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Shear Stress in Key given Torque Transmitted Formula

GoShear Stress in given Force on Key Formula

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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. Check FAQs

𝜏 = 2 \cdot \frac{M t}{b k \cdot l \cdot d s}

𝜏 - Shear Stress in Key?M_t - Transmitted Torque by Keyed Shaft?b_k - Width of Key?l - Length of Key?d_s - Diameter of Shaft using Key?

Shear Stress in Key given Torque Transmitted Example

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Here is how the Shear Stress in Key given Torque Transmitted equation looks like with Values.

Here is how the Shear Stress in Key given Torque Transmitted equation looks like with Units.

Here is how the Shear Stress in Key given Torque Transmitted equation looks like.

57.0159 = 2 \cdot \frac{224500}{5 \cdot 35 \cdot 45}

57.0159N/mm² = 2 \cdot \frac{224500N*mm}{5mm \cdot 35mm \cdot 45mm}

57.0159 = 2 \cdot \frac{224500}{5 \cdot 35 \cdot 45}

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Shear Stress in Key given Torque Transmitted Solution

Follow our step by step solution on how to calculate Shear Stress in Key given Torque Transmitted?

FIRST Step Consider the formula

𝜏 = 2 \cdot \frac{M t}{b k \cdot l \cdot d s}

Next Step Substitute values of Variables

∴

𝜏 = 2 \cdot \frac{224500N*mm}{5mm \cdot 35mm \cdot 45mm}

Next Step Convert Units

∴

𝜏 = 2 \cdot \frac{224.5N*m}{0.005m \cdot 0.035m \cdot 0.045m}

Next Step Prepare to Evaluate

∴

𝜏 = 2 \cdot \frac{224.5}{0.005 \cdot 0.035 \cdot 0.045}

Next Step Evaluate

∴

𝜏 = 57015873.015873Pa

Next Step Convert to Output's Unit

∴

𝜏 = 57.015873015873N/mm²

LAST Step Rounding Answer

∴

𝜏 = 57.0159N/mm²

Shear Stress in Key given Torque Transmitted Formula Elements

Variables

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

Transmitted Torque by Keyed Shaft

Transmitted Torque by Keyed Shaft is defined as the amount of torque or the rotating power transferred from a shaft using a key into it.

Symbol: M_t

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Transmitted Torque by Keyed Shaft

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

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

Diameter of Shaft using Key

Diameter of Shaft using Key is defined as the external surface diameter of a shaft (a rotating machine element) using a key into it.

Symbol: d_s

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft using Key

Other Formulas to find Shear Stress in Key

Go Shear Stress in given Force on Key

𝜏 = \frac{F}{b k \cdot l}

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 Width of Key given Shear Stress in Key

b k = \frac{F}{𝜏 \cdot l}

How to Evaluate Shear Stress in Key given Torque Transmitted?

Shear Stress in Key given Torque Transmitted evaluator uses Shear Stress in Key = 2*Transmitted Torque by Keyed Shaft/(Width of Key*Length of Key*Diameter of Shaft using Key) to evaluate the Shear Stress in Key, Shear Stress in Key given Torque Transmitted is defined as the component of stress coplanar with the key's cross-section. It arises from the shear force, the component of the force vector parallel to the material cross-section. Shear Stress in Key is denoted by 𝜏 symbol.

How to evaluate Shear Stress in Key given Torque Transmitted using this online evaluator? To use this online evaluator for Shear Stress in Key given Torque Transmitted, enter Transmitted Torque by Keyed Shaft (M_t), Width of Key (b_k), Length of Key (l) & Diameter of Shaft using Key (d_s) and hit the calculate button.

FAQs on Shear Stress in Key given Torque Transmitted

What is the formula to find Shear Stress in Key given Torque Transmitted?

The formula of Shear Stress in Key given Torque Transmitted is expressed as Shear Stress in Key = 2*Transmitted Torque by Keyed Shaft/(Width of Key*Length of Key*Diameter of Shaft using Key). Here is an example- 5.7E-5 = 2*224.5/(0.005*0.035*0.045).

How to calculate Shear Stress in Key given Torque Transmitted?

With Transmitted Torque by Keyed Shaft (M_t), Width of Key (b_k), Length of Key (l) & Diameter of Shaft using Key (d_s) we can find Shear Stress in Key given Torque Transmitted using the formula - Shear Stress in Key = 2*Transmitted Torque by Keyed Shaft/(Width of Key*Length of Key*Diameter of Shaft using Key).

What are the other ways to Calculate Shear Stress in Key?

Here are the different ways to Calculate Shear Stress in Key-

Shear Stress in Key=Force on Key/(Width of Key*Length of Key)

Can the Shear Stress in Key given Torque Transmitted be negative?

No, the Shear Stress in Key given Torque Transmitted, measured in Stress cannot be negative.

Which unit is used to measure Shear Stress in Key given Torque Transmitted?

Shear Stress in Key given Torque Transmitted is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Shear Stress in Key given Torque Transmitted can be measured.

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Shear Stress in Key given Torque Transmitted Formula

​GoShear Stress in given Force on Key Formula

Shear Stress in Key given Torque Transmitted Example

Shear Stress in Key given Torque Transmitted Solution

Shear Stress in Key given Torque Transmitted Formula Elements

Other Formulas to find Shear Stress in Key

Other formulas in Design of Square and Flat Keys category

How to Evaluate Shear Stress in Key given Torque Transmitted?

FAQs on Shear Stress in Key given Torque Transmitted

Variable Name

GoShear Stress in given Force on Key Formula