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Angle of twist of hollow cylindrical rod in degrees Formula

GoAngle of twist of solid cylindrical rod in degrees Formula

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

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot (({d ho}^{4}) - ({d hi}^{4}))}) \cdot (\frac{π}{180})

𝜽_d - Angle of twist of shaft in degree?τ - Torsional moment on shaft?l - Length of Shaft?C - Modulus of Rigidity?d_ho - Outer Diameter of Hollow Circular Section?d_hi - Inner Diameter of Hollow Circular Section?π - Archimedes' constant?

Angle of twist of hollow cylindrical rod in degrees Example

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Here is how the Angle of twist of hollow cylindrical rod in degrees equation looks like with Values.

Here is how the Angle of twist of hollow cylindrical rod in degrees equation looks like with Units.

Here is how the Angle of twist of hollow cylindrical rod in degrees equation looks like.

0.443 = (584 \cdot 51000 \cdot \frac{1100}{84000 \cdot ((40^{4}) - (36^{4}))}) \cdot (\frac{3.1416}{180})

0.443° = (584 \cdot 51000N*mm \cdot \frac{1100mm}{84000N/mm² \cdot (({40mm}^{4}) - ({36mm}^{4}))}) \cdot (\frac{3.1416}{180})

0.443 = (584 \cdot 51000 \cdot \frac{1100}{84000 \cdot ((40^{4}) - (36^{4}))}) \cdot (\frac{3.1416}{180})

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Angle of twist of hollow cylindrical rod in degrees Solution

Follow our step by step solution on how to calculate Angle of twist of hollow cylindrical rod in degrees?

FIRST Step Consider the formula

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot (({d ho}^{4}) - ({d hi}^{4}))}) \cdot (\frac{π}{180})

Next Step Substitute values of Variables

∴

𝜽 d = (584 \cdot 51000N*mm \cdot \frac{1100mm}{84000N/mm² \cdot (({40mm}^{4}) - ({36mm}^{4}))}) \cdot (\frac{π}{180})

Next Step Substitute values of Constants

∴

𝜽 d = (584 \cdot 51000N*mm \cdot \frac{1100mm}{84000N/mm² \cdot (({40mm}^{4}) - ({36mm}^{4}))}) \cdot (\frac{3.1416}{180})

Next Step Convert Units

∴

𝜽 d = (584 \cdot 51N*m \cdot \frac{1.1m}{8.4E+10Pa \cdot (({0.04m}^{4}) - ({0.036m}^{4}))}) \cdot (\frac{3.1416}{180})

Next Step Prepare to Evaluate

∴

𝜽 d = (584 \cdot 51 \cdot \frac{1.1}{8.4E+10 \cdot (({0.04}^{4}) - ({0.036}^{4}))}) \cdot (\frac{3.1416}{180})

Next Step Evaluate

∴

𝜽 d = 0.00773217453779084rad

Next Step Convert to Output's Unit

∴

𝜽 d = 0.443020967474017°

LAST Step Rounding Answer

∴

𝜽 d = 0.443°

Angle of twist of hollow cylindrical rod in degrees Formula Elements

Variables

Constants

Angle of twist of shaft in degree

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

Symbol: 𝜽_d

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of twist of shaft in degree

Torsional moment on shaft

Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.

Symbol: τ

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional moment on shaft

Length of Shaft

Length of shaft is defined as the distance between the two opposite ends of a shaft.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Modulus of Rigidity

Modulus of Rigidity 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: C

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Outer Diameter of Hollow Circular Section

Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section.

Symbol: d_ho

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Hollow Circular Section

Inner Diameter of Hollow Circular Section

Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.

Symbol: d_hi

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Diameter of Hollow Circular Section

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 to find Angle of twist of shaft in degree

Go Angle of twist of solid cylindrical rod in degrees

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot ({d c}^{4})}) \cdot (\frac{π}{180})

Other formulas in Design of Shaft for Torsional Moment category

Go Torsional shear stress in shaft due to torsional moment

𝜏 = τ \cdot \frac{r}{J}

Go Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

θ = \frac{τ \cdot l}{J \cdot C}

Go Polar moment of inertia of hollow circular cross-section

J = π \cdot \frac{({d ho}^{4}) - ({d hi}^{4})}{32}

Go Polar moment of inertia of circular cross section

J = π \cdot \frac{{d c}^{4}}{32}

How to Evaluate Angle of twist of hollow cylindrical rod in degrees?

Angle of twist of hollow cylindrical rod in degrees evaluator uses Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180) to evaluate the Angle of twist of shaft in degree, The angle of twist of hollow cylindrical rod in degrees formula is defined as the angle through which the hollow cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod. Angle of twist of shaft in degree is denoted by 𝜽_d symbol.

How to evaluate Angle of twist of hollow cylindrical rod in degrees using this online evaluator? To use this online evaluator for Angle of twist of hollow cylindrical rod in degrees, enter Torsional moment on shaft (τ), Length of Shaft (l), Modulus of Rigidity (C), Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi) and hit the calculate button.

FAQs on Angle of twist of hollow cylindrical rod in degrees

What is the formula to find Angle of twist of hollow cylindrical rod in degrees?

The formula of Angle of twist of hollow cylindrical rod in degrees is expressed as Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180). Here is an example- 25.38323 = (584*51*1.1/(84000000000*((0.04^4)-(0.036^4))))*(pi/180).

How to calculate Angle of twist of hollow cylindrical rod in degrees?

With Torsional moment on shaft (τ), Length of Shaft (l), Modulus of Rigidity (C), Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi) we can find Angle of twist of hollow cylindrical rod in degrees using the formula - Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180). This formula also uses Archimedes' constant .

What are the other ways to Calculate Angle of twist of shaft in degree?

Here are the different ways to Calculate Angle of twist of shaft in degree-

Angle of twist of shaft in degree=(584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180)

Can the Angle of twist of hollow cylindrical rod in degrees be negative?

No, the Angle of twist of hollow cylindrical rod in degrees, measured in Angle cannot be negative.

Which unit is used to measure Angle of twist of hollow cylindrical rod in degrees?

Angle of twist of hollow cylindrical rod in degrees is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of twist of hollow cylindrical rod in degrees can be measured.

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Angle of twist of hollow cylindrical rod in degrees Formula

​GoAngle of twist of solid cylindrical rod in degrees Formula

Angle of twist of hollow cylindrical rod in degrees Example

Angle of twist of hollow cylindrical rod in degrees Solution

Angle of twist of hollow cylindrical rod in degrees Formula Elements

Other Formulas to find Angle of twist of shaft in degree

Other formulas in Design of Shaft for Torsional Moment category

How to Evaluate Angle of twist of hollow cylindrical rod in degrees?

FAQs on Angle of twist of hollow cylindrical rod in degrees

Variable Name

GoAngle of twist of solid cylindrical rod in degrees Formula