Column Slenderness Ratio
Column Slenderness Ratio
Slenderness decides whether a column fails by yielding or by buckling. It is the single most important number in column design.
The radius of gyration is r = √(I/A) and the slenderness ratio is λ = KL/r. where I is the second moment of area, A the cross-section area, K the effective-length factor and L the length.
Inputs
I := 8.0e6 mm^4=8e-06 m^4
A := 3000 mm^2=3e-03 m^2
K := 1=1
L := 3.5 m=3.5 m
The radius of gyration packages the section’s stiffness and area.
r := sqrt(I/A)=51.64 mm
The slenderness ratio scales the effective length by the radius of gyration.
lambda := K·L/r=67.78
Results
Low slenderness (roughly below 50) means a stocky column that yields; high slenderness means an Euler-buckling column. The value steers which design curve applies.
Assumptions & limitations
- Prismatic column, constant section.
- Effective length captures the end restraint.
- Buckling about the weak axis governs unless braced.