Understanding Thick Cylinder Stress Analysis

In mechanical engineering and pressure vessel design, a cylinder is classified as "thick-walled" when the ratio of its wall thickness to its inner diameter is greater than 1/20 (or 5%). Unlike thin-walled cylinders where stress is assumed to be uniform across the thickness, thick cylinders experience significant stress gradients from the inner to the outer surface.

Lame's Equations for Stress Distribution

The calculation of stress in thick-walled cylinders is governed by Lame's Equations. These equations determine the Radial Stress (σᵣ) and Hoop Stress (σθ) at any point within the cylinder wall. The Hoop stress is typically the most critical as it is usually the highest and is responsible for longitudinal cracks.

How to Use the Calculator

To use this thick cylinder stress calculator, simply follow these steps:

• Internal and Outer Radius: Enter the dimensions of your cylinder. Ensure the outer radius is larger than the inner radius.
• Pressure: Input the internal pressure (Pᵢ) and external pressure (Pₒ). In most industrial applications, external pressure is zero (atmospheric).
• Radius of Interest (r): Specify the exact point within the wall (between rᵢ and rₒ) where you wish to calculate the stress. Typically, stresses are highest at the inner radius.

Frequently Asked Questions

What is the difference between Radial and Hoop stress?
Radial stress acts in the direction of the radius (pushing against the wall), while Hoop stress acts circumferentially around the cylinder (trying to pull the material apart).

Why is Hoop stress higher at the inner surface?
Due to the geometry of thick cylinders, the material at the inner surface must withstand the highest concentration of internal pressure, causing the hoop stress to peak at the inner boundary.

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