Moment of area

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Cross sectional area

Moments of area are cross-sectional parameters : they describe how the shape of the cross-sectional area influences the properties of elongated components .

The moments of area up to the 2nd degree ( area moment of inertia ) are used in particular for the strength calculation of components and structures. Moments of area from the 1st degree are related to a certain orientation of the cross-section, so they have different values ​​in different directions (i.e. depending on which axis they are related to).

Moments of area of ​​the nth degree (general definition)

In the following brief descriptions, the bar is parallel to the x-axis of the coordinate system and has the cross-sectional area in the yz-plane. The bar lies symmetrically in the coordinate system (more precisely: the main axes of inertia are parallel to the y and z axes).

The nth degree moment of area has the following general form:


Moment of area of ​​0th degree

The moment of area of ​​the 0th degree corresponds to the cross-sectional area and has the unit  m 2 :

Moment of area 1st degree

The area moments of the 1st degree are also referred to as the static moment and have the unit  m 3 .

In relation to the y-axis:

In relation to the z-axis:

The two coordinates of the center of gravity can be calculated from these moments (if the area is known ) :

Second moment of area

The area moments of the 2nd degree are also known under the term area moment of inertia and have the unit [m 4 ].

They indicate the influence of the shape of the cross-sectional area of ​​a beam on its stiffness . The moment of resistance , which describes the influence of the shape of the cross-sectional area on the strength , is also derived from the area moment of inertia .

Second moment of area related to the y-axis:

Second moment of area related to the z-axis:

biaxial area moment of inertia:

polar area moment of inertia:

Individual evidence

  1. Jens Göttsche, Maritta Petersen: Strength theory - in a nutshell . Hanser Verlag, 2006, ISBN 978-3-446-40415-1 ( limited preview in Google book search).