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Radius of Elementary Ring given Turning Force of Elementary Ring Formula

GoRadius of Elementary Ring given Turning Moment of Elementary Ring Formula

GoRadius of Elementary Ring given Shear Stress of Elementary Ring Formula

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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. Check FAQs

r = \sqrt{\frac{T f \cdot d o}{4 \cdot π \cdot 𝜏 s \cdot b r}}

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

Radius of Elementary Ring given Turning Force of Elementary Ring Example

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Here is how the Radius of Elementary Ring given Turning Force of Elementary Ring equation looks like with Values.

Here is how the Radius of Elementary Ring given Turning Force of Elementary Ring equation looks like with Units.

Here is how the Radius of Elementary Ring given Turning Force of Elementary Ring equation looks like.

2 = \sqrt{\frac{2000.001 \cdot 14}{4 \cdot 3.1416 \cdot 111.4085 \cdot 5}}

2mm = \sqrt{\frac{2000.001N \cdot 14mm}{4 \cdot 3.1416 \cdot 111.4085MPa \cdot 5mm}}

2 = \sqrt{\frac{2000.001 \cdot 14}{4 \cdot 3.1416 \cdot 111.4085 \cdot 5}}

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Radius of Elementary Ring given Turning Force of Elementary Ring Solution

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

FIRST Step Consider the formula

r = \sqrt{\frac{T f \cdot d o}{4 \cdot π \cdot 𝜏 s \cdot b r}}

Next Step Substitute values of Variables

∴

r = \sqrt{\frac{2000.001N \cdot 14mm}{4 \cdot π \cdot 111.4085MPa \cdot 5mm}}

Next Step Substitute values of Constants

∴

r = \sqrt{\frac{2000.001N \cdot 14mm}{4 \cdot 3.1416 \cdot 111.4085MPa \cdot 5mm}}

Next Step Convert Units

∴

r = \sqrt{\frac{2000.001N \cdot 0.014m}{4 \cdot 3.1416 \cdot 1.1E+8Pa \cdot 0.005m}}

Next Step Prepare to Evaluate

∴

r = \sqrt{\frac{2000.001 \cdot 0.014}{4 \cdot 3.1416 \cdot 1.1E+8 \cdot 0.005}}

Next Step Evaluate

∴

r = 0.00200000014243578m

Next Step Convert to Output's Unit

∴

r = 2.00000014243578mm

LAST Step Rounding Answer

∴

r = 2mm

Radius of Elementary Ring given Turning Force of Elementary Ring Formula Elements

Variables

Constants

Functions

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

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

Outer Diameter of Shaft

The Outer Diameter of Shaft is the measurement across the widest part of a hollow circular shaft, influencing its strength and torque transmission capabilities.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter 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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Radius of Elementary Circular Ring

Go Radius of Elementary Ring given Turning Moment of Elementary Ring

r = {(\frac{T \cdot d o}{4 \cdot π \cdot 𝜏 s \cdot b r})}^{\frac{1}{3}}

Go Radius of Elementary Ring given Shear Stress of Elementary Ring

r = \frac{d o \cdot q}{2 \cdot 𝜏 s}

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 Radius of Elementary Ring given Turning Force of Elementary Ring?

Radius of Elementary Ring given Turning Force of Elementary Ring evaluator uses Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring)) to evaluate the Radius of Elementary Circular Ring, Radius of Elementary Ring given Turning Force of Elementary Ring formula is defined as a method to determine the radius of an elementary ring based on the turning force applied, the outer diameter, the shear stress in the shaft, and the width of the ring. Radius of Elementary Circular Ring is denoted by r symbol.

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

FAQs on Radius of Elementary Ring given Turning Force of Elementary Ring

What is the formula to find Radius of Elementary Ring given Turning Force of Elementary Ring?

The formula of Radius of Elementary Ring given Turning Force of Elementary Ring is expressed as Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring)). Here is an example- 118.3216 = sqrt((2000.001*0.014)/(4*pi*111408500*0.005)).

How to calculate Radius of Elementary Ring given Turning Force of Elementary Ring?

With Turning Force (T_f), Outer Diameter of Shaft (d_o), Maximum Shear Stress (𝜏_s) & Thickness of Ring (b_r) we can find Radius of Elementary Ring given Turning Force of Elementary Ring using the formula - Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Radius of Elementary Circular Ring?

Here are the different ways to Calculate Radius of Elementary Circular Ring-

Radius of Elementary Circular Ring=((Turning Moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))^(1/3)
Radius of Elementary Circular Ring=(Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress)

Can the Radius of Elementary Ring given Turning Force of Elementary Ring be negative?

Yes, the Radius of Elementary Ring given Turning Force of Elementary Ring, measured in Length can be negative.

Which unit is used to measure Radius of Elementary Ring given Turning Force of Elementary Ring?

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

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Radius of Elementary Ring given Turning Force of Elementary Ring Formula

​GoRadius of Elementary Ring given Turning Moment of Elementary Ring Formula

​GoRadius of Elementary Ring given Shear Stress of Elementary Ring Formula

Radius of Elementary Ring given Turning Force of Elementary Ring Example

Radius of Elementary Ring given Turning Force of Elementary Ring Solution

Radius of Elementary Ring given Turning Force of Elementary Ring Formula Elements

Other Formulas to find Radius of Elementary Circular Ring

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

How to Evaluate Radius of Elementary Ring given Turning Force of Elementary Ring?

FAQs on Radius of Elementary Ring given Turning Force of Elementary Ring

Variable Name

GoRadius of Elementary Ring given Turning Moment of Elementary Ring Formula

GoRadius of Elementary Ring given Shear Stress of Elementary Ring Formula