# Second Moment of Area

### Glossary Term

The second moment of area, also known as the area moment of inertia is a cross-section property used in the strengths of materials.
The stiffness of a component can be defined by using 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 mm4, cm4, m4 (that is, L4).

There are three types of second moments of area:

• Axial Second Moment of Area:
The axial second 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 second moment of area increases with a constant load. The y-axis is often referred to as the "strong" axis because the second moment of area 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 area centrifugal moment, the moment of deviation, the moment of area deviation, or simply as the centrifugal moment. It is used to calculate deformations on asymmetrical cross-sections and to determine unsymmetrical loads on any cross-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 unsymmetrical cross-sections, the second moments of area are displayed around the cross-section's principal axes u and v.

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