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Equivalent Stress by Distortion Energy Theory Formula

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The Equivalent Stress is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved. Check FAQs

σ e = \frac{1}{\sqrt{2}} \cdot \sqrt{{(σ' 1 - σ' 2)}^{2} + {(σ' 2 - σ 3)}^{2} + {(σ 3 - σ' 1)}^{2}}

σ_e - Equivalent Stress?σ'₁ - Normal Stress 1?σ'₂ - Normal Stress 2?σ₃ - Normal Stress 3?

Equivalent Stress by Distortion Energy Theory Example

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Here is how the Equivalent Stress by Distortion Energy Theory equation looks like with Values.

Here is how the Equivalent Stress by Distortion Energy Theory equation looks like with Units.

Here is how the Equivalent Stress by Distortion Energy Theory equation looks like.

41.0513 = \frac{1}{\sqrt{2}} \cdot \sqrt{{(87.5 - 51.43)}^{2} + {(51.43 - 96.1)}^{2} + {(96.1 - 87.5)}^{2}}

41.0513N/m² = \frac{1}{\sqrt{2}} \cdot \sqrt{{(87.5 - 51.43N/m²)}^{2} + {(51.43N/m² - 96.1N/m²)}^{2} + {(96.1N/m² - 87.5)}^{2}}

41.0513 = \frac{1}{\sqrt{2}} \cdot \sqrt{{(87.5 - 51.43)}^{2} + {(51.43 - 96.1)}^{2} + {(96.1 - 87.5)}^{2}}

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Equivalent Stress by Distortion Energy Theory Solution

Follow our step by step solution on how to calculate Equivalent Stress by Distortion Energy Theory?

FIRST Step Consider the formula

σ e = \frac{1}{\sqrt{2}} \cdot \sqrt{{(σ' 1 - σ' 2)}^{2} + {(σ' 2 - σ 3)}^{2} + {(σ 3 - σ' 1)}^{2}}

Next Step Substitute values of Variables

∴

σ e = \frac{1}{\sqrt{2}} \cdot \sqrt{{(87.5 - 51.43N/m²)}^{2} + {(51.43N/m² - 96.1N/m²)}^{2} + {(96.1N/m² - 87.5)}^{2}}

Next Step Convert Units

∴

σ e = \frac{1}{\sqrt{2}} \cdot \sqrt{{(87.5 - 51.43Pa)}^{2} + {(51.43Pa - 96.1Pa)}^{2} + {(96.1Pa - 87.5)}^{2}}

Next Step Prepare to Evaluate

∴

σ e = \frac{1}{\sqrt{2}} \cdot \sqrt{{(87.5 - 51.43)}^{2} + {(51.43 - 96.1)}^{2} + {(96.1 - 87.5)}^{2}}

Next Step Evaluate

∴

σ e = 41.0512716002805Pa

Next Step Convert to Output's Unit

∴

σ e = 41.0512716002805N/m²

LAST Step Rounding Answer

∴

σ e = 41.0513N/m²

Equivalent Stress by Distortion Energy Theory Formula Elements

Variables

Functions

Equivalent Stress

The Equivalent Stress is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved.

Symbol: σ_e

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Equivalent Stress

Normal Stress 1

Normal Stress 1 is a stress that occurs when a member is loaded by an axial force.

Symbol: σ'₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Normal Stress 1

Normal Stress 2

Normal Stress 2 is a stress that occurs when a member is loaded by an axial force.

Symbol: σ'₂

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Normal Stress 2

Normal Stress 3

Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.

Symbol: σ₃

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Normal Stress 3

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 in Normal Stress category

Go Normal Stress across Oblique Section

σ n = σ \cdot {(\cos (θ o))}^{2}

Go Normal Stress for Principal Planes at Angle of 0 Degrees given Major and Minor Tensile Stress

σ n = \frac{σ 1 + σ 2}{2} + \frac{σ 1 - σ 2}{2}

Go Normal Stress for Principal Planes at Angle of 90 degrees

σ n = \frac{σ 1 + σ 2}{2} - \frac{σ 1 - σ 2}{2}

Go Normal Stress for Principal Planes when Planes are at Angle of 0 Degree

σ n = \frac{σ 1 + σ 2}{2} + \frac{σ 1 - σ 2}{2}

How to Evaluate Equivalent Stress by Distortion Energy Theory?

Equivalent Stress by Distortion Energy Theory evaluator uses Equivalent Stress = 1/sqrt(2)*sqrt((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2) to evaluate the Equivalent Stress, Equivalent Stress by Distortion Energy Theory formula is defined as a method to determine the stress state of a material under different types of loading conditions, providing a comprehensive understanding of the material's behavior under various principal stresses. Equivalent Stress is denoted by σ_e symbol.

How to evaluate Equivalent Stress by Distortion Energy Theory using this online evaluator? To use this online evaluator for Equivalent Stress by Distortion Energy Theory, enter Normal Stress 1 (σ'₁), Normal Stress 2 (σ'₂) & Normal Stress 3 (σ₃) and hit the calculate button.

FAQs on Equivalent Stress by Distortion Energy Theory

What is the formula to find Equivalent Stress by Distortion Energy Theory?

The formula of Equivalent Stress by Distortion Energy Theory is expressed as Equivalent Stress = 1/sqrt(2)*sqrt((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2). Here is an example- 41.05127 = 1/sqrt(2)*sqrt((87.5-51.43)^2+(51.43-96.1)^2+(96.1-87.5)^2).

How to calculate Equivalent Stress by Distortion Energy Theory?

With Normal Stress 1 (σ'₁), Normal Stress 2 (σ'₂) & Normal Stress 3 (σ₃) we can find Equivalent Stress by Distortion Energy Theory using the formula - Equivalent Stress = 1/sqrt(2)*sqrt((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2). This formula also uses Square Root (sqrt) function(s).

Can the Equivalent Stress by Distortion Energy Theory be negative?

Yes, the Equivalent Stress by Distortion Energy Theory, measured in Pressure can be negative.

Which unit is used to measure Equivalent Stress by Distortion Energy Theory?

Equivalent Stress by Distortion Energy Theory is usually measured using the Newton per Square Meter[N/m²] for Pressure. Pascal[N/m²], Kilopascal[N/m²], Bar[N/m²] are the few other units in which Equivalent Stress by Distortion Energy Theory can be measured.

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Equivalent Stress by Distortion Energy Theory Formula

Equivalent Stress by Distortion Energy Theory Example

Equivalent Stress by Distortion Energy Theory Solution

Equivalent Stress by Distortion Energy Theory Formula Elements

Other formulas in Normal Stress category

How to Evaluate Equivalent Stress by Distortion Energy Theory?

FAQs on Equivalent Stress by Distortion Energy Theory

Variable Name