Strain Energy in Torsion given Angle of Twist Calculator

✖Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.ⓘ Polar Moment of Inertia [J]			+10% -10%
✖Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.ⓘ Modulus of Rigidity [G_Torsion]			+10% -10%
✖Angle of Twist is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of Twist [θ]			+10% -10%
✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length of Member [L]			+10% -10%

✖Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.ⓘ Strain Energy in Torsion given Angle of Twist [U]

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Strain Energy in Torsion given Angle of Twist Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)
U = (J*G_Torsion*(θ*(pi/180))^2)/(2*L)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Strain Energy - (Measured in Joule) - Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.
Polar Moment of Inertia - (Measured in Meter⁴) - Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.
Angle of Twist - (Measured in Radian) - Angle of Twist is the angle through which the fixed end of a shaft rotates with respect to the free end.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.

STEP 1: Convert Input(s) to Base Unit

Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)
Angle of Twist: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (J*G_Torsion*(θ*(pi/180))^2)/(2*L) --> (0.0041*40000000000*(0.2617993877991*(pi/180))^2)/(2*3)

Evaluating ... ...

U = 570.669400490482

STEP 3: Convert Result to Output's Unit

570.669400490482 Joule -->570.669400490482 Newton Meter (Check conversion here)

FINAL ANSWER

570.669400490482 ≈ 570.6694 Newton Meter <-- Strain Energy

(Calculation completed in 00.020 seconds)

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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< Strain Energy in Structural Members Calculators

Shear Force using Strain Energy

LaTeX Go Shear Force = sqrt(2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/Length of Member)

Strain Energy in Shear

LaTeX Go Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)

Length over which Deformation takes place given Strain Energy in Shear

LaTeX Go Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)

Stress using Hook's Law

LaTeX Go Direct Stress = Young's Modulus*Lateral Strain

Strain Energy in Torsion given Angle of Twist Formula

LaTeX Go

Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)
U = (J*G_Torsion*(θ*(pi/180))^2)/(2*L)

What does Torsion mean?

The twisting or wrenching of a body by the exertion of forces tending to turn one end or part about a longitudinal axis while the other is held fast or turned in the opposite direction also the state of being twisted. The twisting of a bodily organ or part on its own axis.

What is the Strain Energy in Torsion?

The energy stores in the shaft are equal to work done in twisting i.e., Strain energy stored in a body due to torsion. For example, a solid circular shaft.

How to Calculate Strain Energy in Torsion given Angle of Twist?

Strain Energy in Torsion given Angle of Twist calculator uses Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member) to calculate the Strain Energy, The Strain Energy in Torsion given Angle of Twist formula is defined as the energy stored in a body due to torsional deformation. Strain Energy is denoted by U symbol.

How to calculate Strain Energy in Torsion given Angle of Twist using this online calculator? To use this online calculator for Strain Energy in Torsion given Angle of Twist, enter Polar Moment of Inertia (J), Modulus of Rigidity (G_Torsion), Angle of Twist (θ) & Length of Member (L) and hit the calculate button. Here is how the Strain Energy in Torsion given Angle of Twist calculation can be explained with given input values -> 570.6694 = (0.0041*40000000000*(0.2617993877991*(pi/180))^2)/(2*3).

FAQ

What is Strain Energy in Torsion given Angle of Twist?

The Strain Energy in Torsion given Angle of Twist formula is defined as the energy stored in a body due to torsional deformation and is represented as U = (J*G_Torsion*(θ*(pi/180))^2)/(2*L) or Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member). Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section, Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G, Angle of Twist is the angle through which the fixed end of a shaft rotates with respect to the free end & Length of Member is the measurement or extent of member (beam or column) from end to end.

How to calculate Strain Energy in Torsion given Angle of Twist?

The Strain Energy in Torsion given Angle of Twist formula is defined as the energy stored in a body due to torsional deformation is calculated using Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member). To calculate Strain Energy in Torsion given Angle of Twist, you need Polar Moment of Inertia (J), Modulus of Rigidity (G_Torsion), Angle of Twist (θ) & Length of Member (L). With our tool, you need to enter the respective value for Polar Moment of Inertia, Modulus of Rigidity, Angle of Twist & Length of Member 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 this formula, Strain Energy uses Polar Moment of Inertia, Modulus of Rigidity, Angle of Twist & Length of Member. We can use 3 other way(s) to calculate the same, which is/are as follows -

Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)
Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)
Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)

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