Radius of shaft given shear strain energy in ring of radius r Calculator

✖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 on surface of shaft [𝜏]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.ⓘ Radius 'r' from Center Of Shaft [r_center]			+10% -10%
✖Length of Small Element is a measure of distance.ⓘ Length of Small Element [δx]			+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%
✖Strain Energy in body is defined as the energy stored in a body due to deformation.ⓘ Strain Energy in body [U]			+10% -10%

✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of shaft given shear strain energy in ring of radius r [r_shaft]

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Radius of shaft given shear strain energy in ring of radius r Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Shaft = sqrt((2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Strain Energy in body)))
r_shaft = sqrt((2*pi*(𝜏^2)*L*(r_center^3)*δx)/(2*G*(U)))
This formula uses 1 Constants, 1 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.
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.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Radius 'r' from Center Of Shaft - (Measured in Meter) - Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.
Length of Small Element - (Measured in Meter) - Length of Small Element is a measure of distance.
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.
Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.

STEP 1: Convert Input(s) to Base Unit

Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Radius 'r' from Center Of Shaft: 1500 Millimeter --> 1.5 Meter (Check conversion here)
Length of Small Element: 43.36 Millimeter --> 0.04336 Meter (Check conversion here)
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_shaft = sqrt((2*pi*(𝜏^2)*L*(r_center^3)*δx)/(2*G*(U))) --> sqrt((2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(50000)))

Evaluating ... ...

r_shaft = 0.00507400014385834

STEP 3: Convert Result to Output's Unit

0.00507400014385834 Meter -->5.07400014385834 Millimeter (Check conversion here)

FINAL ANSWER

5.07400014385834 ≈ 5.074 Millimeter <-- Radius of Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Expression for Strain Energy stored in a Body Due to Torsion » Radius of shaft given shear strain energy in ring of radius r

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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)

Radius of shaft given shear strain energy in ring of radius r Formula

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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 Radius of shaft given shear strain energy in ring of radius r?

Radius of shaft given shear strain energy in ring of radius r calculator uses Radius of Shaft = sqrt((2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Strain Energy in body))) to calculate the Radius of Shaft, Radius of shaft given shear strain energy in ring of radius r is a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Radius of Shaft is denoted by r_shaft symbol.

How to calculate Radius of shaft given shear strain energy in ring of radius r using this online calculator? To use this online calculator for Radius of shaft given shear strain energy in ring of radius r, enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Strain Energy in body (U) and hit the calculate button. Here is how the Radius of shaft given shear strain energy in ring of radius r calculation can be explained with given input values -> 1266.157 = sqrt((2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(50000))).

FAQ

What is Radius of shaft given shear strain energy in ring of radius r?

Radius of shaft given shear strain energy in ring of radius r is a line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as r_shaft = sqrt((2*pi*(𝜏^2)*L*(r_center^3)*δx)/(2*G*(U))) or Radius of Shaft = sqrt((2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Strain Energy in body))). 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, The Length of Shaft is the distance between two ends of shaft, Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve, Length of Small Element is a measure of distance, 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 & Strain Energy in body is defined as the energy stored in a body due to deformation.

How to calculate Radius of shaft given shear strain energy in ring of radius r?

Radius of shaft given shear strain energy in ring of radius r is a line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using Radius of Shaft = sqrt((2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Strain Energy in body))). To calculate Radius of shaft given shear strain energy in ring of radius r, you need Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Strain Energy in body (U). With our tool, you need to enter the respective value for Shear stress on surface of shaft, Length of Shaft, Radius 'r' from Center Of Shaft, Length of Small Element, Modulus of rigidity of Shaft & Strain Energy in body 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 Radius of Shaft?

In this formula, Radius of Shaft uses Shear stress on surface of shaft, Length of Shaft, Radius 'r' from Center Of Shaft, Length of Small Element, Modulus of rigidity of Shaft & Strain Energy in body. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Shaft = (Radius 'r' from Center Of Shaft/Shear stress at radius 'r' from shaft)*Shear stress on surface of shaft
Radius of Shaft = sqrt(((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Strain Energy in body)))

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