Theory

One of the most important quantities for the calculation the resistance of a component to the stress on torsion or bending is the area moment of inertia. It can be derived from the cross-section of a component. When dimensioning components, it is used to determine elastic deformations and thus ultimately their resilience. The geometrical moment of inertia must not be confused with the mass moment of inertia, which describes the inertia of a rotating body and its angular acceleration.

There are basically three types of area moments of inertia:

• polar area moment of inertia

describes the area moment of inertia of a surface around a point to be defined. The most important dimension in the cross-section is the expansion in the direction of the applied force.

• axial moment of area

describes the bending of a beam under load depending on the cross-section. The greater the value of the axial geometrical moment of inertia, the smaller the deflection and consequently the internal stresses occurring in the cross-section. Mathematically it can be proven that the axial area moment of inertia is always > 0.

• biaxial moment of area

is also known as the moment of area deviation, is used to calculate the deformation and the stresses in the case of loaded asymmetrical profiles or with asymmetrical loading, symmetrical (or any) profiles.