When to use: Evaluate the compressive capacity of an axially loaded steel column against flexural buckling. Computes the classic Euler critical load Pcr, the slenderness ratio KL/r, and the AISC 360 Chapter E (E3) design strength φPn. The transition limit 4.71√(E/Fy) determines whether the member buckles in the inelastic or elastic range. Use the effective length factor K to capture end conditions.
Calculate the critical buckling load and AISC 360 LRFD design compressive strength for steel columns. Enter cross-section properties, unbraced length, and effective length factor K to instantly evaluate Euler Pcr, slenderness ratio KL/r, and design capacity phiPn.
The calculator first computes the Euler elastic critical load Pcr = π²EI/(KL)² and slenderness ratio λ = KL/r. It then classifies the column as inelastic (λ ≤ 4.71√(E/Fy)) or elastic and applies AISC 360-16 Chapter E Section E3 to find the critical stress Fcr and nominal strength Pn = Fcr·A. The LRFD design strength is φPn = 0.90·Pn.
Euler buckling: Pcr = π²EI/(KL)². Slenderness: λ = KL/r. Inelastic range: Fcr = 0.658^(Fy/Fe)·Fy. Elastic range: Fcr = 0.877·Fe. Transition limit: 4.71√(E/Fy). Design strength: φPn = 0.90·Fcr·A. Effective length factor K = 0.5 (fixed-fixed), 1.0 (pinned-pinned), 2.0 (fixed-free).
Use for preliminary sizing of axially loaded steel columns in buildings, trusses, and braced frames. Input the governing (minimum) radius of gyration r and the larger effective length KL to check the critical axis. Columns with KL/r > 200 are generally impractical and should be resized.
Inelastic buckling occurs when the column yields before reaching the Euler load (λ ≤ 4.71√(E/Fy), or Fy/Fe ≤ 2.25). Elastic buckling governs slender columns that buckle while still in the elastic range. AISC LRFD uses different Fcr equations for each range.
Theoretical K values: 0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, 2.0 fixed-free. AISC recommends slightly larger design values (0.65, 0.80, 1.0, 2.1) to account for partial restraint in real connections.
AISC recommends KL/r ≤ 200 for compression members as a practical upper limit to avoid excessive sensitivity to imperfections and accidental eccentricities.
The column buckles about the axis with the smallest moment of inertia (weakest axis). For wide-flange sections this is typically the weak (y-y) axis unless bracing is provided. Always check both axes with their respective unbraced lengths and K values.