Length of Key given Shear Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of Key = Force on Key/(Width of Key*Shear Stress in Key)
l = F/(bk*𝜏)
This formula uses 4 Variables
Variables Used
Length of Key - (Measured in Meter) - 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.
Force on Key - (Measured in Newton) - Force on Key is the reaction onto the key of a machined assembly.
Width of Key - (Measured in Meter) - 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.
Shear Stress in Key - (Measured in Pascal) - 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.
STEP 1: Convert Input(s) to Base Unit
Force on Key: 9980 Newton --> 9980 Newton No Conversion Required
Width of Key: 5 Millimeter --> 0.005 Meter (Check conversion here)
Shear Stress in Key: 63.9 Newton per Square Millimeter --> 63900000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = F/(bk*𝜏) --> 9980/(0.005*63900000)
Evaluating ... ...
l = 0.0312363067292645
STEP 3: Convert Result to Output's Unit
0.0312363067292645 Meter -->31.2363067292645 Millimeter (Check conversion here)
FINAL ANSWER
31.2363067292645 31.23631 Millimeter <-- Length of Key
(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad
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13 Design of Square and Flat Keys Calculators

Shaft Diameter given Compressive Stress in Key
Go Diameter of Shaft using Key = 4*Transmitted Torque by Keyed Shaft/(Compressive Stress in Key*Length of Key*Height of Key)
Length of Key given Compressive Stress in Key
Go Length of Key = 4*Transmitted Torque by Keyed Shaft/(Diameter of Shaft using Key*Compressive Stress in Key*Height of Key)
Height of Key given Compressive Stress in Key
Go Height of Key = 4*Transmitted Torque by Keyed Shaft/(Diameter of Shaft using Key*Length of Key*Compressive Stress in Key)
Compressive Stress in Key
Go Compressive Stress in Key = 4*Transmitted Torque by Keyed Shaft/(Diameter of Shaft using Key*Length of Key*Height of Key)
Torque Transmitted by Keyed Shaft given Stress in Key
Go Transmitted Torque by Keyed Shaft = Compressive Stress in Key*Diameter of Shaft using Key*Length of Key*Height of Key/4
Shear Stress in Key given Torque Transmitted
Go Shear Stress in Key = 2*Transmitted Torque by Keyed Shaft/(Width of Key*Length of Key*Diameter of Shaft using Key)
Width of Key given Shear Stress in Key
Go Width of Key = Force on Key/(Shear Stress in Key*Length of Key)
Shear Stress in given Force on Key
Go Shear Stress in Key = Force on Key/(Width of Key*Length of Key)
Length of Key given Shear Stress
Go Length of Key = Force on Key/(Width of Key*Shear Stress in Key)
Torque Transmitted by Keyed Shaft given Force on Keys
Go Transmitted Torque by Keyed Shaft = Force on Key*Diameter of Shaft using Key/2
Shaft Diameter given Force on Key
Go Diameter of Shaft using Key = 2*Transmitted Torque by Keyed Shaft/Force on Key
Force on Key
Go Force on Key = 2*Transmitted Torque by Keyed Shaft/Diameter of Shaft using Key
Compressive Stress in Square Key due to Transmitted Torque
Go Compressive Stress in Key = 2*Shear Stress in Key

Length of Key given Shear Stress Formula

Length of Key = Force on Key/(Width of Key*Shear Stress in Key)
l = F/(bk*𝜏)

Define Shear Stress

hear stress, often denoted by τ (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.

How to Calculate Length of Key given Shear Stress?

Length of Key given Shear Stress calculator uses Length of Key = Force on Key/(Width of Key*Shear Stress in Key) to calculate the Length of Key, The Length of Key given Shear Stress is defined as the length of the projection that is fixed in between the key and the shaft. Length of Key is denoted by l symbol.

How to calculate Length of Key given Shear Stress using this online calculator? To use this online calculator for Length of Key given Shear Stress, enter Force on Key (F), Width of Key (bk) & Shear Stress in Key (𝜏) and hit the calculate button. Here is how the Length of Key given Shear Stress calculation can be explained with given input values -> 31236.31 = 9980/(0.005*63900000).

FAQ

What is Length of Key given Shear Stress?
The Length of Key given Shear Stress is defined as the length of the projection that is fixed in between the key and the shaft and is represented as l = F/(bk*𝜏) or Length of Key = Force on Key/(Width of Key*Shear Stress in Key). Force on Key is the reaction onto the key of a machined assembly, 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 & 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.
How to calculate Length of Key given Shear Stress?
The Length of Key given Shear Stress is defined as the length of the projection that is fixed in between the key and the shaft is calculated using Length of Key = Force on Key/(Width of Key*Shear Stress in Key). To calculate Length of Key given Shear Stress, you need Force on Key (F), Width of Key (bk) & Shear Stress in Key (𝜏). With our tool, you need to enter the respective value for Force on Key, Width of Key & Shear Stress in Key and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Length of Key?
In this formula, Length of Key uses Force on Key, Width of Key & Shear Stress in Key. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Length of Key = 4*Transmitted Torque by Keyed Shaft/(Diameter of Shaft using Key*Compressive Stress in Key*Height of Key)
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