Polar moment of inertia of shaft given shear stress and torsional moment Calculator

✖Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.ⓘ Torsional moment on shaft [τ]			+10% -10%
✖Radial Distance from Axis of Rotation is taken as the distance between the projections onto the two planes.ⓘ Radial Distance from Axis of Rotation [r]			+10% -10%
✖Torsional shear stress in twisted shaft or Torsional stress is the shear stress produced in the shaft due to the twisting.ⓘ Torsional shear stress in twisted shaft [𝜏]			+10% -10%

✖Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.ⓘ Polar moment of inertia of shaft given shear stress and torsional moment [J]

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Formula

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Polar moment of inertia of shaft given shear stress and torsional moment

Formula

`"J" = "τ"*"r"/"𝜏"`

Example

`"36428.57mm⁴"="51000N*mm"*"25mm"/"35N/mm²"`

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Polar moment of inertia of shaft given shear stress and torsional moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft
J = τ*r/𝜏
This formula uses 4 Variables

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.
Torsional moment on shaft - (Measured in Newton Meter) - Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.
Radial Distance from Axis of Rotation - (Measured in Meter) - Radial Distance from Axis of Rotation is taken as the distance between the projections onto the two planes.
Torsional shear stress in twisted shaft - (Measured in Pascal) - Torsional shear stress in twisted shaft or Torsional stress is the shear stress produced in the shaft due to the twisting.

STEP 1: Convert Input(s) to Base Unit

Torsional moment on shaft: 51000 Newton Millimeter --> 51 Newton Meter (Check conversion here)
Radial Distance from Axis of Rotation: 25 Millimeter --> 0.025 Meter (Check conversion here)
Torsional shear stress in twisted shaft: 35 Newton per Square Millimeter --> 35000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = τ*r/𝜏 --> 51*0.025/35000000

Evaluating ... ...

J = 3.64285714285714E-08

STEP 3: Convert Result to Output's Unit

3.64285714285714E-08 Meter⁴ -->36428.5714285714 Millimeter⁴ (Check conversion here)

FINAL ANSWER

36428.5714285714 ≈ 36428.57 Millimeter⁴ <-- Polar moment of inertia for circular section

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Machine Design » Design Against Static Load » Design of Shaft for Torsional Moment » Polar moment of inertia of shaft given shear stress and torsional moment

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 9 Design of Shaft for Torsional Moment Calculators

Angle of twist of hollow cylindrical rod in degrees

Go Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180)

Angle of twist of solid cylindrical rod in degrees

Go Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180)

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

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

Polar moment of inertia of shaft given shear stress and torsional moment

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

Torsional shear stress in shaft due to torsional moment

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

Torsional moment on shaft given shear stress

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

Polar moment of inertia of hollow circular cross-section

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

Power transmitted by shaft given speed of shaft and torque

Go Power = 2*pi*Speed of Shaft in RPM*Torsional moment on shaft/(60)

Polar moment of inertia of circular cross section

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

Polar moment of inertia of shaft given shear stress and torsional moment Formula

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

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 shaft given shear stress and torsional moment?

Polar moment of inertia of shaft given shear stress and torsional moment calculator uses Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft to calculate the Polar moment of inertia for circular section, Polar moment of inertia of shaft given shear stress and torsional moment 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 shaft given shear stress and torsional moment using this online calculator? To use this online calculator for Polar moment of inertia of shaft given shear stress and torsional moment, enter Torsional moment on shaft (τ), Radial Distance from Axis of Rotation (r) & Torsional shear stress in twisted shaft (𝜏) and hit the calculate button. Here is how the Polar moment of inertia of shaft given shear stress and torsional moment calculation can be explained with given input values -> 3.6E+16 = 51*0.025/35000000.

FAQ

What is Polar moment of inertia of shaft given shear stress and torsional moment?

Polar moment of inertia of shaft given shear stress and torsional moment 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 = τ*r/𝜏 or Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft. Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force, Radial Distance from Axis of Rotation is taken as the distance between the projections onto the two planes & Torsional shear stress in twisted shaft or Torsional stress is the shear stress produced in the shaft due to the twisting.

How to calculate Polar moment of inertia of shaft given shear stress and torsional moment?

Polar moment of inertia of shaft given shear stress and torsional moment 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 = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft. To calculate Polar moment of inertia of shaft given shear stress and torsional moment, you need Torsional moment on shaft (τ), Radial Distance from Axis of Rotation (r) & Torsional shear stress in twisted shaft (𝜏). With our tool, you need to enter the respective value for Torsional moment on shaft, Radial Distance from Axis of Rotation & Torsional shear stress in twisted shaft 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 Torsional moment on shaft, Radial Distance from Axis of Rotation & Torsional shear stress in twisted shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

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 for circular section = pi*(Diameter of circular section of shaft^4)/32

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