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Maximum Deflection due to Shaft with Uniform Weight Formula

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Deflection is the degree to which a structural element is displaced under a load (due to its deformation). Check FAQs

δ s = \frac{w \cdot L^{4}}{(8 \cdot E) \cdot (\frac{π}{64}) \cdot d^{4}}

δ_s - Deflection?w - Uniformly Distributed Load per Unit Length?L - Length?E - Modulus of Elasticity?d - Diameter of Shaft for Agitator?π - Archimedes' constant?

Maximum Deflection due to Shaft with Uniform Weight Example

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Here is how the Maximum Deflection due to Shaft with Uniform Weight equation looks like with Values.

Here is how the Maximum Deflection due to Shaft with Uniform Weight equation looks like with Units.

Here is how the Maximum Deflection due to Shaft with Uniform Weight equation looks like.

0.0057 = \frac{90 \cdot 100^{4}}{(8 \cdot 195000) \cdot (\frac{3.1416}{64}) \cdot 12^{4}}

0.0057mm = \frac{90N \cdot {100mm}^{4}}{(8 \cdot 195000N/mm²) \cdot (\frac{3.1416}{64}) \cdot {12mm}^{4}}

0.0057 = \frac{90 \cdot 100^{4}}{(8 \cdot 195000) \cdot (\frac{3.1416}{64}) \cdot 12^{4}}

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Maximum Deflection due to Shaft with Uniform Weight Solution

Follow our step by step solution on how to calculate Maximum Deflection due to Shaft with Uniform Weight?

FIRST Step Consider the formula

δ s = \frac{w \cdot L^{4}}{(8 \cdot E) \cdot (\frac{π}{64}) \cdot d^{4}}

Next Step Substitute values of Variables

∴

δ s = \frac{90N \cdot {100mm}^{4}}{(8 \cdot 195000N/mm²) \cdot (\frac{π}{64}) \cdot {12mm}^{4}}

Next Step Substitute values of Constants

∴

δ s = \frac{90N \cdot {100mm}^{4}}{(8 \cdot 195000N/mm²) \cdot (\frac{3.1416}{64}) \cdot {12mm}^{4}}

Next Step Convert Units

∴

δ s = \frac{90N \cdot {0.1m}^{4}}{(8 \cdot 2E+11Pa) \cdot (\frac{3.1416}{64}) \cdot {0.012m}^{4}}

Next Step Prepare to Evaluate

∴

δ s = \frac{90 \cdot {0.1}^{4}}{(8 \cdot 2E+11) \cdot (\frac{3.1416}{64}) \cdot {0.012}^{4}}

Next Step Evaluate

∴

δ s = 5.6679110787712E-06m

Next Step Convert to Output's Unit

∴

δ s = 0.0056679110787712mm

LAST Step Rounding Answer

∴

δ s = 0.0057mm

Maximum Deflection due to Shaft with Uniform Weight Formula Elements

Variables

Constants

Deflection

Deflection is the degree to which a structural element is displaced under a load (due to its deformation).

Symbol: δ_s

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection

Uniformly Distributed Load per Unit Length

Uniformly Distributed Load per Unit Length is Distributed loads are forces which are spread out over a length, area, or volume.

Symbol: w

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Uniformly Distributed Load per Unit Length

Length

Length is the measurement of something from end to end or along its longest side, or a measurement of a particular part.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length

Modulus of Elasticity

Modulus of elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

Symbol: E

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Diameter of Shaft for Agitator

Diameter of Shaft for Agitator is defined as the diameter of the hole in the iron laminations that contains the shaft.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft for Agitator

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Design of Agitation System Components category

Go Maximum Deflection due to Each Load

δ Load = \frac{W \cdot L^{3}}{(3 \cdot E) \cdot (\frac{π}{64}) \cdot d^{4}}

Go Critical Speed for Each Deflection

N c = \frac{946}{\sqrt{δ s}}

How to Evaluate Maximum Deflection due to Shaft with Uniform Weight?

Maximum Deflection due to Shaft with Uniform Weight evaluator uses Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4)) to evaluate the Deflection, Maximum Deflection due to Shaft with Uniform Weight formula is to guarantee continuously smooth operation, shaft deflection should be minimal. A maximum deflection of 0.01 mm between the first and last outer balls in the ball bearing is acceptable. Deflection is denoted by δ_s symbol.

How to evaluate Maximum Deflection due to Shaft with Uniform Weight using this online evaluator? To use this online evaluator for Maximum Deflection due to Shaft with Uniform Weight, enter Uniformly Distributed Load per Unit Length (w), Length (L), Modulus of Elasticity (E) & Diameter of Shaft for Agitator (d) and hit the calculate button.

FAQs on Maximum Deflection due to Shaft with Uniform Weight

What is the formula to find Maximum Deflection due to Shaft with Uniform Weight?

The formula of Maximum Deflection due to Shaft with Uniform Weight is expressed as Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4)). Here is an example- 5.667911 = (90*0.1^(4))/((8*195000000000)*(pi/64)*0.012^(4)).

How to calculate Maximum Deflection due to Shaft with Uniform Weight?

With Uniformly Distributed Load per Unit Length (w), Length (L), Modulus of Elasticity (E) & Diameter of Shaft for Agitator (d) we can find Maximum Deflection due to Shaft with Uniform Weight using the formula - Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4)). This formula also uses Archimedes' constant .

Can the Maximum Deflection due to Shaft with Uniform Weight be negative?

No, the Maximum Deflection due to Shaft with Uniform Weight, measured in Length cannot be negative.

Which unit is used to measure Maximum Deflection due to Shaft with Uniform Weight?

Maximum Deflection due to Shaft with Uniform Weight is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Deflection due to Shaft with Uniform Weight can be measured.

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Maximum Deflection due to Shaft with Uniform Weight Formula

Maximum Deflection due to Shaft with Uniform Weight Example

Maximum Deflection due to Shaft with Uniform Weight Solution

Maximum Deflection due to Shaft with Uniform Weight Formula Elements

Other formulas in Design of Agitation System Components category

How to Evaluate Maximum Deflection due to Shaft with Uniform Weight?

FAQs on Maximum Deflection due to Shaft with Uniform Weight

Variable Name