Shear strain energy in ring of radius 'r' Calculator

✖Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear stress on surface of shaft [𝜏]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.ⓘ Radius 'r' from Center Of Shaft [r_center]			+10% -10%
✖Length of Small Element is a measure of distance.ⓘ Length of Small Element [δx]			+10% -10%
✖Modulus of rigidity of 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 Shaft [G]			+10% -10%
✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of Shaft [r_shaft]			+10% -10%

✖Strain Energy in body is defined as the energy stored in a body due to deformation.ⓘ Shear strain energy in ring of radius 'r' [U]

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Shear strain energy in ring of radius 'r' Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy in body = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))
U = (2*pi*(𝜏^2)*L*(r_center^3)*δx)/(2*G*(r_shaft^2))
This formula uses 1 Constants, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.
Shear stress on surface of shaft - (Measured in Pascal) - Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Radius 'r' from Center Of Shaft - (Measured in Meter) - Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.
Length of Small Element - (Measured in Meter) - Length of Small Element is a measure of distance.
Modulus of rigidity of Shaft - (Measured in Pascal) - Modulus of rigidity of 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.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.

STEP 1: Convert Input(s) to Base Unit

Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Radius 'r' from Center Of Shaft: 1500 Millimeter --> 1.5 Meter (Check conversion here)
Length of Small Element: 43.36 Millimeter --> 0.04336 Meter (Check conversion here)
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (2*pi*(𝜏^2)*L*(r_center^3)*δx)/(2*G*(r_shaft^2)) --> (2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(2^2))

Evaluating ... ...

U = 0.321818468248431

STEP 3: Convert Result to Output's Unit

0.321818468248431 Joule -->0.000321818468248431 Kilojoule (Check conversion here)

FINAL ANSWER

0.000321818468248431 ≈ 0.000322 Kilojoule <-- Strain Energy in body

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Expression for Strain Energy stored in a Body Due to Torsion » Shear strain energy in ring of radius 'r'

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National Institute Of Technology (NIT), Hamirpur

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< Expression for Strain Energy stored in a Body Due to Torsion Calculators

Value of radius 'r' given shear stress at radius 'r' from center

LaTeX Go Radius 'r' from Center Of Shaft = (Shear stress at radius 'r' from shaft*Radius of Shaft)/Shear stress on surface of shaft

Radius of shaft given shear stress at radius r from center

LaTeX Go Radius of Shaft = (Radius 'r' from Center Of Shaft/Shear stress at radius 'r' from shaft)*Shear stress on surface of shaft

Modulus of rigidity given shear strain energy

LaTeX Go Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)

Shear strain energy

LaTeX Go Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)

Shear strain energy in ring of radius 'r' Formula

LaTeX Go

Is strain energy a material property?

The strain energy (i.e. the amount of potential energy stored due to the deformation) is equal to the work expended in deforming the material. The total strain energy corresponds to the area under the load-deflection curve.

How to Calculate Shear strain energy in ring of radius 'r'?

Shear strain energy in ring of radius 'r' calculator uses Strain Energy in body = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)) to calculate the Strain Energy in body, The Shear strain energy in ring of radius 'r' formula is defined as the energy stored in a body due to deformation. Strain Energy in body is denoted by U symbol.

How to calculate Shear strain energy in ring of radius 'r' using this online calculator? To use this online calculator for Shear strain energy in ring of radius 'r', enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Radius of Shaft (r_shaft) and hit the calculate button. Here is how the Shear strain energy in ring of radius 'r' calculation can be explained with given input values -> 2E-8 = (2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(2^2)).

FAQ

What is Shear strain energy in ring of radius 'r'?

The Shear strain energy in ring of radius 'r' formula is defined as the energy stored in a body due to deformation and is represented as U = (2*pi*(𝜏^2)*L*(r_center^3)*δx)/(2*G*(r_shaft^2)) or Strain Energy in body = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)). Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, The Length of Shaft is the distance between two ends of shaft, Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve, Length of Small Element is a measure of distance, Modulus of rigidity of 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 & The Radius of Shaft is the radius of the shaft subjected under torsion.

How to calculate Shear strain energy in ring of radius 'r'?

The Shear strain energy in ring of radius 'r' formula is defined as the energy stored in a body due to deformation is calculated using Strain Energy in body = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)). To calculate Shear strain energy in ring of radius 'r', you need Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Radius of Shaft (r_shaft). With our tool, you need to enter the respective value for Shear stress on surface of shaft, Length of Shaft, Radius 'r' from Center Of Shaft, Length of Small Element, Modulus of rigidity of Shaft & Radius of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Strain Energy in body?

In this formula, Strain Energy in body uses Shear stress on surface of shaft, Length of Shaft, Radius 'r' from Center Of Shaft, Length of Small Element, Modulus of rigidity of Shaft & Radius of Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -

Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)
Strain Energy in body = ((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))
Strain Energy in body = ((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Modulus of rigidity of Shaft)

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