Radial Stress In Thick Cylinder Subjected To External Pressure Calculator

Radial Stress Formula:

\[ \sigma_r = \frac{P_o \cdot d_o^2}{d_o^2 - d_i^2} \cdot \left(1 - \frac{d_i^2}{4 \cdot r^2}\right) \]

External Pressure on Cylinder (Pₒ):

Outer Diameter (dₒ):

Inner Diameter (dᵢ):

Radius (r):

Radial Stress (σᵣ):

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1. What is Radial Stress in Pressurized Cylinder?

Radial stress in pressurized cylinder is defined as the stress produced in the curved surface of a cylinder radially when a cylinder object is subjected to internal or external pressure. It represents the stress component acting perpendicular to the radial direction.

2. How Does the Calculator Work?

The calculator uses the radial stress formula:

\[ \sigma_r = \frac{P_o \cdot d_o^2}{d_o^2 - d_i^2} \cdot \left(1 - \frac{d_i^2}{4 \cdot r^2}\right) \]

Where:

\( \sigma_r \) — Radial stress in pressurized cylinder (Pa)
\( P_o \) — External pressure on cylinder (Pa)
\( d_o \) — Outer diameter of pressurized cylinder (m)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( r \) — Radius of pressurized cylinder (m)

Explanation: This formula calculates the radial stress distribution in thick-walled cylinders subjected to external pressure, considering the geometric parameters and pressure conditions.

3. Importance of Radial Stress Calculation

Details: Accurate radial stress calculation is crucial for designing pressure vessels, pipelines, and cylindrical structures to ensure they can withstand external pressure loads without failure. It helps in determining the safety factor and structural integrity of cylindrical components.

4. Using the Calculator

Tips: Enter external pressure in Pascals, diameters and radius in meters. All values must be positive and valid (outer diameter > inner diameter > 0, radius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between radial stress and hoop stress?
A: Radial stress acts perpendicular to the radial direction, while hoop stress acts circumferentially around the cylinder. Both are important for complete stress analysis.

Q2: When is this formula applicable?
A: This formula applies to thick-walled cylinders subjected to external pressure where the wall thickness is significant compared to the diameter.

Q3: What are typical units for these calculations?
A: Pressure in Pascals (Pa) or MPa, dimensions in meters (m) or millimeters (mm). Consistent units must be used throughout.

Q4: How does external pressure affect radial stress?
A: External pressure creates compressive radial stress that varies through the cylinder wall, being maximum at the outer surface.

Q5: What are the limitations of this formula?
A: This formula assumes isotropic material, linear elastic behavior, and uniform pressure distribution. It may not be accurate for very thin-walled cylinders or under plastic deformation.