Maximum Shear Stress Induced at Outer Surface given Turning Moment on 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 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 Circular Ring [r]			+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 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 Induced at Outer Surface given Turning Moment on Elementary Ring [𝜏_s]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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.
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)
Radius of Elementary Circular Ring: 2 Millimeter --> 0.002 Meter (Check conversion here)
Thickness of Ring: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_s = (T*d_o)/(4*pi*(r^3)*b_r) --> (4*0.014)/(4*pi*(0.002^3)*0.005)

Evaluating ... ...

𝜏_s = 111408460.164327

STEP 3: Convert Result to Output's Unit

111408460.164327 Pascal -->111.408460164327 Megapascal (Check conversion here)

FINAL ANSWER

111.408460164327 ≈ 111.4085 Megapascal <-- Maximum Shear Stress

(Calculation completed in 00.020 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))

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

LaTeX Go

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

What is Elementary Ring?

An elementary ring is a small, thin circular segment within a larger rotating object, often used in physics and engineering to simplify calculations. It’s typically conceptualized as a narrow slice or layer within a cylindrical or spherical body. By analyzing forces, mass, and other properties on this elementary ring, complex rotational and dynamic behavior of the entire body can be understood. This approach is commonly used in studies of moments of inertia, torque, and other rotational properties.

How to Calculate Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring?

Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring calculator uses Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring) to calculate the Maximum Shear Stress, Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring formula is defined as a measure of the maximum shear stress experienced at the outer surface of a hollow circular shaft due to the applied turning moment, which is critical for assessing material strength and safety. Maximum Shear Stress is denoted by 𝜏_s symbol.

How to calculate Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring using this online calculator? To use this online calculator for Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring, enter Turning Moment (T), Outer Diameter of Shaft (d_o), Radius of Elementary Circular Ring (r) & Thickness of Ring (b_r) and hit the calculate button. Here is how the Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring calculation can be explained with given input values -> 0.000738 = (4*0.014)/(4*pi*(0.002^3)*0.005).

FAQ

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

Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring formula is defined as a measure of the maximum shear stress experienced at the outer surface of a hollow circular shaft due to the applied turning moment, which is critical for assessing material strength and safety and is represented as 𝜏_s = (T*d_o)/(4*pi*(r^3)*b_r) or Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring). 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 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 & 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 Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring?

Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring formula is defined as a measure of the maximum shear stress experienced at the outer surface of a hollow circular shaft due to the applied turning moment, which is critical for assessing material strength and safety is calculated using Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring). To calculate Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring, you need Turning Moment (T), Outer Diameter of Shaft (d_o), Radius of Elementary Circular Ring (r) & Thickness of Ring (b_r). With our tool, you need to enter the respective value for Turning Moment, Outer Diameter of Shaft, Radius of Elementary Circular Ring & 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 Maximum Shear Stress?

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

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

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