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Length of the shaft in terms of static deflection Solution

STEP 0: Pre-Calculation Summary
Formula Used
length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4)
l = ((δ*384*E*I)/(5*w))^(1/4)
This formula uses 4 Variables
Variables Used
Static deflection - Static deflection extension or compression of the constraint. (Measured in Meter)
Young's Modulus - Young's Modulus which can also be called elastic modulus is a mechanical property of linear elastic solid substances. It describes the relationship between stress (force per unit area) and strain (proportional deformation in an object). (Measured in Gigapascal)
Moment of inertia of the shaft - Moment of inertia of the shaft can be calculated by taking the distance of each particle from the axis of rotation. (Measured in Kilogram Meter²)
Load per unit length- Load per unit length is the distributed load which is spread over a surface or line.
STEP 1: Convert Input(s) to Base Unit
Static deflection: 2 Meter --> 2 Meter No Conversion Required
Young's Modulus: 100 Gigapascal --> 100000000000 Pascal (Check conversion here)
Moment of inertia of the shaft: 6 Kilogram Meter² --> 6 Kilogram Meter² No Conversion Required
Load per unit length: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = ((δ*384*E*I)/(5*w))^(1/4) --> ((2*384*100000000000*6)/(5*3))^(1/4)
Evaluating ... ...
l = 2354.26476510617
STEP 3: Convert Result to Output's Unit
2354.26476510617 Meter --> No Conversion Required
FINAL ANSWER
2354.26476510617 Meter <-- Length of Shaft
(Calculation completed in 00.016 seconds)

10+ Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of the shaft in terms of circular frequency
length_of_shaft = (((pi^4)/(Natural circular frequency^2))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4) Go
Length of the shaft in terms of natural frequency
length_of_shaft = (((pi^2)/(4*(frequency^2)))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4) Go
Moment of Inertia of shaft in terms of circular frequency
moment_inertia_shaft = ((Natural circular frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^4)*Young's Modulus*Acceleration Due To Gravity) Go
Moment of Inertia of shaft in terms of natural frequency
moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity) Go
Length of the shaft in terms of static deflection
length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4) Go
Uniformly distributed load unit length in terms of static deflection
load_per_unit_length = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*(Length of Shaft^4))) Go
Static deflection of a simply supported shaft due to uniformly distributed load
static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft) Go
Moment of Inertia of shaft in terms of static deflection if load per unit length is known
moment_inertia_shaft = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Static deflection) Go
Circular frequency in terms of static deflection
natural_circular_frequency = 2*pi*(0.5615/(sqrt(Static deflection))) Go
Natural frequency in terms of static deflection
frequency = 0.5615/(sqrt(Static deflection)) Go

Length of the shaft in terms of static deflection Formula

length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4)
l = ((δ*384*E*I)/(5*w))^(1/4)

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 Length of the shaft in terms of static deflection?

Length of the shaft in terms of static deflection calculator uses length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4) to calculate the Length of Shaft, The Length of the shaft in terms of static deflection formula is defined as the term used for identifying the size of a shaft or distance from one end to another end. Length of Shaft and is denoted by l symbol.

How to calculate Length of the shaft in terms of static deflection using this online calculator? To use this online calculator for Length of the shaft in terms of static deflection, enter Static deflection (δ), Young's Modulus (E), Moment of inertia of the shaft (I) and Load per unit length (w) and hit the calculate button. Here is how the Length of the shaft in terms of static deflection calculation can be explained with given input values -> 2354.265 = ((2*384*100000000000*6)/(5*3))^(1/4).

FAQ

What is Length of the shaft in terms of static deflection?
The Length of the shaft in terms of static deflection formula is defined as the term used for identifying the size of a shaft or distance from one end to another end and is represented as l = ((δ*384*E*I)/(5*w))^(1/4) or length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4). Static deflection extension or compression of the constraint, Young's Modulus which can also be called elastic modulus is a mechanical property of linear elastic solid substances. It describes the relationship between stress (force per unit area) and strain (proportional deformation in an object), Moment of inertia of the shaft can be calculated by taking the distance of each particle from the axis of rotation and Load per unit length is the distributed load which is spread over a surface or line.
How to calculate Length of the shaft in terms of static deflection?
The Length of the shaft in terms of static deflection formula is defined as the term used for identifying the size of a shaft or distance from one end to another end is calculated using length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4). To calculate Length of the shaft in terms of static deflection, you need Static deflection (δ), Young's Modulus (E), Moment of inertia of the shaft (I) and Load per unit length (w). With our tool, you need to enter the respective value for Static deflection, Young's Modulus, Moment of inertia of the shaft and Load per unit length 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 Length of Shaft?
In this formula, Length of Shaft uses Static deflection, Young's Modulus, Moment of inertia of the shaft and Load per unit length. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • natural_circular_frequency = 2*pi*(0.5615/(sqrt(Static deflection)))
  • frequency = 0.5615/(sqrt(Static deflection))
  • load_per_unit_length = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*(Length of Shaft^4)))
  • length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4)
  • moment_inertia_shaft = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Static deflection)
  • static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft)
  • moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity)
  • moment_inertia_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 = (((pi^2)/(4*(frequency^2)))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4)
  • length_of_shaft = (((pi^4)/(Natural circular frequency^2))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4)
Where is the Length of the shaft in terms of static deflection calculator used?
Among many, Length of the shaft in terms of static deflection calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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