Radial Stress In Thick Cylinder Subjected To Internal Pressure Calculator

Formula Used:

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

Internal Pressure On Cylinder (Pi):

Inner Diameter Of Pressurized Cylinder (di):

Outer Diameter Of Pressurized Cylinder (do):

Radius Of Pressurized Cylinder (r):

Radial Stress In Pressurized Cylinder (σr):

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1. What Is Radial Stress In A Pressurized Cylinder?

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

2. How Does The Calculator Work?

The calculator uses the formula for radial stress in thick-walled cylinders:

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

Where:

\( \sigma_r \) — Radial stress in pressurized cylinder (Pa)
\( P_i \) — Internal pressure on cylinder (Pa)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( d_o \) — Outer 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 internal pressure, accounting for the geometry and pressure conditions.

3. Importance Of Radial Stress Calculation

Details: Accurate calculation of radial stress is crucial for designing pressure vessels, piping systems, and cylindrical containers to ensure structural integrity and prevent failure under internal pressure.

4. Using The Calculator

Tips: Enter internal pressure in Pascals (Pa), diameters and radius in meters (m). All values must be positive, and the outer diameter must be greater than the inner diameter for valid calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between radial stress and hoop stress?
A: Radial stress acts perpendicular to the radius, while hoop stress acts circumferentially around the cylinder. Both are important in pressure vessel design.

Q2: When is this formula applicable?
A: This formula applies to thick-walled cylinders with uniform internal pressure and homogeneous, isotropic material properties.

Q3: What are typical units for these calculations?
A: Pressure is typically in Pascals (Pa) or MPa, while dimensions are in meters (m) or millimeters (mm) with proper unit conversion.

Q4: How does radial stress vary through the wall thickness?
A: Radial stress is maximum at the inner surface and decreases to zero at the outer surface in internally pressurized cylinders.

Q5: What are the limitations of this formula?
A: This formula assumes elastic behavior, constant material properties, and doesn't account for end effects or external pressures.