Engineering Reference

Radius of gyration

The distance from the axis at which the whole area could be concentrated to give the same moment of inertia.

Definition

Radius of gyration r = √(I ÷ A) converts a section's shape into a single length, and that length is what appears in column buckling formulas as the slenderness ratio K·L/r.

A section with a larger r resists buckling better for the same area, which is why hollow sections beat solid ones in compression: moving material away from the centroid raises I much faster than it raises A.

Common misuse

Comparing sections by area alone for a compression member. The radius of gyration, not the area, governs buckling.

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