From its axis (0), if the radius of gyration about a longitudinal axis through G, aiid 0 the inclin - ation of OG to the vertical, FIG.

This is called the ellipsoid of gyration at 0; it was introduced into the theory by J.

Where K is the radius of gyration about the axis of symmetry, a is the constant distance of G from the plane, and R, F are the normal and tangential components of the reaction of the plane, as shown in fig.

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In the case of an axial moment, the square root of the resulting mean square is called the radius of gyration of the system about the axis in question.

Which we shall meet with presently as the ellipsoid of gyration at G.

The square of the radius of gyration with respect to a diameter is ia2.

It possesses thi property that the radius of gyration about any diameter is half thi distance between the two tangents which are parallel to that diameter, In the case of a uniform triangular plate it may be shown that thi momental ellipse at G is concentric, similar and similarly situatec to the ellipse which touches the sides of the triangle at their middle points.

The radius of gyration of the section is 2a 2.

The formula (16) expresses that the squared radius of gyration about any axis (Ox) exceeds the squared radius of gyration about a parallel axis through G by the square of the distance between the two axes.