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

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

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

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Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations. Check FAQs

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

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

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Here is how the Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load equation looks like with Values.

Here is how the Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load equation looks like with Units.

Here is how the Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load equation looks like.

0.0017 = ({3.573}^{2}) \cdot (\frac{15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4} \cdot 90^{2}})

0.0017 = ({3.573}^{2}) \cdot (\frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4} \cdot {90Hz}^{2}})

0.0017 = ({3.573}^{2}) \cdot (\frac{15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4} \cdot 90^{2}})

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

Follow our step by step solution on how to calculate Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

w = ({3.573}^{2}) \cdot (\frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4} \cdot {90Hz}^{2}})

Next Step Prepare to Evaluate

∴

w = ({3.573}^{2}) \cdot (\frac{15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4} \cdot 90^{2}})

Next Step Evaluate

∴

w = 0.00167596444308245

LAST Step Rounding Answer

∴

w = 0.0017

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

Variables

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

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

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

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 Load per unit length

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

w = (\frac{504 \cdot E \cdot I shaft \cdot g}{{L shaft}^{4} \cdot {ω n}^{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 Frequency for Fixed Shaft and Uniformly Distributed Load?

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

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

FAQs on Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

What is the formula to find Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

The formula of Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load is expressed as 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)). Here is an example- 0.001676 = (3.573^2)*((15*1.085522*9.8)/(3.5^4*90^2)).

How to calculate Load given Natural Frequency for Fixed Shaft and 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) & Frequency (f) we can find Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load using the formula - 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)).

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=((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Natural Circular 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 Frequency for Fixed Shaft and Uniformly Distributed Load Formula

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

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

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

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

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

FAQs on Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

Variable Name

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

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