Torsional Shear Stress given Principal Shear Stress in Shaft Calculator

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Maximum Shear Stress and Principal Stress Theory

Torsional Rigidity

✖Principal Shear Stress in Shaft is defined as the normal stress in the shaft calculated at an angle when shear stress is considered zero.ⓘ Principal Shear Stress in Shaft [τ_max]			+10% -10%
✖Normal Stress in Shaft is the stress that occurs when a shaft is loaded by an axial force.ⓘ Normal Stress in Shaft [σ_x]			+10% -10%

✖Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.ⓘ Torsional Shear Stress given Principal Shear Stress in Shaft [𝜏]

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Formula

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Torsional Shear Stress given Principal Shear Stress in Shaft

Formula

`"𝜏" = sqrt("τ"_{"max"}^2-("σ"_{"x"}/2)^2)`

Example

`"17.38275N/mm²"=sqrt(("126.5N/mm²")^2-("250.6N/mm²"/2)^2)`

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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 shear stress produced in the shaft due to the twisting.
Principal Shear Stress in Shaft - (Measured in Pascal) - Principal Shear Stress in Shaft is defined as the normal stress in the shaft calculated at an angle when shear stress is considered zero.
Normal Stress in Shaft - (Measured in Pascal) - Normal Stress in Shaft is the stress that occurs when a shaft is loaded by an axial force.

STEP 1: Convert Input(s) to Base Unit

Principal Shear Stress in Shaft: 126.5 Newton per Square Millimeter --> 126500000 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(126500000^2-(250600000/2)^2)

Evaluating ... ...

𝜏 = 17382750.0701126

STEP 3: Convert Result to Output's Unit

17382750.0701126 Pascal -->17.3827500701126 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

17.3827500701126 ≈ 17.38275 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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< 16 Shaft Design on Strength Basis Calculators

Diameter of Shaft given Tensile Stress in Shaft

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

Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion

Go Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3)

Torsional Moment given Torsional Shear Stress in Shaft Pure Torsion

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

Torsional Shear Stress in Shaft Pure Torsion

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

Diameter of Shaft given Bending Stress Pure Bending

Go Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3)

Torsional Shear Stress given Principal Shear Stress in Shaft

Go Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2)

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion

Go Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2)

Maximum Shear Stress in Shaft Bending and Torsion

Go Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2)

Bending Stress in Shaft Pure Bending Moment

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

Bending Moment given Bending Stress Pure Bending

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

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

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

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

Power transmitted by Shaft

Go Power Transmitted by Shaft = 2*pi*Speed of Shaft*Torque transmitted by Shaft

Normal Stress given Both Bending and Torsional act on Shaft

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

Tensile Stress given Normal Stress

Go Tensile Stress in Shaft = Normal Stress in Shaft-Bending Stress in Shaft

Bending Stress given Normal Stress

Go Bending Stress in Shaft = Normal Stress in Shaft-Tensile Stress in Shaft

Torsional Shear Stress given Principal Shear Stress in Shaft Formula

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

It is defined as the normal stress calculated at an angle when shear stress is considered as zero. The normal stress can be obtained for maximum and minimum values.

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, The Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as the shear formed by torsion exerted on a beam and this twist causes shear stress to be exerted along the cross-section of the structural member. 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(126500000^2-(250600000/2)^2).

FAQ

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

The Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as the shear formed by torsion exerted on a beam and this twist causes shear stress to be exerted along the cross-section of the structural member 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 defined as the normal stress in the shaft calculated at an angle when shear stress is considered zero & Normal Stress in Shaft is the stress that occurs when a shaft is loaded by an axial force.

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

The Torsional Shear Stress given Principal Shear Stress in Shaft formula is defined as the shear formed by torsion exerted on a beam and this twist causes shear stress to be exerted along the cross-section of the structural member 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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