Factor of Safety for Tri-axial State of Stress Calculator

✖Tensile Yield Strength is the maximum stress a material can withstand without permanent deformation, used in Principal Stress Theory to analyze material failure.ⓘ Tensile Yield Strength [σ_yt]			+10% -10%
✖Normal Stress 1 is the maximum normal stress that occurs on a plane perpendicular to the direction of maximum shear stress.ⓘ Normal Stress 1 [σ₁]			+10% -10%
✖Normal Stress 2 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.ⓘ Normal Stress 2 [σ₂]			+10% -10%
✖Normal Stress 3 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.ⓘ Normal Stress 3 [σ₃]			+10% -10%

✖Factor of Safety is the ratio of maximum shear stress a material can withstand to the maximum shear stress it is subjected to.ⓘ Factor of Safety for Tri-axial State of Stress [fos]

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Factor of Safety for Tri-axial State of Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
fos = σ_yt/sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2))
This formula uses 1 Functions, 5 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

Factor of Safety - Factor of Safety is the ratio of maximum shear stress a material can withstand to the maximum shear stress it is subjected to.
Tensile Yield Strength - (Measured in Pascal) - Tensile Yield Strength is the maximum stress a material can withstand without permanent deformation, used in Principal Stress Theory to analyze material failure.
Normal Stress 1 - Normal Stress 1 is the maximum normal stress that occurs on a plane perpendicular to the direction of maximum shear stress.
Normal Stress 2 - (Measured in Pascal) - Normal Stress 2 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.
Normal Stress 3 - (Measured in Pascal) - Normal Stress 3 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.

STEP 1: Convert Input(s) to Base Unit

Tensile Yield Strength: 154.2899 Newton per Square Millimeter --> 154289900 Pascal (Check conversion here)
Normal Stress 1: 87.5 --> No Conversion Required
Normal Stress 2: 51.43 Newton per Square Millimeter --> 51430000 Pascal (Check conversion here)
Normal Stress 3: 51.43 Newton per Square Millimeter --> 51430000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

fos = σ_yt/sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)) --> 154289900/sqrt(1/2*((87.5-51430000)^2+(51430000-51430000)^2+(51430000-87.5)^2))

Evaluating ... ...

fos = 3.00000315963983

STEP 3: Convert Result to Output's Unit

3.00000315963983 --> No Conversion Required

FINAL ANSWER

3.00000315963983 ≈ 3.000003 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Coupling » Design of Bushed Pin Flexible Coupling » Mechanical » Design Parameters » Factor of Safety for Tri-axial State of Stress

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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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< Design Parameters Calculators

Effective Length of Bush in Contact with Input Flange of Bushed Pin Coupling

LaTeX Go Effective Length of Bush of Coupling = Force on Each Rubber Bush or Pin of Coupling/(Outer Diameter of Bush For Coupling*Intensity of Pressure Between Flange of Coupling)

Thickness of Protective Rim of Coupling

LaTeX Go Thickness of Protecting Rim For Coupling = 0.25*Diameter of Driving Shaft For Coupling

Thickness of Output Flange of Coupling

LaTeX Go Thickness of Output Flange of Coupling = 0.5*Diameter of Driving Shaft For Coupling

Length of Hub of Bushed Pin Coupling given Diameter of Driving Shaft

LaTeX Go Length of Hub For Coupling = 1.5*Diameter of Driving Shaft For Coupling

< Maximum Shear Stress and Principal Stress Theory Calculators

Diameter of Shaft given Permissible Value of Maximum Principle Stress

LaTeX Go Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3)

Permissible Value of Maximum Principle Stress

LaTeX Go Maximum Principle Stress in Shaft = 16/(pi*Diameter of Shaft from MPST^3)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2))

Permissible Value of Maximum Principle Stress using Factor of Safety

LaTeX Go Maximum Principle Stress in Shaft = Yield Strength in Shaft from MPST/Factor of Safety of Shaft

Factor of Safety given Permissible Value of Maximum Principle Stress

LaTeX Go Factor of Safety of Shaft = Yield Strength in Shaft from MPST/Maximum Principle Stress in Shaft

Factor of Safety for Tri-axial State of Stress Formula

LaTeX Go

What is Tri-Axial State of Stress?

A tri-axial state of stress occurs when a material at a point is subjected to normal stresses along all three mutually perpendicular axes (x, y, and z). This means the object experiences stress in three directions simultaneously, typically involving complex loading conditions. It is commonly seen in structures subjected to high pressure or compressive forces from multiple sides, such as in pressure vessels or deep underground formations. Understanding the tri-axial state of stress is essential for accurately assessing material behavior under such conditions and preventing failure.

How to Calculate Factor of Safety for Tri-axial State of Stress?

Factor of Safety for Tri-axial State of Stress calculator uses 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)) to calculate the Factor of Safety, Factor of Safety for Tri-axial State of Stress formula is defined as a measure of the ability of a material to withstand external loads without failing, considering the maximum shear stress and principal stress theory in a tri-axial state of stress. Factor of Safety is denoted by fos symbol.

How to calculate Factor of Safety for Tri-axial State of Stress using this online calculator? To use this online calculator for Factor of Safety for Tri-axial State of Stress, enter Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃) and hit the calculate button. Here is how the Factor of Safety for Tri-axial State of Stress calculation can be explained with given input values -> 3.000003 = 154289900/sqrt(1/2*((87.5-51430000)^2+(51430000-51430000)^2+(51430000-87.5)^2)).

FAQ

What is Factor of Safety for Tri-axial State of Stress?

Factor of Safety for Tri-axial State of Stress formula is defined as a measure of the ability of a material to withstand external loads without failing, considering the maximum shear stress and principal stress theory in a tri-axial state of stress and is represented as fos = σ_yt/sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)) or 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)). Tensile Yield Strength is the maximum stress a material can withstand without permanent deformation, used in Principal Stress Theory to analyze material failure, Normal Stress 1 is the maximum normal stress that occurs on a plane perpendicular to the direction of maximum shear stress, Normal Stress 2 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously & Normal Stress 3 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.

How to calculate Factor of Safety for Tri-axial State of Stress?

Factor of Safety for Tri-axial State of Stress formula is defined as a measure of the ability of a material to withstand external loads without failing, considering the maximum shear stress and principal stress theory in a tri-axial state of stress is calculated using 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)). To calculate Factor of Safety for Tri-axial State of Stress, you need Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃). With our tool, you need to enter the respective value for Tensile Yield Strength, 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.

How many ways are there to calculate Factor of Safety?

In this formula, Factor of Safety uses Tensile Yield Strength, Normal Stress 1, Normal Stress 2 & Normal Stress 3. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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