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

GoLoad given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula

GoLoad using Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

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Load per unit length is the distributed load which is spread over a surface or line. Check FAQs

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

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

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

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

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

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

2.4582 = (\frac{504 \cdot 15 \cdot 6 \cdot 9.8}{4500^{4} \cdot 21^{2}})

2.4582 = (\frac{504 \cdot 15N/m \cdot 6kg·m² \cdot 9.8m/s²}{{4500mm}^{4} \cdot {21rad/s}^{2}})

2.4582 = (\frac{504 \cdot 15 \cdot 6 \cdot 9.8}{4500^{4} \cdot 21^{2}})

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

w = (\frac{504 \cdot 15N/m \cdot 6kg·m² \cdot 9.8m/s²}{{4500mm}^{4} \cdot {21rad/s}^{2}})

Next Step Convert Units

∴

w = (\frac{504 \cdot 15N/m \cdot 6kg·m² \cdot 9.8m/s²}{{4.5m}^{4} \cdot {21rad/s}^{2}})

Next Step Prepare to Evaluate

∴

w = (\frac{504 \cdot 15 \cdot 6 \cdot 9.8}{{4.5}^{4} \cdot 21^{2}})

Next Step Evaluate

∴

w = 2.45816186556927

LAST Step Rounding Answer

∴

w = 2.4582

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

Variables

Load per unit length

Load per unit length is the distributed load which is spread over a surface or line.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

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 can be calculated by taking the distance of each particle from the axis of rotation.

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 acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Length of Shaft

Length of shaft is the distance between two ends of shaft.

Symbol: L_shaft

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Natural Circular Frequency

Natural Circular Frequency is a scalar measure of rotation rate.

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 Load per unit length

Go Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

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

Go Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)

w = (\frac{δ \cdot 384 \cdot E \cdot I shaft}{{L shaft}^{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 Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) evaluator uses 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)) to evaluate the Load per unit length, Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the measure of natural frequency of free transverse vibrations of a shaft under uniformly distributed load, which is essential in determining the shaft's vibrational characteristics and stability in various mechanical systems. Load per unit length is denoted by w symbol.

How to evaluate Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) using this online evaluator? To use this online evaluator for Load 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), Length of Shaft (L_shaft) & Natural Circular Frequency (ω_n) and hit the calculate button.

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

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

The formula of Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) is expressed as 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)). Here is an example- 7.528121 = ((504*15*6*9.8)/(4.5^4*21^2)).

How to calculate Load 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), Length of Shaft (L_shaft) & Natural Circular Frequency (ω_n) we can find Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) using the formula - 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)).

What are the other ways to Calculate Load per unit length?

Here are the different ways to Calculate Load per unit length-

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

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

​GoLoad given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula

​GoLoad using Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

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

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

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

Other Formulas to find Load per unit length

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

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

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

Variable Name

GoLoad given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula

GoLoad using Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula