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Outer Radius of Shaft using Turning Force on Elementary Ring Formula

GoOuter Radius of Shaft using Turning Force on Elementary Ring given Turning Moment Formula

GoOuter Radius of Shaft given Shear Stress of Elementary Ring Formula

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The Outer Radius of Shaft is the distance from the center to the outer edge of a hollow circular shaft, influencing its torque transmission capacity. Check FAQs

r o = \frac{2 \cdot π \cdot 𝜏 s \cdot (r^{2}) \cdot b r}{T f}

r_o - Outer Radius of Shaft?𝜏_s - Maximum Shear Stress?r - Radius of Elementary Circular Ring?b_r - Thickness of Ring?T_f - Turning Force?π - Archimedes' constant?

Outer Radius of Shaft using Turning Force on Elementary Ring Example

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Here is how the Outer Radius of Shaft using Turning Force on Elementary Ring equation looks like with Values.

Here is how the Outer Radius of Shaft using Turning Force on Elementary Ring equation looks like with Units.

Here is how the Outer Radius of Shaft using Turning Force on Elementary Ring equation looks like.

7 = \frac{2 \cdot 3.1416 \cdot 111.4085 \cdot (2^{2}) \cdot 5}{2000.001}

7mm = \frac{2 \cdot 3.1416 \cdot 111.4085MPa \cdot ({2mm}^{2}) \cdot 5mm}{2000.001N}

7 = \frac{2 \cdot 3.1416 \cdot 111.4085 \cdot (2^{2}) \cdot 5}{2000.001}

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Outer Radius of Shaft using Turning Force on Elementary Ring Solution

Follow our step by step solution on how to calculate Outer Radius of Shaft using Turning Force on Elementary Ring?

FIRST Step Consider the formula

r o = \frac{2 \cdot π \cdot 𝜏 s \cdot (r^{2}) \cdot b r}{T f}

Next Step Substitute values of Variables

∴

r o = \frac{2 \cdot π \cdot 111.4085MPa \cdot ({2mm}^{2}) \cdot 5mm}{2000.001N}

Next Step Substitute values of Constants

∴

r o = \frac{2 \cdot 3.1416 \cdot 111.4085MPa \cdot ({2mm}^{2}) \cdot 5mm}{2000.001N}

Next Step Convert Units

∴

r o = \frac{2 \cdot 3.1416 \cdot 1.1E+8Pa \cdot ({0.002m}^{2}) \cdot 0.005m}{2000.001N}

Next Step Prepare to Evaluate

∴

r o = \frac{2 \cdot 3.1416 \cdot 1.1E+8 \cdot ({0.002}^{2}) \cdot 0.005}{2000.001}

Next Step Evaluate

∴

r o = 0.00699999900294967m

Next Step Convert to Output's Unit

∴

r o = 6.99999900294967mm

LAST Step Rounding Answer

∴

r o = 7mm

Outer Radius of Shaft using Turning Force on Elementary Ring Formula Elements

Variables

Constants

Outer Radius of Shaft

The Outer Radius of Shaft is the distance from the center to the outer edge of a hollow circular shaft, influencing its torque transmission capacity.

Symbol: r_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Shaft

Maximum Shear Stress

The Maximum Shear Stress is the highest stress experienced by a material in a hollow circular shaft when subjected to torque, influencing its structural integrity and performance.

Symbol: 𝜏_s

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress

Radius of Elementary Circular Ring

The Radius of Elementary Circular Ring is the distance from the center to the edge of a thin circular section, relevant in analyzing torque in hollow shafts.

Symbol: r

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Elementary Circular Ring

Thickness of Ring

The Thickness of Ring is the measurement of the width of a hollow circular shaft, which influences its strength and the torque it can transmit.

Symbol: b_r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Ring

Turning Force

The Turning Force is the torque transmitted by a hollow circular shaft, influencing its ability to rotate and perform work efficiently in mechanical systems.

