What is the mid-span deflection of a W10x22 beam spanning 5.0 meters under 15.0 kN/m?
⚡ Instant Calculated Answer
A W10x22 steel beam across a 5.0 meter span under a 15.0 kN/m uniform distributed load deflects by 12.43 mm at mid-span, which PASSES the standard building code L/360 serviceability limit (13.89 mm).
12.43 mm
Primary Metric
Limit: 13.89 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 = 5.0 m, Load w = 15.0 kN/m = 15,000 N/m.
- Calculate numerator: 5 × 15,000 × (5.0)⁴ = 5 × 15,000 × 625.00 = 46,875,000.0.
- Calculate denominator: 384 × 200×10⁹ × 4.9100e-05 = 3,770,880,000.0.
- Evaluate deflection: 46,875,000.0 / 3,770,880,000.0 = 0.01243 m = 12.43 mm (compared to L/360 = 13.89 mm).
📊 Nearby Parameter Reference Table
| Span Length | Uniform Load | Mid-Span Deflection | L/360 Code Limit |
|---|---|---|---|
| 4.0 m | 15.0 kN/m | 5.09 mm | 11.11 mm (OK) |
| 4.5 m | 15.0 kN/m | 8.16 mm | 12.5 mm (OK) |
| 5.0 m | 15.0 kN/m | 12.43 mm | 13.89 mm (OK) |
| 5.5 m | 15.0 kN/m | 18.2 mm | 15.28 mm (FAIL) |
| 6.0 m | 15.0 kN/m | 25.78 mm | 16.67 mm (FAIL) |
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