Radius of Elementary Ring given Turning Force of Elementary Ring Calculator

✖The Turning Force is the torque transmitted by a hollow circular shaft, influencing its ability to rotate and perform work efficiently in mechanical systems.ⓘ Turning Force [T_f]			+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 Force of Elementary Ring [r]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Torque Transmitted by a Hollow Circular Shaft Formulas PDF PDF Image

Radius of Elementary Ring given Turning Force of Elementary Ring Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

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 Force - (Measured in Newton) - The Turning Force is the torque transmitted by a hollow circular shaft, influencing its ability to rotate and perform work efficiently 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 Force: 2000.001 Newton --> 2000.001 Newton 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 = sqrt((T_f*d_o)/(4*pi*𝜏_s*b_r)) --> sqrt((2000.001*0.014)/(4*pi*111408500*0.005))

Evaluating ... ...

r = 0.00200000014243578

STEP 3: Convert Result to Output's Unit

0.00200000014243578 Meter -->2.00000014243578 Millimeter (Check conversion here)

FINAL ANSWER

2.00000014243578 ≈ 2 Millimeter <-- Radius of Elementary Circular Ring

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Torque Transmitted by a Hollow Circular Shaft » Radius of Elementary Ring given Turning Force of Elementary Ring

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< 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 Force of Elementary Ring Formula

LaTeX Go

Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))
r = sqrt((T_f*d_o)/(4*pi*𝜏_s*b_r))

What is Shear Shear of Elementary Ring?

The shear stress of an elementary ring refers to the internal stress developed within a small, thin circular segment of a rotating or loaded body when opposing forces act parallel to its cross-sectional area. This stress occurs due to the tendency of forces to slide one layer of the ring over another. Analyzing shear stress in an elementary ring helps understand the material's behavior under rotational or shear forces, ensuring stability and strength in mechanical and structural designs.

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

Radius of Elementary Ring given Turning Force of Elementary Ring calculator uses Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring)) to calculate 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 calculate Radius of Elementary Ring given Turning Force of Elementary Ring using this online calculator? To use this online calculator 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. Here is how the Radius of Elementary Ring given Turning Force of Elementary Ring calculation can be explained with given input values -> 118.3216 = sqrt((2000.001*0.014)/(4*pi*111408500*0.005)).

FAQ

What is Radius of Elementary Ring given Turning Force of Elementary 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 and is represented as r = sqrt((T_f*d_o)/(4*pi*𝜏_s*b_r)) or Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring)). The Turning Force is the torque transmitted by a hollow circular shaft, influencing its ability to rotate and perform work efficiently 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 Force of Elementary 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 is calculated using Radius of Elementary Circular Ring = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring)). To calculate Radius of Elementary Ring given Turning Force of Elementary Ring, you need Turning Force (T_f), 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 Force, 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 Force, 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 = ((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)

Home

FREE PDFs

🔍 Search