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

✖The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.ⓘ Torque [τ]			+10% -10%
✖The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.ⓘ Strain Energy [U]			+10% -10%
✖The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.ⓘ Modulus of Rigidity [G]			+10% -10%

✖The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components.ⓘ 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 Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Polar Moment of Inertia - (Measured in Meter⁴) - The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components.
Torque - (Measured in Newton Meter) - The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.
Length of Rod or Shaft - (Measured in Meter) - The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.
Strain Energy - (Measured in Joule) - The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.
Modulus of Rigidity - (Measured in Pascal) - The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.

STEP 1: Convert Input(s) to Base Unit

Torque: 55005 Newton Millimeter --> 55.005 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1432.449 Millimeter --> 1.432449 Meter (Check conversion here)
Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required
Modulus of Rigidity: 105591 Newton per Square Millimeter --> 105591000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = τ^2*L/(2*U*G) --> 55.005^2*1.432449/(2*37.13919*105591000000)

Evaluating ... ...

J = 5.5257875101012E-10

STEP 3: Convert Result to Output's Unit

5.5257875101012E-10 Meter⁴ -->552.57875101012 Millimeter⁴ (Check conversion here)

FINAL ANSWER

552.57875101012 ≈ 552.5788 Millimeter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.020 seconds)

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< Castigliano's Theorem for Deflection in Complex Structures Calculators

Force Applied on Rod given Strain Energy Stored in Tension Rod

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

Strain Energy Stored in Tension Rod

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

Modulus of Elasticity of Rod given Strain Energy Stored

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

Length of Rod given Strain Energy Stored

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

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

Polar Moment of Inertia = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity)
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 = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity) to calculate the Polar Moment of Inertia, Polar Moment of Inertia of Rod given Strain Energy in Rod formula is defined as a measure of a rod's resistance to torsional deformation when subjected to an applied torque. It relates the strain energy stored in the rod to its geometric and material properties. Polar Moment of Inertia 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 (τ), Length of Rod or Shaft (L), Strain Energy (U) & Modulus of Rigidity (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 -> 5.6E+14 = 55.005^2*1.432449/(2*37.13919*105591000000).

FAQ

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

Polar Moment of Inertia of Rod given Strain Energy in Rod formula is defined as a measure of a rod's resistance to torsional deformation when subjected to an applied torque. It relates the strain energy stored in the rod to its geometric and material properties and is represented as J = τ^2*L/(2*U*G) or Polar Moment of Inertia = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity). The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point, The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis, The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape & The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.

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 formula is defined as a measure of a rod's resistance to torsional deformation when subjected to an applied torque. It relates the strain energy stored in the rod to its geometric and material properties is calculated using Polar Moment of Inertia = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity). To calculate Polar Moment of Inertia of Rod given Strain Energy in Rod, you need Torque (τ), Length of Rod or Shaft (L), Strain Energy (U) & Modulus of Rigidity (G). With our tool, you need to enter the respective value for Torque, Length of Rod or Shaft, Strain Energy & Modulus of Rigidity 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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