Static Deflection at Distance x from End A given Length of Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
y = (w/(24*E*Ishaft))*(x^4+(Lshaft*x)^2-2*Lshaft*x^3)
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Load per unit length: 3 --> No Conversion Required
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
Distance of small section of shaft from end A: 0.05 Meter --> 0.05 Meter No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
y = (w/(24*E*Ishaft))*(x^4+(Lshaft*x)^2-2*Lshaft*x^3) --> (3/(24*15*6))*(0.05^4+(4.5*0.05)^2-2*4.5*0.05^3)
Evaluating ... ...
y = 6.87586805555556E-05
STEP 3: Convert Result to Output's Unit
6.87586805555556E-05 Meter --> No Conversion Required
FINAL ANSWER
6.87586805555556E-05 6.9E-5 Meter <-- Static deflection at distance x from end A
(Calculation completed in 00.020 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 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 at Distance x from End A given Length of Shaft Formula

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

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 at Distance x from End A given Length of Shaft?

Static Deflection at Distance x from End A given Length of Shaft calculator uses 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) to calculate the Static deflection at distance x from end A, The Static deflection at distance x from end A given length of shaft 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 given Length of Shaft using this online calculator? To use this online calculator for Static Deflection at Distance x from End A given Length of Shaft, enter Load per unit length (w), Young's Modulus (E), Moment of inertia of shaft (Ishaft), Distance of small section of shaft from end A (x) & Length of Shaft (Lshaft) and hit the calculate button. Here is how the Static Deflection at Distance x from End A given Length of Shaft calculation can be explained with given input values -> 6.9E-5 = (3/(24*15*6))*(0.05^4+(4.5*0.05)^2-2*4.5*0.05^3).

FAQ

What is Static Deflection at Distance x from End A given Length of Shaft?
The Static deflection at distance x from end A given length of shaft 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/(24*E*Ishaft))*(x^4+(Lshaft*x)^2-2*Lshaft*x^3) or 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). Load per unit length is the distributed load which is spread over a surface or line, 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, 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.
How to calculate Static Deflection at Distance x from End A given Length of Shaft?
The Static deflection at distance x from end A given length of shaft 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/(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). To calculate Static Deflection at Distance x from End A given Length of Shaft, you need Load per unit length (w), Young's Modulus (E), Moment of inertia of shaft (Ishaft), Distance of small section of shaft from end A (x) & Length of Shaft (Lshaft). With our tool, you need to enter the respective value for Load per unit length, Young's Modulus, Moment of inertia of shaft, Distance of small section of shaft from end A & Length 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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