Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Calculator

✖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%
✖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%

✖Diameter of Shaft from MSST is the diameter of the shaft according to the Maximum Shear Stress Theory.ⓘ Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory [d_MSST]

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Formula

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Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory

Formula

d MSST = {(\frac{16}{π \cdot 𝜏 max MSST} \cdot \sqrt{{M b MSST}^{2} + {Mt t}^{2}})}^{\frac{1}{3}}

Example

44.99695 mm = {(\frac{16}{π \cdot 58.9 N/mm²} \cdot \sqrt{{9.8E5 N*mm}^{2} + {3.87E5 N*mm}^{2}})}^{\frac{1}{3}}

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Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
d_MSST = (16/(pi*𝜏_{max MSST})*sqrt(M_{b MSST}^2+Mt_t^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 MSST - (Measured in Meter) - Diameter of Shaft from MSST is the diameter of the shaft according to the 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.
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

Maximum Shear Stress in Shaft from MSST: 58.9 Newton per Square Millimeter --> 58900000 Pascal (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

d_MSST = (16/(pi*𝜏_{max MSST})*sqrt(M_{b MSST}^2+Mt_t^2))^(1/3) --> (16/(pi*58900000)*sqrt(980^2+387^2))^(1/3)

Evaluating ... ...

d_MSST = 0.0449969545387554

STEP 3: Convert Result to Output's Unit

0.0449969545387554 Meter -->44.9969545387554 Millimeter (Check conversion here)

FINAL ANSWER

44.9969545387554 ≈ 44.99695 Millimeter <-- Diameter of Shaft from MSST

(Calculation completed in 00.004 seconds)

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

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Maximum Shear Stress and Principal Stress Theory Calculators

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))

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

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory 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 Principle Shear Stress Maximum Shear Stress Theory?

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

How to calculate Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory using this online calculator? To use this online calculator for Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory, enter Maximum Shear Stress in Shaft from MSST (𝜏_{max 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 Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory calculation can be explained with given input values -> 44996.95 = (16/(pi*58900000)*sqrt(980^2+387^2))^(1/3).

FAQ

What is Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

The Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory is defined as diameter of shaft on which we are applying bending and torsional moment without any axial forces and is represented as d_MSST = (16/(pi*𝜏_{max MSST})*sqrt(M_{b MSST}^2+Mt_t^2))^(1/3) or 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). Maximum Shear Stress in Shaft from MSST is maximum shear stress in a shaft calculated using 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 Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

The Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory is defined as diameter of shaft on which we are applying bending and torsional moment without any axial forces is calculated using 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). To calculate Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory, you need Maximum Shear Stress in Shaft from MSST (𝜏_{max 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 Maximum Shear Stress in 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.

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