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Length of Shaft given Static Deflection Formula

GoLength of Shaft given Natural Frequency Formula

GoLength of Shaft given Circular Frequency 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{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

L_shaft - Length of Shaft?δ - Static Deflection?E - Young's Modulus?I_shaft - Moment of inertia of shaft?w - Load per unit length?

Length of Shaft given Static Deflection Example

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Here is how the Length of Shaft given Static Deflection equation looks like with Values.

Here is how the Length of Shaft given Static Deflection equation looks like with Units.

Here is how the Length of Shaft given Static Deflection equation looks like.

2.3406 = {(\frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{5 \cdot 3})}^{\frac{1}{4}}

2.3406m = {(\frac{0.072m \cdot 384 \cdot 15N/m \cdot 1.0855kg·m²}{5 \cdot 3})}^{\frac{1}{4}}

2.3406 = {(\frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{5 \cdot 3})}^{\frac{1}{4}}

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Length of Shaft given Static Deflection Solution

Follow our step by step solution on how to calculate Length of Shaft given Static Deflection?

FIRST Step Consider the formula

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

Next Step Substitute values of Variables

∴

L shaft = {(\frac{0.072m \cdot 384 \cdot 15N/m \cdot 1.0855kg·m²}{5 \cdot 3})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

L shaft = {(\frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{5 \cdot 3})}^{\frac{1}{4}}

Next Step Evaluate

∴

L shaft = 2.34059130637024m

LAST Step Rounding Answer

∴

L shaft = 2.3406m

Length of Shaft given Static Deflection 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

Static Deflection

Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

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

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

Other Formulas to find Length of Shaft

Go Length of Shaft given Natural Frequency

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

Go Length of Shaft given Circular Frequency

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

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Uniformly Distributed Load Unit Length given Static Deflection

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Go Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

I shaft = \frac{5 \cdot w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

How to Evaluate Length of Shaft given Static Deflection?

Length of Shaft given Static Deflection evaluator uses Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4) to evaluate the Length of Shaft, Length of Shaft given Static Deflection formula is defined as a measure of the distance between two points on a shaft in a mechanical system, considering the static deflection caused by an external load, which is essential in designing and analyzing mechanical components. Length of Shaft is denoted by L_shaft symbol.

How to evaluate Length of Shaft given Static Deflection using this online evaluator? To use this online evaluator for Length of Shaft given Static Deflection, 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.

FAQs on Length of Shaft given Static Deflection

What is the formula to find Length of Shaft given Static Deflection?

The formula of Length of Shaft given Static Deflection is expressed as Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4). Here is an example- 2.340591 = ((0.072*384*15*1.085522)/(5*3))^(1/4).

How to calculate Length of Shaft given Static Deflection?

With Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load per unit length (w) we can find Length of Shaft given Static Deflection using the formula - Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(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=((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Length of Shaft=((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)

Can the Length of Shaft given Static Deflection be negative?

No, the Length of Shaft given Static Deflection, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft given Static Deflection?

Length of Shaft given Static Deflection 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 Static Deflection can be measured.

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Length of Shaft given Static Deflection Formula

​GoLength of Shaft given Natural Frequency Formula

​GoLength of Shaft given Circular Frequency Formula

Length of Shaft given Static Deflection Example

Length of Shaft given Static Deflection Solution

Length of Shaft given Static Deflection Formula Elements

Other Formulas to find Length of Shaft

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Length of Shaft given Static Deflection?

FAQs on Length of Shaft given Static Deflection

Variable Name

GoLength of Shaft given Natural Frequency Formula

GoLength of Shaft given Circular Frequency Formula