Increase In Inner Radius Of Outer Cylinder At Junction Of Compound Cylinder Calculator

Formula Used:

\[ Increase\ in\ radius = \frac{Radius\ at\ Junction}{Modulus\ of\ Elasticity\ Of\ Thick\ Shell} \times \left(Hoop\ Stress\ on\ thick\ shell + \frac{Radial\ Pressure}{Mass\ Of\ Shell}\right) \]

\[ R_i = \frac{r^*}{E} \times \left(\sigma_\theta + \frac{P_v}{M}\right) \]

Radius at Junction (r*):

Modulus of Elasticity Of Thick Shell (E):

Hoop Stress on thick shell (σ_θ):

Radial Pressure (P_v):

Pa/m²

Mass Of Shell (M):

Increase in radius (R_i):

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1. What is Increase in Inner Radius of Outer Cylinder?

The increase in inner radius of outer cylinder at junction of compound cylinder refers to the radial deformation that occurs when a compound cylinder is subjected to internal pressure or thermal loading. This calculation is crucial in pressure vessel design and mechanical engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R_i = \frac{r^*}{E} \times \left(\sigma_\theta + \frac{P_v}{M}\right) \]

Where:

\( R_i \) — Increase in radius (m)
\( r^* \) — Radius at Junction (m)
\( E \) — Modulus of Elasticity Of Thick Shell (Pa)
\( \sigma_\theta \) — Hoop Stress on thick shell (Pa)
\( P_v \) — Radial Pressure (Pa/m²)
\( M \) — Mass Of Shell (kg)

Explanation: The formula calculates the radial deformation by considering the material properties, stress conditions, and geometric parameters of the compound cylinder.

3. Importance of Radius Increase Calculation

Details: Accurate calculation of radius increase is essential for ensuring proper fit and function of compound cylinders, preventing leakage, and maintaining structural integrity under operating conditions.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure radius, modulus of elasticity, and mass values are positive. The calculator provides results in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a compound cylinder?
A: A compound cylinder consists of two or more concentric cylinders assembled with interference fits to create residual stresses that improve pressure containment capability.

Q2: Why is radius increase important in compound cylinders?
A: Calculating radius increase helps determine the deformation under load, ensuring the cylinder maintains its structural integrity and sealing capability.

Q3: What factors affect the increase in radius?
A: Material properties (modulus of elasticity), geometric dimensions, applied pressures, and stress distributions all influence the radial deformation.

Q4: When is this calculation typically used?
A: This calculation is used in pressure vessel design, piping systems, hydraulic cylinders, and any application involving compound cylindrical structures.

Q5: Are there limitations to this formula?
A: The formula assumes linear elastic material behavior, uniform properties, and may have limitations for extreme temperature variations or non-uniform loading conditions.