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Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula

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Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end. Check FAQs

θ hollow = 584 \cdot Mt hollowshaft \cdot \frac{L h}{G h \cdot {d o}^{4} \cdot (1 - C^{4})}

θ_hollow - Angle of Twist of Hollow Shaft?Mt_hollowshaft - Torsional Moment in Hollow Shaft?L_h - Length of Hollow Shaft?G_h - Modulus of Rigidity of Hollow Shaft?d_o - Outer Diameter of Hollow Shaft?C - Ratio of Inner to Outer Diameter of Hollow Shaft?

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Example

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Here is how the Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity equation looks like with Values.

Here is how the Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity equation looks like with Units.

Here is how the Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity equation looks like.

23.5856 = 584 \cdot 320000 \cdot \frac{330}{70000 \cdot 46^{4} \cdot (1 - {0.85}^{4})}

23.5856° = 584 \cdot 320000N*mm \cdot \frac{330mm}{70000N/mm² \cdot {46mm}^{4} \cdot (1 - {0.85}^{4})}

23.5856 = 584 \cdot 320000 \cdot \frac{330}{70000 \cdot 46^{4} \cdot (1 - {0.85}^{4})}

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Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Solution

Follow our step by step solution on how to calculate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

FIRST Step Consider the formula

θ hollow = 584 \cdot Mt hollowshaft \cdot \frac{L h}{G h \cdot {d o}^{4} \cdot (1 - C^{4})}

Next Step Substitute values of Variables

∴

θ hollow = 584 \cdot 320000N*mm \cdot \frac{330mm}{70000N/mm² \cdot {46mm}^{4} \cdot (1 - {0.85}^{4})}

Next Step Convert Units

∴

θ hollow = 584 \cdot 320N*m \cdot \frac{0.33m}{7E+10Pa \cdot {0.046m}^{4} \cdot (1 - {0.85}^{4})}

Next Step Prepare to Evaluate

∴

θ hollow = 584 \cdot 320 \cdot \frac{0.33}{7E+10 \cdot {0.046}^{4} \cdot (1 - {0.85}^{4})}

Next Step Evaluate

∴

θ hollow = 0.411647214046393rad

Next Step Convert to Output's Unit

∴

θ hollow = 23.5856480131812°

LAST Step Rounding Answer

∴

θ hollow = 23.5856°

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula Elements

Variables

Angle of Twist of Hollow Shaft

Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.

Symbol: θ_hollow

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Twist of Hollow Shaft

Torsional Moment in Hollow Shaft

Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.

Symbol: Mt_hollowshaft

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Hollow Shaft

Length of Hollow Shaft

Length of Hollow Shaft is the distance between two ends of a hollow shaft.

Symbol: L_h

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Hollow Shaft

Modulus of Rigidity of Hollow Shaft

Modulus of Rigidity of Hollow 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_h

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity of Hollow Shaft

Outer Diameter of Hollow Shaft

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

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Hollow Shaft

Ratio of Inner to Outer Diameter of Hollow Shaft

The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Ratio of Inner to Outer Diameter of Hollow Shaft

Other formulas in Design of Hollow Shaft category

Go Ratio of Inner Diameter to Outer Diameter

C = \frac{d i}{d o}

Go Inner Diameter of Hollow Shaft given Ratio of Diameters

d i = C \cdot d o

Go Outer Diameter given Ratio of Diameters

d o = \frac{d i}{C}

Go Tensile Stress in Hollow Shaft when Subjected to Axial Force

σ tp = \frac{P ax hollow}{\frac{π}{4} \cdot ({d o}^{2} - {d i}^{2})}

How to Evaluate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity evaluator uses Angle of Twist of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)) to evaluate the Angle of Twist of Hollow Shaft, Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as a measure of the twisting force that a hollow shaft can withstand without deforming, which is critical in designing hollow shafts that can resist torsional stress and maintain their structural integrity. Angle of Twist of Hollow Shaft is denoted by θ_hollow symbol.

How to evaluate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity using this online evaluator? To use this online evaluator for Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity, enter Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button.

FAQs on Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

What is the formula to find Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

The formula of Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity is expressed as Angle of Twist of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). Here is an example- 1351.358 = 584*320*0.33/(70000000000*0.046^4*(1-0.85^4)).

How to calculate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

With Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) we can find Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity using the formula - Angle of Twist of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)).

Can the Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity be negative?

No, the Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity, measured in Angle cannot be negative.

Which unit is used to measure Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity can be measured.

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Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Example

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Solution

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

FAQs on Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Variable Name