Thin-wall and Lamé thick-wall analysis for cylindrical and spherical vessels. Get hoop stress, axial stress, von Mises equivalent, ASME safety factor, and minimum wall thickness instantly.
The fundamental assumption for thin-wall cylinders is that stress is constant through the wall thickness. The primary stresses are the circumferential "hoop" stress and the longitudinal "axial" stress.
$$\sigma_\theta = \frac{P R}{t}, \quad \sigma_a = \frac{P R}{2t}$$Where $P$ is internal pressure, $R$ is the mean radius, and $t$ is wall thickness. Note: $\sigma_\theta$ is twice as large as $\sigma_a$, making it the governing stress for design.
For thick-wall cylinders (t/R ≥ 0.1), Lamé's equations describe how stress varies with radius $r$. The hoop stress is highest at the inner surface.
$$\sigma_\theta(r) = \frac{R_i^2 P}{R_o^2 - R_i^2}\left(1 + \frac{R_o^2}{r^2}\right)$$Where $R_i$ is inner radius, $R_o$ is outer radius, and $r$ is the radial coordinate ($R_i \le r \le R_o$). This gradient is critical for predicting where failure will initiate.
Industrial Boilers & Heat Exchangers: These are classic thin-wall pressure vessels. Engineers use hoop stress calculations to determine the minimum wall thickness required to safely contain high-pressure steam, ensuring routine inspections occur before stress levels approach the material's limits.
High-Pressure Gas Storage (CNG/LNG Tanks): Tanks for compressed natural gas or hydrogen operate at extremely high pressures (250+ bar). They often fall into the thick-wall regime, requiring Lamé analysis to accurately model the high stress concentration at the inner wall and to optimize material use.
Chemical Reactors: Vessels in chemical plants must withstand not only pressure but also corrosive environments and cyclic loading. Von Mises stress and safety factor calculations are combined with material selection to prevent catastrophic failure over the vessel's decades-long lifespan.
Aerospace Propellant Tanks: Rocket fuel tanks are lightweight, thin-wall structures where minimizing mass is critical. Engineers push safety factors as low as reasonably possible, making precise stress analysis non-negotiable. The axial stress formula is key for designing the tank's end caps and attachment points.
When you start using this tool, there are several pitfalls that beginners in CAE often fall into. First and foremost is the misconception that "if the calculation result is safe, it will absolutely not fail." This calculation is only a primary stress evaluation under the ideal condition of "static and uniform internal pressure." In practice, there are numerous factors you must consider, such as stress concentrations at pipe connections, fatigue from repeated pressure, thermal stress from temperature changes, and wall thickness reduction due to corrosion. For example, even with a safety factor of 3.0, stress can locally spike several times higher at a sharp nozzle fillet.
Secondly, the handling of the "thin-wall" and "thick-wall" boundary. The tool switches calculation formulas at a thickness ratio of t/R=0.1, but this is only a guideline. Actual design codes (like the ASME Boiler and Pressure Vessel Code) make judgments based on more detailed conditions. Since results can change significantly near this boundary (e.g., t/R=0.09 vs. 0.11), the key for designs in this region is to perform both calculations and evaluate them carefully.
Finally, material data input errors. Yield strength changes significantly with temperature. A steel with 450 MPa at room temperature might drop to 350 MPa at 300°C. When entering "Yield Strength" in the tool, be sure to use the value at the anticipated maximum operating temperature. Judging something as "safe!" based on a room-temperature value is a very dangerous misunderstanding.