Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Calculator

✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection [δ]			+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%
✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Load per unit length [w]			+10% -10%

✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) [L_shaft]

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Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Formula

`"L"_{"shaft"} = (("δ"*384*"E"*"I"_{"shaft"})/("w"))^(1/4)`

Example

`"5366.563mm"=(("0.072m"*384*"15N/m"*"6kg·m²")/("3"))^(1/4)`

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Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4)
L_shaft = ((δ*384*E*I_shaft)/(w))^(1/4)
This formula uses 5 Variables

Variables Used

Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
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.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.

STEP 1: Convert Input(s) to Base Unit

Static Deflection: 0.072 Meter --> 0.072 Meter 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
Load per unit length: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_shaft = ((δ*384*E*I_shaft)/(w))^(1/4) --> ((0.072*384*15*6)/(3))^(1/4)

Evaluating ... ...

L_shaft = 5.3665631459995

STEP 3: Convert Result to Output's Unit

5.3665631459995 Meter -->5366.5631459995 Millimeter (Check conversion here)

FINAL ANSWER

5366.5631459995 ≈ 5366.563 Millimeter <-- Length of Shaft

(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 of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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National Institute Of Technology (NIT), Hamirpur

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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

Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4)
L_shaft = ((δ*384*E*I_shaft)/(w))^(1/4)

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 Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculator uses Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4) to calculate the Length of Shaft, The Length of shaft in given static deflection (Shaft fixed, uniformly distributed load) formula is defined as the term used for identifying the size of a shaft or distance from one point to another point of shaft. Length of Shaft is denoted by L_shaft symbol.

How to calculate Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load), enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load per unit length (w) and hit the calculate button. Here is how the Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 5.4E+6 = ((0.072*384*15*6)/(3))^(1/4).

FAQ

What is Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

The Length of shaft in given static deflection (Shaft fixed, uniformly distributed load) formula is defined as the term used for identifying the size of a shaft or distance from one point to another point of shaft and is represented as L_shaft = ((δ*384*E*I_shaft)/(w))^(1/4) or Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4). Static deflection is the extension or compression of the constraint, 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 & Load per unit length is the distributed load which is spread over a surface or line.

How to calculate Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

The Length of shaft in given static deflection (Shaft fixed, uniformly distributed load) formula is defined as the term used for identifying the size of a shaft or distance from one point to another point of shaft is calculated using Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4). To calculate Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load), you need Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load per unit length (w). With our tool, you need to enter the respective value for Static Deflection, Young's Modulus, Moment of inertia of shaft & Load per unit length 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 Length of Shaft?

In this formula, Length of Shaft uses Static Deflection, Young's Modulus, Moment of inertia of shaft & Load per unit length. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)
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)

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