Normal Stress given Principal Shear Stress in Shaft Bending and Torsion 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%
✖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 in Shaft [𝜏]			+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 given Principal Shear Stress in Shaft Bending and Torsion [σ_x]

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Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Principal Shear Stress in Shaft: 126.355 Newton per Square Millimeter --> 126355000 Pascal (Check conversion here)
Torsional Shear Stress in Shaft: 16.29 Newton per Square Millimeter --> 16290000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_x = 2*sqrt(τ_max^2-𝜏^2) --> 2*sqrt(126355000^2-16290000^2)

Evaluating ... ...

σ_x = 250601052.870893

STEP 3: Convert Result to Output's Unit

250601052.870893 Pascal -->250.601052870893 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

250.601052870893 ≈ 250.6011 Newton per Square Millimeter <-- Normal Stress in Shaft

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Mechanical » Shaft Design on Strength Basis » Normal Stress given Principal Shear Stress in Shaft Bending and Torsion

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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National Institute Of Technology (NIT), Hamirpur

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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

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion Formula

LaTeX Go

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

Define Principal Shear Stress?

Principal shear stress is the maximum shear stress that occurs on a plane where the normal stresses are equal. It represents the highest value of shear stress that a material experiences under complex loading conditions. Principal shear stress is important in determining how materials will react to forces that cause sliding or deformation between layers. It helps engineers assess the potential for shear failure, particularly in materials subjected to combined stresses, such as in beams, shafts, and other structural elements.

How to Calculate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion calculator uses Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2) to calculate the Normal Stress in Shaft, Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a measure of the stress experienced by a shaft when it is subjected to both bending and torsional loads, providing a critical parameter in shaft design to ensure its strength and reliability. Normal Stress in Shaft is denoted by σ_x symbol.

How to calculate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion using this online calculator? To use this online calculator for Normal Stress given Principal Shear Stress in Shaft Bending and Torsion, enter Principal Shear Stress in Shaft (τ_max) & Torsional Shear Stress in Shaft (𝜏) and hit the calculate button. Here is how the Normal Stress given Principal Shear Stress in Shaft Bending and Torsion calculation can be explained with given input values -> 0.000251 = 2*sqrt(126355000^2-16290000^2).

FAQ

What is Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a measure of the stress experienced by a shaft when it is subjected to both bending and torsional loads, providing a critical parameter in shaft design to ensure its strength and reliability and is represented as σ_x = 2*sqrt(τ_max^2-𝜏^2) or Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^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 & Torsional Shear Stress in Shaft is the stress developed in a shaft due to twisting or rotational force, affecting its strength and structural integrity.

How to calculate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion?

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a measure of the stress experienced by a shaft when it is subjected to both bending and torsional loads, providing a critical parameter in shaft design to ensure its strength and reliability is calculated using Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2). To calculate Normal Stress given Principal Shear Stress in Shaft Bending and Torsion, you need Principal Shear Stress in Shaft (τ_max) & Torsional Shear Stress in Shaft (𝜏). With our tool, you need to enter the respective value for Principal Shear Stress in Shaft & Torsional Shear 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 Normal Stress in Shaft?

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

Normal Stress in Shaft = Bending Stress in Shaft+Tensile Stress in Shaft

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