#### Polar Area Moment of Inertia, Polar Section Modulus Properties of Common Shapes

Polar Area Moment of Inertia and Section Modulus.

The polar moment of inertia, J, of a cross-section with respect to a polar axis, that is, an axis at right angles to the plane of the cross-section, is defined as the moment of inertia of the cross-section with respect to the point of intersection of the axis and the plane. The polar moment of inertia may be found by taking the sum of the moments of inertia about two perpendicular axes lying in the plane of the cross-section and passing through this point.

The polar section modulus (also called section modulus of torsion), Zp, for circular sections may be found by dividing the polar moment of inertia, J, by the distance c from the center of gravity to the most remote fiber. This method may be used to find the approximate value of the polar section modulus of sections that are nearly round. For other than circular cross-sections, however, the polar section modulus does not equal the polar moment of inertia divided by the distance c.

Related: Polar Mass Moment of Inertia About Axis A-A, Axis B-B and Axis C-C.

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 Section Polar Area Moment of Inertia J Polar Area Section Modulus Zp Square Section Area Polar Moment of Inertia Rectangle Section Area Polar Moment of Inertia (d is shorter dimension) Circular Section Area Polar Moment of Inertia Tube Section Area Polar Moment of Inertia Hexagon Section Area Polar Moment of Inertia = 0.12 F4 0.20 F3 Circle with Square Cutout Section Area Polar Moment of Inertia = 0.098 D4 - 0.167 s4 Circle with Socket Head Cutout Section Area Polar Moment of Inertia 0.098 D4 - 1.0825 s4 Triangular Section Area Polar Moment of Inertia

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