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Uniformly Distributed Load Unit Length given Natural Frequency 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

✖Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.ⓘ Frequency [f]			+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%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Uniformly Distributed Load Unit Length given Natural Frequency [w]

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Uniformly Distributed Load Unit Length given Natural Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
w = (pi^2)/(4*f^2)*(E*I_shaft*g)/(L_shaft^4)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.

STEP 1: Convert Input(s) to Base Unit

Frequency: 90 Hertz --> 90 Hertz 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
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second 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 = (pi^2)/(4*f^2)*(E*I_shaft*g)/(L_shaft^4) --> (pi^2)/(4*90^2)*(15*1.085522*9.8)/(3.5^4)

Evaluating ... ...

w = 0.000323920565644122

STEP 3: Convert Result to Output's Unit

0.000323920565644122 --> No Conversion Required

FINAL ANSWER

0.000323920565644122 ≈ 0.000324 <-- Load per unit length

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Natural Frequency of Free Transverse Vibrations » Uniformly Distributed Load Unit Length given Natural Frequency

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National Institute Of Technology (NIT), Hamirpur

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< 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)

Uniformly Distributed Load Unit Length given Natural Frequency Formula

Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
w = (pi^2)/(4*f^2)*(E*I_shaft*g)/(L_shaft^4)

What is transverse and longitudinal vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Uniformly Distributed Load Unit Length given Natural Frequency?

Uniformly Distributed Load Unit Length given Natural Frequency calculator uses Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4) to calculate the Load per unit length, Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as a measure of the load per unit length of a shaft in a mechanical system, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the shaft's modulus of elasticity, moment of inertia, and length. Load per unit length is denoted by w symbol.

How to calculate Uniformly Distributed Load Unit Length given Natural Frequency using this online calculator? To use this online calculator for Uniformly Distributed Load Unit Length given Natural Frequency, enter Frequency (f), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g) & Length of Shaft (L_shaft) and hit the calculate button. Here is how the Uniformly Distributed Load Unit Length given Natural Frequency calculation can be explained with given input values -> 0.00179 = (pi^2)/(4*90^2)*(15*1.085522*9.8)/(3.5^4).

FAQ

What is Uniformly Distributed Load Unit Length given Natural Frequency?

Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as a measure of the load per unit length of a shaft in a mechanical system, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the shaft's modulus of elasticity, moment of inertia, and length and is represented as w = (pi^2)/(4*f^2)*(E*I_shaft*g)/(L_shaft^4) or Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4). Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second, 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, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Length of shaft is the distance between two ends of shaft.

How to calculate Uniformly Distributed Load Unit Length given Natural Frequency?

Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as a measure of the load per unit length of a shaft in a mechanical system, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the shaft's modulus of elasticity, moment of inertia, and length is calculated using Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4). To calculate Uniformly Distributed Load Unit Length given Natural Frequency, you need Frequency (f), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g) & Length of Shaft (L_shaft). With our tool, you need to enter the respective value for Frequency, Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity & Length of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Load per unit length?

In this formula, Load per unit length uses Frequency, Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity & Length of Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -

Load per unit length = (3.573^2)*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Frequency^2))
Load per unit length = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Natural Circular Frequency^2))
Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4))

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