Stress due to Change in Volume with No Distortion Calculator

✖First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component.ⓘ First Principal Stress [σ₁]			+10% -10%
✖Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component.ⓘ Second Principal Stress [σ₂]			+10% -10%
✖Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.ⓘ Third Principal Stress [σ₃]			+10% -10%

✖Stress for Volume Change is defined as the stress in the specimen for a given volume change.ⓘ Stress due to Change in Volume with No Distortion [σ_v]

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Formula

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Stress due to Change in Volume with No Distortion

Formula

`"σ"_{"v"} = ("σ"_{"1"}+"σ"_{"2"}+"σ"_{"3"})/3`

Example

`"49N/mm²"=("35N/mm²"+"47N/mm²"+"65N/mm²")/3`

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Stress due to Change in Volume with No Distortion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3
σ_v = (σ₁+σ₂+σ₃)/3
This formula uses 4 Variables

Variables Used

Stress for Volume Change - (Measured in Pascal) - Stress for Volume Change is defined as the stress in the specimen for a given volume change.
First Principal Stress - (Measured in Pascal) - First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component.
Second Principal Stress - (Measured in Pascal) - Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component.
Third Principal Stress - (Measured in Pascal) - Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

STEP 1: Convert Input(s) to Base Unit

First Principal Stress: 35 Newton per Square Millimeter --> 35000000 Pascal (Check conversion here)
Second Principal Stress: 47 Newton per Square Millimeter --> 47000000 Pascal (Check conversion here)
Third Principal Stress: 65 Newton per Square Millimeter --> 65000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_v = (σ₁+σ₂+σ₃)/3 --> (35000000+47000000+65000000)/3

Evaluating ... ...

σ_v = 49000000

STEP 3: Convert Result to Output's Unit

49000000 Pascal -->49 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

49 Newton per Square Millimeter <-- Stress for Volume Change

(Calculation completed in 00.021 seconds)

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Credits

Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Sagar S Kulkarni

Dayananda Sagar College of Engineering (DSCE), Bengaluru

Sagar S Kulkarni has verified this Calculator and 200+ more calculators!

< 13 Distortion Energy Theory Calculators

Distortion Strain Energy

Go 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)

Tensile Yield Strength by Distortion Energy Theorem Considering Factor of Safety

Go 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 by Distortion Energy Theorem

Go 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))

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

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

Strain Energy due to Change in Volume given Principal Stresses

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

Strain Energy due to Change in Volume with No Distortion

Go Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen

Distortion Strain Energy for Yielding

Go Strain Energy for Distortion = ((1+Poisson's Ratio))/(3*Young's Modulus of Specimen)*Tensile Yield Strength^2

Volumetric Strain with No Distortion

Go Strain for Volume Change = ((1-2*Poisson's Ratio)*Stress for Volume Change)/Young's Modulus of Specimen

Stress due to Change in Volume with No Distortion

Go Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3

Total Strain Energy per Unit Volume

Go Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change

Strain Energy due to Change in Volume given Volumetric Stress

Go Strain Energy for Volume Change = 3/2*Stress for Volume Change*Strain for Volume Change

Shear Yield Strength by Maximum Distortion Energy Theorem

Go Shear Yield Strength = 0.577*Tensile Yield Strength

Shear Yield Strength by Maximum Distortion Energy Theory

Go Shear Yield Strength = 0.577*Tensile Yield Strength

Stress due to Change in Volume with No Distortion Formula

Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3
σ_v = (σ₁+σ₂+σ₃)/3

What is strain energy?

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape. It is usually denoted by U.

How to Calculate Stress due to Change in Volume with No Distortion?

Stress due to Change in Volume with No Distortion calculator uses Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3 to calculate the Stress for Volume Change, Stress due to change in volume with no distortion formula is defined as the average of the principal stresses. Stress for Volume Change is denoted by σ_v symbol.

How to calculate Stress due to Change in Volume with No Distortion using this online calculator? To use this online calculator for Stress due to Change in Volume with No Distortion, enter First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃) and hit the calculate button. Here is how the Stress due to Change in Volume with No Distortion calculation can be explained with given input values -> 4.9E-5 = (35000000+47000000+65000000)/3.

FAQ

What is Stress due to Change in Volume with No Distortion?

Stress due to change in volume with no distortion formula is defined as the average of the principal stresses and is represented as σ_v = (σ₁+σ₂+σ₃)/3 or Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3. First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component, Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component & Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

How to calculate Stress due to Change in Volume with No Distortion?

Stress due to change in volume with no distortion formula is defined as the average of the principal stresses is calculated using Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3. To calculate Stress due to Change in Volume with No Distortion, you need First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃). With our tool, you need to enter the respective value for First Principal Stress, Second Principal Stress & Third Principal Stress and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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