Length of Shaft Calculator

✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection [δ]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%

✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]

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Formula

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Length of Shaft

Formula

`"L" = (("δ"*3*"E"*"I"_{"shaft"})/("W"_{"attached"}))^(1/3)`

Example

`"3343.728mm"=(("0.072m"*3*"15N/m"*"6kg·m²")/("0.52kg"))^(1/3)`

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Download Longitudinal and Transverse Vibrations Formula PDF

Length of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)
L = ((δ*3*E*I_shaft)/(W_attached))^(1/3)
This formula uses 5 Variables

Variables Used

Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.

STEP 1: Convert Input(s) to Base Unit

Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of inertia of shaft: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = ((δ*3*E*I_shaft)/(W_attached))^(1/3) --> ((0.072*3*15*6)/(0.52))^(1/3)

Evaluating ... ...

L = 3.34372823387718

STEP 3: Convert Result to Output's Unit

3.34372823387718 Meter -->3343.72823387718 Millimeter (Check conversion here)

FINAL ANSWER

3343.72823387718 ≈ 3343.728 Millimeter <-- Length of Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Length of Shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 8 Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft

Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)

Static Deflection given Moment of Inertia of Shaft

Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)

Moment of Inertia of Shaft given Static Deflection

Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)

Load at Free End in Free Transverse Vibrations

Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Natural Frequency of Free Transverse Vibrations

Go Frequency = (sqrt(Stiffness of Shaft/Load Attached to Free End of Constraint))/2*pi

Time Period of Free Transverse Vibrations

Go Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft)

Acceleration of Body given Stiffness of Shaft

Go Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint

Restoring Force using Stiffness of Shaft

Go Force = -Stiffness of Shaft*Displacement of Body

Length of Shaft Formula

Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)
L = ((δ*3*E*I_shaft)/(W_attached))^(1/3)

What are transverse vibrations?

A vibration in which the element moves to and fro in a direction perpendicular to the direction of the advance of the wave.

What is free vibration analysis?

Unlike static structural analyses, free vibration analyses do not require that rigid-body motion be prevented. The boundary conditions are important, as they affect the mode shapes and frequencies of the part.

How to Calculate Length of Shaft?

Length of Shaft calculator uses Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3) to calculate the Length of Shaft, The Length of shaft formula is defined as a measure of distance. Length is the term used for identifying the size of an object or distance from one point to Length is a measure of how long an object is or the distance between two points. Length of Shaft is denoted by L symbol.

How to calculate Length of Shaft using this online calculator? To use this online calculator for Length of Shaft, enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load Attached to Free End of Constraint (W_attached) and hit the calculate button. Here is how the Length of Shaft calculation can be explained with given input values -> 3.3E+6 = ((0.072*3*15*6)/(0.52))^(1/3).

FAQ

What is Length of Shaft?

The Length of shaft formula is defined as a measure of distance. Length is the term used for identifying the size of an object or distance from one point to Length is a measure of how long an object is or the distance between two points and is represented as L = ((δ*3*E*I_shaft)/(W_attached))^(1/3) or Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3). Static deflection is the extension or compression of the constraint, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation & Load attached to free end of constraint is a weight or source of pressure.

How to calculate Length of Shaft?

The Length of shaft formula is defined as a measure of distance. Length is the term used for identifying the size of an object or distance from one point to Length is a measure of how long an object is or the distance between two points is calculated using Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3). To calculate Length of Shaft, you need Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load Attached to Free End of Constraint (W_attached). With our tool, you need to enter the respective value for Static Deflection, Young's Modulus, Moment of inertia of shaft & Load Attached to Free End of Constraint 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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