Increase in inner radius of outer cylinder at junction given constants of lame equation Calculator

✖The Radius at Junction is the radius value at the junction of compound cylinders.ⓘ Radius at Junction [r_*]			+10% -10%
✖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.ⓘ Modulus of Elasticity Of Thick Shell [E]			+10% -10%
✖Constant 'b' for outer cylinder is defined as the constant used in lame's equation.ⓘ Constant 'b' for outer cylinder [b₁]			+10% -10%
✖Constant 'a' for outer cylinder is defined as the constant used in lame's equation.ⓘ Constant 'a' for outer cylinder [a₁]			+10% -10%
✖Mass Of Shell is the quantity of matter in a body regardless of its volume or of any forces acting on it.ⓘ Mass Of Shell [M]			+10% -10%

✖Increase in radius is the increase in inner radius of outer cylinder of compound cylinder.ⓘ Increase in inner radius of outer cylinder at junction given constants of lame equation [R_i]

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Increase in inner radius of outer cylinder at junction given constants of lame equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
R_i = r_**(((1/E)*((b₁/r_*)+a₁))+((1/E*M)*((b₁/r_*)-a₁)))
This formula uses 6 Variables

Variables Used

Increase in radius - (Measured in Meter) - Increase in radius is the increase in inner radius of outer cylinder of compound cylinder.
Radius at Junction - (Measured in Meter) - The Radius at Junction is the radius value at the junction of compound cylinders.
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.
Constant 'b' for outer cylinder - Constant 'b' for outer cylinder is defined as the constant used in lame's equation.
Constant 'a' for outer cylinder - Constant 'a' for outer cylinder is defined as the constant used in lame's equation.
Mass Of Shell - (Measured in Kilogram) - Mass Of Shell is the quantity of matter in a body regardless of its volume or of any forces acting on it.

STEP 1: Convert Input(s) to Base Unit

Radius at Junction: 4000 Millimeter --> 4 Meter (Check conversion here)
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
Constant 'b' for outer cylinder: 25 --> No Conversion Required
Constant 'a' for outer cylinder: 4 --> No Conversion Required
Mass Of Shell: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_i = r_**(((1/E)*((b₁/r_*)+a₁))+((1/E*M)*((b₁/r_*)-a₁))) --> 4*(((1/2600000)*((25/4)+4))+((1/2600000*35.45)*((25/4)-4)))

Evaluating ... ...

R_i = 0.000138480769230769

STEP 3: Convert Result to Output's Unit

0.000138480769230769 Meter -->0.138480769230769 Millimeter (Check conversion here)

FINAL ANSWER

0.138480769230769 ≈ 0.138481 Millimeter <-- Increase in radius

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Thick Cylinders And Spheres » Mechanical » Compound Cylinder Shrinkage Radii Change » Increase in inner radius of outer cylinder at junction given constants of lame equation

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< Compound Cylinder Shrinkage Radii Change Calculators

Radius at junction of compound cylinder given increase in inner radius of outer cylinder

LaTeX Go Radius at Junction = (Increase 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

LaTeX Go Increase in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Radial pressure given increase in inner radius of outer cylinder

LaTeX Go Radial Pressure = ((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell

Hoop stress given increase in inner radius of outer cylinder

LaTeX Go Hoop Stress on thick shell = (Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

Increase in inner radius of outer cylinder at junction given constants of lame equation Formula

LaTeX Go

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 Increase in inner radius of outer cylinder at junction given constants of lame equation?

Increase in inner radius of outer cylinder at junction given constants of lame equation calculator uses 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))) to calculate the Increase in radius, The Increase in inner radius of outer cylinder at junction given constants of lame equation formula is defined as an increase in line segment extending from the center of a circle or sphere to the circumference or bounding surface. Increase in radius is denoted by R_i symbol.

How to calculate Increase in inner radius of outer cylinder at junction given constants of lame equation using this online calculator? To use this online calculator for Increase in inner radius of outer cylinder at junction given constants of lame equation, enter Radius at Junction (r_*), Modulus of Elasticity Of Thick Shell (E), Constant 'b' for outer cylinder (b₁), Constant 'a' for outer cylinder (a₁) & Mass Of Shell (M) and hit the calculate button. Here is how the Increase in inner radius of outer cylinder at junction given constants of lame equation calculation can be explained with given input values -> 138.4808 = 4*(((1/2600000)*((25/4)+4))+((1/2600000*35.45)*((25/4)-4))).

FAQ

What is Increase in inner radius of outer cylinder at junction given constants of lame equation?

The Increase in inner radius of outer cylinder at junction given constants of lame equation formula is defined as an increase in line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as R_i = r_**(((1/E)*((b₁/r_*)+a₁))+((1/E*M)*((b₁/r_*)-a₁))) or 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))). The Radius at Junction is the radius value at the junction of compound cylinders, 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, Constant 'b' for outer cylinder is defined as the constant used in lame's equation, Constant 'a' for outer cylinder is defined as the constant used in lame's equation & Mass Of Shell is the quantity of matter in a body regardless of its volume or of any forces acting on it.

How to calculate Increase in inner radius of outer cylinder at junction given constants of lame equation?

The Increase in inner radius of outer cylinder at junction given constants of lame equation formula is defined as an increase in line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using 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))). To calculate Increase in inner radius of outer cylinder at junction given constants of lame equation, you need Radius at Junction (r_*), Modulus of Elasticity Of Thick Shell (E), Constant 'b' for outer cylinder (b₁), Constant 'a' for outer cylinder (a₁) & Mass Of Shell (M). With our tool, you need to enter the respective value for Radius at Junction, Modulus of Elasticity Of Thick Shell, Constant 'b' for outer cylinder, Constant 'a' for outer cylinder & Mass Of 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 Increase in radius?

In this formula, Increase in radius uses Radius at Junction, Modulus of Elasticity Of Thick Shell, Constant 'b' for outer cylinder, Constant 'a' for outer cylinder & Mass Of Shell. We can use 1 other way(s) to calculate the same, which is/are as follows -

Increase in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

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