Fixed Beam Calculator (Built-in / Fixed-Fixed)
Find the support and midspan bending moments, reactions and deflection of a fixed (built-in) beam in seconds. Both ends are rigidly restrained against rotation. Enter the span, load and section, and the result is checked live against the FERS finite-element solver.
Bending moment and reactions are free. Create a free account to unlock deflections and to save your model.
Formulas used
A fixed (built-in / encastré) beam is clamped against rotation at both ends. The largest moment occurs at the supports (hogging), with a smaller sagging moment at midspan:
| Load case | Max moment | Reaction | Max deflection |
|---|---|---|---|
| Central point load P | M_support = P·L / 8, M_mid = P·L / 8 | R = P / 2 | δ_max = P·L³ / (192·E·I) |
| Uniformly distributed load w | M_support = w·L² / 12, M_mid = w·L² / 24 | R = w·L / 2 | δ_max = w·L⁴ / (384·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 fixed (built-in) IPE 240 steel beam (I = 3.89×10⁻⁵ m⁴, E = 210 GPa) with a 10 kN point load at midspan.
- Support moment, P·L/8
- 7.5 kNm
- Midspan moment, P·L/8
- 7.5 kNm
- Reaction at each support, P/2
- 5.0 kN
- Midspan deflection, P·L³/192EI
- 1.4 mm (≈ L/4360)
Frequently asked questions
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Need more than a single beam?
Open the full FERS Cloud app for continuous and multi-span beams, 2D and 3D frames and trusses, load combinations and Eurocode EC3 steel checks.