Diameter of Shaft given Permissible Value of Maximum Principle Stress Calculator

✖Maximum Principle Stress in Shaft is the maximum normal stress a shaft can withstand without yielding, calculated based on maximum shear stress theory.ⓘ Maximum Principle Stress in Shaft [σ_max]			+10% -10%
✖Bending Moment in Shaft is the maximum twisting force that causes shear stress in a shaft, leading to deformation and potential failure.ⓘ Bending Moment in Shaft [M_b]			+10% -10%
✖Torsional Moment in Shaft is the maximum twisting moment that a shaft can withstand without failing, related to maximum shear stress and principal stress theory.ⓘ Torsional Moment in Shaft [Mt_shaft]			+10% -10%

✖Diameter of Shaft from MPST is the diameter of a shaft calculated based on maximum shear stress theory, considering the principal stress theory's principles.ⓘ Diameter of Shaft given Permissible Value of Maximum Principle Stress [d_MPST]

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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*σ_max)*(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 a shaft calculated based on maximum shear stress theory, considering the principal stress theory's principles.
Maximum Principle Stress in Shaft - (Measured in Pascal) - Maximum Principle Stress in Shaft is the maximum normal stress a shaft can withstand without yielding, calculated based on maximum shear stress theory.
Bending Moment in Shaft - (Measured in Newton Meter) - Bending Moment in Shaft is the maximum twisting force that causes shear stress in a shaft, leading to deformation and potential failure.
Torsional Moment in Shaft - (Measured in Newton Meter) - Torsional Moment in Shaft is the maximum twisting moment that a shaft can withstand without failing, related to maximum shear stress and principal stress theory.

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*σ_max)*(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 00.012 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 Permissible Value of Maximum Principle Stress Formula

LaTeX Go

Define Maximum Principle Stress?

Maximum principal stress is the highest normal stress experienced by a material at a specific point when subjected to external forces. It occurs along a particular direction where the shear stress is zero. This stress is important in engineering design because it helps in identifying the point of maximum stress concentration, which can lead to failure if exceeded. Understanding maximum principal stress is essential for ensuring the safety and integrity of structures under load.

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, Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as a measure of the diameter of a shaft based on the maximum principle stress it can withstand, taking into account the bending moment and torsional moment of the shaft, providing a safe and reliable design for mechanical systems. 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 (σ_max), 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?

Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as a measure of the diameter of a shaft based on the maximum principle stress it can withstand, taking into account the bending moment and torsional moment of the shaft, providing a safe and reliable design for mechanical systems and is represented as d_MPST = (16/(pi*σ_max)*(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 the maximum normal stress a shaft can withstand without yielding, calculated based on maximum shear stress theory, Bending Moment in Shaft is the maximum twisting force that causes shear stress in a shaft, leading to deformation and potential failure & Torsional Moment in Shaft is the maximum twisting moment that a shaft can withstand without failing, related to maximum shear stress and principal stress theory.

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

Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as a measure of the diameter of a shaft based on the maximum principle stress it can withstand, taking into account the bending moment and torsional moment of the shaft, providing a safe and reliable design for mechanical systems 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 (σ_max), 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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