# Moment of inertia

### Glossary Term

The second moment of area, also known as the second moment of area. Is a cross -section size used in strength analysis.
The stiffness of a component can be defined with the help of the moment of inertia I. It is determined by the geometry and size of a cross -section.

The symbol for this is I and the unit in SI is mm 4 , cm 4 , m 4 (i.e. L 4 ).

There are 3 types of moments of area:
• Axial second moment of area:
The axial moments of area Iy and Iz describe the stiffnesses against bending about the local axes y and z. The deflection as well as the occurring stresses are smaller as soon as the moment of inertia increases with a constant load. The y-axis is often referred to as the "strong" axis because the moment of inertia Iy is greater here.

Moment of inertia

$$Iy = ∫Az2dAIz = ∫Ay2dA$$

 Iy Second moment of area about the y-axis z Vertical distance of the y-axis to the element dA Iz Second moment of area about the z-axis y Vertical distance of the z-axis to the element dA

• Biaxial moment of area
The biaxial moment of area is often referred to as the surface centrifugal moment, the moment of deviation, the moment of surface deviation or simply as the centrifugal moment. It is used to calculate deformations on asymmetrical sections and to determine non -symmetrical loads on any sections.

$$Izy=Iyz=-∫AzydA$$

• Polar second moment of area
A second moment of area, which describes the resistance of a closed circular ring cross -section or of circular cross -sections against torsion, is referred to as a polar moment of inertia. The polar moment of area Ip is composed of the two moments of area Iy and Iz . It is also to be equated with the torsional moment of inertia IT for circular and circular ring cross-sections, which describes the stiffness against rotation about the longitudinal axis.

$$Ip =∫Ar2dA =∫A(y2 + z2)dA = Iy + Iz$$

For asymmetrical sections, the moments of inertia are displayed around the cross-section's principal axes u and v.

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• Updated 21 January 2021

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