Polar moment of inertia of hollow circular cross-section Calculator

✖Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section.ⓘ Outer Diameter of Hollow Circular Section [d_ho]			+10% -10%
✖Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.ⓘ Inner Diameter of Hollow Circular Section [d_hi]			+10% -10%

✖Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.ⓘ Polar moment of inertia of hollow circular cross-section [J]

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Polar moment of inertia of hollow circular cross-section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32
J = pi*((d_ho^4)-(d_hi^4))/32
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Polar moment of inertia for circular section - (Measured in Meter⁴) - Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.
Outer Diameter of Hollow Circular Section - (Measured in Meter) - Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section.
Inner Diameter of Hollow Circular Section - (Measured in Meter) - Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Hollow Circular Section: 40 Millimeter --> 0.04 Meter (Check conversion here)
Inner Diameter of Hollow Circular Section: 36 Millimeter --> 0.036 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = pi*((d_ho^4)-(d_hi^4))/32 --> pi*((0.04^4)-(0.036^4))/32

Evaluating ... ...

J = 8.64314970855624E-08

STEP 3: Convert Result to Output's Unit

8.64314970855624E-08 Meter⁴ -->86431.4970855624 Millimeter⁴ (Check conversion here)

FINAL ANSWER

86431.4970855624 ≈ 86431.5 Millimeter⁴ <-- Polar moment of inertia for circular section

(Calculation completed in 00.020 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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< Design of Shaft for Torsional Moment Calculators

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

LaTeX Go Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)

Torsional shear stress in shaft due to torsional moment

LaTeX Go Torsional shear stress in twisted shaft = Torsional moment on shaft*Radial Distance from Axis of Rotation/Polar moment of inertia for circular section

Polar moment of inertia of hollow circular cross-section

LaTeX Go Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32

Polar moment of inertia of circular cross section

LaTeX Go Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32

Polar moment of inertia of hollow circular cross-section Formula

LaTeX Go

Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32
J = pi*((d_ho^4)-(d_hi^4))/32

What is polar moment of inertia?

The polar moment of inertia, also known as second polar moment of area, is a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation.

How to Calculate Polar moment of inertia of hollow circular cross-section?

Polar moment of inertia of hollow circular cross-section calculator uses Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32 to calculate the Polar moment of inertia for circular section, The Polar moment of inertia of hollow circular cross-section formula basically describes the cylindrical object's (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object's central axis. Polar moment of inertia for circular section is denoted by J symbol.

How to calculate Polar moment of inertia of hollow circular cross-section using this online calculator? To use this online calculator for Polar moment of inertia of hollow circular cross-section, enter Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi) and hit the calculate button. Here is how the Polar moment of inertia of hollow circular cross-section calculation can be explained with given input values -> 8.6E+16 = pi*((0.04^4)-(0.036^4))/32.

FAQ

What is Polar moment of inertia of hollow circular cross-section?

The Polar moment of inertia of hollow circular cross-section formula basically describes the cylindrical object's (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object's central axis and is represented as J = pi*((d_ho^4)-(d_hi^4))/32 or Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32. Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section & Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.

How to calculate Polar moment of inertia of hollow circular cross-section?

The Polar moment of inertia of hollow circular cross-section formula basically describes the cylindrical object's (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object's central axis is calculated using Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32. To calculate Polar moment of inertia of hollow circular cross-section, you need Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi). With our tool, you need to enter the respective value for Outer Diameter of Hollow Circular Section & Inner Diameter of Hollow Circular Section and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Polar moment of inertia for circular section?

In this formula, Polar moment of inertia for circular section uses Outer Diameter of Hollow Circular Section & Inner Diameter of Hollow Circular Section. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32
Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft

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