Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft))
𝜏 = sqrt((U*(2*G*(rshaft^2)))/(L*Jshaft))
This formula uses 1 Functions, 6 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Shear stress on surface of shaft - (Measured in Pascal) - Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.
Modulus of rigidity of Shaft - (Measured in Pascal) - Modulus of rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
STEP 1: Convert Input(s) to Base Unit
Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜏 = sqrt((U*(2*G*(rshaft^2)))/(L*Jshaft)) --> sqrt((50000*(2*40*(2^2)))/(7*10))
Evaluating ... ...
𝜏 = 478.091443733757
STEP 3: Convert Result to Output's Unit
478.091443733757 Pascal -->0.000478091443733757 Megapascal (Check conversion here)
FINAL ANSWER
0.000478091443733757 0.000478 Megapascal <-- Shear stress on surface of shaft
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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7 Shear Stress Calculators

Shear stress at surface of shaft given shear strain energy in ring of radius 'r'
Go Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element))
Shear stress on surface of shaft given total strain energy in hollow shaft
Go Shear stress on surface of shaft = ((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/(((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft))^(1/2)
Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft
Go Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft))
Shear stress at surface of shaft given total strain energy in shaft due to torsion
Go Shear stress on surface of shaft = sqrt((Strain Energy in body*4*Modulus of rigidity of Shaft)/(Volume of Shaft))
Shear stress given shear strain energy
Go Shear stress on surface of shaft = sqrt((Strain Energy in body*2*Modulus of rigidity of Shaft)/Volume of Shaft)
Shear stress at surface of shaft given shear stress at radius 'r' from center
Go Shear stress on surface of shaft = Shear stress at radius 'r' from shaft/(Radius 'r' from Center Of Shaft/Radius of Shaft)
Shear stress due to torsion at radius 'r' from center
Go Shear stress at radius 'r' from shaft = (Radius 'r' from Center Of Shaft/Radius of Shaft)*Shear stress on surface of shaft

Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft Formula

Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft))
𝜏 = sqrt((U*(2*G*(rshaft^2)))/(L*Jshaft))

Is strain energy a material property?

The strain energy (i.e. the amount of potential energy stored due to the deformation) is equal to the work expended in deforming the material. The total strain energy corresponds to the area under the load-deflection curve and has units of in-lbf in US Customary units and N-m in SI units.

How to Calculate Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?

Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft calculator uses Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft)) to calculate the Shear stress on surface of shaft, The Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Shear stress on surface of shaft is denoted by 𝜏 symbol.

How to calculate Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft using this online calculator? To use this online calculator for Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (rshaft), Length of Shaft (L) & Polar Moment of Inertia of shaft (Jshaft) and hit the calculate button. Here is how the Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft calculation can be explained with given input values -> 4.8E-10 = sqrt((50000*(2*40*(2^2)))/(7*10)).

FAQ

What is Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?
The Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and is represented as 𝜏 = sqrt((U*(2*G*(rshaft^2)))/(L*Jshaft)) or Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft)). Strain Energy in body is defined as the energy stored in a body due to deformation, Modulus of rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is, The Radius of Shaft is the radius of the shaft subjected under torsion, The Length of Shaft is the distance between two ends of shaft & Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
How to calculate Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft?
The Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress is calculated using Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(Length of Shaft*Polar Moment of Inertia of shaft)). To calculate Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft, you need Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (rshaft), Length of Shaft (L) & Polar Moment of Inertia of shaft (Jshaft). With our tool, you need to enter the respective value for Strain Energy in body, Modulus of rigidity of Shaft, Radius of Shaft, Length of Shaft & Polar Moment of Inertia of shaft 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 on surface of shaft?
In this formula, Shear stress on surface of shaft uses Strain Energy in body, Modulus of rigidity of Shaft, Radius of Shaft, Length of Shaft & Polar Moment of Inertia of shaft. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Shear stress on surface of shaft = sqrt((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element))
  • Shear stress on surface of shaft = Shear stress at radius 'r' from shaft/(Radius 'r' from Center Of Shaft/Radius of Shaft)
  • Shear stress on surface of shaft = sqrt((Strain Energy in body*4*Modulus of rigidity of Shaft)/(Volume of Shaft))
  • Shear stress on surface of shaft = sqrt((Strain Energy in body*2*Modulus of rigidity of Shaft)/Volume of Shaft)
  • Shear stress on surface of shaft = ((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/(((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft))^(1/2)
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