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Moment of Inertia of Shaft given Static Deflection given Load per Unit Length 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

✖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 [L_shaft]			+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%
✖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%

✖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 given Static Deflection given Load per Unit Length [I_shaft]

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Moment of Inertia of Shaft given Static Deflection given Load per Unit Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Load per unit length: 3 --> No Conversion Required
Length of Shaft: 3.5 Meter --> 3.5 Meter No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_shaft = (5*w*L_shaft^4)/(384*E*δ) --> (5*3*3.5^4)/(384*15*0.072)

Evaluating ... ...

I_shaft = 5.42760778356481

STEP 3: Convert Result to Output's Unit

5.42760778356481 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

5.42760778356481 ≈ 5.427608 Kilogram Square Meter <-- Moment of inertia of shaft

(Calculation completed in 00.020 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 » Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

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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))

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length Formula

LaTeX Go

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

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 Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length calculator uses Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection) to calculate the Moment of inertia of shaft, Moment of Inertia of Shaft given Static Deflection given Load per Unit Length formula is defined as a measure of an object's resistance to changes in its rotation, which is crucial in determining the natural frequency of free transverse vibrations in a shaft, and is influenced by the shaft's length, load per unit length, and modulus of elasticity. Moment of inertia of shaft is denoted by I_shaft symbol.

How to calculate Moment of Inertia of Shaft given Static Deflection given Load per Unit Length using this online calculator? To use this online calculator for Moment of Inertia of Shaft given Static Deflection given Load per Unit Length, enter Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Static Deflection (δ) and hit the calculate button. Here is how the Moment of Inertia of Shaft given Static Deflection given Load per Unit Length calculation can be explained with given input values -> 5.427608 = (5*3*3.5^4)/(384*15*0.072).

FAQ

What is Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length formula is defined as a measure of an object's resistance to changes in its rotation, which is crucial in determining the natural frequency of free transverse vibrations in a shaft, and is influenced by the shaft's length, load per unit length, and modulus of elasticity and is represented as I_shaft = (5*w*L_shaft^4)/(384*E*δ) or Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection). Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations, Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft, 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 & Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

How to calculate Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length formula is defined as a measure of an object's resistance to changes in its rotation, which is crucial in determining the natural frequency of free transverse vibrations in a shaft, and is influenced by the shaft's length, load per unit length, and modulus of elasticity is calculated using Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection). To calculate Moment of Inertia of Shaft given Static Deflection given Load per Unit Length, you need Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Static Deflection (δ). With our tool, you need to enter the respective value for Load per unit length, Length of Shaft, Young's Modulus & Static Deflection 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 Moment of inertia of shaft?

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

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

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