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

GoMaximum Shear Stress at Outer Surface given Total Turning Moment 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{16 \cdot d o \cdot T}{π \cdot ({d o}^{4} - {d i}^{4})}

𝜏_m - Maximum Shear Stress on Shaft?d_o - Outer Diameter of Shaft?T - Turning Moment?d_i - Inner Diameter of Shaft?π - Archimedes' constant?

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

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

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

Here is how the Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft equation looks like.

-0.1951 = \frac{16 \cdot 14 \cdot 4}{3.1416 \cdot (14^{4} - 35^{4})}

-0.1951MPa = \frac{16 \cdot 14mm \cdot 4N*m}{3.1416 \cdot ({14mm}^{4} - {35mm}^{4})}

-0.1951 = \frac{16 \cdot 14 \cdot 4}{3.1416 \cdot (14^{4} - 35^{4})}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 m = \frac{16 \cdot 14mm \cdot 4N*m}{π \cdot ({14mm}^{4} - {35mm}^{4})}

Next Step Substitute values of Constants

∴

𝜏 m = \frac{16 \cdot 14mm \cdot 4N*m}{3.1416 \cdot ({14mm}^{4} - {35mm}^{4})}

Next Step Convert Units

∴

𝜏 m = \frac{16 \cdot 0.014m \cdot 4N*m}{3.1416 \cdot ({0.014m}^{4} - {0.035m}^{4})}

Next Step Prepare to Evaluate

∴

𝜏 m = \frac{16 \cdot 0.014 \cdot 4}{3.1416 \cdot ({0.014}^{4} - {0.035}^{4})}

Next Step Evaluate

∴

𝜏 m = -195051.225933281Pa

Next Step Convert to Output's Unit

∴

𝜏 m = -0.195051225933281MPa

LAST Step Rounding Answer

∴

𝜏 m = -0.1951MPa

Maximum Shear Stress at Outer Surface given Diameter of Shaft 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

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

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

Inner Diameter of Shaft

The Inner Diameter of Shaft is the measurement of the internal width of a hollow shaft, crucial for determining its torque transmission capacity.

Symbol: d_i

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Inner Diameter of Shaft

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 Total Turning Moment on Hollow Circular Shaft

𝜏 m = \frac{T \cdot 2 \cdot r h}{π \cdot ({r h}^{4} - {r 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 Diameter of Shaft on Hollow Circular Shaft?

Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft evaluator uses Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning Moment)/(pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4)) to evaluate the Maximum Shear Stress on Shaft, Maximum Shear Stress at Outer Surface given Diameter of Shaft 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 when subjected to torque. It helps in assessing the shaft's structural integrity. Maximum Shear Stress on Shaft is denoted by 𝜏_m symbol.

How to evaluate Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft using this online evaluator? To use this online evaluator for Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft, enter Outer Diameter of Shaft (d_o), Turning Moment (T) & Inner Diameter of Shaft (d_i) and hit the calculate button.

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

What is the formula to find Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft?

The formula of Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft is expressed as Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning Moment)/(pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4)). Here is an example- -1.3E-6 = (16*0.014*4)/(pi*(0.014^4-0.035^4)).

How to calculate Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft?

With Outer Diameter of Shaft (d_o), Turning Moment (T) & Inner Diameter of Shaft (d_i) we can find Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft using the formula - Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning Moment)/(pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^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=(Turning Moment*2*Outer Radius Of Hollow circular Cylinder)/(pi*(Outer Radius Of Hollow circular Cylinder^4-Inner Radius Of Hollow Circular Cylinder^4))

Can the Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft be negative?

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

Which unit is used to measure Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft?

Maximum Shear Stress at Outer Surface given Diameter of Shaft 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 Diameter of Shaft on Hollow Circular Shaft can be measured.

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