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Lightest Steel Beam for a Moment

Mediumbeam selectionflexure
A beam has Mu = 160 kN·m, Fy = 345 MPa and φb = 0.90. Four hypothetical compact, fully braced sections have (mass; Zx): A (35 kg/m; 480,000 mm³), B (40 kg/m; 560,000 mm³), C (45 kg/m; 600,000 mm³), D (50 kg/m; 700,000 mm³). All other checks are satisfied. Which is the lightest section whose design flexural strength φbFyZx meets Mu?
  1. ASection B (40 kg/m)
  2. BSection A (35 kg/m)
  3. CSection C (45 kg/m)
  4. DSection D (50 kg/m)
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Answer: A. Section B (40 kg/m)

Equation: Zreq = Mu/(φb Fy). Substitution: Zreq = 160×10⁶/(0.90·345) = 515,298 mm³. A (480,000) fails: φbMn = 149.0 kN·m < 160. B (560,000) passes: 173.9 kN·m. C and D also pass but are heavier, so B is the lightest. Wrong: A passes only if φb is omitted (nominal FyZx = 165.6 kN·m); C and D satisfy flexure but are not the lightest.
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