Steel Beam Flexural Capacity (AISC 360 Ch. F, Compact + Braced)
Whether a compact, laterally-braced steel W-shape carries the moment.
Example
You enter
- Yield stress Fy (ksi) 50
- Plastic section modulus Zx (in³) 101
- Required moment, ASD service-level Ma (kip-ft, 0 to skip) 200
You get
- Nominal Mn 420.8 kip-ft
- ASD allowable Mn/Omega 252.0 kip-ft
- LRFD design phi_b*Mn 378.8 kip-ft
- Demand / capacity (ASD) 0.79
Checked against published worked examples from: AISC.
Details, formula, and sources
ScopeMn = Mp = Fy x Zx, with the ASD allowable Mn/1.67 and the LRFD design 0.90 Mn. A W18x50 in A992 reaches 421 kip-ft nominal, 252 allowable, 379 design - the numbers a detailer reads off AISC Manual Table 3-2. The shape (Zx), not the grade, sizes the beam: the same steel in a section about half the weight (W12x26) carries just over a third of the moment. Compact + braced plastic plateau only (no LTB or slender-element reductions). A design aid, not a substitute for the engineer of record.
Formula or tableMp = Fy x Zx (kip-in); Mn = Mp / 12 (kip-ft); Ma = Mn / 1.67 (ASD); phi_b Mn = 0.90 Mn (LRFD); util = Mu / Ma.
Source and editionAISC 360-22 Chapter F (F2.1) and §B3.1 / §B3.2, by name; Zx is read from the AISC Steel Construction Manual for the actual shape.
Free accessThe Mn = Fy Zx plastic-moment relation and the Omega_b / phi_b factors are stated in AISC 360, whose provisions are published; Zx comes from the AISC Manual shape tables.
What governsEstimate. AHJ and licensed professional govern.
API field namesfy, zx, mu, mn_kipft, ma_kipft, phi_mn, util_asd
- Compact + braced Mn = Mp = Fy Zx is the plastic plateau; a noncompact flange or Lb > Lp reduces Mn below this (F3 / F2.2)AISC 360-22 F2
- Zx user-supplied the plastic section modulus is read from the AISC Manual for the actual rolled shapeAISC Steel Construction Manual
- ASD / LRFD factors Omega_b = 1.67 (ASD) and phi_b = 0.90 (LRFD) per §B3AISC 360-22 B3