Steel Column Design Example -- AISC 360-22 LRFD Worked Solution

Steel column design is a core competency for every structural engineer. Columns carry the gravity load of the building down to the foundation, and their failure — almost always by buckling — can be sudden and catastrophic. The buckling check per AISC 360-22 Chapter E is one of the most safety-critical calculations in structural steel design.

Design parameters

Interior steel column in a multi-storey building: W10x49 section, ASTM A992 steel (Fy = 50 ksi), 14 ft storey height, fixed base and pinned top (K = 0.80). Axial loads: 180 kips dead + 120 kips live. End moment from frame analysis: 45 kip-ft.

Section properties (W10x49)

A = 14.4 in^2, d = 10.0 in, bf = 10.0 in, rx = 4.35 in, ry = 2.54 in, Zx = 60.4 in^3, Sx = 54.6 in^3.

For a complete database of W-shape properties including Ix, Sx, Zx, ry, J, and Cw, see the Section Properties Database.

Step 1: Factored loads

LRFD combination 1.2D + 1.6L gives Pu = 408 kips and Mu = 72 kip-ft (864 kip-in). The moment arises from live load frame action.

Step 2: Flexural buckling check (AISC E3)

KL (weak axis governs) = 0.80 _ 168 = 134.4 in. KL/ry = 52.9. Since 52.9 < 113, inelastic buckling applies: Fcr = 38.3 ksi. Nominal strength Pn = 551.5 kips. Design strength phi_c _ Pn = 496.4 kips. Pu = 408 < 496 — axial check passes (ratio 0.82).

Step 3: Combined axial and flexure (AISC H1)

B1 = 1.19, giving amplified moment Mux = 85.7 kip-ft. phi*b * Mnx = 226.5 kip-ft. Interaction ratio = 0.82 + 8/9 _ 85.7/226.5 = 1.156 — FAILS. The W10x49 is insufficient for combined loading; upgrading to W10x68 (interaction ratio ~0.88) is required.

Key takeaways

The weak-axis radius of gyration (ry) governs column buckling; combined loading is often the governing case; second-order effects amplify moments significantly; and section compactness must be verified before applying the full plastic section modulus.

Educational reference only. All column designs must be independently verified by a licensed Professional Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.

Try It Yourself

Ready to try this yourself? Use our free Column Capacity Calculator. Axial compression and buckling checks per AISC 360-22 Chapter E with K-factor selection and effective length calculation.