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Torsional Shear Stress in Shaft Pure Torsion Formula

GoTorsional Shear Stress given Principal Shear Stress in Shaft Formula

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Torsional Shear Stress in Shaft is the stress developed in a shaft due to twisting or rotational force, affecting its strength and structural integrity. Check FAQs

𝜏 = 16 \cdot \frac{Mt shaft}{π \cdot d^{3}}

𝜏 - Torsional Shear Stress in Shaft?Mt_shaft - Torsional Moment in Shaft?d - Diameter of Shaft on Strength Basis?π - Archimedes' constant?

Torsional Shear Stress in Shaft Pure Torsion Example

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Here is how the Torsional Shear Stress in Shaft Pure Torsion equation looks like with Values.

Here is how the Torsional Shear Stress in Shaft Pure Torsion equation looks like with Units.

Here is how the Torsional Shear Stress in Shaft Pure Torsion equation looks like.

16.29 = 16 \cdot \frac{329966.2}{3.1416 \cdot {46.9}^{3}}

16.29N/mm² = 16 \cdot \frac{329966.2N*mm}{3.1416 \cdot {46.9mm}^{3}}

16.29 = 16 \cdot \frac{329966.2}{3.1416 \cdot {46.9}^{3}}

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Torsional Shear Stress in Shaft Pure Torsion Solution

Follow our step by step solution on how to calculate Torsional Shear Stress in Shaft Pure Torsion?

FIRST Step Consider the formula

𝜏 = 16 \cdot \frac{Mt shaft}{π \cdot d^{3}}

Next Step Substitute values of Variables

∴

𝜏 = 16 \cdot \frac{329966.2N*mm}{π \cdot {46.9mm}^{3}}

Next Step Substitute values of Constants

∴

𝜏 = 16 \cdot \frac{329966.2N*mm}{3.1416 \cdot {46.9mm}^{3}}

Next Step Convert Units

∴

𝜏 = 16 \cdot \frac{329.9662N*m}{3.1416 \cdot {0.0469m}^{3}}

Next Step Prepare to Evaluate

∴

𝜏 = 16 \cdot \frac{329.9662}{3.1416 \cdot {0.0469}^{3}}

Next Step Evaluate

∴

𝜏 = 16289998.2304865Pa

Next Step Convert to Output's Unit

∴

𝜏 = 16.2899982304865N/mm²

LAST Step Rounding Answer

∴

𝜏 = 16.29N/mm²

Torsional Shear Stress in Shaft Pure Torsion Formula Elements

Variables

Constants

Torsional Shear Stress in Shaft

Torsional Shear Stress in Shaft is the stress developed in a shaft due to twisting or rotational force, affecting its strength and structural integrity.

Symbol: 𝜏

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Torsional Shear Stress in Shaft

Torsional Moment in Shaft

Torsional Moment in Shaft is the twisting force that causes rotation in a shaft, affecting its strength and stability in shaft design.

Symbol: Mt_shaft

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Shaft

Diameter of Shaft on Strength Basis

Diameter of Shaft on Strength Basis is the diameter of a shaft calculated based on the strength requirements of the shaft design.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft on Strength Basis

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 Torsional Shear Stress in Shaft

Go Torsional Shear Stress given Principal Shear Stress in Shaft

𝜏 = \sqrt{{τ max}^{2} - {(\frac{σ x}{2})}^{2}}

Other formulas in Shaft Design on Strength Basis category

Go Tensile Stress in Shaft when it is Subjected to Axial Tensile Force

σ t = 4 \cdot \frac{P ax}{π \cdot d^{2}}

Go Diameter of Shaft given Tensile Stress in Shaft

d = \sqrt{4 \cdot \frac{P ax}{π \cdot σ t}}

Go Axial Force given Tensile Stress in Shaft

P ax = σ t \cdot π \cdot \frac{d^{2}}{4}

Go Bending Stress in Shaft Pure Bending Moment

σ b = \frac{32 \cdot M b}{π \cdot d^{3}}

How to Evaluate Torsional Shear Stress in Shaft Pure Torsion?

Torsional Shear Stress in Shaft Pure Torsion evaluator uses Torsional Shear Stress in Shaft = 16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3) to evaluate the Torsional Shear Stress in Shaft, Torsional Shear Stress in Shaft Pure Torsion formula is defined as a measure of the shear stress developed in a shaft when it is subjected to a twisting moment, which is a critical parameter in shaft design to ensure its strength and stability under torsional loading conditions. Torsional Shear Stress in Shaft is denoted by 𝜏 symbol.

How to evaluate Torsional Shear Stress in Shaft Pure Torsion using this online evaluator? To use this online evaluator for Torsional Shear Stress in Shaft Pure Torsion, enter Torsional Moment in Shaft (Mt_shaft) & Diameter of Shaft on Strength Basis (d) and hit the calculate button.

FAQs on Torsional Shear Stress in Shaft Pure Torsion

What is the formula to find Torsional Shear Stress in Shaft Pure Torsion?

The formula of Torsional Shear Stress in Shaft Pure Torsion is expressed as Torsional Shear Stress in Shaft = 16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3). Here is an example- 1.6E-5 = 16*329.9662/(pi*0.0469^3).

How to calculate Torsional Shear Stress in Shaft Pure Torsion?

With Torsional Moment in Shaft (Mt_shaft) & Diameter of Shaft on Strength Basis (d) we can find Torsional Shear Stress in Shaft Pure Torsion using the formula - Torsional Shear Stress in Shaft = 16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3). This formula also uses Archimedes' constant .

What are the other ways to Calculate Torsional Shear Stress in Shaft?

Here are the different ways to Calculate Torsional Shear Stress in Shaft-

Torsional Shear Stress in Shaft=sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2)

Can the Torsional Shear Stress in Shaft Pure Torsion be negative?

No, the Torsional Shear Stress in Shaft Pure Torsion, measured in Stress cannot be negative.

Which unit is used to measure Torsional Shear Stress in Shaft Pure Torsion?

Torsional Shear Stress in Shaft Pure Torsion 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 Torsional Shear Stress in Shaft Pure Torsion can be measured.

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Torsional Shear Stress in Shaft Pure Torsion Formula

​GoTorsional Shear Stress given Principal Shear Stress in Shaft Formula

Torsional Shear Stress in Shaft Pure Torsion Example

Torsional Shear Stress in Shaft Pure Torsion Solution

Torsional Shear Stress in Shaft Pure Torsion Formula Elements

Other Formulas to find Torsional Shear Stress in Shaft

Other formulas in Shaft Design on Strength Basis category

How to Evaluate Torsional Shear Stress in Shaft Pure Torsion?

FAQs on Torsional Shear Stress in Shaft Pure Torsion

Variable Name

GoTorsional Shear Stress given Principal Shear Stress in Shaft Formula