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Width of Key given Shear Stress in Key Formula

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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. Check FAQs

b k = \frac{F}{𝜏 \cdot l}

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

Width of Key given Shear Stress in Key Example

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

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

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

4.4623 = \frac{9980}{63.9 \cdot 35}

4.4623mm = \frac{9980N}{63.9N/mm² \cdot 35mm}

4.4623 = \frac{9980}{63.9 \cdot 35}

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Width of Key given Shear Stress in Key Solution

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

FIRST Step Consider the formula

b k = \frac{F}{𝜏 \cdot l}

Next Step Substitute values of Variables

∴

b k = \frac{9980N}{63.9N/mm² \cdot 35mm}

Next Step Convert Units

∴

b k = \frac{9980N}{6.4E+7Pa \cdot 0.035m}

Next Step Prepare to Evaluate

∴

b k = \frac{9980}{6.4E+7 \cdot 0.035}

Next Step Evaluate

∴

b k = 0.00446232953275207m

Next Step Convert to Output's Unit

∴

b k = 4.46232953275207mm

LAST Step Rounding Answer

∴

b k = 4.4623mm

Width of Key given Shear Stress in Key Formula Elements

Variables

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

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

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

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

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 Width of Key given Shear Stress in Key?

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

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

FAQs on Width of Key given Shear Stress in Key

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

The formula of Width of Key given Shear Stress in Key is expressed as Width of Key = Force on Key/(Shear Stress in Key*Length of Key). Here is an example- 5000 = 9980/(57028570*0.035).

How to calculate Width of Key given Shear Stress in Key?

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

Can the Width of Key given Shear Stress in Key be negative?

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

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

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

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Width of Key given Shear Stress in Key Formula

Width of Key given Shear Stress in Key Example

Width of Key given Shear Stress in Key Solution

Width of Key given Shear Stress in Key Formula Elements

Other formulas in Design of Square and Flat Keys category

How to Evaluate Width of Key given Shear Stress in Key?

FAQs on Width of Key given Shear Stress in Key

Variable Name