Required Plastic Section Modulus for a Steel Beam
The design inverse of the flexural-capacity check.
Example
You enter
- Yield stress Fy (ksi) 50
- Demand moment Mu (LRFD) or Ma (ASD) (kip-ft) 200
- Design method lrfd
You get
- Required plastic section modulus Zx 53.3 in^3
Details, formula, and sources
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 check. Compact, fully braced (Lb <= Lp); the shape lookup and the engineer of record govern.
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.
The Mp = Fy Zx relation and the Omega_b / phi_b factors are stated in AISC 360, whose provisions are published; inverting them for the required Zx is public arithmetic.
Estimate. AHJ and licensed professional govern.
Field names used by the API: fy, moment_kipft, method, zx_req
- Inverse of the forward tile Zx_req solves phi_b Fy Zx / 12 = Mu (LRFD) or Fy Zx / (12 Omega_b) = Ma (ASD); feeding it into steel-beam-flexure returns the demandAISC 360-22 F2 / B3
- Compact + braced Mn = Mp = Fy Zx (the plastic plateau); a noncompact or unbraced beam needs the F3 / F2.2 lateral-torsional-buckling checkAISC 360-22 F2