\[\lambda=\frac{L_e}{r}\]
Variables
lambda[λ]slenderness ratio
Leeffective column length (m)
rradius of gyration (m)
Description
What is this formula?
The slenderness ratio is a dimensionless parameter that measures the susceptibility of a compression member to buckling. It compares the effective length of a member to its radius of gyration.
When to use it
Use this formula when evaluating columns, compression members, truss elements, towers, and structural components that may fail by buckling rather than material yielding.
Example
A steel column has:
Le = 4.0 m
r = 0.050 m
Formula:
λ = Le / r
Substitution:
λ = 4.0 / 0.050
Result:
λ = 80
A higher slenderness ratio generally indicates a greater tendency toward buckling.
Applications
Steel columns, reinforced concrete columns, transmission towers, truss members, industrial structures, bridge components, and structural stability analysis.