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Turning Moment on Elementary Ring Formula

GoTotal Turning Moment on Hollow Circular Shaft given Diameter of Shaft Formula

GoTotal Turning Moment on Hollow Circular Shaft given Radius of Shaft Formula

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The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems. Check FAQs

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

T - Turning Moment?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 Moment on Elementary Ring Example

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

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

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

4 = \frac{4 \cdot 3.1416 \cdot 111.4085 \cdot (2^{3}) \cdot 5}{14}

4N*m = \frac{4 \cdot 3.1416 \cdot 111.4085MPa \cdot ({2mm}^{3}) \cdot 5mm}{14mm}

4 = \frac{4 \cdot 3.1416 \cdot 111.4085 \cdot (2^{3}) \cdot 5}{14}

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Turning Moment on Elementary Ring Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T = \frac{4 \cdot π \cdot 111.4085MPa \cdot ({2mm}^{3}) \cdot 5mm}{14mm}

Next Step Substitute values of Constants

∴

T = \frac{4 \cdot 3.1416 \cdot 111.4085MPa \cdot ({2mm}^{3}) \cdot 5mm}{14mm}

Next Step Convert Units

∴

T = \frac{4 \cdot 3.1416 \cdot 1.1E+8Pa \cdot ({0.002m}^{3}) \cdot 0.005m}{0.014m}

Next Step Prepare to Evaluate

∴

T = \frac{4 \cdot 3.1416 \cdot 1.1E+8 \cdot ({0.002}^{3}) \cdot 0.005}{0.014}

Next Step Evaluate

∴

T = 4.00000143025667N*m

LAST Step Rounding Answer

∴

T = 4N*m

Turning Moment on Elementary Ring Formula Elements

Variables

Constants

Turning Moment

The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems.

Symbol: T

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Turning Moment

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 to find Turning Moment

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 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}

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 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 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 Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring

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

How to Evaluate Turning Moment on Elementary Ring?

Turning Moment on Elementary Ring evaluator uses Turning Moment = (4*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^3)*Thickness of Ring)/Outer Diameter of Shaft to evaluate the Turning Moment, Turning Moment on Elementary Ring formula is defined as a measure of the torque transmitted by a hollow circular shaft, taking into account the shear stress, radius, and width of the ring. It is essential for understanding the mechanical performance of cylindrical structures under load. Turning Moment is denoted by T symbol.

How to evaluate Turning Moment on Elementary Ring using this online evaluator? To use this online evaluator for Turning Moment 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 Moment on Elementary Ring

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

The formula of Turning Moment on Elementary Ring is expressed as Turning Moment = (4*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^3)*Thickness of Ring)/Outer Diameter of Shaft. Here is an example- 4.000001 = (4*pi*111408500*(0.002^3)*0.005)/0.014.

How to calculate Turning Moment 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 Moment on Elementary Ring using the formula - Turning Moment = (4*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^3)*Thickness of Ring)/Outer Diameter of Shaft. This formula also uses Archimedes' constant .

What are the other ways to Calculate Turning Moment?

Here are the different ways to Calculate Turning Moment-

Turning Moment=(pi*Maximum Shear Stress on Shaft*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))/(16*Outer Diameter of Shaft)
Turning Moment=(pi*Maximum Shear Stress on Shaft*((Outer Radius Of Hollow circular Cylinder^4)-(Inner Radius Of Hollow Circular Cylinder^4)))/(2*Outer Radius Of Hollow circular Cylinder)

Can the Turning Moment on Elementary Ring be negative?

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

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

Turning Moment on Elementary Ring is usually measured using the Newton Meter[N*m] for Torque. Newton Centimeter[N*m], Newton Millimeter[N*m], Kilonewton Meter[N*m] are the few other units in which Turning Moment on Elementary Ring can be measured.

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Turning Moment on Elementary Ring Formula

​GoTotal Turning Moment on Hollow Circular Shaft given Diameter of Shaft Formula

​GoTotal Turning Moment on Hollow Circular Shaft given Radius of Shaft Formula

Turning Moment on Elementary Ring Example

Turning Moment on Elementary Ring Solution

Turning Moment on Elementary Ring Formula Elements

Other Formulas to find Turning Moment

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

How to Evaluate Turning Moment on Elementary Ring?

FAQs on Turning Moment on Elementary Ring

Variable Name

GoTotal Turning Moment on Hollow Circular Shaft given Diameter of Shaft Formula

GoTotal Turning Moment on Hollow Circular Shaft given Radius of Shaft Formula