Normal Stress given Principal Shear Stress in Shaft Bending and Torsion 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%
✖Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.ⓘ Torsional Shear Stress in Shaft [𝜏]			+10% -10%

✖Normal Stress in Shaft is the stress that occurs when a shaft is loaded by an axial force.ⓘ Normal Stress given Principal Shear Stress in Shaft Bending and Torsion [σ_x]

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Formula

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Normal Stress given Principal Shear Stress in Shaft Bending and Torsion

Formula

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

Example

`"250.8935N/mm²"=2*sqrt(("126.5N/mm²")^2-("16.29N/mm²")^2)`

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Download Design of Automobile Elements Formula PDF

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 stress that occurs when a shaft is loaded by an axial force.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Principal Shear Stress in Shaft: 126.5 Newton per Square Millimeter --> 126500000 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(126500000^2-16290000^2)

Evaluating ... ...

σ_x = 250893490.549277

STEP 3: Convert Result to Output's Unit

250893490.549277 Pascal -->250.893490549277 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

250.893490549277 ≈ 250.8935 Newton per Square Millimeter <-- Normal Stress in Shaft

(Calculation completed in 00.004 seconds)

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

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

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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

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

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 Normal Stress

A normal stress is a stress that occurs when a member is loaded by an axial force. A normal stress will occur when a member is placed in tension or compression. Examples of members experiencing pure normal forces would include columns, collar ties, etc.

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, The Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a stress that occurs when a member is loaded by an axial force. 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(126500000^2-16290000^2).

FAQ

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

The Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a stress that occurs when a member is loaded by an axial force 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 defined as the normal stress in the shaft calculated at an angle when shear stress is considered zero & Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.

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

The Normal Stress given Principal Shear Stress in Shaft Bending and Torsion formula is defined as a stress that occurs when a member is loaded by an axial force 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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