Understanding the Preferred Failure Theory in Pressure Vessel Design: Reasons and Implications

Pressure Vessels

Introduction to the theory of failure is used in designing pressure vessels and why

When designing pressure vessels, the most commonly used failure theory is the Maximum Principal Stress Theory, also known as Rankine’s Theory of Failure. This theory is particularly suitable for brittle materials, and while pressure vessel materials are generally ductile, the theory provides a conservative approach for design, ensuring safety.

Here’s why the Maximum Principal Stress Theory is used for pressure vessels:


This theory is relatively straightforward and easy to apply. The main focus is on the principal stresses, which are critical in determining if the material will fail.


As mentioned, this theory is more conservative, especially for ductile materials. Using a more conservative approach is desirable in applications where safety is a primary concern, as in the case of pressure vessels.

Historical Precedence:

 Over the years, this theory has been used extensively in the design of pressure vessels, creating a sort of industry standard. The empirical data and experience gained over time have reinforced its suitability.

Safety Factor:

Pressure vessel codes usually incorporate safety factors. When combined with a conservative failure theory, this ensures that the pressure vessel will perform safely under various conditions.

Compliance with Codes and Standards:

Many international codes and standards for pressure vessel design, like the ASME Boiler and Pressure Vessel Code (BPVC), use criteria that align with the Maximum Principal Stress Theory. Adhering to these standards is crucial for ensuring safety, achieving certifications, and avoiding legal complications.

However, it’s essential to note that while Rankine’s Theory is commonly used, the exact approach and criteria for design might vary depending on the specific application, material, and operating conditions of the pressure vessel. Other theories, like the Maximum Shear Stress Theory (Tresca) or the Von Mises Yield Criterion, can also be considered in certain contexts. Engineers always need to be aware of the standards and codes applicable to their specific design scenario.

Material Behavior and Ductility:

Most pressure vessel materials are ductile (e.g., carbon steel, stainless steel). While the Maximum Principal Stress Theory (Rankine’s Theory) is inherently conservative and ideal for brittle materials, other failure criteria like the Maximum Shear Stress Theory (Tresca) or the Von Mises Yield Criterion are more representative of ductile material behavior. For many engineering applications, the Von Mises Criterion (often used in combination with finite element analysis) provides a more accurate representation of how ductile materials yield. But as pressure vessels are critical components where catastrophic failure can be devastating, the use of a more conservative criterion, like Rankine’s, serves as an added layer of protection.

Complex Loading Scenarios:

 Pressure vessels, especially those used in industrial applications, can be subjected to complex loading conditions. These may include internal or external pressures, thermal loads, dynamic loads, and more. In such cases, understanding and calculating the principal stresses becomes vital. Using the Maximum Principal Stress Theory aids engineers in evaluating the most critical stress scenarios, which, if exceeded, might lead to vessel failure.

Evolution of Codes and Standards:

Over the years, as more research and practical knowledge have accumulated regarding material behavior and failure modes, international codes and standards have evolved. While some modern pressure vessel designs might consider more sophisticated analyses or different failure criteria, adherence to established codes remains paramount. For many industries and regions, this means using Rankine’s Theory as the foundation for design.

Design Versatility:

Despite its conservativeness, using Rankine’s Theory allows designers some versatility. For instance, while designing for the worst-case scenarios, they might account for factors like corrosion allowances, potential fatigue, or wear and tear. By ensuring the vessel can handle stresses well below the failure limit, its lifespan and reliability are enhanced.

Cost Considerations:

 A balance always needs to be struck between safety, functionality, and cost. While the Maximum Principal Stress Theory might sometimes result in slightly overdesigned and potentially more expensive vessels, the cost of failure – both in terms of human safety and economic implications – is much higher. Therefore, it’s a worthy investment to use a conservative approach in this context.

In conclusion, while there are various theories of failure available, and modern computational tools can handle complex stress analyses, the design of pressure vessels often favors conservativeness. This ensures that these critical components remain safe under a broad range of conditions. However, engineers must remain updated with evolving codes, material research, and analysis techniques to design vessels that are both safe and efficient.

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FAQ: Pressure Vessel Design and Theory of Failure

1. What theory of failure is commonly used in designing pressure vessels?

In designing pressure vessels, the most commonly used theory of failure is the Maximum Shear Stress Theory, also known as Tresca’s Criterion. This theory is preferred because it effectively predicts the failure of ductile materials, which are commonly used in pressure vessel construction. It states that failure occurs when the maximum shear stress in the material exceeds the shear stress at yield in simple tension.

2. Why is the Maximum Shear Stress Theory preferred over others for pressure vessels?

The Maximum Shear Stress Theory is preferred due to its accuracy in predicting the yielding of ductile materials under complex loading conditions. Pressure vessels often undergo various types of stresses, and this theory provides a reliable safety margin by considering the worst-case scenario of shear stress, which is critical for ensuring the structural integrity and safety of the vessel.

3. Are there other theories of failure considered for pressure vessel design?

Yes, other theories like the Maximum Normal Stress Theory and the Von Mises Criterion are also considered, especially in specific applications. The Von Mises Criterion, for instance, is used for materials where the yield point is not clearly defined, as it accounts for the combined effect of all three principal stresses. However, the choice of theory depends on the material properties and the specific application of the pressure vessel.

4. How does material selection impact the choice of failure theory in pressure vessel design?

Material selection plays a crucial role in determining the appropriate failure theory. For ductile materials, like most metals used in pressure vessels, the Maximum Shear Stress Theory is suitable. However, for more brittle materials, the Maximum Normal Stress Theory might be more appropriate. The material’s yield strength, ductility, and behavior under stress influence the choice of failure theory.

5. What role does safety factor play in the context of failure theories in pressure vessel design?

Safety factor is a critical element in pressure vessel design, acting as a buffer to account for uncertainties in material properties, loading conditions, and potential flaws in the vessel. It is applied to the stress calculations derived from the chosen failure theory. A higher safety factor means a greater margin of safety, ensuring that the vessel can withstand unexpected stresses or flaws in the material. The selection of an appropriate safety factor is as crucial as the choice of the failure theory itself, as it directly impacts the vessel’s reliability and safety.


In the realm of industrial solutions, Red River emerges as a pioneer, offering a diverse range of custom-engineered products and facilities. Among our specialties is the design and production of Custom/OEM Pressure Vessels, meticulously crafted to meet individual client requirements, ensuring performance under various pressure conditions. Our expertise extends to the domain of prefabrication, where Red River leads with distinction.

The company excels in creating prefabricated facilities, modules, and packages, reinforcing its stance as a forerunner in innovation and quality. This proficiency is further mirrored in their Modular Skids offering, where they provide an array of Modular Fabricated Skid Packages and Packaged equipment. Each piece is tailored to client specifications, underlining their commitment to delivering precision and excellence in every project they undertake.

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