Moment of area
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
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:
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: