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Static Deflection at Distance x from End A Calculator

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

✖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%
✖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%
✖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%

✖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 [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 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.
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.
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.

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 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Uniformly Distributed Load Acting Over a Simply Supported Shaft » Static Deflection at Distance x from End A

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National Institute Of Technology (NIT), Hamirpur

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< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

LaTeX Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Static Deflection

LaTeX 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

LaTeX Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

LaTeX Go Frequency = 0.5615/(sqrt(Static Deflection))

Static Deflection at Distance x from End A Formula

LaTeX Go

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 -> 6.175025 = (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 force per unit length applied to a system, affecting its 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, 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.

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.

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