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

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

GoLoad given Natural Circular Frequency (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 = (\frac{δ \cdot 384 \cdot E \cdot I shaft}{{L shaft}^{4}})

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

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

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

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

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

3 = (\frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{{3.5}^{4}})

3 = (\frac{0.072m \cdot 384 \cdot 15N/m \cdot 1.0855kg·m²}{{3.5m}^{4}})

3 = (\frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{{3.5}^{4}})

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

w = (\frac{0.072m \cdot 384 \cdot 15N/m \cdot 1.0855kg·m²}{{3.5m}^{4}})

Next Step Prepare to Evaluate

∴

w = (\frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{{3.5}^{4}})

Next Step Evaluate

∴

w = 3.00000122508955

LAST Step Rounding Answer

∴

w = 3

Load using Static Deflection (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

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

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

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 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}})

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

Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load) evaluator uses Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4)) to evaluate the Load per unit length, Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the load that a shaft can withstand when it is fixed at one end and subjected to a uniformly distributed load, providing insight into the shaft's ability to resist deformation and maintain its structural integrity. Load per unit length is denoted by w symbol.

How to evaluate Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load) using this online evaluator? To use this online evaluator for Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load), enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

The formula of Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load) is expressed as Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4)). Here is an example- 3.000001 = ((0.072*384*15*1.085522)/(3.5^4)).

How to calculate Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

With Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft) we can find Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load) using the formula - Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4)).

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=((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Natural Circular Frequency^2))

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

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

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

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

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

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

FAQs on Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Variable Name

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

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