Tangential Stress In Thick Cylinder Subjected To External Pressure Calculator

Formula Used:

\[ \sigma_{tang} = \frac{P_o \times d_o^2}{d_o^2 - d_i^2} \times \left( \frac{d_i^2}{4 \times r^2} + 1 \right) \]

External Pressure on Cylinder (Pₒ):

Outer Diameter of Pressurized Cylinder (dₒ):

Inner Diameter of Pressurized Cylinder (dᵢ):

Radius of Pressurized Cylinder (r):

Tangential Stress in Pressurized Cylinder (σ_tang):

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1. What is Tangential Stress in Pressurized Cylinder?

Tangential stress in pressurized cylinder is the stress experienced by the cylinder walls when the direction of the deforming force is perpendicular to central axis. It represents the hoop stress that develops in the circumferential direction of the cylinder wall due to internal or external pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{tang} = \frac{P_o \times d_o^2}{d_o^2 - d_i^2} \times \left( \frac{d_i^2}{4 \times r^2} + 1 \right) \]

Where:

\( \sigma_{tang} \) — Tangential 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 tangential (hoop) stress in a thick-walled cylinder subjected to external pressure, accounting for the geometric parameters of the cylinder.

3. Importance of Tangential Stress Calculation

Details: Accurate calculation of tangential stress is crucial for designing pressure vessels, pipelines, and cylindrical containers to ensure structural integrity and prevent failure under pressure loading conditions.

4. Using the Calculator

Tips: Enter external pressure in Pascals, diameters and radius in meters. All values must be positive and the outer diameter must be greater than the inner diameter.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between tangential and radial stress?
A: Tangential stress acts circumferentially around the cylinder, while radial stress acts perpendicular to the cylinder wall surface.

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

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).

Q4: How does external pressure differ from internal pressure?
A: External pressure causes compressive stresses in the cylinder wall, while internal pressure causes tensile stresses.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors of 2-4 depending on the application, material properties, and operating conditions.