Modulus of Rigidity 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 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 [J]			+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 of Rod given Strain Energy in Rod [G]

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Modulus of Rigidity of Rod given Strain Energy in Rod Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.

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)
Polar Moment of Inertia: 553 Millimeter⁴ --> 5.53E-10 Meter⁴ (Check conversion here)
Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = τ^2*L/(2*J*U) --> 55.005^2*1.432449/(2*5.53E-10*37.13919)

Evaluating ... ...

G = 105510565819.005

STEP 3: Convert Result to Output's Unit

105510565819.005 Pascal -->105510.565819005 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

105510.565819005 ≈ 105510.6 Newton per Square Millimeter <-- Modulus of Rigidity

(Calculation completed in 00.004 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

Modulus of Rigidity of Rod given Strain Energy in Rod Formula

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

Define Modulus of Rigidity?

Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus.

How to Calculate Modulus of Rigidity of Rod given Strain Energy in Rod?

Modulus of Rigidity of Rod given Strain Energy in Rod calculator uses Modulus of Rigidity = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Strain Energy) to calculate the Modulus of Rigidity, Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as a measure of a material's ability to resist deformation under shear stress. It relates the energy stored in a deformed rod to its geometric and material properties, providing insights into structural performance. Modulus of Rigidity is denoted by G symbol.

How to calculate Modulus of Rigidity of Rod given Strain Energy in Rod using this online calculator? To use this online calculator for Modulus of Rigidity of Rod given Strain Energy in Rod, enter Torque (τ), Length of Rod or Shaft (L), Polar Moment of Inertia (J) & Strain Energy (U) and hit the calculate button. Here is how the Modulus of Rigidity of Rod given Strain Energy in Rod calculation can be explained with given input values -> 0.105511 = 55.005^2*1.432449/(2*5.53E-10*37.13919).

FAQ

What is Modulus of Rigidity of Rod given Strain Energy in Rod?

Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as a measure of a material's ability to resist deformation under shear stress. It relates the energy stored in a deformed rod to its geometric and material properties, providing insights into structural performance and is represented as G = τ^2*L/(2*J*U) or Modulus of Rigidity = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Strain Energy). 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 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 & 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.

How to calculate Modulus of Rigidity of Rod given Strain Energy in Rod?

Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as a measure of a material's ability to resist deformation under shear stress. It relates the energy stored in a deformed rod to its geometric and material properties, providing insights into structural performance is calculated using Modulus of Rigidity = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Strain Energy). To calculate Modulus of Rigidity of Rod given Strain Energy in Rod, you need Torque (τ), Length of Rod or Shaft (L), Polar Moment of Inertia (J) & Strain Energy (U). With our tool, you need to enter the respective value for Torque, Length of Rod or Shaft, Polar Moment of Inertia & Strain Energy 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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