What is the mid-span deflection of a W10x22 beam spanning 3.0 meters under 10.0 kN/m?
⚡ Instant Calculated Answer
A W10x22 steel beam across a 3.0 meter span under a 10.0 kN/m uniform distributed load deflects by 1.07 mm at mid-span, which PASSES the standard building code L/360 serviceability limit (8.33 mm).
1.07 mm
Primary Metric
Limit: 8.33 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 = 3.0 m, Load w = 10.0 kN/m = 10,000 N/m.
- Calculate numerator: 5 × 10,000 × (3.0)⁴ = 5 × 10,000 × 81.00 = 4,050,000.0.
- Calculate denominator: 384 × 200×10⁹ × 4.9100e-05 = 3,770,880,000.0.
- Evaluate deflection: 4,050,000.0 / 3,770,880,000.0 = 0.00107 m = 1.07 mm (compared to L/360 = 8.33 mm).
📊 Nearby Parameter Reference Table
| Span Length | Uniform Load | Mid-Span Deflection | L/360 Code Limit |
|---|---|---|---|
| 2.0 m | 10.0 kN/m | 0.21 mm | 5.56 mm (OK) |
| 2.5 m | 10.0 kN/m | 0.52 mm | 6.94 mm (OK) |
| 3.0 m | 10.0 kN/m | 1.07 mm | 8.33 mm (OK) |
| 3.5 m | 10.0 kN/m | 1.99 mm | 9.72 mm (OK) |
| 4.0 m | 10.0 kN/m | 3.39 mm | 11.11 mm (OK) |
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