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

✖Strain Energy in body is defined as the energy stored in a body due to deformation.ⓘ Strain Energy in body [U]			+10% -10%
✖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.ⓘ Modulus of rigidity of Shaft [G]			+10% -10%
✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of Shaft [r_shaft]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of shaft [J_shaft]			+10% -10%

✖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.ⓘ Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft [𝜏]

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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*(r_shaft^2)))/(L*J_shaft))
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*(r_shaft^2)))/(L*J_shaft)) --> 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)

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National Institute Of Technology (NIT), Hamirpur

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< Expression for Strain Energy stored in a Body Due to Torsion Calculators

Value of radius 'r' given shear stress at radius 'r' from center

LaTeX Go Radius 'r' from Center Of Shaft = (Shear stress at radius 'r' from shaft*Radius of Shaft)/Shear stress on surface of shaft

Radius of shaft given shear stress at radius r from center

LaTeX Go Radius of Shaft = (Radius 'r' from Center Of Shaft/Shear stress at radius 'r' from shaft)*Shear stress on surface of shaft

Modulus of rigidity given shear strain energy

LaTeX Go Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)

Shear strain energy

LaTeX Go Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)

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

LaTeX Go

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 (r_shaft), Length of Shaft (L) & Polar Moment of Inertia of shaft (J_shaft) 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*(r_shaft^2)))/(L*J_shaft)) 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 (r_shaft), Length of Shaft (L) & Polar Moment of Inertia of shaft (J_shaft). 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 3 other way(s) to calculate the same, which is/are as follows -

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*2*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*(Radius of Shaft^2)))/(2*pi*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element))

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