Steel Beam-Column Combined Axial and Flexure (AISC 360 H1.1)
The single number that decides a beam-column, which no single-action tile produces: 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 member tiles, in the same ASD or LRFD basis; second-order Mr assumed. A design aid, not the engineer of record's stamped design.
Formula and source
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.
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