Cross-section characteristics

Area:

A = \int_A dA\;\;(m^2)

Static moment:

S_y = \int_A z\;dA\;\;(\pm m^3)\\ S_z = \int_A y\;dA\;\; (\pm m^3)

Deviation moment:

D_{yz} = \int_A z y\; dA\;\;(\pm m^4)

Moment of inertia:

I_y = \int_A z^2\;dA\;\;(m^4)\\ I_z = \int_A y^2\;dA\;\; (m^4)

Polar moment of inertia:

I_p = \int_A (y^2+z^2)\;dA\;\;(m^4)

Sectorial static moment:

S_{\omega} = \int_A {\omega} dA\;\;(\pm m^4)

Sectorial deviation moment:

D_{\omega y} = \int_A {\omega} z\;dA\;\;(\pm m^5)\\ D_{\omega z} = \int_A {\omega} y\;dA\;\;(\pm m^5)

Sectorial moment of inertia:

I_\omega = \int_A {\omega}^2\;dA\;\; (mm^6)

Torsion constant:

I_t

Notation
The following notation is used on this page:


 * dA ... infinitezimaly small portion of the area of the cross-section
 * z, y ... cartesian coordinates of element dA
 * \omega ... sectorial coordinate of element dA