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Torsional Shear Stress given Principal Shear Stress in Shaft Formula

GoTorsional Shear Stress in Shaft Pure Torsion 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 = \sqrt{{τ max}^{2} - {(\frac{σ x}{2})}^{2}}

𝜏 - Torsional Shear Stress in Shaft?τ_max - Principal Shear Stress in Shaft?σ_x - Normal Stress in Shaft?

Torsional Shear Stress given Principal Shear Stress in Shaft Example

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Here is how the Torsional Shear Stress given Principal Shear Stress in Shaft equation looks like with Values.

Here is how the Torsional Shear Stress given Principal Shear Stress in Shaft equation looks like with Units.

Here is how the Torsional Shear Stress given Principal Shear Stress in Shaft equation looks like.

16.294 = \sqrt{{126.355}^{2} - {(\frac{250.6}{2})}^{2}}

16.294N/mm² = \sqrt{{126.355N/mm²}^{2} - {(\frac{250.6N/mm²}{2})}^{2}}

16.294 = \sqrt{{126.355}^{2} - {(\frac{250.6}{2})}^{2}}

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Torsional Shear Stress given Principal Shear Stress in Shaft Solution

Follow our step by step solution on how to calculate Torsional Shear Stress given Principal Shear Stress in Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 = \sqrt{{126.355N/mm²}^{2} - {(\frac{250.6N/mm²}{2})}^{2}}

Next Step Convert Units

∴

𝜏 = \sqrt{{1.3E+8Pa}^{2} - {(\frac{2.5E+8Pa}{2})}^{2}}

Next Step Prepare to Evaluate

∴

𝜏 = \sqrt{{1.3E+8}^{2} - {(\frac{2.5E+8}{2})}^{2}}

Next Step Evaluate

∴

𝜏 = 16294048.7602069Pa

Next Step Convert to Output's Unit

∴

𝜏 = 16.2940487602069N/mm²

LAST Step Rounding Answer

∴

𝜏 = 16.294N/mm²

Torsional Shear Stress given Principal Shear Stress in Shaft Formula Elements

Variables

Functions

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

Principal Shear Stress in Shaft

Principal Shear Stress in Shaft is the maximum shear stress that a shaft can withstand without failing, considering the shaft's design and strength parameters.

Symbol: τ_max

Measurement: StressUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Principal Shear Stress in Shaft

Normal Stress in Shaft

Normal Stress in Shaft is the force per unit area that a shaft can withstand without undergoing deformation or failure during its operation.

Symbol: σ_x

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Normal Stress in Shaft

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Torsional Shear Stress in Shaft

Go Torsional Shear Stress in Shaft Pure Torsion

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

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 given Principal Shear Stress in Shaft?

Torsional Shear Stress given Principal Shear Stress in Shaft evaluator uses Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2) to evaluate the Torsional Shear Stress in Shaft, Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as a measure of the shear stress that occurs due to twisting of a shaft, which is a critical parameter in shaft design to ensure the shaft can withstand the torsional load without failure. Torsional Shear Stress in Shaft is denoted by 𝜏 symbol.

How to evaluate Torsional Shear Stress given Principal Shear Stress in Shaft using this online evaluator? To use this online evaluator for Torsional Shear Stress given Principal Shear Stress in Shaft, enter Principal Shear Stress in Shaft (τ_max) & Normal Stress in Shaft (σ_x) and hit the calculate button.

FAQs on Torsional Shear Stress given Principal Shear Stress in Shaft

What is the formula to find Torsional Shear Stress given Principal Shear Stress in Shaft?

The formula of Torsional Shear Stress given Principal Shear Stress in Shaft is expressed as Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2). Here is an example- 1.7E-5 = sqrt(126355000^2-(250600000/2)^2).

How to calculate Torsional Shear Stress given Principal Shear Stress in Shaft?

With Principal Shear Stress in Shaft (τ_max) & Normal Stress in Shaft (σ_x) we can find Torsional Shear Stress given Principal Shear Stress in Shaft using the formula - Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2). This formula also uses Square Root (sqrt) function(s).

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=16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3)

Can the Torsional Shear Stress given Principal Shear Stress in Shaft be negative?

No, the Torsional Shear Stress given Principal Shear Stress in Shaft, measured in Stress cannot be negative.

Which unit is used to measure Torsional Shear Stress given Principal Shear Stress in Shaft?

Torsional Shear Stress given Principal Shear Stress in Shaft 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 given Principal Shear Stress in Shaft can be measured.

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Torsional Shear Stress given Principal Shear Stress in Shaft Formula

​GoTorsional Shear Stress in Shaft Pure Torsion Formula

Torsional Shear Stress given Principal Shear Stress in Shaft Example

Torsional Shear Stress given Principal Shear Stress in Shaft Solution

Torsional Shear Stress given Principal Shear Stress in Shaft 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 given Principal Shear Stress in Shaft?

FAQs on Torsional Shear Stress given Principal Shear Stress in Shaft

Variable Name

GoTorsional Shear Stress in Shaft Pure Torsion Formula