Propped Cantilever Calculator
Find the fixed-end and span bending moments, both reactions and the deflection of a propped cantilever (fixed at one end, simply supported at the other) in seconds. This beam is statically indeterminate — the result is checked live against the FERS finite-element solver.
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Formulas used
A propped cantilever is fixed (built in) at one end and propped on a simple support at the other. The largest moment is the hogging moment at the fixed end:
| Load case | Max moment | Reaction | Max deflection |
|---|---|---|---|
| Central point load P | M_fixed = 3·P·L / 16, M_span = 5·P·L / 32 | R_fixed = 11P/16, R_prop = 5P/16 | δ = 7·P·L³ / (768·E·I) |
| Uniformly distributed load w | M_fixed = w·L² / 8, M_span = 9·w·L² / 128 | R_fixed = 5wL/8, R_prop = 3wL/8 | δ_max ≈ w·L⁴ / (185·E·I) |
where L is the span, P a point load, w a distributed load, E Young's modulus and I the second moment of area. The calculator above runs the FERS finite-element solver on your inputs and shows the analytical and finite-element answers agreeing live.
Worked example
Worked example: a 6 m propped cantilever IPE 300 steel beam (I = 8.36×10⁻⁵ m⁴, E = 210 GPa) under a 10 kN/m uniformly distributed load.
- Fixed-end moment, w·L²/8
- 45.0 kNm
- Max sagging moment, 9w·L²/128
- 25.3 kNm
- Reaction at fixed end, 5wL/8
- 37.5 kN
- Reaction at prop, 3wL/8
- 22.5 kN
- Max deflection, w·L⁴/185EI
- 4.0 mm (≈ L/1500)
Frequently asked questions
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Describe a steel beam in plain English and get an EN 1993-1-1 check computed by the real FERS solver — a limited free demo (a few messages per day); connect your own LLM via MCP for unlimited use.
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