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

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

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Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces. Check FAQs

𝜏 m = \frac{T \cdot 2 \cdot r h}{π \cdot ({r h}^{4} - {r i}^{4})}

𝜏_m - Maximum Shear Stress on Shaft?T - Turning Moment?r_h - Outer Radius Of Hollow circular Cylinder?r_i - Inner Radius Of Hollow Circular Cylinder?π - Archimedes' constant?

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

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Here is how the Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft equation looks like with Values.

Here is how the Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft equation looks like with Units.

Here is how the Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft equation looks like.

4.8E-8 = \frac{4 \cdot 2 \cdot 5500}{3.1416 \cdot (5500^{4} - 5000^{4})}

4.8E-8MPa = \frac{4N*m \cdot 2 \cdot 5500mm}{3.1416 \cdot ({5500mm}^{4} - {5000mm}^{4})}

4.8E-8 = \frac{4 \cdot 2 \cdot 5500}{3.1416 \cdot (5500^{4} - 5000^{4})}

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

Follow our step by step solution on how to calculate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

FIRST Step Consider the formula

𝜏 m = \frac{T \cdot 2 \cdot r h}{π \cdot ({r h}^{4} - {r i}^{4})}

Next Step Substitute values of Variables

∴

𝜏 m = \frac{4N*m \cdot 2 \cdot 5500mm}{π \cdot ({5500mm}^{4} - {5000mm}^{4})}

Next Step Substitute values of Constants

∴

𝜏 m = \frac{4N*m \cdot 2 \cdot 5500mm}{3.1416 \cdot ({5500mm}^{4} - {5000mm}^{4})}

Next Step Convert Units

∴

𝜏 m = \frac{4N*m \cdot 2 \cdot 5.5m}{3.1416 \cdot ({5.5m}^{4} - {5m}^{4})}

Next Step Prepare to Evaluate

∴

𝜏 m = \frac{4 \cdot 2 \cdot 5.5}{3.1416 \cdot ({5.5}^{4} - 5^{4})}

Next Step Evaluate

∴

𝜏 m = 0.048284886850547Pa

Next Step Convert to Output's Unit

∴

𝜏 m = 4.8284886850547E-08MPa

LAST Step Rounding Answer

∴

𝜏 m = 4.8E-8MPa

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

Variables

Constants

Maximum Shear Stress on Shaft

Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.

Symbol: 𝜏_m

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress on Shaft

Turning Moment

The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems.

Symbol: T

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Turning Moment

Outer Radius Of Hollow circular Cylinder

The Outer Radius Of Hollow Circular Cylinder is the distance from the center to the outer edge of a hollow cylinder, crucial for understanding its structural properties and torque transmission.

Symbol: r_h

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius Of Hollow circular Cylinder

Inner Radius Of Hollow Circular Cylinder

The Inner Radius Of Hollow Circular Cylinder is the distance from the center to the inner surface of a hollow cylinder, influencing its structural integrity and torque transmission.

Symbol: r_i

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Radius Of Hollow Circular Cylinder

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Maximum Shear Stress on Shaft

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

𝜏 m = \frac{16 \cdot d o \cdot T}{π \cdot ({d o}^{4} - {d i}^{4})}

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

Go Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft

T = \frac{π \cdot 𝜏 m \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Go Total Turning Moment on Hollow Circular Shaft given Radius of Shaft

T = \frac{π \cdot 𝜏 m \cdot (({r h}^{4}) - ({r i}^{4}))}{2 \cdot r h}

Go Outer Radius of Shaft using Turning Force on Elementary Ring given Turning Moment

r o = \frac{2 \cdot π \cdot 𝜏 s \cdot (r^{2}) \cdot b r}{T}

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

𝜏 s = \frac{T \cdot d o}{4 \cdot π \cdot (r^{3}) \cdot b r}

How to Evaluate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft evaluator uses 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)) to evaluate the Maximum Shear Stress on Shaft, Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft 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 on Shaft is denoted by 𝜏_m symbol.

How to evaluate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft using this online evaluator? To use this online evaluator for Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft, enter Turning Moment (T), Outer Radius Of Hollow circular Cylinder (r_h) & Inner Radius Of Hollow Circular Cylinder (r_i) and hit the calculate button.

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

What is the formula to find Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

The formula of Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft is expressed as 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)). Here is an example- 3.2E-13 = (4*2*5.5)/(pi*(5.5^4-5^4)).

How to calculate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

With Turning Moment (T), Outer Radius Of Hollow circular Cylinder (r_h) & Inner Radius Of Hollow Circular Cylinder (r_i) we can find Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft using the formula - 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)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Maximum Shear Stress on Shaft?

Here are the different ways to Calculate Maximum Shear Stress on Shaft-

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

Can the Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft be negative?

No, the Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft, measured in Pressure cannot be negative.

Which unit is used to measure Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft can be measured.

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

​GoMaximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft Formula

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

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

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

Other Formulas to find Maximum Shear Stress on Shaft

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

How to Evaluate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

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

Variable Name

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