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

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

✖Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Load per unit length [w]			+10% -10%
✖Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖Distance of small section of shaft from end A is the length of a small section of shaft measured from end A in free transverse vibrations.ⓘ Distance of Small Section of Shaft from End A [x]			+10% -10%
✖Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Static deflection at distance x from end A is the maximum displacement of a vibrating beam at a specific point from the fixed end.ⓘ Static Deflection at Distance x from End A given Length of Shaft [y]

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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*I_shaft))*(x^4+(L_shaft*x)^2-2*L_shaft*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 maximum displacement of a vibrating beam at a specific point from the fixed end.
Load per unit length - Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.
Distance of Small Section of Shaft from End A - (Measured in Meter) - Distance of small section of shaft from end A is the length of a small section of shaft measured from end A in free transverse vibrations.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating 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: 1.085522 Kilogram Square Meter --> 1.085522 Kilogram Square Meter 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

y = 0.431819898629415

STEP 3: Convert Result to Output's Unit

0.431819898629415 Meter --> No Conversion Required

FINAL ANSWER

0.431819898629415 ≈ 0.43182 Meter <-- Static deflection at distance x from end A

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Static Deflection at Distance x from End A given Length of Shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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

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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, Static Deflection at Distance x from End A given Length of Shaft formula is defined as a measure of the bending or displacement of a shaft at a specific point due to an applied load, providing insight into the shaft's structural integrity and potential for vibration or failure. 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 (I_shaft), Distance of Small Section of Shaft from End A (x) & Length of Shaft (L_shaft) 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 -> 0.43182 = (3/(24*15*1.085522))*(5^4+(3.5*5)^2-2*3.5*5^3).

FAQ

What is Static Deflection at Distance x from End A given Length of Shaft?

Static Deflection at Distance x from End A given Length of Shaft formula is defined as a measure of the bending or displacement of a shaft at a specific point due to an applied load, providing insight into the shaft's structural integrity and potential for vibration or failure and is represented as y = (w/(24*E*I_shaft))*(x^4+(L_shaft*x)^2-2*L_shaft*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 force per unit length applied to a system, affecting its natural frequency of free transverse vibrations, Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations, Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations, Distance of small section of shaft from end A is the length of a small section of shaft measured from end A in free transverse vibrations & Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

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 formula is defined as a measure of the bending or displacement of a shaft at a specific point due to an applied load, providing insight into the shaft's structural integrity and potential for vibration or failure 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 (I_shaft), Distance of Small Section of Shaft from End A (x) & Length of Shaft (L_shaft). 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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