What is the mid-span deflection of a W18x40 beam spanning 7.0 meters under 25.0 kN/m?
⚡ Instant Calculated Answer
A W18x40 steel beam across a 7.0 meter span under a 25.0 kN/m uniform distributed load deflects by 15.33 mm at mid-span, which PASSES the standard building code L/360 serviceability limit (19.44 mm).
15.33 mm
Primary Metric
Limit: 19.44 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 = 7.0 m, Load w = 25.0 kN/m = 25,000 N/m.
- Calculate numerator: 5 × 25,000 × (7.0)⁴ = 5 × 25,000 × 2401.00 = 300,125,000.0.
- Calculate denominator: 384 × 200×10⁹ × 2.5500e-04 = 19,584,000,000.0.
- Evaluate deflection: 300,125,000.0 / 19,584,000,000.0 = 0.01533 m = 15.33 mm (compared to L/360 = 19.44 mm).
📊 Nearby Parameter Reference Table
| Span Length | Uniform Load | Mid-Span Deflection | L/360 Code Limit |
|---|---|---|---|
| 6.0 m | 25.0 kN/m | 8.27 mm | 16.67 mm (OK) |
| 6.5 m | 25.0 kN/m | 11.39 mm | 18.06 mm (OK) |
| 7.0 m | 25.0 kN/m | 15.33 mm | 19.44 mm (OK) |
| 7.5 m | 25.0 kN/m | 20.2 mm | 20.83 mm (OK) |
| 8.0 m | 25.0 kN/m | 26.14 mm | 22.22 mm (FAIL) |
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