Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion Calculator

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Shaft Design on Strength Basis

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Maximum Shear Stress and Principal Stress Theory

Torsional Rigidity

✖Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment in Shaft [Mt_shaft]			+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%

✖Diameter of Shaft on Strength Basis is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.ⓘ Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion [d]

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Formula

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Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion

Formula

`"d" = (16*"Mt"_{"shaft"}/(pi*"𝜏"))^(1/3)`

Example

`"46.9016mm"=(16*"3.3E5N*mm"/(pi*"16.29N/mm²"))^(1/3)`

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Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3)
d = (16*Mt_shaft/(pi*𝜏))^(1/3)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Diameter of Shaft on Strength Basis - (Measured in Meter) - Diameter of Shaft on Strength Basis is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.
Torsional Moment in Shaft - (Measured in Newton Meter) - Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.
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

Torsional Moment in Shaft: 330000 Newton Millimeter --> 330 Newton Meter (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

d = (16*Mt_shaft/(pi*𝜏))^(1/3) --> (16*330/(pi*16290000))^(1/3)

Evaluating ... ...

d = 0.046901599643428

STEP 3: Convert Result to Output's Unit

0.046901599643428 Meter -->46.901599643428 Millimeter (Check conversion here)

FINAL ANSWER

46.901599643428 ≈ 46.9016 Millimeter <-- Diameter of Shaft on Strength Basis

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Shaft Design on Strength Basis » Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion

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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

Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion Formula

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

Define Torsion

The twisting or wrenching of a body by the exertion of forces tending to turn one end or part about a longitudinal axis while the other is held fast or turned in the opposite direction

How to Calculate Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion?

Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion calculator uses Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3) to calculate the Diameter of Shaft on Strength Basis, The Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion formula is defined as the diameter of the shaft on which we are applying torsional moment. Diameter of Shaft on Strength Basis is denoted by d symbol.

How to calculate Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion using this online calculator? To use this online calculator for Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion, enter Torsional Moment in Shaft (Mt_shaft) & Torsional Shear Stress in Shaft (𝜏) and hit the calculate button. Here is how the Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion calculation can be explained with given input values -> 46901.6 = (16*330/(pi*16290000))^(1/3).

FAQ

What is Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion?

The Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion formula is defined as the diameter of the shaft on which we are applying torsional moment and is represented as d = (16*Mt_shaft/(pi*𝜏))^(1/3) or Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3). Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist & Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.

How to calculate Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion?

The Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion formula is defined as the diameter of the shaft on which we are applying torsional moment is calculated using Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3). To calculate Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion, you need Torsional Moment in Shaft (Mt_shaft) & Torsional Shear Stress in Shaft (𝜏). With our tool, you need to enter the respective value for Torsional Moment 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 Diameter of Shaft on Strength Basis?

In this formula, Diameter of Shaft on Strength Basis uses Torsional Moment in Shaft & Torsional Shear Stress in Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Diameter of Shaft on Strength Basis = sqrt(4*Axial Force on Shaft/(pi*Tensile Stress in Shaft))
Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3)

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