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Inner diameter of shaft given total strain energy in hollow shaft Formula

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

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

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

Inner diameter of shaft given total strain energy in hollow shaft Example

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Here is how the Inner diameter of shaft given total strain energy in hollow shaft equation looks like with Values.

Here is how the Inner diameter of shaft given total strain energy in hollow shaft equation looks like with Units.

Here is how the Inner diameter of shaft given total strain energy in hollow shaft equation looks like.

252345.532 = {((\frac{50 \cdot (4 \cdot 4E-5 \cdot (4000^{2}))}{({4E-6}^{2}) \cdot 125.6}) - (4000^{2}))}^{\frac{1}{2}}

252345.532mm = {((\frac{50KJ \cdot (4 \cdot 4E-5MPa \cdot ({4000mm}^{2}))}{({4E-6MPa}^{2}) \cdot 125.6m³}) - ({4000mm}^{2}))}^{\frac{1}{2}}

252345.532 = {((\frac{50 \cdot (4 \cdot 4E-5 \cdot (4000^{2}))}{({4E-6}^{2}) \cdot 125.6}) - (4000^{2}))}^{\frac{1}{2}}

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Inner diameter of shaft given total strain energy in hollow shaft Solution

Follow our step by step solution on how to calculate Inner diameter of shaft given total strain energy in hollow shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d inner = {((\frac{50KJ \cdot (4 \cdot 4E-5MPa \cdot ({4000mm}^{2}))}{({4E-6MPa}^{2}) \cdot 125.6m³}) - ({4000mm}^{2}))}^{\frac{1}{2}}

Next Step Convert Units

∴

d inner = {((\frac{50000J \cdot (4 \cdot 40Pa \cdot ({4m}^{2}))}{({4Pa}^{2}) \cdot 125.6m³}) - ({4m}^{2}))}^{\frac{1}{2}}

Next Step Prepare to Evaluate

∴

d inner = {((\frac{50000 \cdot (4 \cdot 40 \cdot (4^{2}))}{(4^{2}) \cdot 125.6}) - (4^{2}))}^{\frac{1}{2}}

Next Step Evaluate

∴

d inner = 252.345531991204m

Next Step Convert to Output's Unit

∴

d inner = 252345.531991204mm

LAST Step Rounding Answer

∴

d inner = 252345.532mm

Inner diameter of shaft given total strain energy in hollow shaft Formula Elements

Variables

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

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

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

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 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 Inner diameter of shaft given total strain energy in hollow shaft?

Inner diameter of shaft given total strain energy in hollow shaft evaluator uses Inner Diameter of Shaft = (((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*Volume of Shaft))-(Outer Diameter of Shaft^2))^(1/2) to evaluate the Inner Diameter of Shaft, Inner diameter of shaft given total strain energy in hollow shaft is defined as a chord that runs through the center point of the circle. It is the longest possible chord of any circle. Inner Diameter of Shaft is denoted by d_inner symbol.

How to evaluate Inner diameter of shaft given total strain energy in hollow shaft using this online evaluator? To use this online evaluator for Inner diameter 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), Shear stress on surface of shaft (𝜏) & Volume of Shaft (V) and hit the calculate button.

FAQs on Inner diameter of shaft given total strain energy in hollow shaft

What is the formula to find Inner diameter of shaft given total strain energy in hollow shaft?

The formula of Inner diameter of shaft given total strain energy in hollow shaft is expressed as Inner Diameter of Shaft = (((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*Volume of Shaft))-(Outer Diameter of Shaft^2))^(1/2). Here is an example- 2.5E+8 = (((50000*(4*40*(4^2)))/((4^2)*125.6))-(4^2))^(1/2).

How to calculate Inner diameter 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), Shear stress on surface of shaft (𝜏) & Volume of Shaft (V) we can find Inner diameter of shaft given total strain energy in hollow shaft using the formula - Inner Diameter of Shaft = (((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*Volume of Shaft))-(Outer Diameter of Shaft^2))^(1/2).

Can the Inner diameter of shaft given total strain energy in hollow shaft be negative?

Yes, the Inner diameter of shaft given total strain energy in hollow shaft, measured in Length can be negative.

Which unit is used to measure Inner diameter of shaft given total strain energy in hollow shaft?

Inner diameter of shaft given total strain energy in hollow shaft is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Inner diameter of shaft given total strain energy in hollow shaft can be measured.

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Inner diameter of shaft given total strain energy in hollow shaft Formula

Inner diameter of shaft given total strain energy in hollow shaft Example

Inner diameter of shaft given total strain energy in hollow shaft Solution

Inner diameter of shaft given total strain energy in hollow shaft Formula Elements

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

How to Evaluate Inner diameter of shaft given total strain energy in hollow shaft?

FAQs on Inner diameter of shaft given total strain energy in hollow shaft

Variable Name