Maximum Deflection due to Shaft with Uniform Weight Calculator

✖Uniformly Distributed Load per Unit Length is Distributed loads are forces which are spread out over a length, area, or volume.ⓘ Uniformly Distributed Load per Unit Length [w]			+10% -10%
✖Length is the measurement of something from end to end or along its longest side, or a measurement of a particular part.ⓘ Length [L]			+10% -10%
✖Modulus of elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity [E]			+10% -10%
✖Diameter of Shaft for Agitator is defined as the diameter of the hole in the iron laminations that contains the shaft.ⓘ Diameter of Shaft for Agitator [d]			+10% -10%

✖Deflection is the degree to which a structural element is displaced under a load (due to its deformation).ⓘ Maximum Deflection due to Shaft with Uniform Weight [δ_s]

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Formula

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Maximum Deflection due to Shaft with Uniform Weight

Formula

`"δ"_{"s"} = ("w"*"L"^(4))/((8*"E")*(pi/64)*"d"^(4))`

Example

`"0.005668mm"=("90N"*("100mm")^(4))/((8*"195000N/mm²")*(pi/64)*("12mm")^(4))`

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Maximum Deflection due to Shaft with Uniform Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))
δ_s = (w*L^(4))/((8*E)*(pi/64)*d^(4))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Deflection - (Measured in Meter) - Deflection is the degree to which a structural element is displaced under a load (due to its deformation).
Uniformly Distributed Load per Unit Length - (Measured in Newton) - Uniformly Distributed Load per Unit Length is Distributed loads are forces which are spread out over a length, area, or volume.
Length - (Measured in Meter) - Length is the measurement of something from end to end or along its longest side, or a measurement of a particular part.
Modulus of Elasticity - (Measured in Pascal) - Modulus of elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Diameter of Shaft for Agitator - (Measured in Meter) - Diameter of Shaft for Agitator is defined as the diameter of the hole in the iron laminations that contains the shaft.

STEP 1: Convert Input(s) to Base Unit

Uniformly Distributed Load per Unit Length: 90 Newton --> 90 Newton No Conversion Required
Length: 100 Millimeter --> 0.1 Meter (Check conversion here)
Modulus of Elasticity: 195000 Newton per Square Millimeter --> 195000000000 Pascal (Check conversion here)
Diameter of Shaft for Agitator: 12 Millimeter --> 0.012 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ_s = (w*L^(4))/((8*E)*(pi/64)*d^(4)) --> (90*0.1^(4))/((8*195000000000)*(pi/64)*0.012^(4))

Evaluating ... ...

δ_s = 5.6679110787712E-06

STEP 3: Convert Result to Output's Unit

5.6679110787712E-06 Meter -->0.0056679110787712 Millimeter (Check conversion here)

FINAL ANSWER

0.0056679110787712 ≈ 0.005668 Millimeter <-- Deflection

(Calculation completed in 00.004 seconds)

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< 18 Design of Agitation System Components Calculators

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment

Go Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Maximum Deflection due to Shaft with Uniform Weight

Go Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Maximum Torque for Hollow Shaft

Go Maximum Torque for Hollow Shaft = ((pi/16)*(Hollow Shaft Outer Diameter^3)*(Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))

Outside Diameter of Hollow Shaft based on Equivalent Bending Moment

Go Diameter of Hollow Shaft for Agitator = ((Equivalent Bending Moment)*(32/pi)*(1)/((Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Maximum Deflection due to Each Load

Go Deflection due to each Load = (Concentrated Load*Length^(3))/((3*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Equivalent Twisting Moment for Hollow Shaft

Go Equivalent Twisting Moment for Hollow Shaft = (pi/16)*(Bending Stress)*(Hollow Shaft Outer Diameter^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)

Equivalent Bending Moment for Hollow Shaft

Go Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)

Diameter of Hollow Shaft Subjected to Maximum Bending Moment

Go Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)

Equivalent Bending Moment for Solid Shaft

Go Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))

Diameter of Solid Shaft Subjected to Maximum Bending Moment

Go Diameter of Solid Shaft for Agitator = ((Maximum Bending Moment for Solid Shaft)/((pi/32)*Bending Stress))^(1/3)

Maximum Torque for Solid Shaft

Go Maximum Torque for Solid Shaft = ((pi/16)*(Diameter of Shaft for Agitator^3)*(Torsional Shear Stress in Shaft))

Equivalent Twisting Moment for Solid Shaft

Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))

Diameter of Solid Shaft based on Equivalent Twisting Moment

Go Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)

Diameter of Solid Shaft based on Equivalent Bending Moment

Go Diameter of Solid Shaft for Agitator = (Equivalent Bending Moment*32/pi*1/Bending Stress)^(1/3)

Rated Motor Torque

Go Rated Motor Torque = ((Power*4500)/(2*pi*Speed of Agitator))

Force for Design of Shaft Based on Pure Bending

Go Force = Maximum Torque for Agitator/(0.75*Height of Manometer Liquid)

Maximum Bending Moment subject to Shaft

Go Maximum Bending Moment = Length of Shaft*Force

Critical Speed for Each Deflection

Go Critical Speed = 946/sqrt(Deflection)

< 3 Design of Shaft Based on Critical Speed Calculators

Maximum Deflection due to Shaft with Uniform Weight

Go Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Maximum Deflection due to Each Load

Go Deflection due to each Load = (Concentrated Load*Length^(3))/((3*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Critical Speed for Each Deflection

Go Critical Speed = 946/sqrt(Deflection)

Maximum Deflection due to Shaft with Uniform Weight Formula

Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))
δ_s = (w*L^(4))/((8*E)*(pi/64)*d^(4))

What is Deflection?

Deflection is the degree to which a particular structural element can be displaced with the help of a considerable amount of load. It can also be referred to as the angle or distance. The distance of deflection of a member under a load is directly related to the slope of the deflected shape of the body under that load.

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

Maximum Deflection due to Shaft with Uniform Weight calculator uses Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4)) to calculate 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 calculate Maximum Deflection due to Shaft with Uniform Weight using this online calculator? To use this online calculator 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. Here is how the Maximum Deflection due to Shaft with Uniform Weight calculation can be explained with given input values -> 5.667911 = (90*0.1^(4))/((8*195000000000)*(pi/64)*0.012^(4)).

FAQ

What is Maximum Deflection due to Shaft with Uniform Weight?

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 and is represented as δ_s = (w*L^(4))/((8*E)*(pi/64)*d^(4)) or Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4)). Uniformly Distributed Load per Unit Length is Distributed loads are forces which are spread out over a length, area, or volume, Length is the measurement of something from end to end or along its longest side, or a measurement of a particular part, Modulus of elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Diameter of Shaft for Agitator is defined as the diameter of the hole in the iron laminations that contains the shaft.

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

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 is calculated using Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4)). To calculate Maximum Deflection due to Shaft with Uniform Weight, you need Uniformly Distributed Load per Unit Length (w), Length (L), Modulus of Elasticity (E) & Diameter of Shaft for Agitator (d). With our tool, you need to enter the respective value for Uniformly Distributed Load per Unit Length, Length, Modulus of Elasticity & Diameter of Shaft for Agitator and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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