Column Slenderness Ratio⚠ unverified
Physics / Materials · Compute the slenderness ratio of a column
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| length | length | m | 1.0 | Effective length of the column |
| radius_of_gyration | radiusofgyration | m | 1.0 | Radius of gyration of the cross-section |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | λ | — | Slenderness ratio, dimensionless |
The science & history
Understanding the Parameters
- $L$ — longer columns are more slender (buckling-prone).
- $r$ — larger $r$ (more spread-out section) → lower $\lambda$.
- $\lambda$ — enters Euler and intermediate column formulas; compare to material-dependent limits separating short/intermediate/long columns.
Derivation (Approaching a Proof)
Radius of gyration $r = \sqrt{I/A}$ measures how far area is from the axis. The ratio $L/r$ is the natural dimensionless length for buckling eigenvalue problems ($P_{cr} \propto EI/L^{2} \propto E A /(L/r)^{2}$).
History
Slenderness organises column design from Euler through AISC/Eurocode interaction formulas.
Related Concepts: Euler Buckling Load, Section Modulus, Moment Of Inertia Disk
Notes: Registry calculator materials-column-slenderness-ratio (unverified). Use $KL$ as $L$ for
end conditions.