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Shear stress at surface of shaft given shear strain energy in ring of radius 'r' 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}))}{2 \cdot π \cdot L \cdot ({r center}^{3}) \cdot δx}}

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?r_center - Radius 'r' from Center Of Shaft?δx - Length of Small Element?π - Archimedes' constant?

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

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Here is how the Shear stress at surface of shaft given shear strain energy in ring of radius 'r' equation looks like with Values.

Here is how the Shear stress at surface of shaft given shear strain energy in ring of radius 'r' equation looks like with Units.

Here is how the Shear stress at surface of shaft given shear strain energy in ring of radius 'r' equation looks like.

0.0016 = \sqrt{\frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{2 \cdot 3.1416 \cdot 7000 \cdot (1500^{3}) \cdot 43.36}}

0.0016MPa = \sqrt{\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot 3.1416 \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}}

0.0016 = \sqrt{\frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{2 \cdot 3.1416 \cdot 7000 \cdot (1500^{3}) \cdot 43.36}}

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

Follow our step by step solution on how to calculate Shear stress at surface of shaft given shear strain energy in ring of radius 'r'?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 = \sqrt{\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot π \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}}

Next Step Substitute values of Constants

∴

𝜏 = \sqrt{\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot 3.1416 \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}}

Next Step Convert Units

∴

𝜏 = \sqrt{\frac{50000J \cdot (2 \cdot 40Pa \cdot ({2m}^{2}))}{2 \cdot 3.1416 \cdot 7m \cdot ({1.5m}^{3}) \cdot 0.0434m}}

Next Step Prepare to Evaluate

∴

𝜏 = \sqrt{\frac{50000 \cdot (2 \cdot 40 \cdot (2^{2}))}{2 \cdot 3.1416 \cdot 7 \cdot ({1.5}^{3}) \cdot 0.0434}}

Next Step Evaluate

∴

𝜏 = 1576.66530807717Pa

Next Step Convert to Output's Unit

∴

𝜏 = 0.00157666530807717MPa

LAST Step Rounding Answer

∴

𝜏 = 0.0016MPa

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

Variables

Constants

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

Radius 'r' from Center Of Shaft

Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.

Symbol: r_center

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius 'r' from Center Of Shaft

Length of Small Element

Length of Small Element is a measure of distance.

Symbol: δx

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Small Element

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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}}

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

How to Evaluate Shear stress at surface of shaft given shear strain energy in ring of radius 'r'?

Shear stress at surface of shaft given shear strain energy in ring of radius 'r' evaluator uses 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)) to evaluate the Shear stress on surface of shaft, Shear stress at surface of shaft given shear strain energy in ring of radius 'r' 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 at surface of shaft given shear strain energy in ring of radius 'r' using this online evaluator? To use this online evaluator for Shear stress at surface of shaft given shear strain energy in ring of radius 'r', enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center) & Length of Small Element (δx) and hit the calculate button.

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

What is the formula to find Shear stress at surface of shaft given shear strain energy in ring of radius 'r'?

The formula of Shear stress at surface of shaft given shear strain energy in ring of radius 'r' is expressed as 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)). Here is an example- 6.3E-9 = sqrt((50000*(2*40*(2^2)))/(2*pi*7*(1.5^3)*0.04336)).

How to calculate Shear stress at surface of shaft given shear strain energy in ring of radius 'r'?

With Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center) & Length of Small Element (δx) we can find Shear stress at surface of shaft given shear strain energy in ring of radius 'r' using the formula - 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)). This formula also uses Archimedes' constant and Square Root Function 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)))/(Length of Shaft*Polar Moment of Inertia of shaft))

Can the Shear stress at surface of shaft given shear strain energy in ring of radius 'r' be negative?

No, the Shear stress at surface of shaft given shear strain energy in ring of radius 'r', measured in Pressure cannot be negative.

Which unit is used to measure Shear stress at surface of shaft given shear strain energy in ring of radius 'r'?

Shear stress at surface of shaft given shear strain energy in ring of radius 'r' 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 shear strain energy in ring of radius 'r' can be measured.

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

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

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

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

Variable Name

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

GoShear stress given shear strain energy Formula