Appendix

PROPERTIES OF PLANE SECTIONS

The following symbols will be used:

• \(A=\) Area
• \(x_0, y_c=\) Coordinates of centroid of section in \(x y\) coordinate system.
• \(I_{x_c}, I_{\nu_c}=\) Moment of inertia about an axis through the centroid parallel to the \(x y\) axes.
• \(r_{x_c}, r_{y_c}=\) Radius of gyration of the section with respect to the centroidal axes parallel to the \(x y\) axes.
• \(I_{x_c y_c}=\) Product of inertia with respect to the centroidal axes parallel to the \(x y\) axes.
• \(I_x, I_y=\) Moment of inertia with respect to the \(x y\) axes shown.
• \(r_x, r_y=\) Radius of gyration of the section with respect to the \(x y\) axes shown.
• \(I_{x y}=\) Product of inertia with respect to the \(x y\) axes shown.
• \(I_P\) (same as \(J_O\)) \(=\) Polar moment of inertia about an axis passing through the centroid.
• \(r_{P}=\) Radius of gyration of the section about the polar axis passing through the centroid.
• \(G\) marks the centroid.

PROPERTIES OF HOMOGENEOUS BODIES 

The following symbols will be used:

• \(\rho=\) Mass density
• \(M=\) Mass
• \(x_c, y_c, z_c=\) Coordinates of centroid in \(x y z\) coordinate system.
• \(I_{x_c}, I_{y_c}, I_{z_c}=\) Moment of inertia about an axis through the centroid parallel to the \(x y z\) axes shown.
• \(r_{x_c}, r_{y_c}, r_{z_c}=\) Radius of gyration of the body with respect to the centroidal axes parallel to the \(x y z\) axes shown.
• \(I_{x_c y_c}, I_{x_c z_c}\), etc. = Product of inertia with respect to the centroidal axes parallel to the \(x y z\) axes shown.
• \(I_x, I_y, I_z=\) Moment of inertia with respect to the \(x y z\) axes shown.
• \(r_x, r_y, r_z=\) Radius of gyration of the body with respect to the \(x y z\) axes shown.
• \(I_{x y}, I_{x z}\), etc. \(=\) Product of inertia with respect to the \(x y z\) axes shown.
• \(I_{A A}, r_{A A}=\) Moments of inertia and radii of gyration with respect to special axes shown.
• \(G\) marks the centroid