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:

$D_{yz}=\int _{A}zy\;dA\;\;(\pm m^{4})$

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 $dA$

See Also

• Torsion

 

Home > Topics > Traditional Analysis Methods > Cross-Section Characterictics e
Overview	Overview
Basic Properties	Shear center  · Neutral axis  · Center of gravity  · Sectorial coordinate
Advanced Properties	Torsion constant  · Sectorial moment of intertia (warping constant)