Radius of Gyration in Structural Engineering

Calculate the radius of gyration for various cross-sectional shapes in structural engineering. The radius of gyration describes the distribution of cross-sectional area around the centroidal axis.

Cross Section Type	Formula	Parameters	Radius of Gyration (r)
Rectangle - Centered Axis	r = 0.289h	h = height	0.289 × height
Rectangle - Eccentric Axis	r = 0.577h	h = height	0.577 × height
Rectangle - Tilted Axis I	r = bh / (6√(b² + h²))	b = width, h = height	Width × Height / (6√(b² + h²))
Rectangle - Tilted Axis II	r = √((h²cos²(a) + b²sin²(a)) / 12)	b = width, h = height, a = angle	√((h²cos²(a) + b²sin²(a)) / 12)
Hollow Square	r = √((H² + h²) / 12)	H = outer dimension, h = inner dimension	√((H² + h²) / 12)
Hollow Square - Tilted Axis	r = √((H² + h²) / 12)	H = outer dimension, h = inner dimension	√((H² + h²) / 12)
Equilateral Triangle - Eccentric	r = h / √18	h = height	height / √18
Triangle	r = h / √6	h = height	height / √6
General Formula	r = √(I / A)	I = Area Moment of Inertia, A = cross-sectional area	√(I / A)