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Column Buckling (Euler & AISC)

Euler Pcr · Slenderness KL/r · AISC 360 φPn

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.

Column & Material
ksi
ksi
in²
in⁴
in
ft
Key Formulas
Pcr = π²EI/(KL)²
λ = KL/r
Fe = π²E/λ²
Fcr = 0.658^(Fy/Fe)·Fy (λ≤4.71√(E/Fy))
Fcr = 0.877·Fe (else)
φPn = 0.90·Fcr·A
Design Strength φPn
258.8
kip
Inelastic Range
λ = 67.2 vs limit 113.4
Results
Euler Pcr507.0 kip
Slenderness λ = KL/r67.2
Elastic stress Fe63.38 ksi
Transition 4.71√(E/Fy)113.4
Critical stress Fcr35.94 ksi
Nominal Pn287.5 kip
Design φPn258.8 kip
Buckling RangeInelastic
References
AISC 360-16 Chapter E — Compression
Euler 1757 — elastic buckling
AISC E3 — flexural buckling