Diameter of Shaft given Permissible Value of Maximum Principle Stress Calculator

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Maximum Shear Stress and Principal Stress Theory

ASME Code for Shaft Desgin

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Shaft Design on Strength Basis

Torsional Rigidity

✖Maximum Principle Stress in Shaft is defined as the normal stress calculated in the shaft at an angle when shear stress is considered zero.ⓘ Maximum Principle Stress in Shaft [σ₁]			+10% -10%
✖Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Shaft [M_b]			+10% -10%
✖Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment in Shaft [Mt_shaft]			+10% -10%

✖Diameter of Shaft from MPST is the diameter of the shaft according to the Maximum Principal Stress Theory.ⓘ Diameter of Shaft given Permissible Value of Maximum Principle Stress [d_MPST]

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Formula

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Diameter of Shaft given Permissible Value of Maximum Principle Stress

Formula

`"d"_{"MPST"} = (16/(pi*"σ"_{"1"})*("M"_{"b"}+sqrt("M"_{"b"}^2+"Mt"_{"shaft"}^2)))^(1/3)`

Example

`"51.50622mm"=(16/(pi*"135.3N/mm²")*("1.8E6N*mm"+sqrt(("1.8E6N*mm")^2+("3.3E5N*mm")^2)))^(1/3)`

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Diameter of Shaft given Permissible Value of Maximum Principle Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
d_MPST = (16/(pi*σ₁)*(M_b+sqrt(M_b^2+Mt_shaft^2)))^(1/3)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Diameter of Shaft from MPST - (Measured in Meter) - Diameter of Shaft from MPST is the diameter of the shaft according to the Maximum Principal Stress Theory.
Maximum Principle Stress in Shaft - (Measured in Pascal) - Maximum Principle Stress in Shaft is defined as the normal stress calculated in the shaft at an angle when shear stress is considered zero.
Bending Moment in Shaft - (Measured in Newton Meter) - Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.
Torsional Moment in Shaft - (Measured in Newton Meter) - Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.

STEP 1: Convert Input(s) to Base Unit

Maximum Principle Stress in Shaft: 135.3 Newton per Square Millimeter --> 135300000 Pascal (Check conversion here)
Bending Moment in Shaft: 1800000 Newton Millimeter --> 1800 Newton Meter (Check conversion here)
Torsional Moment in Shaft: 330000 Newton Millimeter --> 330 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_MPST = (16/(pi*σ₁)*(M_b+sqrt(M_b^2+Mt_shaft^2)))^(1/3) --> (16/(pi*135300000)*(1800+sqrt(1800^2+330^2)))^(1/3)

Evaluating ... ...

d_MPST = 0.0515062161581043

STEP 3: Convert Result to Output's Unit

0.0515062161581043 Meter -->51.5062161581043 Millimeter (Check conversion here)

FINAL ANSWER

51.5062161581043 ≈ 51.50622 Millimeter <-- Diameter of Shaft from MPST

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Maximum Shear Stress and Principal Stress Theory » Diameter of Shaft given Permissible Value of Maximum Principle Stress

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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

Diameter of Shaft given Permissible Value of Maximum Principle Stress Formula

Define Maximum Principle Stress

It is defined as the normal stress calculated at an angle when shear stress is considered as zero. The maximum value of normal stress is known as major principal stress and minimum value of normal stress is known as minor principal stress.There are two types of principal stresses; 2-D and 3-D.

How to Calculate Diameter of Shaft given Permissible Value of Maximum Principle Stress?

Diameter of Shaft given Permissible Value of Maximum Principle Stress calculator uses 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) to calculate the Diameter of Shaft from MPST, The Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as the diameter of the shaft on which we are applying bending and torsional moment without any axial forces. Diameter of Shaft from MPST is denoted by d_MPST symbol.

How to calculate Diameter of Shaft given Permissible Value of Maximum Principle Stress using this online calculator? To use this online calculator for Diameter of Shaft given Permissible Value of Maximum Principle Stress, enter Maximum Principle Stress in Shaft (σ₁), Bending Moment in Shaft (M_b) & Torsional Moment in Shaft (Mt_shaft) and hit the calculate button. Here is how the Diameter of Shaft given Permissible Value of Maximum Principle Stress calculation can be explained with given input values -> 51506.22 = (16/(pi*135300000)*(1800+sqrt(1800^2+330^2)))^(1/3).

FAQ

What is Diameter of Shaft given Permissible Value of Maximum Principle Stress?

The Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as the diameter of the shaft on which we are applying bending and torsional moment without any axial forces and is represented as d_MPST = (16/(pi*σ₁)*(M_b+sqrt(M_b^2+Mt_shaft^2)))^(1/3) or 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). Maximum Principle Stress in Shaft is defined as the normal stress calculated in the shaft at an angle when shear stress is considered zero, Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend & Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.

How to calculate Diameter of Shaft given Permissible Value of Maximum Principle Stress?

The Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as the diameter of the shaft on which we are applying bending and torsional moment without any axial forces is calculated using 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). To calculate Diameter of Shaft given Permissible Value of Maximum Principle Stress, you need Maximum Principle Stress in Shaft (σ₁), Bending Moment in Shaft (M_b) & Torsional Moment in Shaft (Mt_shaft). With our tool, you need to enter the respective value for Maximum Principle Stress in Shaft, Bending Moment in Shaft & Torsional Moment in Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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