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Beam Deflection Calculator

Maximum deflection and bending moment of a simply-supported beam, with an L/ratio serviceability check.

Mechanical · Structural
Version1.0.0MethodBeam Deflection

Single concentrated load P at mid-span of a simply-supported beam

1

Beam Data

kN
m
GPa
mm⁴
L /

Beam Diagram

2

Results

Ready to compute?

Enter your beam data and press Calculate Deflection

4

Reference Codes & Standards

  • AISC 360

    Specification for Structural Steel Buildings

    Serviceability deflection guidance (typical L/240, L/360 limits).

  • IBC 1604.3

    International Building Code — Deflection Limits

    Tabulated span/deflection ratios for floor and roof members.

  • EN 1993-1-1

    Eurocode 3 — Design of Steel Structures, General Rules

    Serviceability limit states for beam deflection.

Further Reading

  • Roark's Formulas for Stress and Strain (Young & Budynas) — beam deflection cases.
  • Timoshenko, S. Strength of Materials, Part I — elastic bending of beams.
  • Gere & Goodno, Mechanics of Materials — deflections of beams.
  • Hibbeler, R. C. Structural Analysis — serviceability deflection limits.

Engineering Tips

Single concentrated load P at mid-span of a simply-supported beam.

δ = P·L³ / (48·E·I)
  • L is the full span between supports.
  • Deflection scales with L³ (point) or L⁴ (UDL) — span dominates.
  • Increase I (deeper section) far more effectively than E.
  • Serviceability limits are code-dependent — confirm the governing L/ratio.

For preliminary use — small-deflection theory, simply supported, prismatic, linear-elastic, shear neglected.