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Shear stress on surface of shaft given total strain energy in hollow 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 = {(\frac{U \cdot (4 \cdot G \cdot ({d outer}^{2}))}{(({d outer}^{2}) + ({d inner}^{2})) \cdot V})}^{\frac{1}{2}}

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

Shear stress on surface of shaft given total strain energy in hollow shaft Example

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Here is how the Shear stress on surface of shaft given total strain energy in hollow shaft equation looks like with Values.

Here is how the Shear stress on surface of shaft given total strain energy in hollow shaft equation looks like with Units.

Here is how the Shear stress on surface of shaft given total strain energy in hollow shaft equation looks like.

0.0002 = {(\frac{50 \cdot (4 \cdot 4E-5 \cdot (4000^{2}))}{((4000^{2}) + (1000^{2})) \cdot 125.6})}^{\frac{1}{2}}

0.0002MPa = {(\frac{50KJ \cdot (4 \cdot 4E-5MPa \cdot ({4000mm}^{2}))}{(({4000mm}^{2}) + ({1000mm}^{2})) \cdot 125.6m³})}^{\frac{1}{2}}

0.0002 = {(\frac{50 \cdot (4 \cdot 4E-5 \cdot (4000^{2}))}{((4000^{2}) + (1000^{2})) \cdot 125.6})}^{\frac{1}{2}}

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Shear stress on surface of shaft given total strain energy in hollow shaft Solution

Follow our step by step solution on how to calculate Shear stress on surface of shaft given total strain energy in hollow shaft?

FIRST Step Consider the formula

𝜏 = {(\frac{U \cdot (4 \cdot G \cdot ({d outer}^{2}))}{(({d outer}^{2}) + ({d inner}^{2})) \cdot V})}^{\frac{1}{2}}

Next Step Substitute values of Variables

∴

𝜏 = {(\frac{50KJ \cdot (4 \cdot 4E-5MPa \cdot ({4000mm}^{2}))}{(({4000mm}^{2}) + ({1000mm}^{2})) \cdot 125.6m³})}^{\frac{1}{2}}

Next Step Convert Units

∴

𝜏 = {(\frac{50000J \cdot (4 \cdot 40Pa \cdot ({4m}^{2}))}{(({4m}^{2}) + ({1m}^{2})) \cdot 125.6m³})}^{\frac{1}{2}}

Next Step Prepare to Evaluate

∴

𝜏 = {(\frac{50000 \cdot (4 \cdot 40 \cdot (4^{2}))}{((4^{2}) + (1^{2})) \cdot 125.6})}^{\frac{1}{2}}

Next Step Evaluate

∴

𝜏 = 244.841879377977Pa

Next Step Convert to Output's Unit

∴

𝜏 = 0.000244841879377977MPa

LAST Step Rounding Answer

∴

𝜏 = 0.0002MPa

Shear stress on surface of shaft given total strain energy in hollow shaft Formula Elements

Variables

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

Outer Diameter of Shaft

Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Shaft

Inner Diameter of Shaft

The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

Symbol: d_inner

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Inner Diameter 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

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 Stored in Shaft

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

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 on surface of shaft given total strain energy in hollow shaft?

Shear stress on surface of shaft given total strain energy in hollow shaft evaluator uses Shear stress on surface of shaft = ((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/(((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft))^(1/2) to evaluate the Shear stress on surface of shaft, Shear stress on surface of shaft given total strain energy in hollow shaft 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 on surface of shaft given total strain energy in hollow shaft using this online evaluator? To use this online evaluator for Shear stress on surface of shaft given total strain energy in hollow shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner) & Volume of Shaft (V) and hit the calculate button.

FAQs on Shear stress on surface of shaft given total strain energy in hollow shaft

What is the formula to find Shear stress on surface of shaft given total strain energy in hollow shaft?

The formula of Shear stress on surface of shaft given total strain energy in hollow shaft is expressed as Shear stress on surface of shaft = ((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/(((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft))^(1/2). Here is an example- 2.4E-10 = ((50000*(4*40*(4^2)))/(((4^2)+(1^2))*125.6))^(1/2).

How to calculate Shear stress on surface of shaft given total strain energy in hollow shaft?

With Strain Energy in body (U), Modulus of rigidity of Shaft (G), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner) & Volume of Shaft (V) we can find Shear stress on surface of shaft given total strain energy in hollow shaft using the formula - Shear stress on surface of shaft = ((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/(((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft))^(1/2).

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 on surface of shaft given total strain energy in hollow shaft be negative?

No, the Shear stress on surface of shaft given total strain energy in hollow shaft, measured in Pressure cannot be negative.

Which unit is used to measure Shear stress on surface of shaft given total strain energy in hollow shaft?

Shear stress on surface of shaft given total strain energy in hollow 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 on surface of shaft given total strain energy in hollow shaft can be measured.

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Shear stress on surface of shaft given total strain energy in hollow 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 on surface of shaft given total strain energy in hollow shaft Example

Shear stress on surface of shaft given total strain energy in hollow shaft Solution

Shear stress on surface of shaft given total strain energy in hollow 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 on surface of shaft given total strain energy in hollow shaft?

FAQs on Shear stress on surface of shaft given total strain energy in hollow 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