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Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Formula

GoStatic Deflection using Natural Frequency 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{5 \cdot 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 Simply Supported Shaft due to Uniformly Distributed Load Example

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

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

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

0.36 = \frac{5 \cdot 3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 1.0855}

0.36m = \frac{5 \cdot 3 \cdot {3.5m}^{4}}{384 \cdot 15N/m \cdot 1.0855kg·m²}

0.36 = \frac{5 \cdot 3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 1.0855}

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Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = \frac{5 \cdot 3 \cdot {3.5m}^{4}}{384 \cdot 15N/m \cdot 1.0855kg·m²}

Next Step Prepare to Evaluate

∴

δ = \frac{5 \cdot 3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 1.0855}

Next Step Evaluate

∴

δ = 0.359999852989314m

LAST Step Rounding Answer

∴

δ = 0.36m

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load 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 using Natural Frequency

δ = {(\frac{0.5615}{f})}^{2}

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 Uniformly Distributed Load Unit Length given Static Deflection

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

Go Length of Shaft given Static Deflection

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

How to Evaluate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load evaluator uses Static Deflection = (5*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 Simply Supported Shaft due to Uniformly Distributed Load formula is defined as the maximum displacement of a shaft under a uniformly distributed load, providing a measure of the shaft's flexibility and ability to withstand external forces without deforming excessively. Static Deflection is denoted by δ symbol.

How to evaluate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load using this online evaluator? To use this online evaluator for Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load, 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 Simply Supported Shaft due to Uniformly Distributed Load

What is the formula to find Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

The formula of Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load is expressed as Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft). Here is an example- 0.36 = (5*3*3.5^4)/(384*15*1.085522).

How to calculate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

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 Simply Supported Shaft due to Uniformly Distributed Load using the formula - Static Deflection = (5*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=(0.5615/Frequency)^2

Can the Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load be negative?

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

Which unit is used to measure Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load 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 Simply Supported Shaft due to Uniformly Distributed Load can be measured.

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Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Formula

​GoStatic Deflection using Natural Frequency Formula

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Example

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Solution

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Formula Elements

Other Formulas to find Static Deflection

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

How to Evaluate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

FAQs on Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load

Variable Name

GoStatic Deflection using Natural Frequency Formula