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Shear stress given shear strain energy Formula

GoShear stress at surface of shaft given shear stress at radius 'r' from center Formula

GoShear stress at surface of shaft given shear strain energy in ring of radius 'r' Formula

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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. Check FAQs

𝜏 = \sqrt{\frac{U \cdot 2 \cdot G}{V}}

𝜏 - Shear stress on surface of shaft?U - Strain Energy in body?G - Modulus of rigidity of Shaft?V - Volume of Shaft?

Shear stress given shear strain energy Example

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Here is how the Shear stress given shear strain energy equation looks like with Values.

Here is how the Shear stress given shear strain energy equation looks like with Units.

Here is how the Shear stress given shear strain energy equation looks like.

0.0002 = \sqrt{\frac{50 \cdot 2 \cdot 4E-5}{125.6}}

0.0002MPa = \sqrt{\frac{50KJ \cdot 2 \cdot 4E-5MPa}{125.6m³}}

0.0002 = \sqrt{\frac{50 \cdot 2 \cdot 4E-5}{125.6}}

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Shear stress given shear strain energy Solution

Follow our step by step solution on how to calculate Shear stress given shear strain energy?

FIRST Step Consider the formula

𝜏 = \sqrt{\frac{U \cdot 2 \cdot G}{V}}

Next Step Substitute values of Variables

∴

𝜏 = \sqrt{\frac{50KJ \cdot 2 \cdot 4E-5MPa}{125.6m³}}

Next Step Convert Units

∴

𝜏 = \sqrt{\frac{50000J \cdot 2 \cdot 40Pa}{125.6m³}}

Next Step Prepare to Evaluate

∴

𝜏 = \sqrt{\frac{50000 \cdot 2 \cdot 40}{125.6}}

Next Step Evaluate

∴

𝜏 = 178.457652562062Pa

Next Step Convert to Output's Unit

∴

𝜏 = 0.000178457652562062MPa

LAST Step Rounding Answer

∴

𝜏 = 0.0002MPa

Shear stress given shear strain energy Formula Elements

Variables

Functions

Shear stress on surface of shaft

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.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear stress on surface of shaft

Strain Energy in body

Strain Energy in body is defined as the energy stored in a body due to deformation.

Symbol: U

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Strain Energy in body

Modulus of rigidity of Shaft

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.

Symbol: G

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of rigidity of Shaft

Volume of Shaft

The Volume of Shaft is the volume of cylindical component under torsion.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Volume of Shaft

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Shear stress on surface of shaft

Go Shear stress at surface of shaft given shear stress at radius 'r' from center

𝜏 = \frac{q}{\frac{r center}{r shaft}}

Go Shear stress at surface of shaft given shear strain energy in ring of radius 'r'

𝜏 = \sqrt{\frac{U \cdot (2 \cdot G \cdot ({r shaft}^{2}))}{2 \cdot π \cdot L \cdot ({r center}^{3}) \cdot δx}}

Go Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft

𝜏 = \sqrt{\frac{U \cdot (2 \cdot G \cdot ({r shaft}^{2}))}{L \cdot J shaft}}

Go Shear stress at surface of shaft given total strain energy in shaft due to torsion

𝜏 = \sqrt{\frac{U \cdot 4 \cdot G}{V}}

Other formulas in Expression for Strain Energy stored in a Body Due to Torsion category

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

r center = \frac{q \cdot r shaft}{𝜏}

Go Radius of shaft given shear stress at radius r from center

r shaft = (\frac{r center}{q}) \cdot 𝜏

Go Shear strain energy

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

Go Modulus of rigidity given shear strain energy

G = (𝜏^{2}) \cdot \frac{V}{2 \cdot U}

How to Evaluate Shear stress given shear strain energy?

Shear stress given shear strain energy evaluator uses Shear stress on surface of shaft = sqrt((Strain Energy in body*2*Modulus of rigidity of Shaft)/Volume of Shaft) to evaluate the Shear stress on surface of shaft, Shear stress given shear strain energy is a 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 is denoted by 𝜏 symbol.

How to evaluate Shear stress given shear strain energy using this online evaluator? To use this online evaluator for Shear stress given shear strain energy, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G) & Volume of Shaft (V) and hit the calculate button.

FAQs on Shear stress given shear strain energy

What is the formula to find Shear stress given shear strain energy?

The formula of Shear stress given shear strain energy is expressed as Shear stress on surface of shaft = sqrt((Strain Energy in body*2*Modulus of rigidity of Shaft)/Volume of Shaft). Here is an example- 1.8E-10 = sqrt((50000*2*40)/125.6).

How to calculate Shear stress given shear strain energy?

With Strain Energy in body (U), Modulus of rigidity of Shaft (G) & Volume of Shaft (V) we can find Shear stress given shear strain energy using the formula - Shear stress on surface of shaft = sqrt((Strain Energy in body*2*Modulus of rigidity of Shaft)/Volume of Shaft). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Shear stress on surface of shaft?

Here are the different ways to Calculate Shear stress on surface of shaft-

Shear stress on surface of shaft=Shear stress at radius 'r' from shaft/(Radius 'r' from Center Of Shaft/Radius of Shaft)
Shear stress on surface of shaft=sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element))
Shear stress on surface of shaft=sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft))

Can the Shear stress given shear strain energy be negative?

No, the Shear stress given shear strain energy, measured in Pressure cannot be negative.

Which unit is used to measure Shear stress given shear strain energy?

Shear stress given shear strain energy is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Shear stress given shear strain energy can be measured.

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Shear stress given shear strain energy Formula

​GoShear stress at surface of shaft given shear stress at radius 'r' from center Formula

​GoShear stress at surface of shaft given shear strain energy in ring of radius 'r' Formula

Shear stress given shear strain energy Example

Shear stress given shear strain energy Solution

Shear stress given shear strain energy Formula Elements

Other Formulas to find Shear stress on surface of shaft

Other formulas in Expression for Strain Energy stored in a Body Due to Torsion category

How to Evaluate Shear stress given shear strain energy?

FAQs on Shear stress given shear strain energy

Variable Name

GoShear stress at surface of shaft given shear stress at radius 'r' from center Formula

GoShear stress at surface of shaft given shear strain energy in ring of radius 'r' Formula