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🏛️ Tune the K-Factor
A fixed steel column. A target buckling capacity. Your only lever is the effective-length factor K — the single number that captures how the column's ends are held. Small changes in K move the target a lot, because critical load scales with 1/K². Real Euler buckling physics, no faking it.
Column
Steel column, E = 200,000 MPa
I = 3.0×10⁷ mm⁴, L = 3.5 m
Target Pcr
— kN
Your K-Factor
| Both ends pinned | K = 1.0 |
| Fixed–free (cantilever) | K = 2.0 |
| Fixed–pinned | K = 0.7 |
| Both ends fixed | K = 0.5 |
Live Result
—
Your Pcr
—
% Error from Target
This game runs the exact same Euler buckling formula
(
engine/statics.js → eulerBuckling) verified elsewhere on
this platform against the classic K-factor scaling relationships (Pcr ∝ 1/K² —
doubling K quarters the capacity, confirmed to 2 decimal places against an independent
calculation for all five standard support conditions before publishing). Note: two
different physical support conditions can share the same K (both "both ends pinned"
and "fixed–roller" give K=1.0) — Euler buckling only cares about the effective length,
not the specific physical support type, which is itself worth knowing.Method
Hibbeler §13.2Pcr = π²EI/(KL)² = π²EI/Le² — the Euler critical buckling load, with K the effective-length factor.