Static Deflection using Natural Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Static Deflection = (0.5615/Frequency)^2
δ = (0.5615/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 = (0.5615/f)^2 --> (0.5615/90)^2
Evaluating ... ...
δ = 3.89237345679012E-05
STEP 3: Convert Result to Output's Unit
3.89237345679012E-05 Meter --> No Conversion Required
FINAL ANSWER
3.89237345679012E-05 3.9E-5 Meter <-- Static Deflection
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Verified by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
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17 Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Static Deflection at Distance x from End A
Go Static deflection at distance x from end A = (Load per unit length*(Distance of small section of shaft from end A^4-2*Length of Shaft*Distance of small section of shaft from end A+Length of Shaft^3*Distance of small section of shaft from end A))/(24*Young's Modulus*Moment of inertia of shaft)
Natural Frequency due to Uniformly Distributed Load
Go Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Circular Frequency due to Uniformly Distributed Load
Go Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Maximum Bending Moment at Distance x from End A
Go Bending Moment = (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
Length of Shaft given Circular Frequency
Go Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Uniformly Distributed Load Unit Length given Circular Frequency
Go Load per unit length = (pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Moment of Inertia of Shaft given Circular Frequency
Go Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)
Length of Shaft given Natural Frequency
Go Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Uniformly Distributed Load Unit Length given Natural Frequency
Go 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)
Moment of Inertia of Shaft given Natural Frequency
Go Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)
Length of Shaft given Static Deflection
Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)
Moment of Inertia of Shaft given Static Deflection given Load per Unit Length
Go Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load
Go Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
Uniformly Distributed Load Unit Length given Static Deflection
Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)
Circular Frequency given Static Deflection
Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))
Natural Frequency given Static Deflection
Go Frequency = 0.5615/(sqrt(Static Deflection))
Static Deflection using Natural Frequency
Go Static Deflection = (0.5615/Frequency)^2

Static Deflection using Natural Frequency Formula

Static Deflection = (0.5615/Frequency)^2
δ = (0.5615/f)^2

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 Static Deflection using Natural Frequency?

Static Deflection using Natural Frequency calculator uses Static Deflection = (0.5615/Frequency)^2 to calculate the Static Deflection, The Static deflection using natural frequency 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 using Natural Frequency using this online calculator? To use this online calculator for Static Deflection using Natural Frequency, enter Frequency (f) and hit the calculate button. Here is how the Static Deflection using Natural Frequency calculation can be explained with given input values -> 3.9E-5 = (0.5615/90)^2.

FAQ

What is Static Deflection using Natural Frequency?
The Static deflection using natural frequency 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 = (0.5615/f)^2 or Static Deflection = (0.5615/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 using Natural Frequency?
The Static deflection using natural frequency 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 = (0.5615/Frequency)^2. To calculate Static Deflection using Natural Frequency, 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 = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
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