Beam Deflection Calculator

Calculate beam bending deflection for structural members.

Structures
1

Design Parameters

Beam Span Length (m) must be entered.

Quick Presets

Standard Steel I-Beam (IPE 200)
IPE 200 steel beam with modulus E = 210 GPa, I = 1943 cm4.

Calculated Outputs

Deflection (Metric) mm
0.00
Deflection (Imperial) in
0.0000

Beam Deflection Analysis

Deflection is the vertical displacement of a structural member under service load. Excessive deflection can cause cracks in ceiling plaster, window binding, or structural failures.

Our beam deflection calculator solves elastic beam deflection under point load or UDL conditions to help verify serviceability compliance.

Elastic Deflection Curve Diagram showing deflection curve under bending load.

Elastic Deflection Formulas

Standard deflection equations derived from Euler-Bernoulli beam theory assume linear-elastic material behavior. The maximum vertical deflection is directly proportional to load magnitude and span length, and inversely proportional to material stiffness (Elastic Modulus, E) and member profile inertia (I).

Center Point Load: Max Deflection = (P × L³) ÷ (48 × E × I)
Uniform Distributed Load (UDL): Max Deflection = (5 × w × L⁴) ÷ (384 × E × I)
Example Steel I-Beam Deflection:

1. Beam Span Length (L): 6.0 meters.

2. Steel Modulus of Elasticity (E): 200 GPa (2.0 × 10¹¹ N/m²).

3. Profile Moment of Inertia (I): 8000 cm⁴ (8.0 × 10⁻⁵ m⁴).

4. Concentrated Center Load (P): 20.0 kN (20,000 N).

5. Maximum deflection calculation: (20,000 × 6.0³) ÷ (48 × 2.0 × 10¹¹ × 8.0 × 10⁻⁵) = 4,320,000 ÷ 768,000,000 = 0.0056m = 5.6 mm.

Result: Peak deflection is 5.6 mm, which complies with standard code limits.
Warning: This calculator is for preliminary estimation and educational purposes only. It is NOT a replacement for structural analysis by a licensed professional engineer (PE) or architect. Always verify loads, material properties, and deflection criteria with local building codes (e.g., IBC, Eurocodes).

Code Deflection Limits (L/360 vs. L/240)

Building codes restrict structural element deflection under live loads to prevent crack damage to brittle finishes (like gypsum plaster ceilings) and maintain user comfort:

  • L/360 Limit: Standard limit for beams supporting plaster or drywall ceilings. For a 6m (6000mm) beam, the maximum allowed deflection is 6000 ÷ 360 = 16.6 mm.
  • L/240 Limit: Standard limit for floor members without plaster finishes. For a 6m beam, the maximum deflection is 6000 ÷ 240 = 25.0 mm.

Frequently asked questions

What is a typical code limit for beam deflection?

Building codes typically limit live-load deflection to L/360 or L/240 of the span (e.g., a 6m beam is limited to 16.6 mm deflection).

How does moment of inertia impact deflection?

The Moment of Inertia (I) represents a profile shape's resistance to bending. Deflection is inversely proportional to I; doubling the moment of inertia cut deflection in half.

Does beam deflection depend on structural material strength?

No. Deflection depends on material stiffness (Elastic Modulus E, e.g. 200 GPa for steel) rather than material yield strength (e.g. 350 MPa). A high-strength steel beam deflecs exactly the same amount as a mild steel beam of the same shape.