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

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

GoShear stress given shear strain energy 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 \cdot ({r shaft}^{2}))}{L \cdot J shaft}}

𝜏 - Shear stress on surface of shaft?U - Strain Energy in body?G - Modulus of rigidity of Shaft?r_shaft - Radius of Shaft?L - Length of Shaft?J_shaft - Polar Moment of Inertia of shaft?

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

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Here is how the Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft equation looks like with Values.

Here is how the Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft equation looks like with Units.

Here is how the Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft equation looks like.

0.0005 = \sqrt{\frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{7000 \cdot 10}}

0.0005MPa = \sqrt{\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{7000mm \cdot 10m⁴}}

0.0005 = \sqrt{\frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{7000 \cdot 10}}

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

Follow our step by step solution on how to calculate Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 = \sqrt{\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{7000mm \cdot 10m⁴}}

Next Step Convert Units

∴

𝜏 = \sqrt{\frac{50000J \cdot (2 \cdot 40Pa \cdot ({2m}^{2}))}{7m \cdot 10m⁴}}

Next Step Prepare to Evaluate

∴

𝜏 = \sqrt{\frac{50000 \cdot (2 \cdot 40 \cdot (2^{2}))}{7 \cdot 10}}

Next Step Evaluate

∴

𝜏 = 478.091443733757Pa

Next Step Convert to Output's Unit

∴

𝜏 = 0.000478091443733757MPa

LAST Step Rounding Answer

∴

𝜏 = 0.0005MPa

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

Radius of Shaft

The Radius of Shaft is the radius of the shaft subjected under torsion.

Symbol: r_shaft

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Shaft

Length of Shaft

The Length of Shaft is the distance between two ends of shaft.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Polar Moment of Inertia of shaft

Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

Symbol: J_shaft

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia 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 given shear strain energy

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

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 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 at Surface of Shaft given Total Strain Energy Stored in Shaft?

Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft evaluator uses 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)) to evaluate the Shear stress on surface of shaft, The Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft formula is defined as 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 at Surface of Shaft given Total Strain Energy Stored in Shaft using this online evaluator? To use this online evaluator for Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Length of Shaft (L) & Polar Moment of Inertia of shaft (J_shaft) and hit the calculate button.

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

What is the formula to find Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?

The formula of Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft is expressed as 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)). Here is an example- 4.8E-10 = sqrt((50000*(2*40*(2^2)))/(7*10)).

How to calculate Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?

With Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Length of Shaft (L) & Polar Moment of Inertia of shaft (J_shaft) we can find Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft using the formula - 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)). 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)/Volume 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))

Can the Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft be negative?

No, the Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft, measured in Pressure cannot be negative.

Which unit is used to measure Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?

Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft can be measured.

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

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

​GoShear stress given shear strain energy Formula

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

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

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

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

Variable Name

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

GoShear stress given shear strain energy Formula