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Shear stress on flat key Solution

STEP 0: Pre-Calculation Summary
Formula Used
shear_stress = (2*Transmitted torque)/(Width of Key*Diameter of shaft*Length of Key)
𝜏 = (2*Mt)/(b*d*l)
This formula uses 4 Variables
Variables Used
Transmitted torque - The transmitted torque changes as it increases or decreases speed. Generally, by reducing the speed, a small torque at the input side is transmitted as a larger torque at the output side. (Measured in Newton Centimeter)
Width of Key - Width of Key is defined as the width of the key that is fixed in between the 2 shafts to transmit the power. (Measured in Millimeter)
Diameter of shaft - The Diameter of shaft is defined as the diameter of the hole in the iron laminations that contains the shaft. (Measured in Centimeter)
Length of Key - Length of Key is defined as the length of the projection that is fixed in between the key and the shaft. (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
Transmitted torque: 200 Newton Centimeter --> 2 Newton Meter (Check conversion here)
Width of Key: 50 Millimeter --> 0.05 Meter (Check conversion here)
Diameter of shaft: 10 Centimeter --> 0.1 Meter (Check conversion here)
Length of Key: 100 Millimeter --> 0.1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜏 = (2*Mt)/(b*d*l) --> (2*2)/(0.05*0.1*0.1)
Evaluating ... ...
𝜏 = 8000
STEP 3: Convert Result to Output's Unit
8000 Pascal --> No Conversion Required
FINAL ANSWER
8000 Pascal <-- Shear Stress
(Calculation completed in 00.016 seconds)

10+ Design of Machine Elements Calculators

Factor of Safety for Tri-axial State of Stress
factor_of_safety = Tensile Yield Strength/sqrt((1/2)*(((Normal stress 1-Normal stress 2)^2)+((Normal stress 2-Normal Stress 3)^2)+((Normal Stress 3-Normal stress 1)^2))) Go
Equivalent Stress By Distortion Energy Theory
equivalent_stress = (1/sqrt(2))*sqrt(((Normal stress 1-Normal stress 2)^2)+((Normal stress 2-Normal Stress 3)^2)+((Normal Stress 3-Normal stress 1)^2)) Go
Factor of Safety for bi-axial State of Stress
factor_of_safety = Tensile Yield Strength/(sqrt((Normal stress 1^2)+(Normal stress 2^2)-(Normal stress 1*Normal stress 2))) Go
Tensile Stress In Spigot
tensile_stress = Tensile Force on Rods/(((pi/4)*Diameter of Spigot^(2))-(Diameter of Spigot*Thickness of Cotter)) Go
Permissible Shear Stress for Cotter
permissible_shear_stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter) Go
Permissible Shear Stress for Spigot
permissible_shear_stress = Tensile Force on Rods/(2*Spigot distance*Diameter of Spigot) Go
Compressive Stress of Spigot
compressive_stress_ = Tensile Force on Rods/(Thickness of Cotter*Diameter of Spigot) Go
Stress Amplitude
amplitude_stress = (Maximum stress at crack tip-Minimum Stress)/2 Go
Polar Moment Of Inertia Of Solid Circular Shaft
polar_moment_of_inertia = (pi*(Diameter of shaft)^4)/32 Go
Shear Yield Strength by Maximum Shear Stress Theory
shear_yield_strength = Tensile Yield Strength/2 Go

Shear stress on flat key Formula

shear_stress = (2*Transmitted torque)/(Width of Key*Diameter of shaft*Length of Key)
𝜏 = (2*Mt)/(b*d*l)

What is shear stress in the flat key ?

Design of flat key is based on the two criteria, one is failure due to shear stress and failure due to compressive stress.

How to Calculate Shear stress on flat key?

Shear stress on flat key calculator uses shear_stress = (2*Transmitted torque)/(Width of Key*Diameter of shaft*Length of Key) to calculate the Shear Stress, Shear stress on flat key is the force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. As for the key, it is one of the criteria for testing for failure. Shear Stress is denoted by 𝜏 symbol.

How to calculate Shear stress on flat key using this online calculator? To use this online calculator for Shear stress on flat key, enter Transmitted torque (Mt), Width of Key (b), Diameter of shaft (d) & Length of Key (l) and hit the calculate button. Here is how the Shear stress on flat key calculation can be explained with given input values -> 8000 = (2*2)/(0.05*0.1*0.1).

FAQ

What is Shear stress on flat key?
Shear stress on flat key is the force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. As for the key, it is one of the criteria for testing for failure and is represented as 𝜏 = (2*Mt)/(b*d*l) or shear_stress = (2*Transmitted torque)/(Width of Key*Diameter of shaft*Length of Key). The transmitted torque changes as it increases or decreases speed. Generally, by reducing the speed, a small torque at the input side is transmitted as a larger torque at the output side, Width of Key is defined as the width of the key that is fixed in between the 2 shafts to transmit the power, The Diameter of shaft is defined as the diameter of the hole in the iron laminations that contains the shaft & Length of Key is defined as the length of the projection that is fixed in between the key and the shaft.
How to calculate Shear stress on flat key?
Shear stress on flat key is the force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. As for the key, it is one of the criteria for testing for failure is calculated using shear_stress = (2*Transmitted torque)/(Width of Key*Diameter of shaft*Length of Key). To calculate Shear stress on flat key, you need Transmitted torque (Mt), Width of Key (b), Diameter of shaft (d) & Length of Key (l). With our tool, you need to enter the respective value for Transmitted torque, Width of Key, Diameter of shaft & Length of 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 Shear Stress?
In this formula, Shear Stress uses Transmitted torque, Width of Key, Diameter of shaft & Length of Key. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • amplitude_stress = (Maximum stress at crack tip-Minimum Stress)/2
  • factor_of_safety = Tensile Yield Strength/sqrt((1/2)*(((Normal stress 1-Normal stress 2)^2)+((Normal stress 2-Normal Stress 3)^2)+((Normal Stress 3-Normal stress 1)^2)))
  • equivalent_stress = (1/sqrt(2))*sqrt(((Normal stress 1-Normal stress 2)^2)+((Normal stress 2-Normal Stress 3)^2)+((Normal Stress 3-Normal stress 1)^2))
  • factor_of_safety = Tensile Yield Strength/(sqrt((Normal stress 1^2)+(Normal stress 2^2)-(Normal stress 1*Normal stress 2)))
  • tensile_stress = Tensile Force on Rods/(((pi/4)*Diameter of Spigot^(2))-(Diameter of Spigot*Thickness of Cotter))
  • permissible_shear_stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter)
  • permissible_shear_stress = Tensile Force on Rods/(2*Spigot distance*Diameter of Spigot)
  • compressive_stress_ = Tensile Force on Rods/(Thickness of Cotter*Diameter of Spigot)
  • shear_yield_strength = Tensile Yield Strength/2
  • polar_moment_of_inertia = (pi*(Diameter of shaft)^4)/32
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