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Factor of Safety for Bi-Axial State of Stress Formula

GoFactor of Safety given Ultimate Stress and Working Stress Formula

GoFactor of Safety for Tri-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{{σ 1}^{2} + {σ 2}^{2} - σ 1 \cdot σ 2}}

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

Factor of Safety for Bi-Axial State of Stress Example

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

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

Here is how the Factor of Safety for Bi-Axial State of Stress equation looks like.

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

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

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

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Design of Machine Elements » fx Factor of Safety for Bi-Axial State of Stress

Factor of Safety for Bi-Axial State of Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

fos = 3.00000060761927

LAST Step Rounding Answer

∴

fos = 3

Factor of Safety for Bi-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

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 Tri-axial State of Stress

fos = \frac{σ yt}{\sqrt{\frac{1}{2} \cdot ({(σ 1 - σ 2)}^{2} + {(σ 2 - σ 3)}^{2} + {(σ 3 - σ 1)}^{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 Bi-Axial State of Stress?

Factor of Safety for Bi-Axial State of Stress evaluator uses Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2)) to evaluate the Factor of Safety, Factor of Safety for Bi-Axial State of Stress formula is defined as a measure of the ability of a material to withstand failure under bi-axial stress conditions, providing a safety margin against failure by considering the maximum shear stress and principal stress theory. Factor of Safety is denoted by fos symbol.

How to evaluate Factor of Safety for Bi-Axial State of Stress using this online evaluator? To use this online evaluator for Factor of Safety for Bi-Axial State of Stress, enter Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁) & Normal Stress 2 (σ₂) and hit the calculate button.

FAQs on Factor of Safety for Bi-Axial State of Stress

What is the formula to find Factor of Safety for Bi-Axial State of Stress?

The formula of Factor of Safety for Bi-Axial State of Stress is expressed as Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2)). Here is an example- 3.000001 = 154289900/(sqrt(87.5^2+51430000^2-87.5*51430000)).

How to calculate Factor of Safety for Bi-Axial State of Stress?

With Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁) & Normal Stress 2 (σ₂) we can find Factor of Safety for Bi-Axial State of Stress using the formula - Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 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(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))

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