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

GoMaximum Shear Stress at Outer Surface given Turning Force on Elementary Ring Formula

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

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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. Check FAQs

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

𝜏_s - Maximum Shear Stress?T - Turning Moment?d_o - Outer Diameter of Shaft?r - Radius of Elementary Circular Ring?b_r - Thickness of Ring?π - Archimedes' constant?

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

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Here is how the Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring equation looks like with Values.

Here is how the Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring equation looks like with Units.

Here is how the Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring equation looks like.

111.4085 = \frac{4 \cdot 14}{4 \cdot 3.1416 \cdot (2^{3}) \cdot 5}

111.4085MPa = \frac{4N*m \cdot 14mm}{4 \cdot 3.1416 \cdot ({2mm}^{3}) \cdot 5mm}

111.4085 = \frac{4 \cdot 14}{4 \cdot 3.1416 \cdot (2^{3}) \cdot 5}

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

Follow our step by step solution on how to calculate Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 s = \frac{4N*m \cdot 14mm}{4 \cdot π \cdot ({2mm}^{3}) \cdot 5mm}

Next Step Substitute values of Constants

∴

𝜏 s = \frac{4N*m \cdot 14mm}{4 \cdot 3.1416 \cdot ({2mm}^{3}) \cdot 5mm}

Next Step Convert Units

∴

𝜏 s = \frac{4N*m \cdot 0.014m}{4 \cdot 3.1416 \cdot ({0.002m}^{3}) \cdot 0.005m}

Next Step Prepare to Evaluate

∴

𝜏 s = \frac{4 \cdot 0.014}{4 \cdot 3.1416 \cdot ({0.002}^{3}) \cdot 0.005}

Next Step Evaluate

∴

𝜏 s = 111408460.164327Pa

Next Step Convert to Output's Unit

∴

𝜏 s = 111.408460164327MPa

LAST Step Rounding Answer

∴

𝜏 s = 111.4085MPa

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

Variables

Constants

Maximum Shear Stress

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.

Symbol: 𝜏_s

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress

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 Diameter of Shaft

The Outer Diameter of Shaft is the measurement across the widest part of a hollow circular shaft, influencing its strength and torque transmission capabilities.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Shaft

Radius of Elementary Circular Ring

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.

Symbol: r

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Elementary Circular Ring

Thickness of Ring

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.

Symbol: b_r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Ring

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

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

𝜏 s = \frac{T f \cdot d o}{4 \cdot π \cdot (r^{2}) \cdot b r}

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

𝜏 s = \frac{d o \cdot q}{2 \cdot r}

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

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})}

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

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

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}

How to Evaluate 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 evaluator uses Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring) to evaluate 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 evaluate Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring using this online evaluator? To use this online evaluator 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.

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

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

The formula of Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring is expressed as Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring). Here is an example- 0.000738 = (4*0.014)/(4*pi*(0.002^3)*0.005).

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

With Turning Moment (T), Outer Diameter of Shaft (d_o), Radius of Elementary Circular Ring (r) & Thickness of Ring (b_r) we can find Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring using the formula - Maximum Shear Stress = (Turning Moment*Outer Diameter of Shaft)/(4*pi*(Radius of Elementary Circular Ring^3)*Thickness of Ring). This formula also uses Archimedes' constant .

What are the other ways to Calculate Maximum Shear Stress?

Here are the different ways to Calculate Maximum Shear Stress-

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)

Can the Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring be negative?

Yes, the Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring, measured in Stress can be negative.

Which unit is used to measure 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 is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring can be measured.

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

​GoMaximum Shear Stress at Outer Surface given Turning Force on Elementary Ring Formula

​GoMaximum shear stress induced at outer surface given shear stress of elementary ring Formula

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

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

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

Other Formulas to find Maximum Shear Stress

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

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

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

Variable Name

GoMaximum Shear Stress at Outer Surface given Turning Force on Elementary Ring Formula

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