Calculator
Engineering
MathColumn Buckling Calculator
Free column buckling calculator: Euler critical load, slenderness KL/r and AISC 360 design capacity φPn. IPE sections built in, with full step-by-step math.
Have feedback? Report bugs, suggest features, or share your thoughts — we read them allWhat is the Column Buckling Calculator?
This calculator checks a steel column against flexural buckling. It computes the effective length KL from the end conditions, the slenderness ratio KL/r, the Euler critical load Ncr = π²EI/(KL)², and the design compressive capacity φPn following the AISC 360 E3 curve, which smoothly blends inelastic buckling (short/intermediate columns) and elastic Euler buckling (slender columns). Pick a European IPE section from the built-in EN 10365 table (the weak axis governs) or enter area and moment of inertia manually — every intermediate value is shown step by step.
Features
- Four standard end conditions with their effective length factors K (1.0, 0.5, 0.7, 2.0)
- Built-in IPE 80–600 section table (EN 10365) using the governing weak axis
- Manual mode for any section: enter A and Imin directly
- Euler critical load and stress, slenderness KL/r and the 4.71√(E/Fy) limit
- AISC 360-16 E3 critical stress: inelastic 0.658^(Fy/Fe)·Fy or elastic 0.877·Fe
- Design capacity φPn (LRFD, φ = 0.90) and utilization check against your applied load
- Complete step-by-step derivation for verification and homework
How to use
- Choose the end condition — pinned–pinned (K = 1.0) is the common default
- Enter the column length in metres
- Pick an IPE section, or switch to manual input and enter A (cm²) and Imin (cm⁴)
- Adjust E and Fy if needed (defaults: 200 000 MPa, S355 steel)
- Optionally enter the applied load P to get a PASS/FAIL utilization check
- Press Calculate and review the results table and the step-by-step math
Typical uses
- Sizing a steel column or post for a mezzanine, canopy or frame
- Checking whether an existing column can take an increased load
- Civil engineering coursework: Euler buckling and column-curve problems
- Comparing how end fixity (K factor) changes column capacity
Engineering notes
- Buckling always happens about the axis with the largest KL/r — for an IPE column free in both directions that is the weak (z) axis, which this tool uses
- Recommended K values are theoretical; codes suggest slightly higher design values when connection rigidity is uncertain
- Keep KL/r ≤ 200 for compression members, per common code practice
- This tool covers flexural buckling of doubly symmetric sections; torsional and local buckling need separate checks
Frequently Asked Questions
The AISC 360-16 E3 column curve. First Fe = π²E/(KL/r)² is computed. If KL/r ≤ 4.71√(E/Fy) the column buckles inelastically and Fcr = 0.658^(Fy/Fe)·Fy; otherwise it buckles elastically and Fcr = 0.877·Fe. The design capacity is φPn = 0.90·Fcr·A (LRFD).
K converts the real column length into the equivalent pinned-pinned buckling length: 1.0 for pinned–pinned, 0.5 for fixed–fixed, 0.7 for fixed–pinned and 2.0 for a cantilever (fixed–free). The Euler load uses (KL)² in the denominator, so K has a squared effect on capacity.
A column that is not braced differently in the two directions always buckles about the axis with the larger slenderness — for I-shaped sections that is the weak (z) axis with the smaller radius of gyration. If your column is braced about the weak axis, use manual mode with the strong-axis properties.
No. The Euler load is the theoretical elastic limit for a perfect column. Real columns have residual stresses and initial imperfections, which is why the AISC curve reduces capacity — use φPn, not Ncr, for design.
Yes for the Euler part — set E for aluminium, timber, etc. The AISC E3 curve, however, is calibrated for hot-rolled steel; for other materials use the appropriate design standard.
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