Max Deflection of a Simply Supported Beam
Harddeflectionuniform load
A simply supported steel beam has span L = 6 m, uniform load w = 12 kN/m, E = 200 GPa and I = 300 × 106 mm4. What is the maximum deflection?
- A3.4 mm
- B6.8 mm
- C1.7 mm
- D13.5 mm
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Answer: A. 3.4 mm
δmax = 5 w L4 / (384 E I). Work in N and m: w = 12000 N/m, I = 300 × 106 mm4 = 3 × 10-4 m4, E I = 200 × 109 · 3 × 10-4 = 6 × 107 N·m2. δ = 5 · 12000 · 64 / (384 · 6 × 107) = 77.76 × 106 / 2.304 × 1010 = 0.00338 m ≈ 3.4 mm. Unit conversion of I is where most errors happen: 1 mm4 = 10-12 m4.
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