Maximum Shear Stress in Shafts Calculator

✖Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability.ⓘ Diameter of Shaft from MSST [d_MSST]			+10% -10%
✖Bending Moment in Shaft for MSST is the maximum twisting force that causes shear stress in a shaft, affecting its structural integrity and stability.ⓘ Bending Moment in Shaft for MSST [M_{b MSST}]			+10% -10%
✖Torsional Moment in Shaft for MSST is the maximum twisting moment that a shaft can withstand without failing, considering maximum shear stress and principal stress theory.ⓘ Torsional Moment in Shaft for MSST [Mt_t]			+10% -10%

✖Maximum Shear Stress in Shaft from MSST is the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity.ⓘ Maximum Shear Stress in Shafts [𝜏_{max MSST}]

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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 the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity.
Diameter of Shaft from MSST - (Measured in Meter) - Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability.
Bending Moment in Shaft for MSST - (Measured in Newton Meter) - Bending Moment in Shaft for MSST is the maximum twisting force that causes shear stress in a shaft, affecting its structural integrity and stability.
Torsional Moment in Shaft for MSST - (Measured in Newton Meter) - Torsional Moment in Shaft for MSST is the maximum twisting moment that a shaft can withstand without failing, considering maximum shear stress and principal stress theory.

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: 387582.1 Newton Millimeter --> 387.5821 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+387.5821^2)

Evaluating ... ...

𝜏_{max MSST} = 58899999.4843198

STEP 3: Convert Result to Output's Unit

58899999.4843198 Pascal -->58.8999994843198 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

58.8999994843198 ≈ 58.9 Newton per Square Millimeter <-- Maximum Shear Stress in Shaft from MSST

(Calculation completed in 00.004 seconds)

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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

LaTeX 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

LaTeX 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

LaTeX 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

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

Maximum Shear Stress in Shafts Formula

LaTeX Go

Define Principle Stress?

Principal stress refers to the normal stress acting on a particular plane within a material where the shear stress is zero. These stresses occur along the principal planes, which are oriented such that only normal stresses, not shear stresses, are present. Principal stresses include both maximum and minimum values, and they help in analyzing the behavior of materials under complex loading conditions. Understanding principal stresses is important for assessing the potential for material failure and ensuring the safety and reliability of structures.

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, Maximum Shear Stress in Shafts formula is defined as a measure of the maximum shear stress that occurs in a shaft, which is a critical parameter in mechanical engineering to ensure the structural integrity and reliability of rotating machines and mechanisms. 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+387.5821^2).

FAQ

What is Maximum Shear Stress in Shafts?

Maximum Shear Stress in Shafts formula is defined as a measure of the maximum shear stress that occurs in a shaft, which is a critical parameter in mechanical engineering to ensure the structural integrity and reliability of rotating machines and mechanisms 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 a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability, Bending Moment in Shaft for MSST is the maximum twisting force that causes shear stress in a shaft, affecting its structural integrity and stability & Torsional Moment in Shaft for MSST is the maximum twisting moment that a shaft can withstand without failing, considering maximum shear stress and principal stress theory.

How to calculate Maximum Shear Stress in Shafts?

Maximum Shear Stress in Shafts formula is defined as a measure of the maximum shear stress that occurs in a shaft, which is a critical parameter in mechanical engineering to ensure the structural integrity and reliability of rotating machines and mechanisms 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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