Column Slenderness Ratio Formula
Determines the propensity of a structural column to buckle elastically vs. yield in compression based on effective length and radius of gyration r.
\[ \lambda = \frac{K \cdot L}{r} \quad \text{where } r = \sqrt{\frac{I}{A}} \]
Plain Text Formula:
lambda = (K * L) / r where r = sqrt(I / A)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \lambda \] | Slenderness Ratio | dimensionless | Dimensionless buckling indicator (columns with lambda > 120 buckle elastically) |
| \[ K \cdot L \] | Effective Buckling Length | mm | Unsupported length scaled by boundary condition factor |
| \[ r \] | Radius of Gyration | mm | Geometric distribution of area: sqrt(I / A) |
| \[ A \] | Cross-Sectional Area | mm² | Gross metal area |
💡 Worked Engineering Example
Problem Statement:
A steel column (A=6,000 mm², I_min=5.4e6 mm⁴) has effective length KL=3,000 mm. Find its slenderness ratio.
Step-by-Step Solution:
- r = sqrt(5.4e6 / 6,000) = sqrt(900) = 30 mm
- lambda = 3,000 / 30 = 100
🎯 Result: The column has a slenderness ratio of 100, placing it in the intermediate column transition zone.