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Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Formula

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

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Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness. Check FAQs

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

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

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Example

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Here is how the Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft equation looks like with Values.

Here is how the Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft equation looks like with Units.

Here is how the Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft equation looks like.

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

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

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

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Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

δ = \frac{3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 1.0855}

Next Step Evaluate

∴

δ = 0.0719999705978629m

LAST Step Rounding Answer

∴

δ = 0.072m

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Formula Elements

Variables

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

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

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

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

Other Formulas to find Static Deflection

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

δ = {(\frac{0.571}{f})}^{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 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}

Go Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

How to Evaluate Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft?

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft evaluator uses Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft) to evaluate the Static Deflection, Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft formula is defined as a measure of the maximum displacement of a shaft under a uniformly distributed load, providing insight into the shaft's ability to withstand external forces and maintain its structural integrity. Static Deflection is denoted by δ symbol.

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

FAQs on Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft

What is the formula to find Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft?

The formula of Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft is expressed as Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft). Here is an example- 0.072 = (3*3.5^4)/(384*15*1.085522).

How to calculate Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft?

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

What are the other ways to Calculate Static Deflection?

Here are the different ways to Calculate Static Deflection-

Static Deflection=(0.571/Frequency)^2

Can the Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft be negative?

No, the Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft, measured in Length cannot be negative.

Which unit is used to measure Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft?

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft can be measured.

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Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Formula

​GoStatic Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Example

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Solution

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft Formula Elements

Other Formulas to find Static Deflection

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

How to Evaluate Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft?

FAQs on Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft

Variable Name

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