# Moment of 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:

- With

## 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

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