Equivalent Stress by Distortion Energy Theory Calculator

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✖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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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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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 9 Design of Coupling Calculators

Factor of Safety for Tri-axial State of Stress

Go Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))

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)

Factor of Safety for Bi-Axial State of Stress

Go Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))

Tensile Stress in Spigot

Go Tensile Stress = Tensile Force on Rods/((pi/4*Diameter of Spigot^(2))-(Diameter of Spigot*Thickness of Cotter))

Polar Moment of Inertia of Hollow Circular Shaft

Go Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32

Permissible Shear Stress for Cotter

Go Permissible Shear Stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter)

Permissible Shear Stress for Spigot

Go Permissible Shear Stress = Tensile Force on Rods/(2*Spigot Distance*Diameter of Spigot)

Stress Amplitude

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

Polar Moment of Inertia of Solid Circular Shaft

Go Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32

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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