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)
σe = 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
σe = 1/sqrt(2)*sqrt((σ12)^2+(σ23)^2+(σ31)^2) --> 1/sqrt(2)*sqrt((87.5-51.43)^2+(51.43-96.1)^2+(96.1-87.5)^2)
Evaluating ... ...
σe = 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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Osmania University (OU), Hyderabad
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Normal Stress Calculators

Normal Stress for Principal Planes at Angle of 0 Degrees given Major and Minor Tensile Stress
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2-(Major Tensile Stress-Minor Tensile Stress)/2
Normal Stress across Oblique Section
​ LaTeX ​ Go Normal Stress = Stress in Bar*(cos(Angle made by Oblique Section with Normal))^2

Equivalent Stress by Distortion Energy Theory Formula

​LaTeX ​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)
σe = 1/sqrt(2)*sqrt((σ1-σ2)^2+(σ2-σ3)^2+(σ3-σ1)^2)

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 σe 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 1), Normal Stress 2 2) & Normal Stress 3 3) 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 σe = 1/sqrt(2)*sqrt((σ12)^2+(σ23)^2+(σ31)^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 1), Normal Stress 2 2) & Normal Stress 3 3). 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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