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Length of Shaft Calculator

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General Shaft Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Shaft Subjected to a Number of Point Loads Uniformly Distributed Load Acting Over a Simply Supported Shaft

✖Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.ⓘ Static Deflection [δ]			+10% -10%
✖Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%

✖Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.ⓘ Length of Shaft [L_shaft]

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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_shaft = ((δ*3*E*I_shaft)/(W_attached))^(1/3)
This formula uses 5 Variables

Variables Used

Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.
Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.

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: 1.085522 Kilogram Square Meter --> 1.085522 Kilogram Square Meter No Conversion Required
Load Attached to Free End of Constraint: 0.453411 Kilogram --> 0.453411 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_shaft = ((δ*3*E*I_shaft)/(W_attached))^(1/3) --> ((0.072*3*15*1.085522)/(0.453411))^(1/3)

Evaluating ... ...

L_shaft = 1.97953808889316

STEP 3: Convert Result to Output's Unit

1.97953808889316 Meter --> No Conversion Required

FINAL ANSWER

1.97953808889316 ≈ 1.979538 Meter <-- 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 » Mechanical » General Shaft » Length of Shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< General Shaft Calculators

Length of Shaft

LaTeX 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

LaTeX 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

LaTeX 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

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

Length of Shaft Formula

LaTeX Go

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

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, Length of Shaft formula is defined as the distance between the points of support in a shaft, which is a critical parameter in determining the natural frequency of free transverse vibrations, and is influenced by factors such as the shaft's modulus of elasticity, moment of inertia, and the weight of the attached load. Length of Shaft is denoted by L_shaft 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 -> 1.979538 = ((0.072*3*15*1.085522)/(0.453411))^(1/3).

FAQ

What is Length of Shaft?

Length of Shaft formula is defined as the distance between the points of support in a shaft, which is a critical parameter in determining the natural frequency of free transverse vibrations, and is influenced by factors such as the shaft's modulus of elasticity, moment of inertia, and the weight of the attached load and is represented as L_shaft = ((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 maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness, Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations, Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations & Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.

How to calculate Length of Shaft?

Length of Shaft formula is defined as the distance between the points of support in a shaft, which is a critical parameter in determining the natural frequency of free transverse vibrations, and is influenced by factors such as the shaft's modulus of elasticity, moment of inertia, and the weight of the attached load 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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