Static Deflection given Moment of Inertia of Shaft Calculator

✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%

✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection given Moment of Inertia of Shaft [δ]

⎘ Copy

👎

Formula

✖

Static Deflection given Moment of Inertia of Shaft

Formula

`"δ" = ("W"_{"attached"}*"L"^3)/(3*"E"*"I"_{"shaft"})`

Example

`"0.660593m"=("0.52kg"*("7000mm")^3)/(3*"15N/m"*"6kg·m²")`

Calculator

LaTeX

Reset

👍

Download Longitudinal and Transverse Vibrations Formula PDF PDF Image

Static Deflection given Moment of Inertia of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)
δ = (W_attached*L^3)/(3*E*I_shaft)
This formula uses 5 Variables

Variables Used

Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
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.
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.

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
Moment of inertia of shaft: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (W_attached*L^3)/(3*E*I_shaft) --> (0.52*7^3)/(3*15*6)

Evaluating ... ...

δ = 0.660592592592593

STEP 3: Convert Result to Output's Unit

0.660592592592593 Meter --> No Conversion Required

FINAL ANSWER

0.660592592592593 ≈ 0.660593 Meter <-- Static Deflection

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Static Deflection given Moment of Inertia of Shaft

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

Static Deflection given Moment of Inertia of Shaft Formula

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

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 Static Deflection given Moment of Inertia of Shaft?

Static Deflection given Moment of Inertia of Shaft calculator uses Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft) to calculate the Static Deflection, The Static Deflection given Moment of Inertia of Shaft formula is defined as a deflection resulting from an applied load which remains after the removal of the load. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection given Moment of Inertia of Shaft using this online calculator? To use this online calculator for Static Deflection given Moment of Inertia of Shaft, enter Load Attached to Free End of Constraint (W_attached), Length of Shaft (L), Young's Modulus (E) & Moment of inertia of shaft (I_shaft) and hit the calculate button. Here is how the Static Deflection given Moment of Inertia of Shaft calculation can be explained with given input values -> 0.660593 = (0.52*7^3)/(3*15*6).

FAQ

What is Static Deflection given Moment of Inertia of Shaft?

The Static Deflection given Moment of Inertia of Shaft formula is defined as a deflection resulting from an applied load which remains after the removal of the load and is represented as δ = (W_attached*L^3)/(3*E*I_shaft) or Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft). 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 & Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.

How to calculate Static Deflection given Moment of Inertia of Shaft?

The Static Deflection given Moment of Inertia of Shaft formula is defined as a deflection resulting from an applied load which remains after the removal of the load is calculated using Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft). To calculate Static Deflection given Moment of Inertia of Shaft, you need Load Attached to Free End of Constraint (W_attached), Length of Shaft (L), Young's Modulus (E) & Moment of inertia of shaft (I_shaft). With our tool, you need to enter the respective value for Load Attached to Free End of Constraint, Length of Shaft, Young's Modulus & Moment of inertia of shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search