\[r=\sqrt{\frac{I}{A}}\]
Variables
rradius of gyration (m)
Isecond moment of area (m⁴)
Across-sectional area (m²)
Description
What is this formula?
The radius of gyration is a geometric property that describes how the area of a cross-section is distributed relative to a centroidal axis. It provides an equivalent distance at which the entire area could be concentrated while maintaining the same second moment of area.
When to use it
Use this formula in column design, buckling analysis, structural stability calculations, and whenever the slenderness ratio of a member must be determined.
Example
A steel column section has:
I = 8.0×10^-5 m⁴
A = 0.0040 m²
Formula:
r = √(I/A)
Substitution:
r = √((8.0×10^-5)/0.0040)
r = √(0.020)
Result:
r = 0.141 m
Applications
Column design, Euler buckling calculations, slenderness ratio determination, steel structures, reinforced concrete columns, towers, and structural stability assessments.