Maximum Shear Stress in Shafts Calculator

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Maximum Shear Stress and Principal Stress Theory

ASME Code for Shaft Desgin

Design of Hollow Shaft

Shaft Design on Strength Basis

Torsional Rigidity

✖Diameter of Shaft from MSST is the diameter of the shaft according to the Maximum Shear Stress Theory.ⓘ Diameter of Shaft from MSST [d_MSST]			+10% -10%
✖Bending Moment in Shaft for MSST 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 for MSST [M_{b MSST}]			+10% -10%
✖Torsional Moment in Shaft for MSST 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 for MSST [Mt_t]			+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 Shafts [𝜏_{max MSST}]

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Formula

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Maximum Shear Stress in Shafts

Formula

`"𝜏"_{"max MSST"} = 16/(pi*"d"_{"MSST"}^3)*sqrt("M"_{"b MSST"}^2+"Mt"_{"t"}^2)`

Example

`"58.88804N/mm²"=16/(pi*("45mm")^3)*sqrt(("9.8E5N*mm")^2+("3.87E5N*mm")^2)`

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Maximum Shear Stress in Shafts Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
𝜏_{max MSST} = 16/(pi*d_MSST^3)*sqrt(M_{b MSST}^2+Mt_t^2)
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

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.
Diameter of Shaft from MSST - (Measured in Meter) - Diameter of Shaft from MSST is the diameter of the shaft according to the Maximum Shear Stress Theory.
Bending Moment in Shaft for MSST - (Measured in Newton Meter) - Bending Moment in Shaft for MSST 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 for MSST - (Measured in Newton Meter) - Torsional Moment in Shaft for MSST 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

Diameter of Shaft from MSST: 45 Millimeter --> 0.045 Meter (Check conversion here)
Bending Moment in Shaft for MSST: 980000 Newton Millimeter --> 980 Newton Meter (Check conversion here)
Torsional Moment in Shaft for MSST: 387000 Newton Millimeter --> 387 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_{max MSST} = 16/(pi*d_MSST^3)*sqrt(M_{b MSST}^2+Mt_t^2) --> 16/(pi*0.045^3)*sqrt(980^2+387^2)

Evaluating ... ...

𝜏_{max MSST} = 58888042.2981432

STEP 3: Convert Result to Output's Unit

58888042.2981432 Pascal -->58.8880422981432 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

58.8880422981432 ≈ 58.88804 Newton per Square Millimeter <-- Maximum Shear Stress in Shaft from MSST

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Maximum Shear Stress and Principal Stress Theory » Maximum Shear Stress in Shafts

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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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

Maximum Shear Stress in Shafts Formula

Define 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 Maximum Shear Stress in Shafts?

Maximum Shear Stress in Shafts calculator uses 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) to calculate the Maximum Shear Stress in Shaft from MSST, The Maximum Shear Stress in shafts formula is defined as the maximum limit of the principal stress induced in the shaft. Maximum Shear Stress in Shaft from MSST is denoted by 𝜏_{max MSST} symbol.

How to calculate Maximum Shear Stress in Shafts using this online calculator? To use this online calculator for Maximum Shear Stress in Shafts, enter Diameter of Shaft from MSST (d_MSST), Bending Moment in Shaft for MSST (M_{b MSST}) & Torsional Moment in Shaft for MSST (Mt_t) and hit the calculate button. Here is how the Maximum Shear Stress in Shafts calculation can be explained with given input values -> 5.9E-5 = 16/(pi*0.045^3)*sqrt(980^2+387^2).

FAQ

What is Maximum Shear Stress in Shafts?

The Maximum Shear Stress in shafts formula is defined as the maximum limit of the principal stress induced in the shaft and is represented as 𝜏_{max MSST} = 16/(pi*d_MSST^3)*sqrt(M_{b MSST}^2+Mt_t^2) or 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). Diameter of Shaft from MSST is the diameter of the shaft according to the Maximum Shear Stress Theory, Bending Moment in Shaft for MSST 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 for MSST 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 Maximum Shear Stress in Shafts?

The Maximum Shear Stress in shafts formula is defined as the maximum limit of the principal stress induced in the shaft is calculated using 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). To calculate Maximum Shear Stress in Shafts, you need Diameter of Shaft from MSST (d_MSST), Bending Moment in Shaft for MSST (M_{b MSST}) & Torsional Moment in Shaft for MSST (Mt_t). With our tool, you need to enter the respective value for Diameter of Shaft from MSST, Bending Moment in Shaft for MSST & Torsional Moment in Shaft for 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 Maximum Shear Stress in Shaft from MSST?

In this formula, Maximum Shear Stress in Shaft from MSST uses Diameter of Shaft from MSST, Bending Moment in Shaft for MSST & Torsional Moment in Shaft for MSST. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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