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Distortion Strain Energy for Yielding Formula

GoDistortion Strain Energy Formula

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Strain Energy for Distortion with no volume change is defined as the energy stored in the body per unit volume due to deformation. Check FAQs

U d = \frac{(1 + 𝛎)}{3 \cdot E} \cdot {σ y}^{2}

U_d - Strain Energy for Distortion?𝛎 - Poisson's Ratio?E - Young's Modulus of Specimen?σ_y - Tensile Yield Strength?

Distortion Strain Energy for Yielding Example

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Here is how the Distortion Strain Energy for Yielding equation looks like with Values.

Here is how the Distortion Strain Energy for Yielding equation looks like with Units.

Here is how the Distortion Strain Energy for Yielding equation looks like.

16.4781 = \frac{(1 + 0.3)}{3 \cdot 190} \cdot 85^{2}

16.4781kJ/m³ = \frac{(1 + 0.3)}{3 \cdot 190GPa} \cdot {85N/mm²}^{2}

16.4781 = \frac{(1 + 0.3)}{3 \cdot 190} \cdot 85^{2}

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Distortion Strain Energy for Yielding Solution

Follow our step by step solution on how to calculate Distortion Strain Energy for Yielding?

FIRST Step Consider the formula

U d = \frac{(1 + 𝛎)}{3 \cdot E} \cdot {σ y}^{2}

Next Step Substitute values of Variables

∴

U d = \frac{(1 + 0.3)}{3 \cdot 190GPa} \cdot {85N/mm²}^{2}

Next Step Convert Units

∴

U d = \frac{(1 + 0.3)}{3 \cdot 1.9E+11Pa} \cdot {8.5E+7Pa}^{2}

Next Step Prepare to Evaluate

∴

U d = \frac{(1 + 0.3)}{3 \cdot 1.9E+11} \cdot {8.5E+7}^{2}

Next Step Evaluate

∴

U d = 16478.0701754386J/m³

Next Step Convert to Output's Unit

∴

U d = 16.4780701754386kJ/m³

LAST Step Rounding Answer

∴

U d = 16.4781kJ/m³

Distortion Strain Energy for Yielding Formula Elements

Variables

Strain Energy for Distortion

Strain Energy for Distortion with no volume change is defined as the energy stored in the body per unit volume due to deformation.

Symbol: U_d

Measurement: Energy DensityUnit: kJ/m³

Note: Value should be greater than 0.

Formulas to find Strain Energy for Distortion

Poisson's Ratio

Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 0.5.

Formulas to find Poisson's Ratio

Young's Modulus of Specimen

Young's Modulus of Specimen is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Young's Modulus of Specimen

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

Other Formulas to find Strain Energy for Distortion

Go Distortion Strain Energy

U d = \frac{(1 + 𝛎)}{6 \cdot E} \cdot ({(σ 1 - σ 2)}^{2} + {(σ 2 - σ 3)}^{2} + {(σ 3 - σ 1)}^{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 Distortion Strain Energy for Yielding?

Distortion Strain Energy for Yielding evaluator uses Strain Energy for Distortion = ((1+Poisson's Ratio))/(3*Young's Modulus of Specimen)*Tensile Yield Strength^2 to evaluate the Strain Energy for Distortion, Distortion Strain Energy for Yielding formula is defined as the energy stored in a body due to deformation. This energy is the energy stored when volume does not change with distortion. Strain Energy for Distortion is denoted by U_d symbol.

How to evaluate Distortion Strain Energy for Yielding using this online evaluator? To use this online evaluator for Distortion Strain Energy for Yielding, enter Poisson's Ratio (𝛎), Young's Modulus of Specimen (E) & Tensile Yield Strength (σ_y) and hit the calculate button.

FAQs on Distortion Strain Energy for Yielding

What is the formula to find Distortion Strain Energy for Yielding?

The formula of Distortion Strain Energy for Yielding is expressed as Strain Energy for Distortion = ((1+Poisson's Ratio))/(3*Young's Modulus of Specimen)*Tensile Yield Strength^2. Here is an example- 0.016478 = ((1+0.3))/(3*190000000000)*85000000^2.

How to calculate Distortion Strain Energy for Yielding?

With Poisson's Ratio (𝛎), Young's Modulus of Specimen (E) & Tensile Yield Strength (σ_y) we can find Distortion Strain Energy for Yielding using the formula - Strain Energy for Distortion = ((1+Poisson's Ratio))/(3*Young's Modulus of Specimen)*Tensile Yield Strength^2.

What are the other ways to Calculate Strain Energy for Distortion?

Here are the different ways to Calculate Strain Energy for Distortion-

Strain Energy for Distortion=((1+Poisson's Ratio))/(6*Young's Modulus of Specimen)*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2)

Can the Distortion Strain Energy for Yielding be negative?

No, the Distortion Strain Energy for Yielding, measured in Energy Density cannot be negative.

Which unit is used to measure Distortion Strain Energy for Yielding?

Distortion Strain Energy for Yielding is usually measured using the Kilojoule per Cubic Meter[kJ/m³] for Energy Density. Joule per Cubic Meter[kJ/m³], Megajoule per Cubic Meter[kJ/m³] are the few other units in which Distortion Strain Energy for Yielding can be measured.

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Distortion Strain Energy for Yielding Formula

​GoDistortion Strain Energy Formula

Distortion Strain Energy for Yielding Example

Distortion Strain Energy for Yielding Solution

Distortion Strain Energy for Yielding Formula Elements

Other Formulas to find Strain Energy for Distortion

Other formulas in Distortion Energy Theory category

How to Evaluate Distortion Strain Energy for Yielding?

FAQs on Distortion Strain Energy for Yielding

Variable Name

GoDistortion Strain Energy Formula