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Tensile Yield Strength by Distortion Energy Theorem Formula

GoTensile Yield Strength by Distortion Energy Theorem Considering Factor of Safety Formula

GoTensile Yield Strength for Biaxial Stress by Distortion Energy Theorem Considering Factor of Safety Formula

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Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions. Check FAQs

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

σ_y - Tensile Yield Strength?σ₁ - First Principal Stress?σ₂ - Second Principal Stress?σ₃ - Third Principal Stress?

Tensile Yield Strength by Distortion Energy Theorem Example

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Here is how the Tensile Yield Strength by Distortion Energy Theorem equation looks like with Values.

Here is how the Tensile Yield Strength by Distortion Energy Theorem equation looks like with Units.

Here is how the Tensile Yield Strength by Distortion Energy Theorem equation looks like.

25.9931 = \sqrt{\frac{1}{2} \cdot ({(35.2 - 47)}^{2} + {(47 - 65)}^{2} + {(65 - 35.2)}^{2})}

25.9931N/mm² = \sqrt{\frac{1}{2} \cdot ({(35.2N/mm² - 47N/mm²)}^{2} + {(47N/mm² - 65N/mm²)}^{2} + {(65N/mm² - 35.2N/mm²)}^{2})}

25.9931 = \sqrt{\frac{1}{2} \cdot ({(35.2 - 47)}^{2} + {(47 - 65)}^{2} + {(65 - 35.2)}^{2})}

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Tensile Yield Strength by Distortion Energy Theorem Solution

Follow our step by step solution on how to calculate Tensile Yield Strength by Distortion Energy Theorem?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ y = \sqrt{\frac{1}{2} \cdot ({(35.2N/mm² - 47N/mm²)}^{2} + {(47N/mm² - 65N/mm²)}^{2} + {(65N/mm² - 35.2N/mm²)}^{2})}

Next Step Convert Units

∴

σ y = \sqrt{\frac{1}{2} \cdot ({(3.5E+7Pa - 4.7E+7Pa)}^{2} + {(4.7E+7Pa - 6.5E+7Pa)}^{2} + {(6.5E+7Pa - 3.5E+7Pa)}^{2})}

Next Step Prepare to Evaluate

∴

σ y = \sqrt{\frac{1}{2} \cdot ({(3.5E+7 - 4.7E+7)}^{2} + {(4.7E+7 - 6.5E+7)}^{2} + {(6.5E+7 - 3.5E+7)}^{2})}

Next Step Evaluate

∴

σ y = 25993076.00112Pa

Next Step Convert to Output's Unit

∴

σ y = 25.99307600112N/mm²

LAST Step Rounding Answer

∴

σ y = 25.9931N/mm²

Tensile Yield Strength by Distortion Energy Theorem Formula Elements

Variables

Functions

Tensile Yield Strength

Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions.

Symbol: σ_y

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Tensile Yield Strength

First Principal Stress

First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

Symbol: σ₁

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find First Principal Stress

Second Principal Stress

Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

Symbol: σ₂

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Second Principal Stress

Third Principal Stress

Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

Symbol: σ₃

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Third Principal Stress

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 Tensile Yield Strength

Go Tensile Yield Strength by Distortion Energy Theorem Considering Factor of Safety

σ y = f s \cdot \sqrt{\frac{1}{2} \cdot ({(σ 1 - σ 2)}^{2} + {(σ 2 - σ 3)}^{2} + {(σ 3 - σ 1)}^{2})}

Go Tensile Yield Strength for Biaxial Stress by Distortion Energy Theorem Considering Factor of Safety

σ y = f s \cdot \sqrt{{σ 1}^{2} + {σ 2}^{2} - σ 1 \cdot σ 2}

Other formulas in Distortion Energy Theory category

Go Shear Yield Strength by Maximum Distortion Energy Theory

S sy = 0.577 \cdot σ y

Go Total Strain Energy per Unit Volume

U Total = U d + U v

Go Strain Energy due to Change in Volume given Volumetric Stress

U v = \frac{3}{2} \cdot σ v \cdot ε v

Go Stress due to Change in Volume with No Distortion

σ v = \frac{σ 1 + σ 2 + σ 3}{3}

How to Evaluate Tensile Yield Strength by Distortion Energy Theorem?

Tensile Yield Strength by Distortion Energy Theorem evaluator uses Tensile Yield Strength = sqrt(1/2*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2)) to evaluate the Tensile Yield Strength, Tensile yield strength by distortion energy theorem formula is defined as the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions. Tensile Yield Strength is denoted by σ_y symbol.

How to evaluate Tensile Yield Strength by Distortion Energy Theorem using this online evaluator? To use this online evaluator for Tensile Yield Strength by Distortion Energy Theorem, enter First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃) and hit the calculate button.

FAQs on Tensile Yield Strength by Distortion Energy Theorem

What is the formula to find Tensile Yield Strength by Distortion Energy Theorem?

The formula of Tensile Yield Strength by Distortion Energy Theorem is expressed as Tensile Yield Strength = sqrt(1/2*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2)). Here is an example- 2.6E-5 = sqrt(1/2*((35200000-47000000)^2+(47000000-65000000)^2+(65000000-35200000)^2)).

How to calculate Tensile Yield Strength by Distortion Energy Theorem?

With First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃) we can find Tensile Yield Strength by Distortion Energy Theorem using the formula - Tensile Yield Strength = sqrt(1/2*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Tensile Yield Strength?

Here are the different ways to Calculate Tensile Yield Strength-

Tensile Yield Strength=Factor of Safety*sqrt(1/2*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2))
Tensile Yield Strength=Factor of Safety*sqrt(First Principal Stress^2+Second Principal Stress^2-First Principal Stress*Second Principal Stress)

Can the Tensile Yield Strength by Distortion Energy Theorem be negative?

No, the Tensile Yield Strength by Distortion Energy Theorem, measured in Stress cannot be negative.

Which unit is used to measure Tensile Yield Strength by Distortion Energy Theorem?

Tensile Yield Strength by Distortion Energy Theorem 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 Tensile Yield Strength by Distortion Energy Theorem can be measured.

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Tensile Yield Strength by Distortion Energy Theorem Formula

​GoTensile Yield Strength by Distortion Energy Theorem Considering Factor of Safety Formula

​GoTensile Yield Strength for Biaxial Stress by Distortion Energy Theorem Considering Factor of Safety Formula

Tensile Yield Strength by Distortion Energy Theorem Example

Tensile Yield Strength by Distortion Energy Theorem Solution

Tensile Yield Strength by Distortion Energy Theorem Formula Elements

Other Formulas to find Tensile Yield Strength

Other formulas in Distortion Energy Theory category

How to Evaluate Tensile Yield Strength by Distortion Energy Theorem?

FAQs on Tensile Yield Strength by Distortion Energy Theorem

Variable Name

GoTensile Yield Strength by Distortion Energy Theorem Considering Factor of Safety Formula

GoTensile Yield Strength for Biaxial Stress by Distortion Energy Theorem Considering Factor of Safety Formula