What is the mid-span deflection of a W12x26 beam spanning 6.0 meters under 20.0 kN/m?
⚡ Instant Calculated Answer
A W12x26 steel beam across a 6.0 meter span under a 20.0 kN/m uniform distributed load deflects by 19.88 mm at mid-span, which EXCEEDS the standard building code L/360 serviceability limit (16.67 mm).
19.88 mm
Primary Metric
Limit: 16.67 mm
Secondary Metric
📐 Mathematical Formula & Step-by-Step Substitution
- Identify beam properties: Section W12x26, Moment of Inertia I_x = 8,490 cm⁴ (8.4900e-05 m⁴), Young's Modulus E = 200 GPa.
- Convert units: Span L = 6.0 m, Load w = 20.0 kN/m = 20,000 N/m.
- Calculate numerator: 5 × 20,000 × (6.0)⁴ = 5 × 20,000 × 1296.00 = 129,600,000.0.
- Calculate denominator: 384 × 200×10⁹ × 8.4900e-05 = 6,520,320,000.0.
- Evaluate deflection: 129,600,000.0 / 6,520,320,000.0 = 0.01988 m = 19.88 mm (compared to L/360 = 16.67 mm).
📊 Nearby Parameter Reference Table
| Span Length | Uniform Load | Mid-Span Deflection | L/360 Code Limit |
|---|---|---|---|
| 5.0 m | 20.0 kN/m | 9.59 mm | 13.89 mm (OK) |
| 5.5 m | 20.0 kN/m | 14.03 mm | 15.28 mm (OK) |
| 6.0 m | 20.0 kN/m | 19.88 mm | 16.67 mm (FAIL) |
| 6.5 m | 20.0 kN/m | 27.38 mm | 18.06 mm (FAIL) |
| 7.0 m | 20.0 kN/m | 36.82 mm | 19.44 mm (FAIL) |
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