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Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Formula

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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. Check FAQs

G = \frac{32 \cdot τ \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}{π \cdot θ \cdot (D 2 - D 1)}

G - Modulus of rigidity of Shaft?τ - Torque Exerted on Wheel?L - Length of Shaft?D₁ - Diameter of shaft at left end?D₂ - Diameter of shaft at right end?θ - Angle of twist?π - Archimedes' constant?

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Example

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Here is how the Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft equation looks like with Values.

Here is how the Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft equation looks like with Units.

Here is how the Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft equation looks like.

1.7E-6 = \frac{32 \cdot 50 \cdot 7000 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}{3.1416 \cdot 30 \cdot (5000 - 3000)}

1.7E-6MPa = \frac{32 \cdot 50N*m \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}{3.1416 \cdot 30 \cdot (5000mm - 3000mm)}

1.7E-6 = \frac{32 \cdot 50 \cdot 7000 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}{3.1416 \cdot 30 \cdot (5000 - 3000)}

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Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Solution

Follow our step by step solution on how to calculate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

FIRST Step Consider the formula

G = \frac{32 \cdot τ \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}{π \cdot θ \cdot (D 2 - D 1)}

Next Step Substitute values of Variables

∴

G = \frac{32 \cdot 50N*m \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}{π \cdot 30 \cdot (5000mm - 3000mm)}

Next Step Substitute values of Constants

∴

G = \frac{32 \cdot 50N*m \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}{3.1416 \cdot 30 \cdot (5000mm - 3000mm)}

Next Step Convert Units

∴

G = \frac{32 \cdot 50N*m \cdot 7m \cdot (\frac{1}{{3m}^{3}} - \frac{1}{{5m}^{3}})}{3.1416 \cdot 30 \cdot (5m - 3m)}

Next Step Prepare to Evaluate

∴

G = \frac{32 \cdot 50 \cdot 7 \cdot (\frac{1}{3^{3}} - \frac{1}{5^{3}})}{3.1416 \cdot 30 \cdot (5 - 3)}

Next Step Evaluate

∴

G = 1.72531817814977Pa

Next Step Convert to Output's Unit

∴

G = 1.72531817814977E-06MPa

LAST Step Rounding Answer

∴

G = 1.7E-6MPa

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Formula Elements

Variables

Constants

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

Torque Exerted on Wheel

Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

Symbol: τ

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Torque Exerted on Wheel

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

Diameter of shaft at left end

Diameter of shaft at left end is the shorter side diameter of tapering shaft.

Symbol: D₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of shaft at left end

Diameter of shaft at right end

Diameter of shaft at right end is the longer side diameter of tapering shaft.

Symbol: D₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of shaft at right end

Angle of twist

Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Angle of twist

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

Other formulas in Torsion of Tapering Shafts category

Go Torque on Tapering Shaft

τ = \frac{𝜏 \cdot π \cdot d s}{16}

Go Shear Stress on Left Surface of Shaft

𝜏 = \frac{16 \cdot τ}{π \cdot d s}

Go Diameter of Shaft at Left End

d s = \frac{16 \cdot τ}{𝜏 \cdot π}

Go Total Angle of Twist for Shaft

θ = \frac{32 \cdot τ \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}{π \cdot G \cdot (D 2 - D 1)}

How to Evaluate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft evaluator uses Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end)) to evaluate the Modulus of rigidity of Shaft, Modulus of rigidity of shaft given total angle of twist for shaft is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Modulus of rigidity of Shaft is denoted by G symbol.

How to evaluate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft using this online evaluator? To use this online evaluator for Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Diameter of shaft at left end (D₁), Diameter of shaft at right end (D₂) & Angle of twist (θ) and hit the calculate button.

FAQs on Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft

What is the formula to find Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

The formula of Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft is expressed as Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end)). Here is an example- 1.7E-12 = (32*50*7*(1/(3^3)-1/(5^3)))/(pi*30*(5-3)).

How to calculate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

With Torque Exerted on Wheel (τ), Length of Shaft (L), Diameter of shaft at left end (D₁), Diameter of shaft at right end (D₂) & Angle of twist (θ) we can find Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft using the formula - Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end)). This formula also uses Archimedes' constant .

Can the Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft be negative?

No, the Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft can be measured.

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Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Formula

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Example

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Solution

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Formula Elements

Other formulas in Torsion of Tapering Shafts category

How to Evaluate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

FAQs on Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft

Variable Name