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M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load Calculator

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

✖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.ⓘ M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load [I_shaft]

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M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
I_shaft = (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 = (w*L_shaft^4)/(384*E*δ) --> (3*3.5^4)/(384*15*0.072)

Evaluating ... ...

I_shaft = 1.08552155671296

STEP 3: Convert Result to Output's Unit

1.08552155671296 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

1.08552155671296 ≈ 1.085522 Kilogram Square Meter <-- Moment of inertia of shaft

(Calculation completed in 00.004 seconds)

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< Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Frequency = 0.571/(sqrt(Static Deflection))

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Static Deflection = (0.571/Frequency)^2

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load Formula

LaTeX Go

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

What is a Transverse Wave definition?

Transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

How to Calculate M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load?

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load calculator uses Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection) to calculate the Moment of inertia of shaft, M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load formula is defined as a measure of the moment of inertia of a shaft under static deflection, which is essential in determining the natural frequency of free transverse vibrations in a shaft subjected to a uniformly distributed load. Moment of inertia of shaft is denoted by I_shaft symbol.

How to calculate M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load using this online calculator? To use this online calculator for M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load, 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 M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load calculation can be explained with given input values -> 1.085522 = (3*3.5^4)/(384*15*0.072).

FAQ

What is M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load?

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load formula is defined as a measure of the moment of inertia of a shaft under static deflection, which is essential in determining the natural frequency of free transverse vibrations in a shaft subjected to a uniformly distributed load and is represented as I_shaft = (w*L_shaft^4)/(384*E*δ) or Moment of inertia of shaft = (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 M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load?

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load formula is defined as a measure of the moment of inertia of a shaft under static deflection, which is essential in determining the natural frequency of free transverse vibrations in a shaft subjected to a uniformly distributed load is calculated using Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection). To calculate M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load, 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 = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity)
Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity)

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