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

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

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

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