Static Deflection at Distance x from End A Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
y = (w*(x^4-2*Lshaft*x+Lshaft^3*x))/(24*E*Ishaft)
This formula uses 6 Variables
Variables Used
Static deflection at distance x from end A - (Measured in Meter) - Static deflection at distance x from end A is the degree to which a structural element is displaced under a load.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Distance of small section of shaft from end A - (Measured in Meter) - Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.
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.
STEP 1: Convert Input(s) to Base Unit
Load per unit length: 3 --> No Conversion Required
Distance of small section of shaft from end A: 5 Meter --> 5 Meter No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of inertia of shaft: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
y = (w*(x^4-2*Lshaft*x+Lshaft^3*x))/(24*E*Ishaft) --> (3*(5^4-2*4.5*5+4.5^3*5))/(24*15*6)
Evaluating ... ...
y = 1.43836805555556
STEP 3: Convert Result to Output's Unit
1.43836805555556 Meter --> No Conversion Required
FINAL ANSWER
1.43836805555556 1.438368 Meter <-- Static deflection at distance x from end A
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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 at Distance x from End A Formula

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)
y = (w*(x^4-2*Lshaft*x+Lshaft^3*x))/(24*E*Ishaft)

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 at Distance x from End A?

Static Deflection at Distance x from End A calculator uses 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) to calculate the Static deflection at distance x from end A, The Static deflection at distance x from end A formula is defined as the degree to which a structural element is displaced under a load (due to its deformation). Static deflection at distance x from end A is denoted by y symbol.

How to calculate Static Deflection at Distance x from End A using this online calculator? To use this online calculator for Static Deflection at Distance x from End A, enter Load per unit length (w), Distance of small section of shaft from end A (x), Length of Shaft (Lshaft), Young's Modulus (E) & Moment of inertia of shaft (Ishaft) and hit the calculate button. Here is how the Static Deflection at Distance x from End A calculation can be explained with given input values -> 0.005703 = (3*(5^4-2*4.5*5+4.5^3*5))/(24*15*6).

FAQ

What is Static Deflection at Distance x from End A?
The Static deflection at distance x from end A formula is defined as the degree to which a structural element is displaced under a load (due to its deformation) and is represented as y = (w*(x^4-2*Lshaft*x+Lshaft^3*x))/(24*E*Ishaft) or 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). Load per unit length is the distributed load which is spread over a surface or line, Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are, Length of shaft is the distance between two ends of shaft, 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.
How to calculate Static Deflection at Distance x from End A?
The Static deflection at distance x from end A 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 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). To calculate Static Deflection at Distance x from End A, you need Load per unit length (w), Distance of small section of shaft from end A (x), Length of Shaft (Lshaft), Young's Modulus (E) & Moment of inertia of shaft (Ishaft). With our tool, you need to enter the respective value for Load per unit length, Distance of small section of shaft from end A, Length of Shaft, Young's Modulus & Moment of inertia of shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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