Beam Calculator

Structural beam analysis and load calculations

Quick answer

Beam Calculator

Calculate beam moments, shear forces, deflections, and stresses for various loading conditions and support types.

Formula

M = wL²/8 (distributed), M = PL/4 (center point load)

🏢 Beam Configuration

⚖️ Loading Conditions

📊 Analysis Results

Enter beam parameters and loads to see analysis results

🏗️ Design Notes

  • • This is a simplified analysis tool
  • • Always verify with detailed calculations
  • • Consider dynamic loads and buckling
  • • Check local building codes
  • • Consult a structural engineer for critical applications

🏢Formula

M = wL²/8 (distributed), M = PL/4 (center point load)

💡How it works

Calculate beam moments, shear forces, deflections, and stresses for various loading conditions and support types.

ℹ️ What is Beam Deflection Calculator?

A beam deflection calculator determines how much a structural beam bends (deflects) under applied loads. Engineers use it to ensure beams stay within safe deflection limits — critical for floor beams, bridges, shelves, and any structure where excessive bending would be unsafe or unacceptable.

📐 Formula

δ_max = FL³ / 48EI (simply supported, center load)
F— Applied load (Newtons or lbs)
L— Span length of the beam
E— Young's modulus of the beam material
I— Moment of inertia of the beam cross-section
δ— Maximum deflection at critical point

✏️ Worked Example

Load F: 10,000 N
Span L: 5 m
E (Steel): 200 GPa
I (W200×100): 113 × 10⁶ mm⁴
  1. 1δ = FL³/(48EI)
  2. 2δ = (10000 × 5³) / (48 × 200×10⁹ × 113×10⁻⁶)
  3. 3δ = 1,250,000 / (1,084,800) ≈ 1.15 mm
✅ Result: Maximum deflection ≈ 1.15 mm

💡 How to Interpret Results

  • ▸Typical allowable deflection limit: L/360 for floors, L/240 for roofs, L/180 for live load only.
  • ▸For a 5m beam: L/360 = 13.9 mm — the 1.15mm is well within limits.
  • ▸Doubling the span quadruples deflection (cubic relationship with L).
  • ▸Stiffer material (higher E) or deeper section (higher I) directly reduces deflection.
  • ▸Cantilever beams deflect 8× more than equivalent simply supported beams under the same load.

❓ Frequently Asked Questions

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