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## Credits

National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 1000+ more calculators!
Indian Institute of Information Technology (IIIT), Guwahati
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## Static deflection of a simply supported shaft due to uniformly distributed load Solution

STEP 0: Pre-Calculation Summary
Formula Used
static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft)
δ = (5*w*(l^4))/(384*E*I)
This formula uses 4 Variables
Variables Used
Load per unit length- Load per unit length is the distributed load which is spread over a surface or line.
Length of Shaft - The Length of Shaft is the distance between two ends of shaft. (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)
STEP 1: Convert Input(s) to Base Unit
Load per unit length: 3 --> No Conversion Required
Length of Shaft: 50 Meter --> 50 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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δ = (5*w*(l^4))/(384*E*I) --> (5*3*(50^4))/(384*100000000000*6)
Evaluating ... ...
δ = 4.06901041666667E-07
STEP 3: Convert Result to Output's Unit
4.06901041666667E-07 Meter --> No Conversion Required
FINAL ANSWER
4.06901041666667E-07 Meter <-- Static deflection
(Calculation completed in 00.015 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

### Static deflection of a simply supported shaft due to uniformly distributed load Formula

static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft)
δ = (5*w*(l^4))/(384*E*I)

## 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 of a simply supported shaft due to uniformly distributed load?

Static deflection of a simply supported shaft due to uniformly distributed load calculator uses static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft) to calculate the Static deflection, The Static deflection of a simply supported shaft due to 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 and is denoted by δ symbol.

How to calculate Static deflection of a simply supported shaft due to uniformly distributed load using this online calculator? To use this online calculator for Static deflection of a simply supported shaft due to uniformly distributed load, enter Load per unit length (w), Length of Shaft (l), Young's Modulus (E) and Moment of inertia of the shaft (I) and hit the calculate button. Here is how the Static deflection of a simply supported shaft due to uniformly distributed load calculation can be explained with given input values -> 4.069E-7 = (5*3*(50^4))/(384*100000000000*6).

### FAQ

What is Static deflection of a simply supported shaft due to uniformly distributed load?
The Static deflection of a simply supported shaft due to 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 = (5*w*(l^4))/(384*E*I) or static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft). Load per unit length is the distributed load which is spread over a surface or line, The Length of Shaft is the distance between two ends of shaft, 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) and Moment of inertia of the shaft can be calculated by taking the distance of each particle from the axis of rotation.
How to calculate Static deflection of a simply supported shaft due to uniformly distributed load?
The Static deflection of a simply supported shaft due to 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 = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft). To calculate Static deflection of a simply supported shaft due to uniformly distributed load, you need Load per unit length (w), Length of Shaft (l), Young's Modulus (E) and Moment of inertia of the shaft (I). With our tool, you need to enter the respective value for Load per unit length, Length of Shaft, Young's Modulus and Moment of inertia of the 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 Static deflection?
In this formula, Static deflection uses Load per unit length, Length of Shaft, Young's Modulus and Moment of inertia of the shaft. 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)
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