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Length of Key given Shear Stress Formula

GoLength of Key given Compressive Stress in Key Formula

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The Length of Key is defined as the length of the key which is used to prevent rotation of a machine component or it is the major dimension of the key. Check FAQs

l = \frac{F}{b k \cdot 𝜏}

l - Length of Key?F - Force on Key?b_k - Width of Key?𝜏 - Shear Stress in Key?

Length of Key given Shear Stress Example

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Here is how the Length of Key given Shear Stress equation looks like with Values.

Here is how the Length of Key given Shear Stress equation looks like with Units.

Here is how the Length of Key given Shear Stress equation looks like.

31.2363 = \frac{9980}{5 \cdot 63.9}

31.2363mm = \frac{9980N}{5mm \cdot 63.9N/mm²}

31.2363 = \frac{9980}{5 \cdot 63.9}

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Length of Key given Shear Stress Solution

Follow our step by step solution on how to calculate Length of Key given Shear Stress?

FIRST Step Consider the formula

l = \frac{F}{b k \cdot 𝜏}

Next Step Substitute values of Variables

∴

l = \frac{9980N}{5mm \cdot 63.9N/mm²}

Next Step Convert Units

∴

l = \frac{9980N}{0.005m \cdot 6.4E+7Pa}

Next Step Prepare to Evaluate

∴

l = \frac{9980}{0.005 \cdot 6.4E+7}

Next Step Evaluate

∴

l = 0.0312363067292645m

Next Step Convert to Output's Unit

∴

l = 31.2363067292645mm

LAST Step Rounding Answer

∴

l = 31.2363mm

Length of Key given Shear Stress Formula Elements

Variables

Length of Key

The Length of Key is defined as the length of the key which is used to prevent rotation of a machine component or it is the major dimension of the key.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Key

Force on Key

Force on Key is the reaction onto the key of a machined assembly.

Symbol: F

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force on Key

Width of Key

Width of Key is defined as the width of the key that is fixed in between the shaft and the hub to prevent relative movement between a power transmitting shaft and an attached component.

Symbol: b_k

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Key

Shear Stress in Key

Shear Stress in Key is the force per unit area tending to cause deformation of the key by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Shear Stress in Key

Other Formulas to find Length of Key

Go Length of Key given Compressive Stress in Key

l = 4 \cdot \frac{M t}{d s \cdot σ c \cdot h}

Other formulas in Design of Square and Flat Keys category

Go Force on Key

F = 2 \cdot \frac{M t}{d s}

Go Torque Transmitted by Keyed Shaft given Force on Keys

M t = F \cdot \frac{d s}{2}

Go Shaft Diameter given Force on Key

d s = 2 \cdot \frac{M t}{F}

Go Shear Stress in given Force on Key

𝜏 = \frac{F}{b k \cdot l}

How to Evaluate Length of Key given Shear Stress?

Length of Key given Shear Stress evaluator uses Length of Key = Force on Key/(Width of Key*Shear Stress in Key) to evaluate the Length of Key, Length of Key given Shear Stress formula is defined as a method to determine the appropriate dimensions of a key in mechanical design, ensuring it can withstand the applied shear stress without failure. This is crucial for maintaining the integrity and functionality of mechanical assemblies. Length of Key is denoted by l symbol.

How to evaluate Length of Key given Shear Stress using this online evaluator? To use this online evaluator for Length of Key given Shear Stress, enter Force on Key (F), Width of Key (b_k) & Shear Stress in Key (𝜏) and hit the calculate button.

FAQs on Length of Key given Shear Stress

What is the formula to find Length of Key given Shear Stress?

The formula of Length of Key given Shear Stress is expressed as Length of Key = Force on Key/(Width of Key*Shear Stress in Key). Here is an example- 35000 = 9980/(0.005*63900000).

How to calculate Length of Key given Shear Stress?

With Force on Key (F), Width of Key (b_k) & Shear Stress in Key (𝜏) we can find Length of Key given Shear Stress using the formula - Length of Key = Force on Key/(Width of Key*Shear Stress in Key).

What are the other ways to Calculate Length of Key?

Here are the different ways to Calculate Length of Key-

Length of Key=4*Transmitted Torque by Keyed Shaft/(Diameter of Shaft using Key*Compressive Stress in Key*Height of Key)

Can the Length of Key given Shear Stress be negative?

No, the Length of Key given Shear Stress, measured in Length cannot be negative.

Which unit is used to measure Length of Key given Shear Stress?

Length of Key given Shear Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Key given Shear Stress can be measured.

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Length of Key given Shear Stress Formula

​GoLength of Key given Compressive Stress in Key Formula

Length of Key given Shear Stress Example

Length of Key given Shear Stress Solution

Length of Key given Shear Stress Formula Elements

Other Formulas to find Length of Key

Other formulas in Design of Square and Flat Keys category

How to Evaluate Length of Key given Shear Stress?

FAQs on Length of Key given Shear Stress

Variable Name

GoLength of Key given Compressive Stress in Key Formula