Symbol: T_f

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Turning Force

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 to find Outer Radius of Shaft

Go Outer Radius of Shaft using Turning Force on Elementary Ring given Turning Moment

r o = \frac{2 \cdot π \cdot 𝜏 s \cdot (r^{2}) \cdot b r}{T}

Go Outer Radius of Shaft given Shear Stress of Elementary Ring

r o = \frac{𝜏 s \cdot r}{q}

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

Go Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft

𝜏 m = \frac{16 \cdot d o \cdot T}{π \cdot ({d o}^{4} - {d i}^{4})}

Go Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft

T = \frac{π \cdot 𝜏 m \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Go Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft

𝜏 m = \frac{T \cdot 2 \cdot r h}{π \cdot ({r h}^{4} - {r i}^{4})}

Go Total Turning Moment on Hollow Circular Shaft given Radius of Shaft

T = \frac{π \cdot 𝜏 m \cdot (({r h}^{4}) - ({r i}^{4}))}{2 \cdot r h}

How to Evaluate Outer Radius of Shaft using Turning Force on Elementary Ring?

Outer Radius of Shaft using Turning Force on Elementary Ring evaluator uses Outer Radius of Shaft = (2*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^2)*Thickness of Ring)/Turning Force to evaluate the Outer Radius of Shaft, Outer Radius of Shaft using Turning Force on Elementary Ring formula is defined as a method to determine the outer radius of a shaft based on the turning force applied to an elementary ring. It helps in analyzing the torque transmission capabilities of hollow circular shafts. Outer Radius of Shaft is denoted by r_o symbol.

How to evaluate Outer Radius of Shaft using Turning Force on Elementary Ring using this online evaluator? To use this online evaluator for Outer Radius of Shaft using Turning Force on Elementary Ring, enter Maximum Shear Stress (𝜏_s), Radius of Elementary Circular Ring (r), Thickness of Ring (b_r) & Turning Force (T_f) and hit the calculate button.

FAQs on Outer Radius of Shaft using Turning Force on Elementary Ring

What is the formula to find Outer Radius of Shaft using Turning Force on Elementary Ring?

The formula of Outer Radius of Shaft using Turning Force on Elementary Ring is expressed as Outer Radius of Shaft = (2*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^2)*Thickness of Ring)/Turning Force. Here is an example- 6999.999 = (2*pi*111408500*(0.002^2)*0.005)/2000.001.

How to calculate Outer Radius of Shaft using Turning Force on Elementary Ring?

With Maximum Shear Stress (𝜏_s), Radius of Elementary Circular Ring (r), Thickness of Ring (b_r) & Turning Force (T_f) we can find Outer Radius of Shaft using Turning Force on Elementary Ring using the formula - Outer Radius of Shaft = (2*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^2)*Thickness of Ring)/Turning Force. This formula also uses Archimedes' constant .

What are the other ways to Calculate Outer Radius of Shaft?

Here are the different ways to Calculate Outer Radius of Shaft-

Outer Radius of Shaft=(2*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^2)*Thickness of Ring)/Turning Moment
Outer Radius of Shaft=(Maximum Shear Stress*Radius of Elementary Circular Ring)/Shear Stress at Elementary Ring

Can the Outer Radius of Shaft using Turning Force on Elementary Ring be negative?

No, the Outer Radius of Shaft using Turning Force on Elementary Ring, measured in Length cannot be negative.

Which unit is used to measure Outer Radius of Shaft using Turning Force on Elementary Ring?

Outer Radius of Shaft using Turning Force on Elementary Ring is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Outer Radius of Shaft using Turning Force on Elementary Ring can be measured.

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Outer Radius of Shaft using Turning Force on Elementary Ring Formula

​GoOuter Radius of Shaft using Turning Force on Elementary Ring given Turning Moment Formula

​GoOuter Radius of Shaft given Shear Stress of Elementary Ring Formula

Outer Radius of Shaft using Turning Force on Elementary Ring Example

Outer Radius of Shaft using Turning Force on Elementary Ring Solution

Outer Radius of Shaft using Turning Force on Elementary Ring Formula Elements

Other Formulas to find Outer Radius of Shaft

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

How to Evaluate Outer Radius of Shaft using Turning Force on Elementary Ring?

FAQs on Outer Radius of Shaft using Turning Force on Elementary Ring

Variable Name

GoOuter Radius of Shaft using Turning Force on Elementary Ring given Turning Moment Formula

GoOuter Radius of Shaft given Shear Stress of Elementary Ring Formula