Increase In Inner Radius Of Outer Cylinder At Junction Given Constants Of Lame Equation Calculator

Formula Used:

\[ Increase\ in\ radius = Radius\ at\ Junction \times \left( \left( \frac{1}{Modulus\ of\ Elasticity} \times \left( \frac{Constant\ 'b'\ for\ outer\ cylinder}{Radius\ at\ Junction} + Constant\ 'a'\ for\ outer\ cylinder \right) \right) + \left( \frac{1}{Modulus\ of\ Elasticity \times Mass\ Of\ Shell} \times \left( \frac{Constant\ 'b'\ for\ outer\ cylinder}{Radius\ at\ Junction} - Constant\ 'a'\ for\ outer\ cylinder \right) \right) \right) \]

Radius at Junction:

Modulus of Elasticity Of Thick Shell:

Constant 'b' for outer cylinder:

Constant 'a' for outer cylinder:

Mass Of Shell:

Increase in radius:

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1. What is Increase In Inner Radius Of Outer Cylinder?

The increase in inner radius of outer cylinder at junction given constants of lame equation calculates the change in radius at the junction of compound cylinders when subjected to internal pressure, using Lame's constants and material properties.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

Radius at Junction — The radius value at the junction of compound cylinders (m)
Modulus of Elasticity — Measures resistance to deformation (Pa)
Constant 'b' for outer cylinder — Constant used in Lame's equation
Constant 'a' for outer cylinder — Constant used in Lame's equation
Mass Of Shell — Mass of the cylindrical shell (kg)

Explanation: This formula calculates the radial displacement at the junction of compound cylinders under pressure, considering material properties and Lame's constants.

3. Importance of the Calculation

Details: Calculating the increase in radius is crucial for designing compound cylinders that can withstand internal pressures without failure, ensuring structural integrity in pressure vessels and piping systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Radius and modulus of elasticity must be positive values. The constants 'a' and 'b' are specific to the material and geometry of the cylinder.

5. Frequently Asked Questions (FAQ)

Q1: What are Lame's constants?
A: Lame's constants are material parameters that describe the elastic properties of isotropic materials, relating stresses to strains in elastic deformation.

Q2: When is this calculation most important?
A: This calculation is critical in the design of pressure vessels, hydraulic cylinders, and compound cylinders where precise dimensional changes under pressure must be accounted for.

Q3: What factors affect the increase in radius?
A: The increase depends on the internal pressure, material properties (modulus of elasticity), geometry of the cylinder, and the specific Lame's constants for the material.

Q4: How accurate is this calculation?
A: The calculation provides a theoretical value based on elastic theory. Actual measurements may vary slightly due to material imperfections and manufacturing tolerances.

Q5: Can this be used for non-cylindrical structures?
A: No, this specific formula is derived for compound cylindrical structures under internal pressure.