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Static Deflection of Shaft due to Uniformly Distributed Load 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%
✖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 is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.ⓘ Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft [δ]

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Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
δ = (w*L_shaft^4)/(384*E*I_shaft)
This formula uses 5 Variables

Variables Used

Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.
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.
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
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

δ = (w*L_shaft^4)/(384*E*I_shaft) --> (3*3.5^4)/(384*15*1.085522)

Evaluating ... ...

δ = 0.0719999705978629

STEP 3: Convert Result to Output's Unit

0.0719999705978629 Meter --> No Conversion Required

FINAL ANSWER

0.0719999705978629 ≈ 0.072 Meter <-- Static Deflection

(Calculation completed in 00.004 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 of Shaft due to Uniformly Distributed Load given Length of Shaft

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< Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Frequency = 0.571/(sqrt(Static Deflection))

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Static Deflection = (0.571/Frequency)^2

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Formula

LaTeX Go

Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
δ = (w*L_shaft^4)/(384*E*I_shaft)

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 of Shaft due to Uniformly Distributed Load given Length of Shaft?

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft calculator uses Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft) to calculate the Static Deflection, Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft formula is defined as a measure of the maximum displacement of a shaft under a uniformly distributed load, providing insight into the shaft's ability to withstand external forces and maintain its structural integrity. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft using this online calculator? To use this online calculator for Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft, enter Load per unit length (w), 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 of Shaft due to Uniformly Distributed Load given Length of Shaft calculation can be explained with given input values -> 0.072 = (3*3.5^4)/(384*15*1.085522).

FAQ

What is Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft?

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft formula is defined as a measure of the maximum displacement of a shaft under a uniformly distributed load, providing insight into the shaft's ability to withstand external forces and maintain its structural integrity and is represented as δ = (w*L_shaft^4)/(384*E*I_shaft) or Static Deflection = (Load per unit length*Length of Shaft^4)/(384*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, 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 of Shaft due to Uniformly Distributed Load given Length of Shaft?

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft formula is defined as a measure of the maximum displacement of a shaft under a uniformly distributed load, providing insight into the shaft's ability to withstand external forces and maintain its structural integrity is calculated using Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft). To calculate Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft, you need Load per unit length (w), 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, 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?

In this formula, Static Deflection uses Load per unit length, 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 = (0.571/Frequency)^2

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