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Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Formula

GoNormal Stress given Both Bending and Torsional act on Shaft Formula

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

σ x = 2 \cdot \sqrt{{τ max}^{2} - 𝜏^{2}}

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

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Example

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Here is how the Normal Stress given Principal Shear Stress in Shaft Bending and Torsion equation looks like with Values.

Here is how the Normal Stress given Principal Shear Stress in Shaft Bending and Torsion equation looks like with Units.

Here is how the Normal Stress given Principal Shear Stress in Shaft Bending and Torsion equation looks like.

250.6011 = 2 \cdot \sqrt{{126.355}^{2} - {16.29}^{2}}

250.6011N/mm² = 2 \cdot \sqrt{{126.355N/mm²}^{2} - {16.29N/mm²}^{2}}

250.6011 = 2 \cdot \sqrt{{126.355}^{2} - {16.29}^{2}}

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Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Solution

Follow our step by step solution on how to calculate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

FIRST Step Consider the formula

σ x = 2 \cdot \sqrt{{τ max}^{2} - 𝜏^{2}}

Next Step Substitute values of Variables

∴

σ x = 2 \cdot \sqrt{{126.355N/mm²}^{2} - {16.29N/mm²}^{2}}

Next Step Convert Units

∴

σ x = 2 \cdot \sqrt{{1.3E+8Pa}^{2} - {1.6E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ x = 2 \cdot \sqrt{{1.3E+8}^{2} - {1.6E+7}^{2}}

Next Step Evaluate

∴

σ x = 250601052.870893Pa

Next Step Convert to Output's Unit

∴

σ x = 250.601052870893N/mm²

LAST Step Rounding Answer

∴

σ x = 250.6011N/mm²

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Formula Elements

Variables

Functions

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

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

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

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 Normal Stress in Shaft

Go Normal Stress given Both Bending and Torsional act on Shaft

σ x = σ b + σ t

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 Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion evaluator uses Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2) to evaluate the Normal Stress in Shaft, Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a measure of the stress experienced by a shaft when it is subjected to both bending and torsional loads, providing a critical parameter in shaft design to ensure its strength and reliability. Normal Stress in Shaft is denoted by σ_x symbol.

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

FAQs on Normal Stress given Principal Shear Stress in Shaft Bending and Torsion

What is the formula to find Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

The formula of Normal Stress given Principal Shear Stress in Shaft Bending and Torsion is expressed as Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2). Here is an example- 0.000251 = 2*sqrt(126355000^2-16290000^2).

How to calculate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

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

What are the other ways to Calculate Normal Stress in Shaft?

Here are the different ways to Calculate Normal Stress in Shaft-

Normal Stress in Shaft=Bending Stress in Shaft+Tensile Stress in Shaft

Can the Normal Stress given Principal Shear Stress in Shaft Bending and Torsion be negative?

No, the Normal Stress given Principal Shear Stress in Shaft Bending and Torsion, measured in Stress cannot be negative.

Which unit is used to measure Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

Normal Stress given Principal Shear Stress in Shaft Bending and 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 Normal Stress given Principal Shear Stress in Shaft Bending and Torsion can be measured.

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Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Formula

​GoNormal Stress given Both Bending and Torsional act on Shaft Formula

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Example

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Solution

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Formula Elements

Other Formulas to find Normal Stress in Shaft

Other formulas in Shaft Design on Strength Basis category

How to Evaluate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

FAQs on Normal Stress given Principal Shear Stress in Shaft Bending and Torsion

Variable Name

GoNormal Stress given Both Bending and Torsional act on Shaft Formula