📏 Beam Deflection Calculator
Calculate beam deflection and slope for simply supported and cantilever beams under point and distributed loads.
Beam Deflection Under Load — Serviceability Check
BrainyCalculators editorial insight — unique to this tool
Simply supported beam with center point load: max deflection δ = PL³/(48EI). L/360 limit is common for live load floor comfort — excessive deflection cracks drywall before structural failure. Steel I-beams vs wood joists differ vastly in moment of inertia I.
When to use this calculator
Use for structural beam deflection estimates in design review. For weight of steel itself, use Steel Weight.
Combining dead and live loads on a slab?
This page computes beam bending deflection. For load combination totals, use the Structural Load Calculator →
Beam Type
Load Type
GPa (Gigapascals)
cm⁴ (centimetres to the 4th)
What is Beam Deflection?
Beam deflection analysis computes how far a structural member bends under load using elastic modulus, moment of inertia, span, and support conditions.
Use this page when you have beam geometry and load layout and need displacement limits. Structural load calculator aggregates dead/live load combinations on slabs and frames.
Force and torque are scalar mechanics primitives; deflection is deformation result on a member.
Beam Deflection Formulas
Where: P = point load (kN), w = UDL (kN/m), L = span (m), E = elastic modulus (Pa), I = moment of inertia (m⁴). Ensure consistent SI units throughout.
Worked Example
Simply supported steel beam: Span = 6 m, point load P = 30 kN at midspan, E = 200 GPa, I = 85,500 cm⁴.
How the Beam Deflection Calculator Works
Formula, assumptions, and calculation steps for this engineering tool.
Methodology
Engineering calculators apply standard unit conversions and formula relationships after normalizing measurements to compatible units.
Calculation Steps
- Enter dimensions, loads, rates, or electrical values.
- Convert the inputs into the formula unit system.
- Apply the engineering equation or conversion factor.
- Return the result with units and supporting context.
Assumptions and Limits
- Material behavior is assumed ideal unless fields specify otherwise.
- Code checks, safety factors, and site conditions may require professional review.
- Use a qualified engineer for design-critical decisions.
Frequently Asked Questions
The moment of inertia (I) — also called the second moment of area — measures a cross-section's resistance to bending. A larger I means less deflection for the same load. It depends on both the area and how that area is distributed relative to the neutral axis. Deep sections (like I-beams) have much higher I values than equivalent solid rectangular sections, which is why I-beams are structurally efficient. I is measured in m⁴ or cm⁴.
Excessive deflection causes: (1) cracking of brittle finishes like plaster or tiles; (2) doors and windows jamming; (3) ponding of water on flat roofs; (4) visual distress to occupants; (5) secondary structural effects (P-delta effects). Building codes set deflection limits to prevent these issues. Common limits: L/250 for general floors, L/360 when supporting brittle finishes, L/500 for facades, L/1000 for sensitive equipment floors.
Elastic modulus (E) measures a material's stiffness — its resistance to elastic deformation under stress. A higher E means the material is stiffer and deflects less under the same load. Steel (200 GPa) is about 3× stiffer than aluminum (69 GPa) and 6.5× stiffer than concrete (30 GPa). E is used in beam deflection formulas as EI (flexural rigidity), so increasing either E or I reduces deflection proportionally.
A simply supported beam rests on two supports (pinned and roller) and is free to rotate at both ends. The maximum deflection is at midspan. A cantilever beam is fixed at one end and free at the other. It deflects more than an equivalent simply supported beam — a cantilever with a point load deflects 16× more than a simply supported beam (PL³/3EI vs PL³/48EI). Cantilevers develop large hogging moments at the fixed support.
To reduce deflection: (1) Increase depth of section — deflection reduces with the cube of depth increase; (2) Use a stiffer material (higher E); (3) Reduce span — deflection increases with L³ or L⁴, so halving span reduces deflection by 8–16×; (4) Add intermediate supports to create a continuous beam; (5) Pre-camber the beam so it deflects to level under service load; (6) Increase moment of inertia by choosing a deeper or wider section.
Real-World Applications of Beam Deflection
Common Beam Deflection Mistakes
Typical Deflection Limits (Building Codes)
| Application | Live Load Limit | Total Load Limit |
|---|---|---|
| Floor beams (IBC/AISC) | L/360 | L/240 |
| Roof beams (not plaster) | L/240 | L/180 |
| Roof supporting plaster | L/360 | L/240 |
| Crane runway beams | L/1000 | L/600 |
| Bridge girders (AASHTO) | L/800 | — |
| Timber floors (Eurocode 5) | L/300 | L/250 |
References
- American Institute of Steel Construction. Steel Construction Manual. 16th ed. AISC, 2022.
- International Building Code. IBC 2021 — Chapter 16: Structural Design. ICC, 2021.
- Timoshenko SP, Gere JM. Mechanics of Materials. 4th ed. PWS-KENT, 1990.
- Eurocode 3. Design of Steel Structures — EN 1993-1-1. CEN, 2005.
- AASHTO. LRFD Bridge Design Specifications. 9th ed. AASHTO, 2020.
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