Radius of Elementary Ring given Shear Stress of Elementary Ring Calculator

✖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 Shear Stress at Elementary Ring is the internal stress experienced by a thin ring in a hollow shaft due to the applied torque, affecting its structural integrity.ⓘ Shear Stress at Elementary Ring [q]			+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 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 Shear Stress of Elementary Ring [r]

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Radius of Elementary Ring given Shear Stress of Elementary Ring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Elementary Circular Ring = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress)
r = (d_o*q)/(2*𝜏_s)
This formula uses 4 Variables

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.
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.
Shear Stress at Elementary Ring - (Measured in Pascal) - The Shear Stress at Elementary Ring is the internal stress experienced by a thin ring in a hollow shaft due to the applied torque, affecting its structural integrity.
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.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 14 Millimeter --> 0.014 Meter (Check conversion here)
Shear Stress at Elementary Ring: 31.831 Megapascal --> 31831000 Pascal (Check conversion here)
Maximum Shear Stress: 111.4085 Megapascal --> 111408500 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = (d_o*q)/(2*𝜏_s) --> (0.014*31831000)/(2*111408500)

Evaluating ... ...

r = 0.002

STEP 3: Convert Result to Output's Unit

0.002 Meter -->2 Millimeter (Check conversion here)

FINAL ANSWER

2 Millimeter <-- Radius of Elementary Circular Ring

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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 Shear Stress of Elementary Ring Formula

LaTeX Go

Radius of Elementary Circular Ring = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress)
r = (d_o*q)/(2*𝜏_s)

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 Shear Stress of Elementary Ring?

Radius of Elementary Ring given Shear Stress of Elementary Ring calculator uses Radius of Elementary Circular Ring = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress) to calculate the Radius of Elementary Circular Ring, Radius of Elementary Ring given Shear Stress of Elementary Ring formula is defined as a method to determine the radius of an elementary ring in a hollow circular shaft based on the outer diameter and the shear stress experienced by the shaft, which is crucial for torque analysis. Radius of Elementary Circular Ring is denoted by r symbol.

How to calculate Radius of Elementary Ring given Shear Stress of Elementary Ring using this online calculator? To use this online calculator for Radius of Elementary Ring given Shear Stress of Elementary Ring, enter Outer Diameter of Shaft (d_o), Shear Stress at Elementary Ring (q) & Maximum Shear Stress (𝜏_s) and hit the calculate button. Here is how the Radius of Elementary Ring given Shear Stress of Elementary Ring calculation can be explained with given input values -> 6.999969 = (0.014*31831000)/(2*111408500).

FAQ

What is Radius of Elementary Ring given Shear Stress of Elementary Ring?

Radius of Elementary Ring given Shear Stress of Elementary Ring formula is defined as a method to determine the radius of an elementary ring in a hollow circular shaft based on the outer diameter and the shear stress experienced by the shaft, which is crucial for torque analysis and is represented as r = (d_o*q)/(2*𝜏_s) or Radius of Elementary Circular Ring = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress). 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 Shear Stress at Elementary Ring is the internal stress experienced by a thin ring in a hollow shaft due to the applied torque, affecting its structural integrity & 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.

How to calculate Radius of Elementary Ring given Shear Stress of Elementary Ring?

Radius of Elementary Ring given Shear Stress of Elementary Ring formula is defined as a method to determine the radius of an elementary ring in a hollow circular shaft based on the outer diameter and the shear stress experienced by the shaft, which is crucial for torque analysis is calculated using Radius of Elementary Circular Ring = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Maximum Shear Stress). To calculate Radius of Elementary Ring given Shear Stress of Elementary Ring, you need Outer Diameter of Shaft (d_o), Shear Stress at Elementary Ring (q) & Maximum Shear Stress (𝜏_s). With our tool, you need to enter the respective value for Outer Diameter of Shaft, Shear Stress at Elementary Ring & Maximum Shear Stress 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 Outer Diameter of Shaft, Shear Stress at Elementary Ring & Maximum Shear Stress. 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 = sqrt((Turning Force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of Ring))

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