Free Steel Buckling Calculator — Column & Plate

Q: What is the difference between Euler buckling and inelastic buckling?

Euler buckling is elastic buckling below the proportional limit. Inelastic buckling accounts for residual stresses and partial yielding, reducing capacity below the Euler curve for intermediate slenderness. The transition is at KL/r approximately 4.71 times sqrt(E/Fy) per AISC 360.

Q: What is flexural-torsional buckling and when does it govern?

Flexural-torsional buckling is coupled bending and twisting in singly-symmetric sections (channels, T-sections, angles). Unlike doubly-symmetric W-shapes where pure flexural buckling governs, single angles can have FTB capacities up to 40 percent lower.

Check steel buckling across all major modes — flexural (Euler) buckling of columns, torsional and flexural-torsional buckling of singly-symmetric sections, lateral-torsional buckling (LTB) of beams, and local buckling of plates. Covers AISC 360-22 Sections E, F, and B4, AS 4100 Sections 5 and 6, EN 1993-1-1 Section 6.3, and CSA S16 Sections 13 and 14.

Buckling Modes

Mode	Sections Affected	AISC 360	AS 4100	EN 1993-1-1	CSA S16
Flexural (Euler)	All columns, compression members	E3	Cl 6.3	Cl 6.3.1	Cl 13.3
Torsional	Cruciform, thin-walled closed	E4	Cl 6.4	Cl 6.3.1.4	Cl 13.3.2
Flexural-torsional	Single angles, T-sections, channels	E4	Cl 6.4	Cl 6.3.1.4	Cl 13.3.2
Lateral-torsional (LTB)	Beams, unbraced compression flange	F2	Cl 5.6	Cl 6.3.2.2	Cl 13.6
Local (flange/web)	All sections with slender elements	B4	Cl 5.2	Table 5.2	Cl 11.2

Key Equations

Euler buckling (AISC 360-22 Eq E3-3): Fe = π²E / (KL/r)²

Inelastic buckling (AISC 360-22 Eq E3-2): When KL/r ≤ 4.71√(E/Fy): Fcr = (0.658^(Fy/Fe)) × Fy When KL/r > 4.71√(E/Fy): Fcr = 0.877 × Fe

LTB moment (AISC 360-22 Eq F2-3): Mn = Fcr × Sx, where Fcr = Cb × π² × E / (Lb/rts)² × √(1 + 0.078 × Jc/(Sx×ho) × (Lb/rts)²)

Frequently Asked Questions

What is the difference between Euler buckling and inelastic buckling? Euler buckling describes elastic buckling of a perfectly straight column, valid when the critical stress remains below the proportional limit. Inelastic buckling accounts for material nonlinearity (residual stresses, partial yielding), which reduces capacity below the Euler curve for intermediate slenderness ratios. The transition occurs at KL/r ≈ 4.71√(E/Fy) per AISC 360.

What is flexural-torsional buckling and when does it govern? Flexural-torsional buckling is a coupled mode involving simultaneous bending and twisting, occurring in singly-symmetric sections (channels, T-sections, single angles, double angles with a gap). Unlike doubly-symmetric sections (W-shapes with equal flanges) where pure flexural buckling governs, single angles can have FTB capacities up to 40% lower than flexural buckling.

How does lateral-torsional buckling differ from column buckling? LTB is a beam instability where the compression flange buckles laterally while the cross-section twists, reducing flexural capacity. Column buckling (flexural) is a compression member instability. LTB depends on unbraced length (Lb), section torsional properties (J, Cw), and moment gradient (Cb). Column buckling depends on KL/r, which is purely a section radius of gyration and effective length.

What is the local buckling limit for flange and web elements? AISC 360-22 Table B4.1b defines width-to-thickness limits for compression elements. Flanges: λ_p = 0.38√(E/Fy) (compact limit), λ_r = 1.0√(E/Fy) (slender limit). Webs: λ_p = 3.76√(E/Fy) (compact), λ_r = 5.70√(E/Fy) (slender). Beyond λ_r, effective width concepts are required (Section E7 for columns, F5 for beams).

Is this buckling calculator free? Yes, completely free with unlimited calculations.

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