Equivalent Stress by Distortion Energy Theory Calculator

✖Normal Stress 1 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 1 [σ'₁]			+10% -10%
✖Normal Stress 2 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 2 [σ'₂]			+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 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((σ'₁-σ'₂)^2+(σ'₂-σ₃)^2+(σ₃-σ'₁)^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 - Normal Stress 1 is a stress that occurs when a member is loaded by an axial force.
Normal Stress 2 - (Measured in Pascal) - 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((σ'₁-σ'₂)^2+(σ'₂-σ₃)^2+(σ₃-σ'₁)^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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< Normal Stress Calculators

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

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, Equivalent Stress by Distortion Energy Theory formula is defined as a method to determine the stress state of a material under different types of loading conditions, providing a comprehensive understanding of the material's behavior under various principal stresses. 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 (σ'₁), Normal Stress 2 (σ'₂) & 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?

Equivalent Stress by Distortion Energy Theory formula is defined as a method to determine the stress state of a material under different types of loading conditions, providing a comprehensive understanding of the material's behavior under various principal stresses and is represented as σ_e = 1/sqrt(2)*sqrt((σ'₁-σ'₂)^2+(σ'₂-σ₃)^2+(σ₃-σ'₁)^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). Normal Stress 1 is a stress that occurs when a member is loaded by an axial force, 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?

Equivalent Stress by Distortion Energy Theory formula is defined as a method to determine the stress state of a material under different types of loading conditions, providing a comprehensive understanding of the material's behavior under various principal stresses 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 (σ'₁), Normal Stress 2 (σ'₂) & 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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