What does the radius of gyration k of an area about an axis represent?

The distance from the axis at which the whole area could be concentrated at a point while giving the same moment of inertia

The distance from the axis to the centroid of the area

The distance to the farthest point of the area from the axis

The distance at which the area has zero moment of inertia

For a rectangle b × d, what is k about the centroidal axis parallel to b, and where is k used?

k = d/12; it is used in beam shear stress calculation

k = d/2; it is used for finding the centroid

k = d/sqrt(3); it is used in torsion of shafts

2076 Asoj · 2 marks

Radius of gyration

Short answer

The radius of gyration k is the distance from an axis where the total area would be concentrated to give the same moment of inertia: k = √(I/A). It indicates the spread of area and is used in column design through the slenderness ratio L_e/k_min.

What is radius of gyration?

The radius of gyration $k$ of an area about an axis is the distance from that axis at which the whole area could be assumed concentrated at a point so that the moment of inertia remains the same:

I = Ak^2 \quad\Longrightarrow\quad k = \sqrt{\frac{I}{A}}

Unit: length (mm, m). For example, $k_x = \sqrt{I_x/A}$ and $k_y = \sqrt{I_y/A}$ ; for a rectangle $b\times d$ , $k_x = d/\sqrt{12}$ about the centroidal axis parallel to $b$ . It measures how far the area is spread from the axis and is used in column design through the slenderness ratio $L_e/k_{min}$ .

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