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Length of Shaft given Static Deflection Calculator

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

✖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 per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Load per unit length [w]			+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 given Static Deflection [L_shaft]

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Length of Shaft given Static Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)
L_shaft = ((δ*384*E*I_shaft)/(5*w))^(1/4)
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 per unit length - Load per unit length is the force per unit length applied to a system, affecting its natural frequency of 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 per unit length: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_shaft = ((δ*384*E*I_shaft)/(5*w))^(1/4) --> ((0.072*384*15*1.085522)/(5*3))^(1/4)

Evaluating ... ...

L_shaft = 2.34059130637024

STEP 3: Convert Result to Output's Unit

2.34059130637024 Meter --> No Conversion Required

FINAL ANSWER

2.34059130637024 ≈ 2.340591 Meter <-- Length of Shaft

(Calculation completed in 00.016 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Uniformly Distributed Load Acting Over a Simply Supported Shaft » Length of Shaft given Static Deflection

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< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

LaTeX Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Static Deflection

LaTeX Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)

Circular Frequency given Static Deflection

LaTeX Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

LaTeX Go Frequency = 0.5615/(sqrt(Static Deflection))

Length of Shaft given Static Deflection Formula

LaTeX Go

Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)
L_shaft = ((δ*384*E*I_shaft)/(5*w))^(1/4)

What is Transverse and Longitudinal Vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Length of Shaft given Static Deflection?

Length of Shaft given Static Deflection calculator uses Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4) to calculate the Length of Shaft, Length of Shaft given Static Deflection formula is defined as a measure of the distance between two points on a shaft in a mechanical system, considering the static deflection caused by an external load, which is essential in designing and analyzing mechanical components. Length of Shaft is denoted by L_shaft symbol.

How to calculate Length of Shaft given Static Deflection using this online calculator? To use this online calculator for Length of Shaft given Static Deflection, enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load per unit length (w) and hit the calculate button. Here is how the Length of Shaft given Static Deflection calculation can be explained with given input values -> 2.340591 = ((0.072*384*15*1.085522)/(5*3))^(1/4).

FAQ

What is Length of Shaft given Static Deflection?

Length of Shaft given Static Deflection formula is defined as a measure of the distance between two points on a shaft in a mechanical system, considering the static deflection caused by an external load, which is essential in designing and analyzing mechanical components and is represented as L_shaft = ((δ*384*E*I_shaft)/(5*w))^(1/4) or Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4). 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 per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

How to calculate Length of Shaft given Static Deflection?

Length of Shaft given Static Deflection formula is defined as a measure of the distance between two points on a shaft in a mechanical system, considering the static deflection caused by an external load, which is essential in designing and analyzing mechanical components is calculated using Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4). To calculate Length of Shaft given Static Deflection, you need Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load per unit length (w). With our tool, you need to enter the respective value for Static Deflection, Young's Modulus, Moment of inertia of shaft & Load per unit length 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 Length of Shaft?

In this formula, Length of Shaft uses Static Deflection, Young's Modulus, Moment of inertia of shaft & Load per unit length. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)

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