Euler-Bernoulli Beam Deflection Calculator
Calculates maximum deflection and bending moment for simply supported and cantilever beams according to Euler-Bernoulli beam theory.
Euler-Bernoulli Beam Deflection
Calculates maximum elastica deflection δ_max, bending moments M_max, reaction forces, and IBC building code span limits.
IBC limit: L/360 for live loads, L/240 total.
Deflection: δ_max = (P · L³) / (48 · E · I)
Moment: M_max = (P · L) / 4
Reaction Forces: Ra = 5 kN, Rb = 5 kN
What is Beam Deflection?
Beam deflection is the vertical displacement of a structural beam under the influence of an applied lateral load, governed by the span length, Young’s modulus, and area moment of inertia.
Formula & Step-by-Step Calculation
Euler-Bernoulli deflection and bending moment formula.
Worked Step-by-Step Examples
Simply supported 4m steel beam (E=200 GPa, I=50×10⁶ mm⁴) with 10 kN center load
Common Real-World & Academic Use Cases
- ✓ Floor joist structural deflection building code verification (L/360 rule)
- ✓ Crane gantry girder bending moment sizing
- ✓ Bridge deck longitudinal support beam checks
How to Use the Euler-Bernoulli Beam Deflection Calculator
Select Support Condition
Choose Simply Supported or Cantilever.
Enter Span & Applied Load
Input length (m) and force (N).
Read Deflection
Inspect maximum deflection in mm and L/span ratio.
Frequently Asked Questions
Q: What is the L/360 building deflection limit?
A common structural building code threshold specifying that a floor beam under live load must not deflect by more than 1/360th of its clear span length to prevent plaster ceiling cracking.