Required Plastic Section Modulus for a Steel Beam
The design inverse of the flexural-capacity check: enter the demand moment and Fy, get the plastic section modulus Zx to pick a W-shape. LRFD Zx >= 12 Mu/(0.90 Fy); ASD Zx >= 12(1.67)Ma/Fy (AISC 360 Ch. F, Mp = Fy Zx, inverted). A 200 kip-ft LRFD demand on 50 ksi steel needs Zx 53.3 in^3 (a W16x31 works); design it by ASD and the required Zx jumps to 80.2. Feeds straight back into the flexural-capacity tile. Compact, fully braced (Lb <= Lp); the shape lookup and the engineer of record govern.
Formula and source
LRFD: Zx_req = 12 Mu / (0.90 Fy); ASD: Zx_req = 12 (1.67) Ma / Fy (in^3, the 12 converts kip-ft to kip-in).
AISC 360-22 Chapter F (F2.1) Mp = Fy Zx and the §B3 resistance/safety factors, inverted for the required plastic section modulus, by name.
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