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Beam Deflection & Moment

⚙️ Mechanical · Deflection and maximum moment calculation for 4 support/load cases

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δ=PL348EI\delta = \frac{PL^3}{48EI}

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.

📖 Sourced Formula · Single Verification

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.

Results are for educational and preliminary-sizing purposes; final engineering design decisions must reference the relevant standards and a licensed engineer's approval.