Polar Moment of Inertia of Hollow Circular Shaft Calculator

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✖Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_outer]			+10% -10%
✖The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Shaft [d_inner]			+10% -10%

✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of Hollow Circular Shaft [J_shaft]

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Formula

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Polar Moment of Inertia of Hollow Circular Shaft

Formula

`"J"_{"shaft"} = (pi*("d"_{"outer"}^(4)-"d"_{"inner"}^(4)))/32`

Example

`"25.03457m⁴"=(pi*(("4000mm")^(4)-("1000mm")^(4)))/32`

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Polar Moment of Inertia of Hollow Circular Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32
J_shaft = (pi*(d_outer^(4)-d_inner^(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 of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Inner Diameter of Shaft - (Measured in Meter) - The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Inner Diameter of Shaft: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32 --> (pi*(4^(4)-1^(4)))/32

Evaluating ... ...

J_shaft = 25.0345664582937

STEP 3: Convert Result to Output's Unit

25.0345664582937 Meter⁴ --> No Conversion Required

FINAL ANSWER

25.0345664582937 ≈ 25.03457 Meter⁴ <-- Polar Moment of Inertia of shaft

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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National Institute Of Technology (NIT), Hamirpur

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< 9 Design of Coupling Calculators

Factor of Safety for Tri-axial State of Stress

Go Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))

Equivalent Stress by Distortion Energy Theory

Go Equivalent Stress = 1/sqrt(2)*sqrt((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2)

Factor of Safety for Bi-Axial State of Stress

Go Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))

Tensile Stress in Spigot

Go Tensile Stress = Tensile Force on Rods/((pi/4*Diameter of Spigot^(2))-(Diameter of Spigot*Thickness of Cotter))

Polar Moment of Inertia of Hollow Circular Shaft

Go Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32

Permissible Shear Stress for Cotter

Go Permissible Shear Stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter)

Permissible Shear Stress for Spigot

Go Permissible Shear Stress = Tensile Force on Rods/(2*Spigot Distance*Diameter of Spigot)

Stress Amplitude

Go Stress Amplitude = (Maximum Stress at Crack Tip-Minimum Stress)/2

Polar Moment of Inertia of Solid Circular Shaft

Go Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32

Polar Moment of Inertia of Hollow Circular Shaft Formula

Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32
J_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32

Define polar moment of inertia?

Polar Moment of Inertia is a measure of an object’s capacity to oppose or resist torsion when some amount of torque is applied to it on a specified axis. Torsion, on the other hand, is nothing but the twisting of an object due to an applied torque. Polar moment of inertia 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.

How to Calculate Polar Moment of Inertia of Hollow Circular Shaft?

Polar Moment of Inertia of Hollow Circular Shaft calculator uses Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32 to calculate the Polar Moment of Inertia of shaft, The Polar moment of inertia of hollow circular shaft formula is a quantity used to describe resistance to torsional deformation, in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia of shaft is denoted by J_shaft symbol.

How to calculate Polar Moment of Inertia of Hollow Circular Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Hollow Circular Shaft, enter Outer Diameter of Shaft (d_outer) & Inner Diameter of Shaft (d_inner) and hit the calculate button. Here is how the Polar Moment of Inertia of Hollow Circular Shaft calculation can be explained with given input values -> 25.03457 = (pi*(4^(4)-1^(4)))/32.

FAQ

What is Polar Moment of Inertia of Hollow Circular Shaft?

The Polar moment of inertia of hollow circular shaft formula is a quantity used to describe resistance to torsional deformation, in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation and is represented as J_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32 or Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32. Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

How to calculate Polar Moment of Inertia of Hollow Circular Shaft?

The Polar moment of inertia of hollow circular shaft formula is a quantity used to describe resistance to torsional deformation, in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation is calculated using Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32. To calculate Polar Moment of Inertia of Hollow Circular Shaft, you need Outer Diameter of Shaft (d_outer) & Inner Diameter of Shaft (d_inner). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Inner Diameter of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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