Torsional Shear Stress given Principal Shear Stress in Shaft Calculator

✖Principal Shear Stress in Shaft is the maximum shear stress that a shaft can withstand without failing, considering the shaft's design and strength parameters.ⓘ Principal Shear Stress in Shaft [τ_max]			+10% -10%
✖Normal Stress in Shaft is the force per unit area that a shaft can withstand without undergoing deformation or failure during its operation.ⓘ Normal Stress in Shaft [σ_x]			+10% -10%

✖Torsional Shear Stress in Shaft is the stress developed in a shaft due to twisting or rotational force, affecting its strength and structural integrity.ⓘ Torsional Shear Stress given Principal Shear Stress in Shaft [𝜏]

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Torsional Shear Stress given Principal Shear Stress in Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2)
𝜏 = sqrt(τ_max^2-(σ_x/2)^2)
This formula uses 1 Functions, 3 Variables

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 Shear Stress in Shaft - (Measured in Pascal) - Torsional Shear Stress in Shaft is the stress developed in a shaft due to twisting or rotational force, affecting its strength and structural integrity.
Principal Shear Stress in Shaft - (Measured in Pascal) - Principal Shear Stress in Shaft is the maximum shear stress that a shaft can withstand without failing, considering the shaft's design and strength parameters.
Normal Stress in Shaft - (Measured in Pascal) - Normal Stress in Shaft is the force per unit area that a shaft can withstand without undergoing deformation or failure during its operation.

STEP 1: Convert Input(s) to Base Unit

Principal Shear Stress in Shaft: 126.355 Newton per Square Millimeter --> 126355000 Pascal (Check conversion here)
Normal Stress in Shaft: 250.6 Newton per Square Millimeter --> 250600000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = sqrt(τ_max^2-(σ_x/2)^2) --> sqrt(126355000^2-(250600000/2)^2)

Evaluating ... ...

𝜏 = 16294048.7602069

STEP 3: Convert Result to Output's Unit

16294048.7602069 Pascal -->16.2940487602069 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

16.2940487602069 ≈ 16.29405 Newton per Square Millimeter <-- Torsional Shear Stress in Shaft

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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National Institute of Technology (NIT), Srinagar

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< Shaft Design on Strength Basis Calculators

Diameter of Shaft given Tensile Stress in Shaft

LaTeX Go Diameter of Shaft on Strength Basis = sqrt(4*Axial Force on Shaft/(pi*Tensile Stress in Shaft))

Bending Stress in Shaft Pure Bending Moment

LaTeX Go Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3)

Tensile Stress in Shaft when it is Subjected to Axial Tensile Force

LaTeX Go Tensile Stress in Shaft = 4*Axial Force on Shaft/(pi*Diameter of Shaft on Strength Basis^2)

Axial Force given Tensile Stress in Shaft

LaTeX Go Axial Force on Shaft = Tensile Stress in Shaft*pi*(Diameter of Shaft on Strength Basis^2)/4

Torsional Shear Stress given Principal Shear Stress in Shaft Formula

LaTeX Go

Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2)
𝜏 = sqrt(τ_max^2-(σ_x/2)^2)

Define Principle Shear Stress?

Principal shear stress is the maximum shear stress that occurs on a particular plane within a material when it is subjected to combined normal and shear stresses. It represents the highest possible shear stress acting on a material and is critical in determining potential failure modes, particularly in areas prone to shear failure. Principal shear stress helps in analyzing how materials behave under complex loading conditions, such as in beams, shafts, or pressure vessels, and is essential for ensuring structural safety and integrity.

How to Calculate Torsional Shear Stress given Principal Shear Stress in Shaft?

Torsional Shear Stress given Principal Shear Stress in Shaft calculator uses Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2) to calculate the Torsional Shear Stress in Shaft, Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as a measure of the shear stress that occurs due to twisting of a shaft, which is a critical parameter in shaft design to ensure the shaft can withstand the torsional load without failure. Torsional Shear Stress in Shaft is denoted by 𝜏 symbol.

How to calculate Torsional Shear Stress given Principal Shear Stress in Shaft using this online calculator? To use this online calculator for Torsional Shear Stress given Principal Shear Stress in Shaft, enter Principal Shear Stress in Shaft (τ_max) & Normal Stress in Shaft (σ_x) and hit the calculate button. Here is how the Torsional Shear Stress given Principal Shear Stress in Shaft calculation can be explained with given input values -> 1.7E-5 = sqrt(126355000^2-(250600000/2)^2).

FAQ

What is Torsional Shear Stress given Principal Shear Stress in Shaft?

Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as a measure of the shear stress that occurs due to twisting of a shaft, which is a critical parameter in shaft design to ensure the shaft can withstand the torsional load without failure and is represented as 𝜏 = sqrt(τ_max^2-(σ_x/2)^2) or Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2). Principal Shear Stress in Shaft is the maximum shear stress that a shaft can withstand without failing, considering the shaft's design and strength parameters & Normal Stress in Shaft is the force per unit area that a shaft can withstand without undergoing deformation or failure during its operation.

How to calculate Torsional Shear Stress given Principal Shear Stress in Shaft?

Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as a measure of the shear stress that occurs due to twisting of a shaft, which is a critical parameter in shaft design to ensure the shaft can withstand the torsional load without failure is calculated using Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2). To calculate Torsional Shear Stress given Principal Shear Stress in Shaft, you need Principal Shear Stress in Shaft (τ_max) & Normal Stress in Shaft (σ_x). With our tool, you need to enter the respective value for Principal Shear Stress in Shaft & Normal Stress in Shaft 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 Shear Stress in Shaft?

In this formula, Torsional Shear Stress in Shaft uses Principal Shear Stress in Shaft & Normal Stress in Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

Torsional Shear Stress in Shaft = 16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3)

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