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Load at Free End in Free Transverse Vibrations 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

✖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%
✖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%
✖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 [I_shaft]			+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%

✖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 at Free End in Free Transverse Vibrations [W_attached]

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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_shaft^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 the force applied to the free end of a constraint in a system undergoing 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.
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.
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.
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.

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: 1.085522 Kilogram Square Meter --> 1.085522 Kilogram Square Meter No Conversion Required
Length of Shaft: 3.5 Meter --> 3.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_attached = (δ*3*E*I_shaft)/(L_shaft^3) --> (0.072*3*15*1.085522)/(3.5^3)

Evaluating ... ...

W_attached = 0.0820312834985423

STEP 3: Convert Result to Output's Unit

0.0820312834985423 Kilogram --> No Conversion Required

FINAL ANSWER

0.0820312834985423 ≈ 0.082031 Kilogram <-- Load Attached to Free End of Constraint

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » General Shaft » Load at Free End in Free Transverse Vibrations

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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)

Load at Free End in Free Transverse Vibrations Formula

LaTeX Go

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_shaft^3)

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, Load at Free End in Free Transverse Vibrations formula is defined as the maximum weight that can be attached to the free end of a shaft without causing it to vibrate excessively, which is critical in designing and optimizing mechanical systems to ensure stability and performance. 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_shaft) 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 -> 0.082031 = (0.072*3*15*1.085522)/(3.5^3).

FAQ

What is Load at Free End in Free Transverse Vibrations?

Load at Free End in Free Transverse Vibrations formula is defined as the maximum weight that can be attached to the free end of a shaft without causing it to vibrate excessively, which is critical in designing and optimizing mechanical systems to ensure stability and performance and is represented as W_attached = (δ*3*E*I_shaft)/(L_shaft^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 maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness, 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, 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 & Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

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

Load at Free End in Free Transverse Vibrations formula is defined as the maximum weight that can be attached to the free end of a shaft without causing it to vibrate excessively, which is critical in designing and optimizing mechanical systems to ensure stability and performance 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_shaft). 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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