Maximum shear stress induced at outer surface 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 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 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 shear stress of elementary ring [𝜏_s]

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Maximum shear stress induced at outer surface given shear stress of elementary ring Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_s = (d_o*q)/(2*r) --> (0.014*31831000)/(2*0.002)

Evaluating ... ...

𝜏_s = 111408500

STEP 3: Convert Result to Output's Unit

111408500 Pascal -->111.4085 Megapascal (Check conversion here)

FINAL ANSWER

111.4085 Megapascal <-- Maximum Shear Stress

(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))

Maximum shear stress induced at outer surface given shear stress of elementary ring Formula

LaTeX Go

Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring)
𝜏_s = (d_o*q)/(2*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 shear stress of elementary ring?

Maximum shear stress induced at outer surface given shear stress of elementary ring calculator uses Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring) to calculate the Maximum Shear Stress, Maximum shear stress induced at outer surface given shear stress of 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 torque, which is crucial 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 shear stress of elementary ring using this online calculator? To use this online calculator for Maximum shear stress induced at outer surface given shear stress of elementary ring, enter Outer Diameter of Shaft (d_o), Shear Stress at Elementary Ring (q) & Radius of Elementary Circular Ring (r) and hit the calculate button. Here is how the Maximum shear stress induced at outer surface given shear stress of elementary ring calculation can be explained with given input values -> 3.9E-7 = (0.014*31831000)/(2*0.002).

FAQ

What is Maximum shear stress induced at outer surface given shear stress of elementary ring?

Maximum shear stress induced at outer surface given shear stress of 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 torque, which is crucial for assessing material strength and safety and is represented as 𝜏_s = (d_o*q)/(2*r) or Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring). 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 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.

How to calculate Maximum shear stress induced at outer surface given shear stress of elementary ring?

Maximum shear stress induced at outer surface given shear stress of 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 torque, which is crucial for assessing material strength and safety is calculated using Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring). To calculate Maximum shear stress induced at outer surface given shear stress of elementary ring, you need Outer Diameter of Shaft (d_o), Shear Stress at Elementary Ring (q) & Radius of Elementary Circular Ring (r). With our tool, you need to enter the respective value for Outer Diameter of Shaft, Shear Stress at Elementary Ring & Radius of Elementary Circular 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 Outer Diameter of Shaft, Shear Stress at Elementary Ring & Radius of Elementary Circular Ring. We can use 2 other way(s) to calculate the same, which is/are as follows -

Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring)
Maximum Shear Stress = (Turning Force*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^2)*Thickness of Ring)

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