Factor of Safety given Permissible Value of Maximum Shear Stress Calculator

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Maximum Shear Stress and Principal Stress Theory

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Torsional Rigidity

✖Yield Strength in Shaft from MSST is the yield stress of the considered shaft from Maximum Shear Stress Theory.ⓘ Yield Strength in Shaft from MSST [σ_yt]			+10% -10%
✖Maximum Shear Stress in Shaft from MSST is maximum shear stress in a shaft calculated using Maximum Shear Stress Theory.ⓘ Maximum Shear Stress in Shaft from MSST [𝜏_{max MSST}]			+10% -10%

✖Factor of Safety of Shaft expresses how much stronger a shaft is than it needs to be for an intended load.ⓘ Factor of Safety given Permissible Value of Maximum Shear Stress [f_s]

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Formula

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Factor of Safety given Permissible Value of Maximum Shear Stress

Formula

`"f"_{"s"} = 0.5*"σ"_{"yt"}/"𝜏"_{"max MSST"}`

Example

`"1.88455"=0.5*"222N/mm²"/"58.9N/mm²"`

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Factor of Safety given Permissible Value of Maximum Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST
f_s = 0.5*σ_yt/𝜏_{max MSST}
This formula uses 3 Variables

Variables Used

Factor of Safety of Shaft - Factor of Safety of Shaft expresses how much stronger a shaft is than it needs to be for an intended load.
Yield Strength in Shaft from MSST - (Measured in Pascal) - Yield Strength in Shaft from MSST is the yield stress of the considered shaft from Maximum Shear Stress Theory.
Maximum Shear Stress in Shaft from MSST - (Measured in Pascal) - Maximum Shear Stress in Shaft from MSST is maximum shear stress in a shaft calculated using Maximum Shear Stress Theory.

STEP 1: Convert Input(s) to Base Unit

Yield Strength in Shaft from MSST: 222 Newton per Square Millimeter --> 222000000 Pascal (Check conversion here)
Maximum Shear Stress in Shaft from MSST: 58.9 Newton per Square Millimeter --> 58900000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = 0.5*σ_yt/𝜏_{max MSST} --> 0.5*222000000/58900000

Evaluating ... ...

f_s = 1.88455008488964

STEP 3: Convert Result to Output's Unit

1.88455008488964 --> No Conversion Required

FINAL ANSWER

1.88455008488964 ≈ 1.88455 <-- Factor of Safety of Shaft

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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< 17 Maximum Shear Stress and Principal Stress Theory Calculators

Factor of Safety for Tri-axial State of Stress

Go 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))

Diameter of Shaft given Permissible Value of Maximum Principle Stress

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

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))

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory

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

Bending Moment given Maximum Shear Stress

Go Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2)

Torsional Moment given Maximum Shear Stress

Go Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2)

Maximum Shear Stress in Shafts

Go Maximum Shear Stress in Shaft from MSST = 16/(pi*Diameter of Shaft from MSST^3)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)

Factor of Safety for Bi-Axial State of Stress

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

Torsional Moment given Equivalent Bending Moment

Go Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)

Equivalent Bending Moment given Torsional Moment

Go Equivalent Bending Moment from MSST = Bending Moment in Shaft for MSST+sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)

Factor of Safety given Permissible Value of Maximum Shear Stress

Go Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST

Yield Strength in Shear Maximum Shear Stress Theory

Go Shear Yield Strength in Shaft from MSST = 0.5*Factor of Safety of Shaft*Maximum Principle Stress in Shaft

Permissible Value of Maximum Shear Stress

Go Maximum Shear Stress in Shaft from MSST = 0.5*Yield Strength in Shaft from MSST/Factor of Safety of Shaft

Yield Stress in Shear given Permissible Value of Maximum Principle Stress

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

Permissible Value of Maximum Principle Stress using Factor of Safety

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

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

Factor of Safety given Ultimate Stress and Working Stress

Go Factor of Safety = Fracture Stress/Working Stress

Factor of Safety given Permissible Value of Maximum Shear Stress Formula

Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST
f_s = 0.5*σ_yt/𝜏_{max MSST}

Define Shear Stress

Shear stress, often denoted by τ, is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.

How to Calculate Factor of Safety given Permissible Value of Maximum Shear Stress?

Factor of Safety given Permissible Value of Maximum Shear Stress calculator uses Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST to calculate the Factor of Safety of Shaft, The Factor of Safety given Permissible Value of Maximum Shear Stress formula is defined as the ratio of the ultimate strength of a member or piece of material (as in an airplane) to the actual working stress or the maximum permissible stress when in use. Factor of Safety of Shaft is denoted by f_s symbol.

How to calculate Factor of Safety given Permissible Value of Maximum Shear Stress using this online calculator? To use this online calculator for Factor of Safety given Permissible Value of Maximum Shear Stress, enter Yield Strength in Shaft from MSST (σ_yt) & Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}) and hit the calculate button. Here is how the Factor of Safety given Permissible Value of Maximum Shear Stress calculation can be explained with given input values -> 1.88455 = 0.5*222000000/58900000.

FAQ

What is Factor of Safety given Permissible Value of Maximum Shear Stress?

The Factor of Safety given Permissible Value of Maximum Shear Stress formula is defined as the ratio of the ultimate strength of a member or piece of material (as in an airplane) to the actual working stress or the maximum permissible stress when in use and is represented as f_s = 0.5*σ_yt/𝜏_{max MSST} or Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST. Yield Strength in Shaft from MSST is the yield stress of the considered shaft from Maximum Shear Stress Theory & Maximum Shear Stress in Shaft from MSST is maximum shear stress in a shaft calculated using Maximum Shear Stress Theory.

How to calculate Factor of Safety given Permissible Value of Maximum Shear Stress?

The Factor of Safety given Permissible Value of Maximum Shear Stress formula is defined as the ratio of the ultimate strength of a member or piece of material (as in an airplane) to the actual working stress or the maximum permissible stress when in use is calculated using Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST. To calculate Factor of Safety given Permissible Value of Maximum Shear Stress, you need Yield Strength in Shaft from MSST (σ_yt) & Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}). With our tool, you need to enter the respective value for Yield Strength in Shaft from MSST & Maximum Shear Stress in Shaft from MSST 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 of Shaft?

In this formula, Factor of Safety of Shaft uses Yield Strength in Shaft from MSST & Maximum Shear Stress in Shaft from MSST. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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