Radius of Elementary Ring given Turning Moment of Elementary Ring Calculator

✖The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems.ⓘ Turning Moment [T]			+10% -10%
✖The Outer Diameter of Shaft is the measurement across the widest part of a hollow circular shaft, influencing its strength and torque transmission capabilities.ⓘ Outer Diameter of Shaft [d_o]			+10% -10%
✖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.ⓘ Maximum Shear Stress [𝜏_s]			+10% -10%
✖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.ⓘ Thickness of Ring [b_r]			+10% -10%

✖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.ⓘ Radius of Elementary Ring given Turning Moment of Elementary Ring [r]

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Radius of Elementary Ring given Turning Moment of Elementary Ring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Elementary Circular Ring = ((Turning Moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))^(1/3)
r = ((T*d_o)/(4*pi*𝜏_s*b_r))^(1/3)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Radius of Elementary Circular Ring - (Measured in Meter) - 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.
Turning Moment - (Measured in Newton Meter) - The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems.
Outer Diameter of Shaft - (Measured in Meter) - The Outer Diameter of Shaft is the measurement across the widest part of a hollow circular shaft, influencing its strength and torque transmission capabilities.
Maximum Shear Stress - (Measured in Pascal) - 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.
Thickness of Ring - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Turning Moment: 4 Newton Meter --> 4 Newton Meter No Conversion Required
Outer Diameter of Shaft: 14 Millimeter --> 0.014 Meter (Check conversion here)
Maximum Shear Stress: 111.4085 Megapascal --> 111408500 Pascal (Check conversion here)
Thickness of Ring: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = ((T*d_o)/(4*pi*𝜏_s*b_r))^(1/3) --> ((4*0.014)/(4*pi*111408500*0.005))^(1/3)

Evaluating ... ...

r = 0.00199999976162395

STEP 3: Convert Result to Output's Unit

0.00199999976162395 Meter -->1.99999976162395 Millimeter (Check conversion here)

FINAL ANSWER

1.99999976162395 ≈ 2 Millimeter <-- Radius of Elementary Circular Ring

(Calculation completed in 00.004 seconds)

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< Torque Transmitted by a Hollow Circular Shaft Calculators

Total Turning Moment on Hollow Circular Shaft given Radius of Shaft

LaTeX Go 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)

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

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

Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft

LaTeX Go Turning Moment = (pi*Maximum Shear Stress on Shaft*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))/(16*Outer Diameter of Shaft)

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

LaTeX Go Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning Moment)/(pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))

Radius of Elementary Ring given Turning Moment of Elementary Ring Formula

LaTeX Go

Radius of Elementary Circular Ring = ((Turning Moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))^(1/3)
r = ((T*d_o)/(4*pi*𝜏_s*b_r))^(1/3)

What is Turning Moment?

The turning moment, also known as torque, is the measure of a force's ability to cause an object to rotate around a specific axis or pivot point. It depends on the force's magnitude and its perpendicular distance from the pivot. Turning moments are crucial in mechanics and engineering as they help determine the effectiveness of forces applied to rotate or stabilize structures, machines, and vehicles.

How to Calculate Radius of Elementary Ring given Turning Moment of Elementary Ring?

Radius of Elementary Ring given Turning Moment of Elementary Ring calculator uses Radius of Elementary Circular Ring = ((Turning Moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))^(1/3) to calculate the Radius of Elementary Circular Ring, Radius of Elementary Ring given Turning Moment of Elementary Ring formula is defined as a method to determine the radius of an elementary ring based on the turning moment, outer diameter, shear stress, and width of the ring, which is essential in analyzing torque transmission in hollow circular shafts. Radius of Elementary Circular Ring is denoted by r symbol.

How to calculate Radius of Elementary Ring given Turning Moment of Elementary Ring using this online calculator? To use this online calculator for Radius of Elementary Ring given Turning Moment of Elementary Ring, enter Turning Moment (T), Outer Diameter of Shaft (d_o), Maximum Shear Stress (𝜏_s) & Thickness of Ring (b_r) and hit the calculate button. Here is how the Radius of Elementary Ring given Turning Moment of Elementary Ring calculation can be explained with given input values -> 3756.726 = ((4*0.014)/(4*pi*111408500*0.005))^(1/3).

FAQ

What is Radius of Elementary Ring given Turning Moment of Elementary Ring?

Radius of Elementary Ring given Turning Moment of Elementary Ring formula is defined as a method to determine the radius of an elementary ring based on the turning moment, outer diameter, shear stress, and width of the ring, which is essential in analyzing torque transmission in hollow circular shafts and is represented as r = ((T*d_o)/(4*pi*𝜏_s*b_r))^(1/3) or Radius of Elementary Circular Ring = ((Turning Moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))^(1/3). The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems, The Outer Diameter of Shaft is the measurement across the widest part of a hollow circular shaft, influencing its strength and torque transmission capabilities, 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 & 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.

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

Radius of Elementary Ring given Turning Moment of Elementary Ring formula is defined as a method to determine the radius of an elementary ring based on the turning moment, outer diameter, shear stress, and width of the ring, which is essential in analyzing torque transmission in hollow circular shafts is calculated using Radius of Elementary Circular Ring = ((Turning Moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))^(1/3). To calculate Radius of Elementary Ring given Turning Moment of Elementary Ring, you need Turning Moment (T), Outer Diameter of Shaft (d_o), Maximum Shear Stress (𝜏_s) & Thickness of Ring (b_r). With our tool, you need to enter the respective value for Turning Moment, Outer Diameter of Shaft, Maximum Shear Stress & Thickness of Ring and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radius of Elementary Circular Ring?

In this formula, Radius of Elementary Circular Ring uses Turning Moment, Outer Diameter of Shaft, Maximum Shear Stress & Thickness of Ring. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))
Radius of Elementary Circular Ring = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress)

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