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Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Formula

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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. Check FAQs

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

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

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Example

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

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

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

70016.7668 = 584 \cdot 320000 \cdot \frac{330}{23.58 \cdot 46^{4} \cdot (1 - {0.85}^{4})}

70016.7668N/mm² = 584 \cdot 320000N*mm \cdot \frac{330mm}{23.58° \cdot {46mm}^{4} \cdot (1 - {0.85}^{4})}

70016.7668 = 584 \cdot 320000 \cdot \frac{330}{23.58 \cdot 46^{4} \cdot (1 - {0.85}^{4})}

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Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

G h = 584 \cdot 320000N*mm \cdot \frac{330mm}{23.58° \cdot {46mm}^{4} \cdot (1 - {0.85}^{4})}

Next Step Convert Units

∴

G h = 584 \cdot 320N*m \cdot \frac{0.33m}{0.4115rad \cdot {0.046m}^{4} \cdot (1 - {0.85}^{4})}

Next Step Prepare to Evaluate

∴

G h = 584 \cdot 320 \cdot \frac{0.33}{0.4115 \cdot {0.046}^{4} \cdot (1 - {0.85}^{4})}

Next Step Evaluate

∴

G h = 70016766790.6141Pa

Next Step Convert to Output's Unit

∴

G h = 70016.7667906141N/mm²

LAST Step Rounding Answer

∴

G h = 70016.7668N/mm²

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Formula Elements

Variables

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

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

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

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 Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity evaluator uses Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)) to evaluate the Modulus of Rigidity of Hollow Shaft, Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as the measure of the shaft's stiffness in torsion, which is essential in designing hollow shafts to withstand twisting forces and resist deformation. Modulus of Rigidity of Hollow Shaft is denoted by G_h symbol.

How to evaluate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity using this online evaluator? To use this online evaluator for Modulus of Rigidity given 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), Angle of Twist of Hollow Shaft (θ_hollow), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button.

FAQs on Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity

What is the formula to find Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

The formula of Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity is expressed as Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). Here is an example- 0.070017 = 584*320*0.33/(0.411548637620186*0.046^4*(1-0.85^4)).

How to calculate Modulus of Rigidity given 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), Angle of Twist of Hollow Shaft (θ_hollow), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) we can find Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity using the formula - Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)).

Can the Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity be negative?

No, the Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity, measured in Stress cannot be negative.

Which unit is used to measure Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity can be measured.

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Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Formula

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Example

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Solution

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

FAQs on Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity

Variable Name