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.
$I_{x_{c}}, I_{ν_{c}} =$ 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:

$ρ =$ 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