What is the mid-span deflection of a W18x40 beam spanning 4.0 meters under 12.0 kN/m?
⚡ Instant Calculated Answer
A W18x40 steel beam across a 4.0 meter span under a 12.0 kN/m uniform distributed load deflects by 0.78 mm at mid-span, which PASSES the standard building code L/360 serviceability limit (11.11 mm).
0.78 mm
Primary Metric
Limit: 11.11 mm
Secondary Metric
📐 Mathematical Formula & Step-by-Step Substitution
- Identify beam properties: Section W18x40, Moment of Inertia I_x = 25,500 cm⁴ (2.5500e-04 m⁴), Young's Modulus E = 200 GPa.
- Convert units: Span L = 4.0 m, Load w = 12.0 kN/m = 12,000 N/m.
- Calculate numerator: 5 × 12,000 × (4.0)⁴ = 5 × 12,000 × 256.00 = 15,360,000.0.
- Calculate denominator: 384 × 200×10⁹ × 2.5500e-04 = 19,584,000,000.0.
- Evaluate deflection: 15,360,000.0 / 19,584,000,000.0 = 0.00078 m = 0.78 mm (compared to L/360 = 11.11 mm).
📊 Nearby Parameter Reference Table
| Span Length | Uniform Load | Mid-Span Deflection | L/360 Code Limit |
|---|---|---|---|
| 3.0 m | 12.0 kN/m | 0.25 mm | 8.33 mm (OK) |
| 3.5 m | 12.0 kN/m | 0.46 mm | 9.72 mm (OK) |
| 4.0 m | 12.0 kN/m | 0.78 mm | 11.11 mm (OK) |
| 4.5 m | 12.0 kN/m | 1.26 mm | 12.5 mm (OK) |
| 5.0 m | 12.0 kN/m | 1.91 mm | 13.89 mm (OK) |
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