Torsional Moment given Maximum Shear Stress 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%
✖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 given Maximum Shear Stress [Mt_t]

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Torsional Moment given Maximum Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Diameter of Shaft from MSST: 45 Millimeter --> 0.045 Meter (Check conversion here)
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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Mt_t = sqrt((pi*d_MSST^3*𝜏_{max MSST}/16)^2-M_{b MSST}^2) --> sqrt((pi*0.045^3*58900000/16)^2-980^2)

Evaluating ... ...

Mt_t = 387.582125088048

STEP 3: Convert Result to Output's Unit

387.582125088048 Newton Meter -->387582.125088048 Newton Millimeter (Check conversion here)

FINAL ANSWER

387582.125088048 ≈ 387582.1 Newton Millimeter <-- Torsional Moment in Shaft for MSST

(Calculation completed in 00.004 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

Torsional Moment given Maximum Shear Stress Formula

LaTeX Go

Define Torsional Moment?

Torsional moment, also known as torque, is the measure of the twisting force that causes an object to rotate around its axis. It is generated when a force is applied at a distance from the axis of rotation, resulting in a rotational effect. The magnitude of the torsional moment depends on the size of the applied force and the distance from the axis at which the force acts. Torsional moment is crucial in various mechanical systems, including engines, shafts, and gearboxes, as it determines how effectively rotational power is transmitted. Proper management of torsional moments is essential to prevent mechanical failure and ensure the performance of rotating components.

How to Calculate Torsional Moment given Maximum Shear Stress?

Torsional Moment given Maximum Shear Stress calculator uses 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) to calculate the Torsional Moment in Shaft for MSST, Torsional Moment given Maximum Shear Stress formula is defined as a measure of the twisting force that causes shear stress in a shaft, which is a critical parameter in mechanical engineering to determine the shaft's ability to resist twisting and potential failure. Torsional Moment in Shaft for MSST is denoted by Mt_t symbol.

How to calculate Torsional Moment given Maximum Shear Stress using this online calculator? To use this online calculator for Torsional Moment given Maximum Shear Stress, enter Diameter of Shaft from MSST (d_MSST), Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}) & Bending Moment in Shaft for MSST (M_{b MSST}) and hit the calculate button. Here is how the Torsional Moment given Maximum Shear Stress calculation can be explained with given input values -> 3.9E+8 = sqrt((pi*0.045^3*58900000/16)^2-980^2).

FAQ

What is Torsional Moment given Maximum Shear Stress?

Torsional Moment given Maximum Shear Stress formula is defined as a measure of the twisting force that causes shear stress in a shaft, which is a critical parameter in mechanical engineering to determine the shaft's ability to resist twisting and potential failure and is represented as Mt_t = sqrt((pi*d_MSST^3*𝜏_{max MSST}/16)^2-M_{b MSST}^2) or 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). 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 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.

How to calculate Torsional Moment given Maximum Shear Stress?

Torsional Moment given Maximum Shear Stress formula is defined as a measure of the twisting force that causes shear stress in a shaft, which is a critical parameter in mechanical engineering to determine the shaft's ability to resist twisting and potential failure is calculated using 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). To calculate Torsional Moment given Maximum Shear Stress, you need Diameter of Shaft from MSST (d_MSST), Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}) & Bending Moment in Shaft for MSST (M_{b MSST}). With our tool, you need to enter the respective value for Diameter of Shaft from MSST, Maximum Shear Stress in Shaft from MSST & Bending 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 Torsional Moment in Shaft for MSST?

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

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)

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