The radius of gyration of a rectangular section (depth D, width B) from a centroidal axis parallel to the width is

The radius of gyration k about an axis is given by the formula:

k = √(I/A)

Where:

• I is the moment of inertia about the axis
• A is the area of the section

For a rectangle of depth D and width B, the moment of inertia about the centroidal axis parallel to the width (i.e., the horizontal centroidal axis) is:

I = (B × D³) / 12

The area is:

A = B × D

Substituting into the formula for k:

k = √[ (B × D³) / (12 × B × D) ] = √(D² / 12) = D / (2√3)

Therefore, the radius of gyration is:

k = D / (2√3)