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Turning Force on Elementary Ring Formula

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

T f = \frac{4 \cdot π \cdot 𝜏 s \cdot r^{2} \cdot b r}{d o}

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

Turning Force on Elementary Ring Example

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Here is how the Turning Force on Elementary Ring equation looks like with Values.

Here is how the Turning Force on Elementary Ring equation looks like with Units.

Here is how the Turning Force on Elementary Ring equation looks like.

2000.0007 = \frac{4 \cdot 3.1416 \cdot 111.4085 \cdot 2^{2} \cdot 5}{14}

2000.0007N = \frac{4 \cdot 3.1416 \cdot 111.4085MPa \cdot {2mm}^{2} \cdot 5mm}{14mm}

2000.0007 = \frac{4 \cdot 3.1416 \cdot 111.4085 \cdot 2^{2} \cdot 5}{14}

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Turning Force on Elementary Ring Solution

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

FIRST Step Consider the formula

T f = \frac{4 \cdot π \cdot 𝜏 s \cdot r^{2} \cdot b r}{d o}

Next Step Substitute values of Variables

∴

T f = \frac{4 \cdot π \cdot 111.4085MPa \cdot {2mm}^{2} \cdot 5mm}{14mm}

Next Step Substitute values of Constants

∴

T f = \frac{4 \cdot 3.1416 \cdot 111.4085MPa \cdot {2mm}^{2} \cdot 5mm}{14mm}

Next Step Convert Units

∴

T f = \frac{4 \cdot 3.1416 \cdot 1.1E+8Pa \cdot {0.002m}^{2} \cdot 0.005m}{0.014m}

Next Step Prepare to Evaluate

∴

T f = \frac{4 \cdot 3.1416 \cdot 1.1E+8 \cdot {0.002}^{2} \cdot 0.005}{0.014}

Next Step Evaluate

∴

T f = 2000.00071512833N

LAST Step Rounding Answer

∴

T f = 2000.0007N

Turning Force on Elementary Ring Formula Elements

Variables

Constants

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

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

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

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 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 Turning Force on Elementary Ring?

Turning Force on Elementary Ring evaluator uses Turning Force = (4*pi*Maximum Shear Stress*Radius of Elementary Circular Ring^2*Thickness of Ring)/Outer Diameter of Shaft to evaluate the Turning Force, Turning Force on Elementary Ring formula is defined as a representation of the torque exerted on a hollow circular shaft. It illustrates the relationship between shear stress, radius, and the dimensions of the ring, providing insight into the mechanical behavior of rotating systems. Turning Force is denoted by T_f symbol.

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

FAQs on Turning Force on Elementary Ring

What is the formula to find Turning Force on Elementary Ring?

The formula of Turning Force on Elementary Ring is expressed as Turning Force = (4*pi*Maximum Shear Stress*Radius of Elementary Circular Ring^2*Thickness of Ring)/Outer Diameter of Shaft. Here is an example- 2000.001 = (4*pi*111408500*0.002^2*0.005)/0.014.

How to calculate Turning Force on Elementary Ring?

With Maximum Shear Stress (𝜏_s), Radius of Elementary Circular Ring (r), Thickness of Ring (b_r) & Outer Diameter of Shaft (d_o) we can find Turning Force on Elementary Ring using the formula - Turning Force = (4*pi*Maximum Shear Stress*Radius of Elementary Circular Ring^2*Thickness of Ring)/Outer Diameter of Shaft. This formula also uses Archimedes' constant .

Can the Turning Force on Elementary Ring be negative?

No, the Turning Force on Elementary Ring, measured in Force cannot be negative.

Which unit is used to measure Turning Force on Elementary Ring?

Turning Force on Elementary Ring is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Turning Force on Elementary Ring can be measured.

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Turning Force on Elementary Ring Formula

Turning Force on Elementary Ring Example

Turning Force on Elementary Ring Solution

Turning Force on Elementary Ring Formula Elements

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

How to Evaluate Turning Force on Elementary Ring?

FAQs on Turning Force on Elementary Ring

Variable Name