Polar Moment of Inertia of Rod given Strain Energy in Rod Calculator

✖Torque on Rod or Shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.ⓘ Torque on Rod or Shaft [τ]			+10% -10%
✖Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy in Rod or Shaft [U]			+10% -10%
✖Modulus of rigidity of rod or shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.ⓘ Modulus of rigidity of rod or shaft [G]			+10% -10%

✖Polar Moment of Inertia of rod or shaft is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia of Rod given Strain Energy in Rod [J]

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Polar Moment of Inertia of Rod given Strain Energy in Rod

Formula

`"J" = ("τ"^2)*"L"/(2*"U"*"G")`

Example

`"205770mm⁴"=(("1.14E6N*mm")^2)*"1330mm"/(2*"40J"*"1.05E5N/mm²")`

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Polar Moment of Inertia of Rod given Strain Energy in Rod Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)
J = (τ^2)*L/(2*U*G)
This formula uses 5 Variables

Variables Used

Polar Moment of Inertia of rod or shaft - (Measured in Meter⁴) - Polar Moment of Inertia of rod or shaft is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.
Torque on Rod or Shaft - (Measured in Newton Meter) - Torque on Rod or Shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.
Length of Rod or Shaft - (Measured in Meter) - Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
Strain Energy in Rod or Shaft - (Measured in Joule) - Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.
Modulus of rigidity of rod or shaft - (Measured in Pascal) - Modulus of rigidity of rod or shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

STEP 1: Convert Input(s) to Base Unit

Torque on Rod or Shaft: 1140000 Newton Millimeter --> 1140 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
Modulus of rigidity of rod or shaft: 105000 Newton per Square Millimeter --> 105000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (τ^2)*L/(2*U*G) --> (1140^2)*1.33/(2*40*105000000000)

Evaluating ... ...

J = 2.0577E-07

STEP 3: Convert Result to Output's Unit

2.0577E-07 Meter⁴ -->205770 Millimeter⁴ (Check conversion here)

FINAL ANSWER

205770 Millimeter⁴ <-- Polar Moment of Inertia of rod or shaft

(Calculation completed in 00.004 seconds)

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< 14 Castigliano's Theorem for Deflection in Complex Structures Calculators

Torque given Strain Energy in Rod Subjected to External Torque

Go Torque on Rod or Shaft = sqrt(2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft/Length of Rod or Shaft)

Force Applied on Rod given Strain Energy Stored in Tension Rod

Go Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

Go Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Modulus of elasticity of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Area Moment of Inertia of rod or shaft)

Strain Energy Stored in Rod Subjected to Bending Moment

Go Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Length of Rod or Shaft = 2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^2)

Length of Shaft when Strain Energy in Shaft Subjected to External Torque

Go Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)

Strain Energy in Rod when it is Subjected to External Torque

Go Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)

Polar Moment of Inertia of Rod given Strain Energy in Rod

Go Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)

Modulus of Rigidity of Rod given Strain Energy in Rod

Go Modulus of rigidity of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Strain Energy in Rod or Shaft)

Strain Energy Stored in Tension Rod

Go Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)

Cross-sectional Area of Rod given Strain Energy stored in Rod

Go Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft)

Modulus of Elasticity of Rod given Strain Energy Stored

Go Modulus of elasticity of rod or shaft = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy in Rod or Shaft)

Length of Rod given Strain Energy Stored

Go Length of Rod or Shaft = Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2

Polar Moment of Inertia of Rod given Strain Energy in Rod Formula

Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)
J = (τ^2)*L/(2*U*G)

Define 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.[1] It is a constituent of the second moment of area, linked through the perpendicular axis theorem.

How to Calculate Polar Moment of Inertia of Rod given Strain Energy in Rod?

Polar Moment of Inertia of Rod given Strain Energy in Rod calculator uses Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft) to calculate the Polar Moment of Inertia of rod or shaft, The Polar Moment of Inertia of Rod given Strain Energy in Rod formula is defined as the quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia of rod or shaft is denoted by J symbol.

How to calculate Polar Moment of Inertia of Rod given Strain Energy in Rod using this online calculator? To use this online calculator for Polar Moment of Inertia of Rod given Strain Energy in Rod, enter Torque on Rod or Shaft (τ), Length of Rod or Shaft (L), Strain Energy in Rod or Shaft (U) & Modulus of rigidity of rod or shaft (G) and hit the calculate button. Here is how the Polar Moment of Inertia of Rod given Strain Energy in Rod calculation can be explained with given input values -> 2.1E+17 = (1140^2)*1.33/(2*40*105000000000).

FAQ

What is Polar Moment of Inertia of Rod given Strain Energy in Rod?

The Polar Moment of Inertia of Rod given Strain Energy in Rod formula is defined as the quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects with an invariant cross-section and no significant warping or out-of-plane deformation and is represented as J = (τ^2)*L/(2*U*G) or Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft). Torque on Rod or Shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force, Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom, Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation & Modulus of rigidity of rod or shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

How to calculate Polar Moment of Inertia of Rod given Strain Energy in Rod?

The Polar Moment of Inertia of Rod given Strain Energy in Rod formula is defined as the quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects with an invariant cross-section and no significant warping or out-of-plane deformation is calculated using Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft). To calculate Polar Moment of Inertia of Rod given Strain Energy in Rod, you need Torque on Rod or Shaft (τ), Length of Rod or Shaft (L), Strain Energy in Rod or Shaft (U) & Modulus of rigidity of rod or shaft (G). With our tool, you need to enter the respective value for Torque on Rod or Shaft, Length of Rod or Shaft, Strain Energy in Rod or Shaft & Modulus of rigidity of rod or 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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