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
Jshaft = (pi*(douter^(4)-dinner^(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
Jshaft = (pi*(douter^(4)-dinner^(4)))/32 --> (pi*(4^(4)-1^(4)))/32
Evaluating ... ...
Jshaft = 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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21 Design of Machine Elements 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)
Collar Friction Torque in Accordance of Uniform Pressure Theory
Go Collar Friction Torque = ((Coefficient of Friction*Load)*(Outer Diameter of Collar^3-Inner Diameter of Collar^3))/(3*(Outer Diameter of Collar^2-Inner Diameter of Collar^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))
Unit Bearing Pressure
Go Unit Bearing Pressure = (4*Force on Unit)/(pi*Number of Threads*(Nominal Diameter^2-Core Diameter^2))
Shear Stress on Flat Key
Go Shear Stress = (2*Torque Transmitted by Shaft)/(Width of Key*Diameter of Shaft*Length of Key)
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
Ratio Factor for External Gears
Go Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear+Number of Teeth on Spur Pinion)
Ratio Factor for Internal Gears
Go Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion)
Permissible Shear Stress for Cotter
Go Permissible Shear Stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter)
Compressive Stress of Spigot
Go Compressive Stress in Spigot = Load on Cotter Joint/(Thickness of Cotter*Spigot Diameter)
Permissible Shear Stress for Spigot
Go Permissible Shear Stress = Tensile Force on Rods/(2*Spigot Distance*Diameter of Spigot)
Pitchline Velocity of Meshing Gears
Go Velocity = pi*Diameter of Pitch Circle*Speed in RPM/60
Power Transmitted
Go Shaft Power = 2*pi*Speed of Rotation*Torque applied
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
Factor of Safety given Ultimate Stress and Working Stress
Go Factor of Safety = Fracture Stress/Working Stress
Thickness of Cotter Joint
Go Thickness of Cotter = 0.31*Diameter of Rod of Cotter Joint
Shear Yield Strength by Maximum Distortion Energy Theory
Go Shear Yield Strength = 0.577*Tensile Yield Strength
Shear Yield Strength by Maximum Shear Stress Theory
Go Shear Yield Strength = Tensile Yield Strength/2

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
Jshaft = (pi*(douter^(4)-dinner^(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 Jshaft 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 (douter) & Inner Diameter of Shaft (dinner) 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 Jshaft = (pi*(douter^(4)-dinner^(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 (douter) & Inner Diameter of Shaft (dinner). 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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