FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

Fx Copy

LaTeX Copy

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 = (\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

With values

With units

Only example

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.

3.123 = (\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4} \cdot {13.1}^{2}})

3.123 = (\frac{504 \cdot 15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4} \cdot {13.1rad/s}^{2}})

3.123 = (\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4} \cdot {13.1}^{2}})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

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 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4} \cdot {13.1rad/s}^{2}})

Next Step Prepare to Evaluate

∴

w = (\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4} \cdot {13.1}^{2}})

Next Step Evaluate

∴

w = 3.12299818691884

LAST Step Rounding Answer

∴

w = 3.123

Load given Natural Circular Frequency (Shaft Fixed, 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

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 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- 3.122998 = ((504*15*1.085522*9.8)/(3.5^4*13.1^2)).

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))

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

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