18.2 Steel Columns and Beam-Columns

A steel column is a member inside a stability system, not an isolated area multiplied by yield stress. Compression can trigger local, flexural, torsional, or flexural-torsional buckling before gross yielding. For July 2026, use the April 2024 PE Civil: Structural specification, current PE Civil Reference Handbook, and the AISC Steel Construction Manual 15th edition. Do not import the April 2027 editions.

Section Capacity Is Not System Stability

A short compact cross-section can approach a squash-type axial limit related to F_yA_g, but a real column's nominal compressive strength depends on its buckling behavior. Flange and web width-thickness ratios identify local slenderness. Global flexural buckling depends on E, I, unbraced segment length, and restraint about each axis. Singly symmetric or open sections may have torsional or flexural-torsional modes. Residual stress, initial crookedness, and inelastic response are reflected in AISC's calibrated column provisions.

The frame can also lose stability through story sway even when each isolated section looks adequate. Braces, diaphragms, connections, and adjacent members provide the restraint assumed in analysis; they need strength, stiffness, and a complete force path. A brace shown as a point restraint but attached to a flexible support may not create the modeled unbraced length.

Axis-Specific Length and Slenderness

For a traditional effective-length description, slenderness is KL/r about the relevant axis. L is the segment between restraints effective for that mode, not automatically floor height or total fabricated length. K represents frame and end restraint in the chosen method. Because r_x and r_y differ, the weak-axis mode often governs, but unequal bracing can reverse that expectation.

Local element slenderness is a plate width-to-thickness issue and is not the same as member KL/r. Beam lateral-torsional unbraced length is another distinct parameter. Label every length by mode before using it.

Choose One Compatible Stability Method

The AISC 15th-edition framework offers stability-analysis approaches with coordinated assumptions. A direct-analysis route includes required second-order effects, prescribed stiffness treatment, and initial imperfection representation such as notional loads; member checks use the compatible effective-length assumption of that route. An effective-length route evaluates frame stability and assigns K consistently with its permitted analysis assumptions.

Do not take reduced stiffness from direct analysis, a favorable K from a separate idealization, and first-order moments from another model. That mixture has no calibrated basis. State whether moments include P-Delta global sway and P-delta member curvature. The method determines which amplification, stiffness, and resistance provisions belong together.

Column Design Workflow

1. Generate LRFD or ASD demands from the controlling load combinations.
2. Build the system model with actual supports, releases, braces, and connection stiffness assumptions.
3. Apply the selected AISC stability method, including required second-order and imperfection effects.
4. Classify section elements and calculate axial strength for every plausible buckling mode and axis.
5. Calculate flexural strengths with the correct unbraced lengths and local limits.
6. Apply axial-flexural interaction using demands and capacities from the same design route.
7. Check splices, bases, anchors, braces, and load transfer to foundations.

A column can pass member interaction yet belong to an unstable frame; it can also sit in a stable frame and fail local or member buckling. Both levels must pass.

Worked Biaxial Beam-Column Interaction

A problem supplies LRFD demands from a compatible second-order analysis: P_u = 180 kips, M_ux = 90 kip-ft, and M_uy = 20 kip-ft. It supplies design strengths φP_n = 400 kips, φM_nx = 240 kip-ft, and φM_ny = 120 kip-ft. The problem identifies the applicable AISC high-axial-load interaction form as

P_u/(φP_n) + (8/9)[M_ux/(φM_nx) + M_uy/(φM_ny)] ≤ 1.0

Ratios are:

P_u/(φP_n) = 180/400 = 0.450

M_ux/(φM_nx) = 90/240 = 0.375

M_uy/(φM_ny) = 20/120 = 0.167

Interaction:

0.450 + (8/9)(0.375 + 0.167) = 0.932 ≤ 1.0

The stated interaction passes. It would be invalid to replace φP_n with an ASD allowable P_n/Ω while retaining factored P_u, or to use first-order moments if the selected route requires second-order effects. The interaction result also assumes the supplied strengths already address their applicable member limit states; it does not separately prove frame stability or connection adequacy.

Compression, Bending, and Load Introduction

Moment can arise from frame action, beam reactions, eccentric connections, initial crookedness, or load not applied through the effective centroid. Biaxial moments can change sign by combination, so envelope both axes. A base plate distributes compression to concrete while anchor rods and bearing transfer shear and uplift as detailed. Column splices transfer axial force and may need moment or shear according to the system.

At concentrated beam-column joints, check panel-zone, web, flange, stiffener, and connection demands as the applicable provisions require. A member line in an analysis model does not resolve local force introduction. Likewise, a leaning gravity column can add destabilizing load to a lateral frame through diaphragm compatibility even if it carries little lateral shear.

Final Consistency Audit

Write four labels beside the interaction result: LRFD or ASD, stability method, second-order status, and unbraced length by axis. Then confirm local slenderness, member buckling, system stability, and connections were not collapsed into one ratio.

Two screens remain outside the interaction equation: service drift can govern even when strength passes, and fire, corrosion, or damaged bracing can change section properties or support conditions. The design model must represent the required current condition.