Polar Moment of Inertia of Solid Circular Shaft Calculator

⤿

Design of Coupling

Basics Of Machine Design

Design of Gears

⤿

Design of Bushed-Pin Flexible Coupling

Design of Clamp and Muff Coupling

Design of Cotter Joint

Design of Knuckle Joint

Design of Rigid Flange Coupling

Design of Threaded Fastener

Packing

Retaining Rings and Circlips

Riveted Joints

Seals

Threaded Bolted Joints

Welded Joints

✖The Diameter of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.ⓘ Diameter of Shaft [d_s]

+10%

-10%

✖The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia of Solid Circular Shaft [J]

⎘ Copy

👎

Formula

✖

Polar Moment of Inertia of Solid Circular Shaft

Formula

`"J" = (pi*"d"_{"s"}^4)/32`

Example

`"0.203575m⁴"=(pi*("1200mm")^4)/32`

Calculator

LaTeX

Reset

👍

Download Design of Coupling Formula PDF PDF Image

Polar Moment of Inertia of Solid Circular Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32
J = (pi*d_s^4)/32
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Polar Moment of Inertia - (Measured in Meter⁴) - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.
Diameter of Shaft - (Measured in Meter) - The Diameter of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

STEP 1: Convert Input(s) to Base Unit

Diameter of Shaft: 1200 Millimeter --> 1.2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (pi*d_s^4)/32 --> (pi*1.2^4)/32

Evaluating ... ...

J = 0.203575203952619

STEP 3: Convert Result to Output's Unit

0.203575203952619 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.203575203952619 ≈ 0.203575 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Design of Machine Elements » Design of Coupling » Polar Moment of Inertia of Solid Circular Shaft

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 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 Solid Circular Shaft Formula

Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32
J = (pi*d_s^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 Solid Circular Shaft?

Polar Moment of Inertia of Solid Circular Shaft calculator uses Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32 to calculate the Polar Moment of Inertia, The Polar Moment of Inertia of Solid 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 is denoted by J symbol.

How to calculate Polar Moment of Inertia of Solid Circular Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Solid Circular Shaft, enter Diameter of Shaft (d_s) and hit the calculate button. Here is how the Polar Moment of Inertia of Solid Circular Shaft calculation can be explained with given input values -> 0.203575 = (pi*1.2^4)/32.

FAQ

What is Polar Moment of Inertia of Solid Circular Shaft?

The Polar Moment of Inertia of Solid 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 = (pi*d_s^4)/32 or Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32. The Diameter of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

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

The Polar Moment of Inertia of Solid 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 = (pi*Diameter of Shaft^4)/32. To calculate Polar Moment of Inertia of Solid Circular Shaft, you need Diameter of Shaft (d_s). With our tool, you need to enter the respective value for Diameter of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search