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)
Ishaft = (Wattached*L^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 can be calculated by taking the distance of each particle from the axis of rotation.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
STEP 1: Convert Input(s) to Base Unit
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
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
Ishaft = (Wattached*L^3)/(3*E*δ) --> (0.52*7^3)/(3*15*0.072)
Evaluating ... ...
Ishaft = 55.0493827160494
STEP 3: Convert Result to Output's Unit
55.0493827160494 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
55.0493827160494 55.04938 Kilogram Square Meter <-- Moment of inertia of shaft
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
Dipto Mandal has verified this Calculator and 400+ more calculators!

8 Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft
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
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
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
Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)
Natural Frequency of Free Transverse Vibrations
Go Frequency = (sqrt(Stiffness of Shaft/Load Attached to Free End of Constraint))/2*pi
Time Period of Free Transverse Vibrations
Go Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft)
Acceleration of Body given Stiffness of Shaft
Go Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint
Restoring Force using Stiffness of Shaft
Go Force = -Stiffness of Shaft*Displacement of Body

Moment of Inertia of Shaft given Static Deflection Formula

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

What is free vibration analysis?

Unlike static structural analyses, free vibration analyses do not require that rigid-body motion be prevented. The boundary conditions are important, as they affect the mode shapes and frequencies of the part.

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, The Moment of Inertia of Shaft given Static Deflection can be calculated by taking the distance of each particle from the axis of rotation. Moment of inertia of shaft is denoted by Ishaft 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 (Wattached), Length of Shaft (L), 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 -> 55.04938 = (0.52*7^3)/(3*15*0.072).

FAQ

What is Moment of Inertia of Shaft given Static Deflection?
The Moment of Inertia of Shaft given Static Deflection can be calculated by taking the distance of each particle from the axis of rotation and is represented as Ishaft = (Wattached*L^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 a weight or source of pressure, The Length of Shaft is the distance between two ends of shaft, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain & Static deflection is the extension or compression of the constraint.
How to calculate Moment of Inertia of Shaft given Static Deflection?
The Moment of Inertia of Shaft given Static Deflection can be calculated by taking the distance of each particle from the axis of rotation 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 (Wattached), Length of Shaft (L), 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!