Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) Solution

STEP 0: Pre-Calculation Summary
Formula Used
Static Deflection = (0.571/Frequency)^2
δ = (0.571/f)^2
This formula uses 2 Variables
Variables Used
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
STEP 1: Convert Input(s) to Base Unit
Frequency: 90 Hertz --> 90 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δ = (0.571/f)^2 --> (0.571/90)^2
Evaluating ... ...
δ = 4.0251975308642E-05
STEP 3: Convert Result to Output's Unit
4.0251975308642E-05 Meter --> No Conversion Required
FINAL ANSWER
4.0251975308642E-05 4E-5 Meter <-- Static Deflection
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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17 Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

Static Deflection at Distance x from End A given Length of Shaft
Go Static deflection at distance x from end A = (Load per unit length/(24*Young's Modulus*Moment of inertia of shaft))*(Distance of small section of shaft from end A^4+(Length of Shaft*Distance of small section of shaft from end A)^2-2*Length of Shaft*Distance of small section of shaft from end A^3)
Bending Moment at Some Distance from One End
Go Bending Moment = ((Load per unit length*Length of Shaft^2)/12)+((Load per unit length*Distance of small section of shaft from end A^2)/2)-((Load per unit length*Length of Shaft*Distance of small section of shaft from end A)/2)
Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load
Go Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load
Go Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Length of Shaft = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Natural Circular Frequency^2))^(1/4)
Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)
Go 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))
M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity)
Length of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Length of Shaft = 3.573^2*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Frequency^2))^(1/4)
Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load
Go 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))
M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load
Go Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity)
Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4)
Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4))
M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load
Go Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft
Go Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))
Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Frequency = 0.571/(sqrt(Static Deflection))
Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Static Deflection = (0.571/Frequency)^2

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

Static Deflection = (0.571/Frequency)^2
δ = (0.571/f)^2

What is a transverse wave definition?

Transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

How to Calculate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) calculator uses Static Deflection = (0.571/Frequency)^2 to calculate the Static Deflection, The Static deflection given natural frequency (Shaft fixed, uniformly distributed load) formula is defined as the degree to which a structural element is displaced under a load (due to its deformation). Static Deflection is denoted by δ symbol.

How to calculate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load), enter Frequency (f) and hit the calculate button. Here is how the Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 4E-5 = (0.571/90)^2.

FAQ

What is Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?
The Static deflection given natural frequency (Shaft fixed, uniformly distributed load) formula is defined as the degree to which a structural element is displaced under a load (due to its deformation) and is represented as δ = (0.571/f)^2 or Static Deflection = (0.571/Frequency)^2. Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
How to calculate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?
The Static deflection given natural frequency (Shaft fixed, uniformly distributed load) formula is defined as the degree to which a structural element is displaced under a load (due to its deformation) is calculated using Static Deflection = (0.571/Frequency)^2. To calculate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load), you need Frequency (f). With our tool, you need to enter the respective value for Frequency 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 Static Deflection?
In this formula, Static Deflection uses Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
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