Load at Free End in Free Transverse Vibrations Calculator

✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection [δ]			+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%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%

✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load at Free End in Free Transverse Vibrations [W_attached]

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Formula

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Load at Free End in Free Transverse Vibrations

Formula

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

Example

`"0.056676kg"=("0.072m"*3*"15N/m"*"6kg·m²")/(("7000mm")^3)`

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Download Longitudinal and Transverse Vibrations Formula PDF

Load at Free End in Free Transverse Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
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.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.

STEP 1: Convert Input(s) to Base Unit

Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required
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
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_attached = (δ*3*E*I_shaft)/(L^3) --> (0.072*3*15*6)/(7^3)

Evaluating ... ...

W_attached = 0.0566763848396501

STEP 3: Convert Result to Output's Unit

0.0566763848396501 Kilogram --> No Conversion Required

FINAL ANSWER

0.0566763848396501 ≈ 0.056676 Kilogram <-- Load Attached to Free End of Constraint

(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 » Load at Free End in Free Transverse Vibrations

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 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

Load at Free End in Free Transverse Vibrations Formula

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

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 Load at Free End in Free Transverse Vibrations?

Load at Free End in Free Transverse Vibrations calculator uses Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3) to calculate the Load Attached to Free End of Constraint, The Load at Free End in Free Transverse Vibrations formula is defined as a large quantity or heavy object, which is being carried at the end of the shaft. Load Attached to Free End of Constraint is denoted by W_attached symbol.

How to calculate Load at Free End in Free Transverse Vibrations using this online calculator? To use this online calculator for Load at Free End in Free Transverse Vibrations, enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L) and hit the calculate button. Here is how the Load at Free End in Free Transverse Vibrations calculation can be explained with given input values -> 0.056676 = (0.072*3*15*6)/(7^3).

FAQ

What is Load at Free End in Free Transverse Vibrations?

The Load at Free End in Free Transverse Vibrations formula is defined as a large quantity or heavy object, which is being carried at the end of the shaft and is represented as W_attached = (δ*3*E*I_shaft)/(L^3) or Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3). Static deflection is the extension or compression of the constraint, 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 & The Length of Shaft is the distance between two ends of shaft.

How to calculate Load at Free End in Free Transverse Vibrations?

The Load at Free End in Free Transverse Vibrations formula is defined as a large quantity or heavy object, which is being carried at the end of the shaft is calculated using Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3). To calculate Load at Free End in Free Transverse Vibrations, you need Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L). With our tool, you need to enter the respective value for Static Deflection, Young's Modulus, Moment of inertia of shaft & Length of Shaft 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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