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), 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
Square Section

Square Section Polar Equation
Polar Section Modulus

Rectangle Section
Area Polar Moment of Inertia
Rectangle

polar Moment Equation 2

Polar Section Modulus
(d is shorter dimension)

Circular Section
Area Polar Moment of Inertia
Circle Section

Polar Moment of inertia
Polar Section Modulus

Tube Section
Area Polar Moment of Inertia
Tube

Open
Tube Section Polar Moment of Inertia Calculator

Polar Moment of inertia

Polar Section Modulus

Hexagon Section
Area Polar Moment of Inertia
Penta

Open
Hexagon Section Polar Moment of Inertia Calculator

Polar Moment of inertia

= 0.12 F4

0.20 F3

Circle with Square Cutout Section
Area Polar Moment of Inertia
Square Drive

Open
Circle with Square Cutout Section Polar Moment of Inertia Calculator

Polar Moment of inertia

= 0.098 D4 - 0.167 s4

Polar Section Modulus

Circle with Socket Head Cutout
Section Area Polar Moment of Inertia
Socket Head

Open
Circle with Socket Cutout Section Polar Moment of Inertia Calculator

Polar Moment of inertia

0.098 D4 - 1.0825 s4

Polar Section Modulus

Polar Section Modulus

Triangular Section
Area Polar Moment of Inertia
Trinagle

Open
Triangular Section Polar Moment of Inertia Calculator

Polar Moment of inertia
Polar Section Modulus
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