# 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:

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

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

$I_t$

## Notation

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

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