First moment of area

Moments of area are cross-sectional characteristics. Describe the influence of the shape of the cross-sectional area of the elongate members to their properties.

Application will find the area moments to 2nd degree, particularly in the context of the strength calculation of components and structures. Area moments from the first grade are related to a specific orientation of the cross section, they have, therefore, in different directions, different values.

Defining area moments of degree n

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

The area moment of n- th degree is of the following general form:

Area moment of degree 0

The area moment of 0 degree corresponds to the cross-sectional area, and has the unit: [m 2 ]

Moment of area 1 degree

The area moments of first degree are also called static moment and have the unit [ m3]

Of the two moments can be calculated ( in a known area ) the two coordinates of the center of gravity.

Moment of area 1 degree relative to the y -axis:

Moment of area 1 degree relative to the z-axis

Moment of area 2nd degree

The area moments of 2nd degree are also known under the term moment of area and have the unit: [ m4 ].

Indicate the influence of the shape of the cross -sectional area of a beam on its stiffness. And the moment of resistance is derived from the geometrical moment of inertia, which describes the influence of the shape of the cross-sectional area of the strength.

Moment of area 2 degree based on the y -axis:

Second moment of area with respect to the degree of the z-axis:

Biaxial area moment of inertia:

Polar area moment of inertia: