Tensile Yield Strength by Distortion Energy Theorem 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%

✖Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions.ⓘ Tensile Yield Strength by Distortion Energy Theorem [σ_y]

⎘ Copy

👎

Formula

Reset

👍

Download Mechanical Formula PDF PDF Image

Tensile Yield Strength by Distortion Energy Theorem Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σ_y = sqrt(1/2*((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

Tensile Yield Strength - (Measured in Pascal) - Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions.
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: 35.2 Newton per Square Millimeter --> 35200000 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_y = sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)) --> sqrt(1/2*((35200000-47000000)^2+(47000000-65000000)^2+(65000000-35200000)^2))

Evaluating ... ...

σ_y = 25993076.00112

STEP 3: Convert Result to Output's Unit

25993076.00112 Pascal -->25.99307600112 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

25.99307600112 ≈ 25.99308 Newton per Square Millimeter <-- Tensile Yield Strength

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Machine Design » Design Against Static Load » Theories of Failure » Distortion Energy Theory » Tensile Yield Strength by Distortion Energy Theorem

Credits

Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< Distortion Energy Theory Calculators

Stress due to Change in Volume with No Distortion

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

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

Total Strain Energy per Unit Volume

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

Shear Yield Strength by Maximum Distortion Energy Theory

Go Shear Yield Strength = 0.577*Tensile Yield Strength

Tensile Yield Strength by Distortion Energy Theorem Formula

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 Tensile Yield Strength by Distortion Energy Theorem?

Tensile Yield Strength by Distortion Energy Theorem calculator uses 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)) to calculate the Tensile Yield Strength, Tensile yield strength by distortion energy theorem formula is defined as the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions. Tensile Yield Strength is denoted by σ_y symbol.

How to calculate Tensile Yield Strength by Distortion Energy Theorem using this online calculator? To use this online calculator for Tensile Yield Strength by Distortion Energy Theorem, enter First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃) and hit the calculate button. Here is how the Tensile Yield Strength by Distortion Energy Theorem calculation can be explained with given input values -> 2.6E-5 = sqrt(1/2*((35200000-47000000)^2+(47000000-65000000)^2+(65000000-35200000)^2)).

FAQ

What is Tensile Yield Strength by Distortion Energy Theorem?

Tensile yield strength by distortion energy theorem formula is defined as the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions and is represented as σ_y = sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)) or 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)). 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 Tensile Yield Strength by Distortion Energy Theorem?

Tensile yield strength by distortion energy theorem formula is defined as the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions is calculated using 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)). To calculate Tensile Yield Strength by Distortion Energy Theorem, 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.

How many ways are there to calculate Tensile Yield Strength?

In this formula, Tensile Yield Strength uses First Principal Stress, Second Principal Stress & Third Principal Stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search