction) and fixed-end moment,
- the bending stress at the support,
- the tip deflection (and its L/x ratio) and tip rotation.
The formulas
With distance a measured from the fixed end, length L, stiffness EI:
- Moment: M = Σ P·a + wL²/2
- Shear: V = Σ P + wL
- Tip deflection: δ = Σ P·a²(3L − a)/(6EI) + wL⁴/(8EI)
- Tip rotation: θ = Σ P·a²/(2EI) + wL³/(6EI)
How to use it
- Enter the cantilever length.
- List point loads, one per line, as
distance, load(meters, kN). - Add a uniform load if there is one.
- Enter I and c for your section and choose a material (or a custom E).
For a simply supported beam or a single load, use the Beam Load Calculator or Beam Deflection Calculator.
Frequently asked questions
Does it include the beam's own weight? No — add it as a uniform load (weight per meter × 9.81 for kN/m).
Are results design-ready? No. They are linear-elastic estimates; apply load factors and check your governing code.