Beam Deflection & Moment
⚙️ Mechanical · Deflection and maximum moment calculation for 4 support/load cases
Beam deflection is one of the fundamental criteria that determines a structure’s serviceability — a beam can become unusable due to excessive deflection (door/window binding, floor vibration, brittle material cracking) even before it breaks.
This tool covers four common support/load combinations: a simply supported beam with a point load or distributed load at the center, and a cantilever beam (fixed at one end, free at the other) with a point load or distributed load at the tip. Each case uses a closed-form (directly applicable, no integration needed) deflection and moment formula.
Worth noting: cantilever beams deflect far more than simply supported beams under the same load and span (exactly 16 times more for a point load) — this is why cantilever elements are designed more conservatively.
Serviceability rule: most structural standards commonly accept a deflection limit of δ ≤ L/300 (L: span). This tool automatically generates a warning when that limit is exceeded.
This tool's formula is based on a reliable source (see the Sources tab below) and has been checked against a hand-computed numerical example. A second, independent literature cross-check has not yet been added. As with any engineering calculation, we recommend independently confirming results before relying on them for critical decisions.
- [2] Hibbeler, R. C.. Mechanics of Materials, 10 ed.. Pearson, 2017. ↗
Beam Deflection & Moment — EngineersLab calc card
Formula: δ = PL³/48EI (simply supported, point load at center)
Sources: [2] Mechanics of Materials
Tool version: 1.1.0 · Date:
Source URL: https://engineerslab.com.tr/en/araclar/kiris
Results are for educational and preliminary-sizing purposes; final engineering design decisions must reference the relevant standards and a licensed engineer's approval.