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Uniformly Distributed Load Unit Length given Static Deflection Formula

GoUniformly Distributed Load Unit Length given Natural Frequency Formula

GoUniformly Distributed Load Unit Length given Circular Frequency 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}{5 \cdot {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?

Uniformly Distributed Load Unit Length given Static Deflection Example

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Here is how the Uniformly Distributed Load Unit Length given Static Deflection equation looks like with Values.

Here is how the Uniformly Distributed Load Unit Length given Static Deflection equation looks like with Units.

Here is how the Uniformly Distributed Load Unit Length given Static Deflection equation looks like.

0.6 = \frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{5 \cdot {3.5}^{4}}

0.6 = \frac{0.072m \cdot 384 \cdot 15N/m \cdot 1.0855kg·m²}{5 \cdot {3.5m}^{4}}

0.6 = \frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{5 \cdot {3.5}^{4}}

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Uniformly Distributed Load Unit Length given Static Deflection Solution

Follow our step by step solution on how to calculate Uniformly Distributed Load Unit Length given Static Deflection?

FIRST Step Consider the formula

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Next Step Substitute values of Variables

∴

w = \frac{0.072m \cdot 384 \cdot 15N/m \cdot 1.0855kg·m²}{5 \cdot {3.5m}^{4}}

Next Step Prepare to Evaluate

∴

w = \frac{0.072 \cdot 384 \cdot 15 \cdot 1.0855}{5 \cdot {3.5}^{4}}

Next Step Evaluate

∴

w = 0.600000245017909

LAST Step Rounding Answer

∴

w = 0.6

Uniformly Distributed Load Unit Length given Static Deflection 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 Uniformly Distributed Load Unit Length given Natural Frequency

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

Go Uniformly Distributed Load Unit Length given Circular Frequency

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

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Length of Shaft given Static Deflection

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

Go Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

I shaft = \frac{5 \cdot w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

How to Evaluate Uniformly Distributed Load Unit Length given Static Deflection?

Uniformly Distributed Load Unit Length given Static Deflection evaluator uses Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4) to evaluate the Load per unit length, Uniformly Distributed Load Unit Length given Static Deflection formula is defined as a measure of the load per unit length of a shaft in terms of its static deflection, modulus of elasticity, and moment of inertia, providing a crucial parameter in the analysis of transverse vibrations in mechanical systems. Load per unit length is denoted by w symbol.

How to evaluate Uniformly Distributed Load Unit Length given Static Deflection using this online evaluator? To use this online evaluator for Uniformly Distributed Load Unit Length given Static Deflection, 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 Uniformly Distributed Load Unit Length given Static Deflection

What is the formula to find Uniformly Distributed Load Unit Length given Static Deflection?

The formula of Uniformly Distributed Load Unit Length given Static Deflection is expressed as Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4). Here is an example- 0.6 = (0.072*384*15*1.085522)/(5*3.5^4).

How to calculate Uniformly Distributed Load Unit Length given Static Deflection?

With Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft) we can find Uniformly Distributed Load Unit Length given Static Deflection using the formula - Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*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=(pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Load per unit length=(pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)

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Uniformly Distributed Load Unit Length given Static Deflection Formula

​GoUniformly Distributed Load Unit Length given Natural Frequency Formula

​GoUniformly Distributed Load Unit Length given Circular Frequency Formula

Uniformly Distributed Load Unit Length given Static Deflection Example

Uniformly Distributed Load Unit Length given Static Deflection Solution

Uniformly Distributed Load Unit Length given Static Deflection Formula Elements

Other Formulas to find Load per unit length

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Uniformly Distributed Load Unit Length given Static Deflection?

FAQs on Uniformly Distributed Load Unit Length given Static Deflection

Variable Name

GoUniformly Distributed Load Unit Length given Natural Frequency Formula

GoUniformly Distributed Load Unit Length given Circular Frequency Formula