AISC 360-22

AISC 360-22 Chapter H | Combined Axial Force and Flexural Bending

Steel members in building frames rarely carry pure axial load or pure bending alone. AISC 360-22 Chapter H provides piecewise bilinear interaction equations that govern beam-columns carrying simultaneous compression and bi-axial moments.

Code Equation

Governing Formula

\begin{cases} \dfrac{P_r}{P_c} + \dfrac{8}{9}\left( \dfrac{M_{rx}}{M_{cx}} + \dfrac{M_{ry}}{M_{cy}} \right) \le 1.0 & \text{ for } \dfrac{P_r}{P_c} \ge 0.2 \\[12pt] \dfrac{P_r}{2 P_c} + \left( \dfrac{M_{rx}}{M_{cx}} + \dfrac{M_{ry}}{M_{cy}} \right) \le 1.0 & \text{ for } \dfrac{P_r}{P_c} < 0.2 \end{cases}

Standard: AISC 360-22Dual US Customary & SI Metric

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Notation & Variables

P_r

Required axial compressive or tensile strength

kips or kN

P_c

Available axial strength (phi_c * Pn for LRFD)

kips or kN

M_{rx}, M_{ry}

Required flexural strength about x and y principal axes

kip-ft or kN·m

M_{cx}, M_{cy}

Available flexural strength about x and y axes (phi_b * Mn)

kip-ft or kN·m

Worked Example

Calculate axial force ratio Pr / Pc

For a W12x65 column with Pr = 150 kips and Pc = 520 kips: Pr / Pc = 150 / 520 = 0.288.

Select governing interaction equation

Because Pr / Pc = 0.288 >= 0.20, Equation H1-1a governs.

Evaluate unity interaction value

Substitute moment ratios: 0.288 + (8/9)*(Mrx/Mcx + Mry/Mcy) = 0.842 <= 1.0 (PASS).

Governing Criteria

When does this govern?

Controls sizing of all multi-story moment frame columns, braced frame columns, and crane runaway building columns.

Common Pitfall

Common Mistake

Omitting second-order P-delta and P-Delta moment magnification when evaluating required moments Mrx and Mry per Appendix 8.

Related Resources

Notation & Variables

P_r

Required axial compressive or tensile strength

kips or kN

P_c

Available axial strength (phi_c * Pn for LRFD)

kips or kN

M_{rx}, M_{ry}

Required flexural strength about x and y principal axes

kip-ft or kN·m

M_{cx}, M_{cy}

Available flexural strength about x and y axes (phi_b * Mn)

kip-ft or kN·m

Worked Example

Calculate axial force ratio Pr / Pc

For a W12x65 column with Pr = 150 kips and Pc = 520 kips: Pr / Pc = 150 / 520 = 0.288.

Select governing interaction equation

Because Pr / Pc = 0.288 >= 0.20, Equation H1-1a governs.

Evaluate unity interaction value

Substitute moment ratios: 0.288 + (8/9)*(Mrx/Mcx + Mry/Mcy) = 0.842 <= 1.0 (PASS).