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

✖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 Shaft from MSST [𝜏_{max 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%

✖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 given Principle Shear Stress Maximum Shear Stress Theory [d_MSST]

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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 a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability.
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.
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

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: 387582.1 Newton Millimeter --> 387.5821 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+387.5821^2))^(1/3)

Evaluating ... ...

d_MSST = 0.0449999998686723

STEP 3: Convert Result to Output's Unit

0.0449999998686723 Meter -->44.9999998686723 Millimeter (Check conversion here)

FINAL ANSWER

44.9999998686723 ≈ 45 Millimeter <-- Diameter of Shaft from MSST

(Calculation completed in 00.020 seconds)

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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

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

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What is Principle Stress?

Principal stress refers to the normal stress acting on a plane where the shear stress is zero. These are the maximum and minimum stresses experienced by a material at a point, acting along specific directions known as principal planes. Principal stresses help in analyzing the strength of materials under complex loading conditions by identifying the extreme values of stress, which are crucial for assessing failure risks and ensuring the structural integrity of components.

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, Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory formula is defined as a measure of the diameter of a shaft under maximum shear stress, considering the principal stress theory, which is essential in mechanical engineering to design and analyze shafts for various applications. 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 -> 45000 = (16/(pi*58900000)*sqrt(980^2+387.5821^2))^(1/3).

FAQ

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

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory formula is defined as a measure of the diameter of a shaft under maximum shear stress, considering the principal stress theory, which is essential in mechanical engineering to design and analyze shafts for various applications 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 the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity, 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 Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory formula is defined as a measure of the diameter of a shaft under maximum shear stress, considering the principal stress theory, which is essential in mechanical engineering to design and analyze shafts for various applications 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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