Opening reinforcement: Differences between the equal area method and the pressure area method

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The pressure area method is an opening reinforcement technique adopted in the West German AD code, and its scope of application is broader than that of the equal area method. When the porosity exceeds the range applicable to the equal-area method, the HG standard recommends using this method for pore reinforcement calculations. In fact, both the pressure area method and the equal area method are based on the theory of static strength, and they are calculation methods that take the balance between the load-bearing capacity of the shell’s cross-section and the internal pressure as their principle. Although the two calculation methods differ in form, their essence is exactly the same. However, the two methods differ in terms of the range of effective reinforcement widths for the shell. Pressure vessel designers often encounter situations where the equal-area method cannot be used for reinforcement calculations; in such cases, they usually switch to analytical methods for calculation. If even analytical methods are not applicable, then the pressure area method must be used for verification. Yet, it is often said that the pressure area method does not provide reliable results. In my opinion, this is true in most cases, as the pressure area method tends to be too aggressive and not conservative enough, which may result in insufficient reinforcement area. But in a few cases, the pressure area method might actually be more conservative than the equal-area method, and in such instances the results obtained using this method are reliable for reinforcement purposes. What’s needed is simply an understanding of the rules governing the effective reinforcement ranges for both methods, as follows: Equal-area method: The effective reinforcement area B for the shell is taken to be twice the diameter of the opening, i.e., B=2d. This value is determined based on the range over which stress concentration decreases in the case of an opening in a large plate. Pressure area method: The effective reinforcement area of the shell is taken as B = (Dt)^0.5, where D is the inner diameter of the shell and t is its thickness; this value is determined by taking into account the range of reduction in local circumferential membrane stress caused by structural discontinuities at the openings in the shell. As can be seen from the above, the effective reinforcement width of the shell according to the equal-area method depends only on the diameter of the opening, whereas the pressure-area method depends on both the diameter and thickness of the shell. Therefore, for small orifice nozzles on shells with larger diameters, the effective reinforcement width obtained using the pressure area method can be much greater than that of the equal area method; in other words, the effective reinforcement area A1 tends to be larger, resulting in a lower required reinforcement area. In such cases, if the reinforcement calculation using the equal area method fails, the calculation using the pressure area method might succeed. However, in these situations, the results obtained from the pressure area method are overly aggressive and unreliable. Conversely, for larger orifice nozzles on shells with smaller diameters, the effective reinforcement width of the shell calculated using the pressure area method may be even smaller than that obtained using the equal area method; in such cases, the reinforcement calculation based on the pressure area method is more conservative than that based on the equal area method. Therefore, for the reinforcement calculation of orifice nozzles on such shells, when the equal area method cannot be used, the pressure area method is a completely reliable and more conservative approach.