Steel Beam-Column Combined Axial and Flexure (AISC 360 H1.1)
The single number that decides a steel beam-column.
Example
You enter
- Required axial Pr (kip, 2nd-order) 100
- Available axial Pc (kip) 400
- Required strong-axis moment Mrx (kip-ft) 80
- Available strong-axis moment Mcx (kip-ft) 200
You get
- Axial ratio Pr/Pc 0.250
- Interaction (<= 1.0 passes) 0.606 (OK)
Details, formula, and sources
AISC H1.1 combines axial and bending in a bilinear interaction - Pr/Pc + (8/9)(Mrx/Mcx + Mry/Mcy) for Pr/Pc >= 0.2, Pr/(2Pc) + (sum Mr/Mc) below. Pr 100 / Pc 400 with Mrx 80 / Mcx 200 passes at 0.61; drop the axial and the low-axial branch gives it a lighter half-weight, so a beam with only incidental axial is governed by its moment. Pc/Mc from the individual member checks, in the same ASD or LRFD basis; second-order Mr assumed. A design aid, not the engineer of record's stamped design.
ratio = Pr/Pc; ratio >= 0.2: I = Pr/Pc + (8/9)(Mrx/Mcx + Mry/Mcy); ratio < 0.2: I = Pr/(2Pc) + (Mrx/Mcx + Mry/Mcy); pass when I <= 1.0.
The AISC 360-22 Section H1.1 combined-force (axial plus flexure) bilinear interaction equations, consistent for ASD or LRFD, by name.
AISC 360 is free to read at aisc.org (Specification for Structural Steel Buildings); the H1.1 interaction equations are in the published specification.
Estimate. AHJ and licensed professional govern.
Field names used by the API: pr_kip, pc_kip, mrx_kft, mcx_kft, ratio, interaction
- Bilinear interaction the 8/9 form for Pr/Pc >= 0.2, the half-axial form below, capped at 1.0AISC 360-22 Eq. H1-1a/H1-1b
- Available strengths Pc and Mc entered from the member tiles in a consistent ASD or LRFD basisAISC 360-22 H1.1
- Second-order the P-delta/P-Delta amplification is already carried in the required moment MrAISC 360-22 Ch. C / App. 8