Radius at junction of compound cylinder given original difference of radii at junction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell)
r* = Δroriginal/(2*(a1-a2)/E)
This formula uses 5 Variables
Variables Used
Radius at Junction - (Measured in Meter) - The Radius at Junction is the radius value at the junction of compound cylinders.
Original difference of radii - (Measured in Meter) - Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder.
Constant 'a' for outer cylinder - Constant 'a' for outer cylinder is defined as the constant used in lame's equation.
Constant 'a' for inner cylinder - Constant 'a' for inner cylinder is defined as the constant used in lame's equation.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
STEP 1: Convert Input(s) to Base Unit
Original difference of radii: 0.02 Millimeter --> 2E-05 Meter (Check conversion here)
Constant 'a' for outer cylinder: 4 --> No Conversion Required
Constant 'a' for inner cylinder: 3 --> No Conversion Required
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r* = Δroriginal/(2*(a1-a2)/E) --> 2E-05/(2*(4-3)/2600000)
Evaluating ... ...
r* = 26
STEP 3: Convert Result to Output's Unit
26 Meter -->26000 Millimeter (Check conversion here)
FINAL ANSWER
26000 Millimeter <-- Radius at Junction
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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21 Compound Cylinder Shrinkage Radii Change Calculators

Decrease in outer radius of inner cylinder at junction given constants of lame equation
Go Decrease in radius = -Radius at Junction*(((1/Modulus of Elasticity Of Thick Shell)*((Constant 'b' for inner cylinder/Radius at Junction)+Constant 'a' for inner cylinder))+((1/Modulus of Elasticity Of Thick Shell*Mass Of Shell)*((Constant 'b' for inner cylinder/Radius at Junction)-Constant 'a' for inner cylinder)))
Increase in inner radius of outer cylinder at junction given constants of lame equation
Go Increase in radius = Radius at Junction*(((1/Modulus of Elasticity Of Thick Shell)*((Constant 'b' for outer cylinder/Radius at Junction)+Constant 'a' for outer cylinder))+((1/Modulus of Elasticity Of Thick Shell*Mass Of Shell)*((Constant 'b' for outer cylinder/Radius at Junction)-Constant 'a' for outer cylinder)))
Modulus of elasticity given decrease in outer radius of inner cylinder and constants
Go Modulus of Elasticity Of Thick Shell = -Radius at Junction*(((1/Decrease in radius)*((Constant 'b' for inner cylinder/Radius at Junction)+Constant 'a' for inner cylinder))+((1/Decrease in radius*Mass Of Shell)*((Constant 'b' for inner cylinder/Radius at Junction)-Constant 'a' for inner cylinder)))
Modulus of elasticity given increase in inner radius of outer cylinder and constants
Go Modulus of Elasticity Of Thick Shell = Radius at Junction*(((1/Increase in radius)*((Constant 'b' for outer cylinder/Radius at Junction)+Constant 'a' for outer cylinder))+((1/Increase in radius*Mass Of Shell)*((Constant 'b' for outer cylinder/Radius at Junction)-Constant 'a' for outer cylinder)))
Radius at junction of compound cylinder given increase in inner radius of outer cylinder
Go Radius at Junction = (Increase in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
Radius at junction of compound cylinder given decrease in outer radius of inner cylinder
Go Radius at Junction = (Decrease in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
Increase in inner radius of outer cylinder at junction of compound cylinder
Go Increase in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
Decrease in outer radius of inner cylinder at junction of compound cylinder
Go Decrease in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
Mass of compound cylinder given increase in inner radius of outer cylinder
Go Mass Of Shell = Radial Pressure/((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)
Mass of compound cylinder given decrease in outer radius of inner cylinder
Go Mass Of Shell = Radial Pressure/((Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)
Modulus of elasticity given increase in inner radius of outer cylinder
Go Modulus of Elasticity Of Thick Shell = (Radius at Junction/Increase in radius)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
Radial pressure given increase in inner radius of outer cylinder
Go Radial Pressure = ((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell
Radial pressure given decrease in outer radius of inner cylinder
Go Radial Pressure = ((Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell
Modulus of elasticity decrease in outer radius of inner cylinder
Go Modulus of Elasticity Of Thick Shell = (Radius at Junction/Decrease in radius)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
Hoop stress given increase in inner radius of outer cylinder
Go Hoop Stress on thick shell = (Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)
Hoop stress given decrease in outer radius of inner cylinder
Go Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)
Radius at junction of compound cylinder given original difference of radii at junction
Go Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell)
Constant 'a' for inner cylinder given original difference of radii at junction
Go Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))
Constant for outer cylinder given original difference of radii at junction
Go Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder
Modulus of elasticity given original difference of radii at junction
Go Modulus of Elasticity Of Thick Shell = 2*Radius at Junction*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Original difference of radii
Original difference of radii at junction
Go Original difference of radii = 2*Radius at Junction*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell

Radius at junction of compound cylinder given original difference of radii at junction Formula

Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell)
r* = Δroriginal/(2*(a1-a2)/E)

What is meant by hoop stress?

The hoop stress is the force over the area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.

How to Calculate Radius at junction of compound cylinder given original difference of radii at junction?

Radius at junction of compound cylinder given original difference of radii at junction calculator uses Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell) to calculate the Radius at Junction, The Radius at junction of compound cylinder given original difference of radii at junction formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Radius at Junction is denoted by r* symbol.

How to calculate Radius at junction of compound cylinder given original difference of radii at junction using this online calculator? To use this online calculator for Radius at junction of compound cylinder given original difference of radii at junction, enter Original difference of radii (Δroriginal), Constant 'a' for outer cylinder (a1), Constant 'a' for inner cylinder (a2) & Modulus of Elasticity Of Thick Shell (E) and hit the calculate button. Here is how the Radius at junction of compound cylinder given original difference of radii at junction calculation can be explained with given input values -> 2.6E+7 = 2E-05/(2*(4-3)/2600000).

FAQ

What is Radius at junction of compound cylinder given original difference of radii at junction?
The Radius at junction of compound cylinder given original difference of radii at junction formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as r* = Δroriginal/(2*(a1-a2)/E) or Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell). Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder, Constant 'a' for outer cylinder is defined as the constant used in lame's equation, Constant 'a' for inner cylinder is defined as the constant used in lame's equation & Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
How to calculate Radius at junction of compound cylinder given original difference of radii at junction?
The Radius at junction of compound cylinder given original difference of radii at junction formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell). To calculate Radius at junction of compound cylinder given original difference of radii at junction, you need Original difference of radii (Δroriginal), Constant 'a' for outer cylinder (a1), Constant 'a' for inner cylinder (a2) & Modulus of Elasticity Of Thick Shell (E). With our tool, you need to enter the respective value for Original difference of radii, Constant 'a' for outer cylinder, Constant 'a' for inner cylinder & Modulus of Elasticity Of Thick Shell 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 at Junction?
In this formula, Radius at Junction uses Original difference of radii, Constant 'a' for outer cylinder, Constant 'a' for inner cylinder & Modulus of Elasticity Of Thick Shell. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Radius at Junction = (Increase in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
  • Radius at Junction = (Decrease in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))
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