✖A normal stress 1 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 1 [σ₁]			+10% -10%
✖A normal stress 2 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 2 [σ₂]			+10% -10%
✖Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 3 [σ₃]			+10% -10%

✖The Equivalent Stress is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved.ⓘ Equivalent Stress by Distortion Energy Theory [σ_e]

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Formula

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Equivalent Stress by Distortion Energy Theory

Formula

`"σ"_{"e"} = 1/sqrt(2)*sqrt(("σ"_{"1"}-"σ"_{"2"})^2+("σ"_{"2"}-"σ"_{"3"})^2+("σ"_{"3"}-"σ"_{"1"})^2)`

Example

`"41.05127N/m²"=1/sqrt(2)*sqrt(("87.5"-"51.43N/m²")^2+("51.43N/m²"-"96.1N/m²")^2+("96.1N/m²"-"87.5")^2)`

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Equivalent Stress by Distortion Energy Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
σ_e = 1/sqrt(2)*sqrt((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Equivalent Stress - (Measured in Pascal) - The Equivalent Stress is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved.
Normal Stress 1 - A normal stress 1 is a stress that occurs when a member is loaded by an axial force.
Normal Stress 2 - (Measured in Pascal) - A normal stress 2 is a stress that occurs when a member is loaded by an axial force.
Normal Stress 3 - (Measured in Pascal) - Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.

STEP 1: Convert Input(s) to Base Unit

Normal Stress 1: 87.5 --> No Conversion Required
Normal Stress 2: 51.43 Newton per Square Meter --> 51.43 Pascal (Check conversion here)
Normal Stress 3: 96.1 Newton per Square Meter --> 96.1 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_e = 1/sqrt(2)*sqrt((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2) --> 1/sqrt(2)*sqrt((87.5-51.43)^2+(51.43-96.1)^2+(96.1-87.5)^2)

Evaluating ... ...

σ_e = 41.0512716002805

STEP 3: Convert Result to Output's Unit

41.0512716002805 Pascal -->41.0512716002805 Newton per Square Meter (Check conversion here)

FINAL ANSWER

41.0512716002805 ≈ 41.05127 Newton per Square Meter <-- Equivalent Stress

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Stress and Strain » Principal Stresses and Strains » Principal Stresses » Mechanical » Normal Stress » Equivalent Stress by Distortion Energy Theory

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< 8 Normal Stress Calculators

Equivalent Stress by Distortion Energy Theory

Go 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)

Normal Stress on Oblique Section given Stress in Perpendicular Directions

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2*cos(2*Angle made by Oblique Section with Normal)

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

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2

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

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2

Normal Stress for Principal Planes at Angle of 90 degrees

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2-(Major Tensile Stress-Minor Tensile Stress)/2

Normal Stress across Oblique Section

Go Normal Stress = Stress in Bar*(cos(Angle made by Oblique Section with Normal))^2

Normal Stress using Obliquity

Go Normal Stress = Shear Stress/tan(Angle of Obliquity)

Stress Amplitude

Go Stress Amplitude = (Maximum Stress at Crack Tip-Minimum Stress)/2

Equivalent Stress by Distortion Energy Theory Formula

Define Distortion energy theory?

The distortion energy theory says that failure occurs due to distortion of a part, not due to volumetric changes in the part (distortion causes shearing, but volumetric changes due not). As examples: Rocks below the earth's surface.

How to Calculate Equivalent Stress by Distortion Energy Theory?

Equivalent Stress by Distortion Energy Theory calculator 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 calculate the Equivalent Stress, The Equivalent Stress by Distortion Energy Theory is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved. Equivalent Stress is denoted by σ_e symbol.

How to calculate Equivalent Stress by Distortion Energy Theory using this online calculator? To use this online calculator for Equivalent Stress by Distortion Energy Theory, enter Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃) and hit the calculate button. Here is how the Equivalent Stress by Distortion Energy Theory calculation can be explained with given input values -> 41.05127 = 1/sqrt(2)*sqrt((87.5-51.43)^2+(51.43-96.1)^2+(96.1-87.5)^2).

FAQ

What is Equivalent Stress by Distortion Energy Theory?

The Equivalent Stress by Distortion Energy Theory is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved and is represented as σ_e = 1/sqrt(2)*sqrt((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2) or 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). A normal stress 1 is a stress that occurs when a member is loaded by an axial force, A normal stress 2 is a stress that occurs when a member is loaded by an axial force & Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.

How to calculate Equivalent Stress by Distortion Energy Theory?

The Equivalent Stress by Distortion Energy Theory is the value of uniaxial tensile stress that would produce the same level of distortion energy as the actual stresses involved is calculated using 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 calculate Equivalent Stress by Distortion Energy Theory, you need Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃). With our tool, you need to enter the respective value for Normal Stress 1, Normal Stress 2 & Normal Stress 3 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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