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

GoMaximum 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

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

𝜏 max = \frac{d outer \cdot q}{2 \cdot r}

𝜏_max - Maximum Shear Stress?d_outer - Outer Diameter of Shaft?q - Shear Stress at Elementary Ring?r - Radius of Elementary Circular Ring?

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

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Here is how the Maximum shear stress induced at outer surface given shear stress of elementary ring equation looks like with Values.

Here is how the Maximum shear stress induced at outer surface given shear stress of elementary ring equation looks like with Units.

Here is how the Maximum shear stress induced at outer surface given shear stress of elementary ring equation looks like.

31831 = \frac{4000 \cdot 31.831}{2 \cdot 2}

31831MPa = \frac{4000mm \cdot 31.831MPa}{2 \cdot 2mm}

31831 = \frac{4000 \cdot 31.831}{2 \cdot 2}

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

Follow our step by step solution on how to calculate Maximum shear stress induced at outer surface given shear stress of elementary ring?

FIRST Step Consider the formula

𝜏 max = \frac{d outer \cdot q}{2 \cdot r}

Next Step Substitute values of Variables

∴

𝜏 max = \frac{4000mm \cdot 31.831MPa}{2 \cdot 2mm}

Next Step Convert Units

∴

𝜏 max = \frac{4m \cdot 3.2E+7Pa}{2 \cdot 0.002m}

Next Step Prepare to Evaluate

∴

𝜏 max = \frac{4 \cdot 3.2E+7}{2 \cdot 0.002}

Next Step Evaluate

∴

𝜏 max = 31831000000Pa

LAST Step Convert to Output's Unit

∴

𝜏 max = 31831MPa

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

Variables

Maximum Shear Stress

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

Symbol: 𝜏_max

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress

Outer Diameter of Shaft

Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Shaft

Shear Stress at Elementary Ring

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.

Symbol: q

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress at Elementary Ring

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

Other Formulas to find Maximum Shear Stress

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

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

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

𝜏 max = \frac{T f \cdot d outer}{4 \cdot π \cdot (r^{2}) \cdot b 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 max = \frac{16 \cdot d outer \cdot T}{π \cdot (({d outer}^{4}) - ({d inner}^{4}))}

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

T = \frac{π \cdot 𝜏 max \cdot (({d outer}^{4}) - ({d inner}^{4}))}{16 \cdot d outer}

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

𝜏 max = \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 max \cdot (({r h}^{4}) - ({r i}^{4}))}{2 \cdot r h}

How to Evaluate 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 evaluator uses Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring) to evaluate 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_max symbol.

How to evaluate Maximum shear stress induced at outer surface given shear stress of elementary ring using this online evaluator? To use this online evaluator for Maximum shear stress induced at outer surface given shear stress of elementary ring, enter Outer Diameter of Shaft (d_outer), Shear Stress at Elementary Ring (q) & Radius of Elementary Circular Ring (r) and hit the calculate button.

FAQs on Maximum shear stress induced at outer surface given shear stress of elementary ring

What is the formula to find Maximum shear stress induced at outer surface given shear stress of elementary ring?

The formula of Maximum shear stress induced at outer surface given shear stress of elementary ring is expressed as Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring). Here is an example- 3.9E-7 = (0.014*31831000)/(2*0.002).

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

With Outer Diameter of Shaft (d_outer), Shear Stress at Elementary Ring (q) & Radius of Elementary Circular Ring (r) we can find Maximum shear stress induced at outer surface given shear stress of elementary ring using the formula - Maximum Shear Stress = (Outer Diameter of Shaft*Shear Stress at Elementary Ring)/(2*Radius of Elementary Circular Ring).

What are the other ways to Calculate Maximum Shear Stress?

Here are the different ways to Calculate Maximum Shear Stress-

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)

Can the Maximum shear stress induced at outer surface given shear stress of elementary ring be negative?

Yes, the Maximum shear stress induced at outer surface given shear stress of elementary ring, measured in Stress can be negative.

Which unit is used to measure 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 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 shear stress of elementary ring can be measured.

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

​GoMaximum 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

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

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

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

FAQs on Maximum shear stress induced at outer surface given shear stress of elementary ring

Variable Name

GoMaximum 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