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Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

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

GoLength of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

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Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft. Check FAQs

L shaft = {(\frac{504 \cdot E \cdot I shaft \cdot g}{w \cdot {ω n}^{2}})}^{\frac{1}{4}}

L_shaft - Length of Shaft?E - Young's Modulus?I_shaft - Moment of inertia of shaft?g - Acceleration due to Gravity?w - Load per unit length?ω_n - Natural Circular Frequency?

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Example

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Here is how the Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) equation looks like with Values.

Here is how the Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) equation looks like with Units.

Here is how the Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) equation looks like.

3.5353 = {(\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{3 \cdot {13.1}^{2}})}^{\frac{1}{4}}

3.5353m = {(\frac{504 \cdot 15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {13.1rad/s}^{2}})}^{\frac{1}{4}}

3.5353 = {(\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{3 \cdot {13.1}^{2}})}^{\frac{1}{4}}

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Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Solution

Follow our step by step solution on how to calculate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

FIRST Step Consider the formula

L shaft = {(\frac{504 \cdot E \cdot I shaft \cdot g}{w \cdot {ω n}^{2}})}^{\frac{1}{4}}

Next Step Substitute values of Variables

∴

L shaft = {(\frac{504 \cdot 15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {13.1rad/s}^{2}})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

L shaft = {(\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{3 \cdot {13.1}^{2}})}^{\frac{1}{4}}

Next Step Evaluate

∴

L shaft = 3.5353357398968m

LAST Step Rounding Answer

∴

L shaft = 3.5353m

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula Elements

Variables

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Young's Modulus

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.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of inertia of shaft

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.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Acceleration due to Gravity

Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

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.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Other Formulas to find Length of Shaft

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

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{w})}^{\frac{1}{4}}

Go Length of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

L shaft = {3.573}^{2} \cdot {(\frac{E \cdot I shaft \cdot g}{w \cdot f^{2}})}^{\frac{1}{4}}

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

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

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

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

δ = {(\frac{0.571}{f})}^{2}

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

f = \frac{0.571}{\sqrt{δ}}

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

I shaft = \frac{w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

How to Evaluate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) evaluator uses 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) to evaluate the Length of Shaft, Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the distance from one end of a shaft to the other, which is a critical parameter in determining the natural frequency of free transverse vibrations of a shaft under uniformly distributed load when fixed at both ends. Length of Shaft is denoted by L_shaft symbol.

How to evaluate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) using this online evaluator? To use this online evaluator for Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load), enter Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g), Load per unit length (w) & Natural Circular Frequency (ω_n) and hit the calculate button.

FAQs on Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

What is the formula to find Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

The formula of Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) is expressed as 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). Here is an example- 3.535336 = ((504*15*1.085522*9.8)/(3*13.1^2))^(1/4).

How to calculate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

With Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g), Load per unit length (w) & Natural Circular Frequency (ω_n) we can find Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) using the formula - 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).

What are the other ways to Calculate Length of Shaft?

Here are the different ways to Calculate Length of Shaft-

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

Can the Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) be negative?

No, the Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load), measured in Length cannot be negative.

Which unit is used to measure Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) can be measured.

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Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

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

​GoLength of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Example

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Solution

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula Elements

Other Formulas to find Length of Shaft

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

How to Evaluate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

FAQs on Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Variable Name

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

GoLength of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) Formula