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Moment of Inertia of Shaft given Static Deflection 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

✖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]			+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 [I_shaft]

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Moment of Inertia of Shaft given Static Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)
I_shaft = (W_attached*L_shaft^3)/(3*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 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.
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 Attached to Free End of Constraint: 0.453411 Kilogram --> 0.453411 Kilogram 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_attached*L_shaft^3)/(3*E*δ) --> (0.453411*3.5^3)/(3*15*0.072)

Evaluating ... ...

I_shaft = 5.99999895833333

STEP 3: Convert Result to Output's Unit

5.99999895833333 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

5.99999895833333 ≈ 5.999999 Kilogram Square Meter <-- Moment of inertia 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 » Moment of Inertia of Shaft given Static Deflection

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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)

Moment of Inertia of Shaft given Static Deflection Formula

LaTeX Go

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

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 Moment of Inertia of Shaft given Static Deflection?

Moment of Inertia of Shaft given Static Deflection calculator uses Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection) to calculate the Moment of inertia of shaft, Moment of Inertia of Shaft given Static Deflection formula is defined as a measure of the shaft's resistance to changes in its rotation, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the attached weight, length, and static deflection of the shaft. Moment of inertia of shaft is denoted by I_shaft symbol.

How to calculate Moment of Inertia of Shaft given Static Deflection using this online calculator? To use this online calculator for Moment of Inertia of Shaft given Static Deflection, enter Load Attached to Free End of Constraint (W_attached), 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 calculation can be explained with given input values -> 5.999999 = (0.453411*3.5^3)/(3*15*0.072).

FAQ

What is Moment of Inertia of Shaft given Static Deflection?

Moment of Inertia of Shaft given Static Deflection formula is defined as a measure of the shaft's resistance to changes in its rotation, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the attached weight, length, and static deflection of the shaft and is represented as I_shaft = (W_attached*L_shaft^3)/(3*E*δ) or Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection). 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, 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?

Moment of Inertia of Shaft given Static Deflection formula is defined as a measure of the shaft's resistance to changes in its rotation, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the attached weight, length, and static deflection of the shaft is calculated using Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection). To calculate Moment of Inertia of Shaft given Static Deflection, you need Load Attached to Free End of Constraint (W_attached), Length of Shaft (L_shaft), Young's Modulus (E) & Static Deflection (δ). With our tool, you need to enter the respective value for Load Attached to Free End of Constraint, 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.

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