Length of Shaft Subjected to Torsional Moment given Angle of Twist Calculator

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✖Angle of Twist in Shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of Twist in Shaft [θ]			+10% -10%
✖Modulus of Rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid is s shaft.ⓘ Modulus of Rigidity of Shaft [G]			+10% -10%
✖Diameter of Shaft from Torsional Rigidity is the diameter of the external surface of a shaft calculated on the basis of torsional rigidity.ⓘ Diameter of Shaft from Torsional Rigidity [d_torl]			+10% -10%
✖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%

✖Length of Shaft from Torsional Rigidity is the length of the shaft calculated on the basis of torsional rigidity.ⓘ Length of Shaft Subjected to Torsional Moment given Angle of Twist [L]

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Formula

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Length of Shaft Subjected to Torsional Moment given Angle of Twist

Formula

`"L" = "θ"*("G"*"d"_{"torl"}^4)/(584*"Mt"_{"shaft"})`

Example

`"450.0228mm"="15.42°"*("90000N/mm²"*("43.5mm")^4)/(584*"3.3E5N*mm")`

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Length of Shaft Subjected to Torsional Moment given Angle of Twist Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Shaft from Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(584*Torsional Moment in Shaft)
L = θ*(G*d_torl^4)/(584*Mt_shaft)
This formula uses 5 Variables

Variables Used

Length of Shaft from Torsional Rigidity - (Measured in Meter) - Length of Shaft from Torsional Rigidity is the length of the shaft calculated on the basis of torsional rigidity.
Angle of Twist in Shaft - (Measured in Radian) - Angle of Twist in Shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.
Modulus of Rigidity of Shaft - (Measured in Pascal) - Modulus of Rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid is s shaft.
Diameter of Shaft from Torsional Rigidity - (Measured in Meter) - Diameter of Shaft from Torsional Rigidity is the diameter of the external surface of a shaft calculated on the basis of torsional rigidity.
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.

STEP 1: Convert Input(s) to Base Unit

Angle of Twist in Shaft: 15.42 Degree --> 0.269129770657475 Radian (Check conversion here)
Modulus of Rigidity of Shaft: 90000 Newton per Square Millimeter --> 90000000000 Pascal (Check conversion here)
Diameter of Shaft from Torsional Rigidity: 43.5 Millimeter --> 0.0435 Meter (Check conversion here)
Torsional Moment in Shaft: 330000 Newton Millimeter --> 330 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = θ*(G*d_torl^4)/(584*Mt_shaft) --> 0.269129770657475*(90000000000*0.0435^4)/(584*330)

Evaluating ... ...

L = 0.45002277316367

STEP 3: Convert Result to Output's Unit

0.45002277316367 Meter -->450.02277316367 Millimeter (Check conversion here)

FINAL ANSWER

450.02277316367 ≈ 450.0228 Millimeter <-- Length of Shaft from Torsional Rigidity

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 5 Torsional Rigidity Calculators

Shaft Diameter given Angle of Twist in Shaft

Go Diameter of Shaft from Torsional Rigidity = (584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Modulus of Rigidity of Shaft*Angle of Twist in Shaft))^(1/4)

Length of Shaft Subjected to Torsional Moment given Angle of Twist

Go Length of Shaft from Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(584*Torsional Moment in Shaft)

Torsional Moment given Angle of Twist in Shaft

Go Torsional Moment in Shaft = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(Length of Shaft from Torsional Rigidity*584)

Modulus of Rigidity given Angle of Twist

Go Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4)

Angle of Twist of Shaft

Go Angle of Twist in Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)

Length of Shaft Subjected to Torsional Moment given Angle of Twist Formula

Define Torsional Moment?

Torsion is the twisting of a beam under the action of a torque (twisting moment). In the case of a torque, the force is tangential and the distance is the radial distance between this tangent and the axis of rotation.

How to Calculate Length of Shaft Subjected to Torsional Moment given Angle of Twist?

Length of Shaft Subjected to Torsional Moment given Angle of Twist calculator uses Length of Shaft from Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(584*Torsional Moment in Shaft) to calculate the Length of Shaft from Torsional Rigidity, The Length of Shaft Subjected to Torsional Moment given Angle of Twist formula is defined as the length of the shaft on which we are applying the torsional moment. Length of Shaft from Torsional Rigidity is denoted by L symbol.

How to calculate Length of Shaft Subjected to Torsional Moment given Angle of Twist using this online calculator? To use this online calculator for Length of Shaft Subjected to Torsional Moment given Angle of Twist, enter Angle of Twist in Shaft (θ), Modulus of Rigidity of Shaft (G), Diameter of Shaft from Torsional Rigidity (d_torl) & Torsional Moment in Shaft (Mt_shaft) and hit the calculate button. Here is how the Length of Shaft Subjected to Torsional Moment given Angle of Twist calculation can be explained with given input values -> 450022.8 = 0.269129770657475*(90000000000*0.0435^4)/(584*330).

FAQ

What is Length of Shaft Subjected to Torsional Moment given Angle of Twist?

The Length of Shaft Subjected to Torsional Moment given Angle of Twist formula is defined as the length of the shaft on which we are applying the torsional moment and is represented as L = θ*(G*d_torl^4)/(584*Mt_shaft) or Length of Shaft from Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(584*Torsional Moment in Shaft). Angle of Twist in Shaft is the angle through which the fixed end of a shaft rotates with respect to the free end, Modulus of Rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid is s shaft, Diameter of Shaft from Torsional Rigidity is the diameter of the external surface of a shaft calculated on the basis of 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.

How to calculate Length of Shaft Subjected to Torsional Moment given Angle of Twist?

The Length of Shaft Subjected to Torsional Moment given Angle of Twist formula is defined as the length of the shaft on which we are applying the torsional moment is calculated using Length of Shaft from Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(584*Torsional Moment in Shaft). To calculate Length of Shaft Subjected to Torsional Moment given Angle of Twist, you need Angle of Twist in Shaft (θ), Modulus of Rigidity of Shaft (G), Diameter of Shaft from Torsional Rigidity (d_torl) & Torsional Moment in Shaft (Mt_shaft). With our tool, you need to enter the respective value for Angle of Twist in Shaft, Modulus of Rigidity of Shaft, Diameter of Shaft from Torsional Rigidity & Torsional Moment in Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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