Total strain energy in hollow shaft due to torsion 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%
✖Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_outer]			+10% -10%
✖The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Shaft [d_inner]			+10% -10%
✖The Volume of Shaft is the volume of cylindical component under torsion.ⓘ Volume of Shaft [V]			+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%

✖Strain Energy in body is defined as the energy stored in a body due to deformation.ⓘ Total strain energy in hollow shaft due to torsion [U]

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Total strain energy in hollow shaft due to torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2))
U = ((𝜏^2)*((d_outer^2)+(d_inner^2))*V)/(4*G*(d_outer^2))
This formula uses 6 Variables

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.
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.
Volume of Shaft - (Measured in Cubic Meter) - The Volume of Shaft is the volume of cylindical component under torsion.
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.

STEP 1: Convert Input(s) to Base Unit

Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Inner Diameter of Shaft: 1000 Millimeter --> 1 Meter (Check conversion here)
Volume of Shaft: 125.6 Cubic Meter --> 125.6 Cubic Meter No Conversion Required
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = ((𝜏^2)*((d_outer^2)+(d_inner^2))*V)/(4*G*(d_outer^2)) --> ((4^2)*((4^2)+(1^2))*125.6)/(4*40*(4^2))

Evaluating ... ...

U = 13.345

STEP 3: Convert Result to Output's Unit

13.345 Joule -->0.013345 Kilojoule (Check conversion here)

FINAL ANSWER

0.013345 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 » Total strain energy in hollow shaft due to torsion

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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)

Total strain energy in hollow shaft due to torsion Formula

LaTeX Go

What is the difference between strain energy and resilience?

Strain energy is elastic that is, the material tends to recover when the load is removed. Resilience is typically expressed as the modulus of resilience, which is the amount of strain energy the material can store per unit of volume without causing permanent deformation.

How to Calculate Total strain energy in hollow shaft due to torsion?

Total strain energy in hollow shaft due to torsion calculator uses Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)) to calculate the Strain Energy in body, Total strain energy in hollow shaft due to torsion formula is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. Strain Energy in body is denoted by U symbol.

How to calculate Total strain energy in hollow shaft due to torsion using this online calculator? To use this online calculator for Total strain energy in hollow shaft due to torsion, enter Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Modulus of rigidity of Shaft (G) and hit the calculate button. Here is how the Total strain energy in hollow shaft due to torsion calculation can be explained with given input values -> 1.3E-5 = ((4^2)*((4^2)+(1^2))*125.6)/(4*40*(4^2)).

FAQ

What is Total strain energy in hollow shaft due to torsion?

Total strain energy in hollow shaft due to torsion formula is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation and is represented as U = ((𝜏^2)*((d_outer^2)+(d_inner^2))*V)/(4*G*(d_outer^2)) or Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter 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, 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, The Volume of Shaft is the volume of cylindical component under torsion & 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.

How to calculate Total strain energy in hollow shaft due to torsion?

Total strain energy in hollow shaft due to torsion formula is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation is calculated using Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)). To calculate Total strain energy in hollow shaft due to torsion, you need Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Modulus of rigidity of Shaft (G). With our tool, you need to enter the respective value for Shear stress on surface of shaft, Outer Diameter of Shaft, Inner Diameter of Shaft, Volume of Shaft & Modulus of rigidity 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, Outer Diameter of Shaft, Inner Diameter of Shaft, Volume of Shaft & Modulus of rigidity 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 = (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))
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))

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