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Static Deflection at Distance x from End A Calculator

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General Shaft Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Shaft Subjected to a Number of Point Loads Uniformly Distributed Load Acting Over a Simply Supported Shaft

✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Load per unit length [w]			+10% -10%
✖Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are.ⓘ Distance of small section of shaft from end A [x]			+10% -10%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%

✖Static deflection at distance x from end A is the degree to which a structural element is displaced under a load.ⓘ Static Deflection at Distance x from End A [y]

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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*L_shaft*x+L_shaft^3*x))/(24*E*I_shaft)
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: 3.5 Meter --> 3.5 Meter No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of inertia of shaft: 1.085522 Kilogram Square Meter --> 1.085522 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = (w*(x^4-2*L_shaft*x+L_shaft^3*x))/(24*E*I_shaft) --> (3*(5^4-2*3.5*5+3.5^3*5))/(24*15*1.085522)

Evaluating ... ...

y = 6.17502455040064

STEP 3: Convert Result to Output's Unit

6.17502455040064 Meter --> No Conversion Required

FINAL ANSWER

6.17502455040064 ≈ 6.175025 Meter <-- Static deflection at distance x from end A

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Natural Frequency of Free Transverse Vibrations » Static Deflection at Distance x from End A

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National Institute Of Technology (NIT), Hamirpur

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< Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft

Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)

Static Deflection given Moment of Inertia of Shaft

Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)

Moment of Inertia of Shaft given Static Deflection

Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)

Load at Free End in Free Transverse Vibrations

Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Static Deflection at Distance x from End A Formula

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, Static Deflection at Distance x from End A formula is defined as a measure of the bending or deformation of a shaft at a specific point due to an applied load, providing insight into the shaft's mechanical behavior and stress distribution under various loading conditions. 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 (L_shaft), Young's Modulus (E) & Moment of inertia of shaft (I_shaft) 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 -> 1.117188 = (3*(5^4-2*3.5*5+3.5^3*5))/(24*15*1.085522).

FAQ

What is Static Deflection at Distance x from End A?

Static Deflection at Distance x from End A formula is defined as a measure of the bending or deformation of a shaft at a specific point due to an applied load, providing insight into the shaft's mechanical behavior and stress distribution under various loading conditions and is represented as y = (w*(x^4-2*L_shaft*x+L_shaft^3*x))/(24*E*I_shaft) 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?

Static Deflection at Distance x from End A formula is defined as a measure of the bending or deformation of a shaft at a specific point due to an applied load, providing insight into the shaft's mechanical behavior and stress distribution under various loading conditions 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 (L_shaft), Young's Modulus (E) & Moment of inertia of shaft (I_shaft). 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.

How many ways are there to calculate Static deflection at distance x from end A?

In this formula, Static deflection at distance x from end A uses Load per unit length, Distance of small section of shaft from end A, Length of Shaft, Young's Modulus & Moment of inertia of shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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