AISC 360-22 Chapter E | Compressive Strength of Steel Columns
Steel columns under compression fail either by yielding or buckling. Short stocky columns fail by inelastic crushing, while long slender columns buckle elastically at much lower stresses according to Euler's classic column formula.
Governing Formula
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Notation & Variables
Worked Example
Calculate slenderness ratio
For a W12x53 column with unbraced length L = 14 ft (168"), ry = 2.48", pinned ends (K = 1.0): KL/r = (1.0 * 168) / 2.48 = 67.74.
Check slenderness boundary
Compute limit: 4.71 * sqrt(29000 / 50) = 113.4. Since 67.74 ≤ 113.4, inelastic buckling controls.
Calculate critical stress
Compute Fe = π²(29000) / (67.74)² = 62.38 ksi. Critical stress Fcr = (0.658^(50/62.38)) * 50 = 35.80 ksi.
When does this govern?
Governs all building gravity columns, diagonal bracing members, and truss compression chords.
Common Mistake
Using K = 1.0 for unbraced sway frames. Sway frames have effective length factors K > 1.0 (often 1.5 to 2.5), which cuts buckling strength by more than half if neglected.