What is the mid-span deflection of a W10x22 beam spanning 4.0 meters under 12.0 kN/m?
⚡ Instant Calculated Answer
A W10x22 steel beam across a 4.0 meter span under a 12.0 kN/m uniform distributed load deflects by 4.07 mm at mid-span, which PASSES the standard building code L/360 serviceability limit (11.11 mm).
4.07 mm
Primary Metric
Limit: 11.11 mm
Secondary Metric
📐 Mathematical Formula & Step-by-Step Substitution
- Identify beam properties: Section W10x22, Moment of Inertia I_x = 4,910 cm⁴ (4.9100e-05 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 × 4.9100e-05 = 3,770,880,000.0.
- Evaluate deflection: 15,360,000.0 / 3,770,880,000.0 = 0.00407 m = 4.07 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 | 1.29 mm | 8.33 mm (OK) |
| 3.5 m | 12.0 kN/m | 2.39 mm | 9.72 mm (OK) |
| 4.0 m | 12.0 kN/m | 4.07 mm | 11.11 mm (OK) |
| 4.5 m | 12.0 kN/m | 6.52 mm | 12.5 mm (OK) |
| 5.0 m | 12.0 kN/m | 9.94 mm | 13.89 mm (OK) |
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