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

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

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

δ = {(\frac{0.571}{f})}^{2}

δ - Static Deflection?f - Frequency?

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

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

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

Here is how the Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) equation looks like.

4E-5 = {(\frac{0.571}{90})}^{2}

4E-5m = {(\frac{0.571}{90Hz})}^{2}

4E-5 = {(\frac{0.571}{90})}^{2}

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

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

FIRST Step Consider the formula

δ = {(\frac{0.571}{f})}^{2}

Next Step Substitute values of Variables

∴

δ = {(\frac{0.571}{90Hz})}^{2}

Next Step Prepare to Evaluate

∴

δ = {(\frac{0.571}{90})}^{2}

Next Step Evaluate

∴

δ = 4.0251975308642E-05m

LAST Step Rounding Answer

∴

δ = 4E-5m

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

Variables

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

Frequency

Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency

Other Formulas to find Static Deflection

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

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

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 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}

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}}

How to Evaluate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) evaluator uses Static Deflection = (0.571/Frequency)^2 to evaluate the Static Deflection, Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the maximum displacement of a shaft under uniformly distributed load, which is a critical parameter in mechanical engineering to determine the stability and performance of rotating machines. Static Deflection is denoted by δ symbol.

How to evaluate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) using this online evaluator? To use this online evaluator for Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load), enter Frequency (f) and hit the calculate button.

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

What is the formula to find Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?

The formula of Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) is expressed as Static Deflection = (0.571/Frequency)^2. Here is an example- 4E-5 = (0.571/90)^2.

How to calculate Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?

With Frequency (f) we can find Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) using the formula - Static Deflection = (0.571/Frequency)^2.

What are the other ways to Calculate Static Deflection?

Here are the different ways to Calculate Static Deflection-

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

Can the Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) be negative?

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

Which unit is used to measure Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)?

Static Deflection given Natural 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 Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) can be measured.

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