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Factor of Safety for Tri-axial State of Stress Formula

GoFactor of Safety given Ultimate Stress and Working Stress Formula

GoFactor of Safety for Bi-Axial State of Stress Formula

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Factor of Safety is the ratio of maximum shear stress a material can withstand to the maximum shear stress it is subjected to. Check FAQs

fos = \frac{σ yt}{\sqrt{\frac{1}{2} \cdot ({(σ 1 - σ 2)}^{2} + {(σ 2 - σ 3)}^{2} + {(σ 3 - σ 1)}^{2})}}

fos - Factor of Safety?σ_yt - Tensile Yield Strength?σ₁ - Normal Stress 1?σ₂ - Normal Stress 2?σ₃ - Normal Stress 3?

Factor of Safety for Tri-axial State of Stress Example

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Here is how the Factor of Safety for Tri-axial State of Stress equation looks like with Values.

Here is how the Factor of Safety for Tri-axial State of Stress equation looks like with Units.

Here is how the Factor of Safety for Tri-axial State of Stress equation looks like.

3 = \frac{154.2899}{\sqrt{\frac{1}{2} \cdot ({(87.5 - 51.43)}^{2} + {(51.43 - 51.43)}^{2} + {(51.43 - 87.5)}^{2})}}

3 = \frac{154.2899N/mm²}{\sqrt{\frac{1}{2} \cdot ({(87.5 - 51.43N/mm²)}^{2} + {(51.43N/mm² - 51.43N/mm²)}^{2} + {(51.43N/mm² - 87.5)}^{2})}}

3 = \frac{154.2899}{\sqrt{\frac{1}{2} \cdot ({(87.5 - 51.43)}^{2} + {(51.43 - 51.43)}^{2} + {(51.43 - 87.5)}^{2})}}

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Design of Machine Elements » fx Factor of Safety for Tri-axial State of Stress

Factor of Safety for Tri-axial State of Stress Solution

Follow our step by step solution on how to calculate Factor of Safety for Tri-axial State of Stress?

FIRST Step Consider the formula

fos = \frac{σ yt}{\sqrt{\frac{1}{2} \cdot ({(σ 1 - σ 2)}^{2} + {(σ 2 - σ 3)}^{2} + {(σ 3 - σ 1)}^{2})}}

Next Step Substitute values of Variables

∴

fos = \frac{154.2899N/mm²}{\sqrt{\frac{1}{2} \cdot ({(87.5 - 51.43N/mm²)}^{2} + {(51.43N/mm² - 51.43N/mm²)}^{2} + {(51.43N/mm² - 87.5)}^{2})}}

Next Step Convert Units

∴

fos = \frac{1.5E+8Pa}{\sqrt{\frac{1}{2} \cdot ({(87.5 - 5.1E+7Pa)}^{2} + {(5.1E+7Pa - 5.1E+7Pa)}^{2} + {(5.1E+7Pa - 87.5)}^{2})}}

Next Step Prepare to Evaluate

∴

fos = \frac{1.5E+8}{\sqrt{\frac{1}{2} \cdot ({(87.5 - 5.1E+7)}^{2} + {(5.1E+7 - 5.1E+7)}^{2} + {(5.1E+7 - 87.5)}^{2})}}

Next Step Evaluate

∴

fos = 3.00000315963983

LAST Step Rounding Answer

∴

fos = 3

Factor of Safety for Tri-axial State of Stress Formula Elements

Variables

Functions

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.

Symbol: fos

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

Tensile Yield Strength

Tensile Yield Strength is the maximum stress a material can withstand without permanent deformation, used in Principal Stress Theory to analyze material failure.

Symbol: σ_yt

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Tensile Yield Strength

Normal Stress 1

Normal Stress 1 is the maximum normal stress that occurs on a plane perpendicular to the direction of maximum shear stress.

Symbol: σ₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Normal Stress 1

Normal Stress 2

Normal Stress 2 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.

Symbol: σ₂

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Normal Stress 2

Normal Stress 3

Normal Stress 3 is a type of stress that occurs when a material is subjected to a combination of normal and shear stresses simultaneously.

Symbol: σ₃

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Normal Stress 3

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.

Syntax: sqrt(Number)

Other Formulas to find Factor of Safety

Go Factor of Safety given Ultimate Stress and Working Stress

fos = \frac{f s}{W s}

Go Factor of Safety for Bi-Axial State of Stress

fos = \frac{σ yt}{\sqrt{{σ 1}^{2} + {σ 2}^{2} - σ 1 \cdot σ 2}}

Other formulas in Design Parameters category

Go Permissible Value of Maximum Principle Stress

σ max = \frac{16}{π \cdot {d MPST}^{3}} \cdot (M b + \sqrt{{M b}^{2} + {Mt shaft}^{2}})

Go Diameter of Shaft given Permissible Value of Maximum Principle Stress

d MPST = {(\frac{16}{π \cdot σ max} \cdot (M b + \sqrt{{M b}^{2} + {Mt shaft}^{2}}))}^{\frac{1}{3}}

Go Permissible Value of Maximum Principle Stress using Factor of Safety

σ max = \frac{F ce}{fos shaft}

Go Factor of Safety given Permissible Value of Maximum Principle Stress

fos shaft = \frac{F ce}{σ max}

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

Factor of Safety for Tri-axial State of Stress evaluator 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 evaluate 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 evaluate Factor of Safety for Tri-axial State of Stress using this online evaluator? To use this online evaluator 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.

FAQs on Factor of Safety for Tri-axial State of Stress

What is the formula to find Factor of Safety for Tri-axial State of Stress?

The formula of Factor of Safety for Tri-axial State of Stress is expressed as 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)). Here is an example- 3.000003 = 154289900/sqrt(1/2*((87.5-51430000)^2+(51430000-51430000)^2+(51430000-87.5)^2)).

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

With Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃) we can find Factor of Safety for Tri-axial State of Stress using the formula - 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)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Factor of Safety?

Here are the different ways to Calculate Factor of Safety-

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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Factor of Safety for Tri-axial State of Stress Formula

​GoFactor of Safety given Ultimate Stress and Working Stress Formula

​GoFactor of Safety for Bi-Axial State of Stress Formula

Factor of Safety for Tri-axial State of Stress Example

Factor of Safety for Tri-axial State of Stress Solution

Factor of Safety for Tri-axial State of Stress Formula Elements

Other Formulas to find Factor of Safety

Other formulas in Design Parameters category

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

FAQs on Factor of Safety for Tri-axial State of Stress

Variable Name

GoFactor of Safety given Ultimate Stress and Working Stress Formula

GoFactor of Safety for Bi-Axial State of Stress Formula