Calculation of Working Pressure for Cylindrical Vessel Under External Pressure

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Initial geometric imperfections have a significant effect on the load carrying capacity of asymmetrical cylindrical pressure vessels. This research paper presents a comparison of a reliability technique that employs a Fourier series representation of random asymmetric imperfections in a defined cylindrical pressure vessel subjected to external pressure. Evaluations as prescribed by the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 rules are also presented and discussed in light of the proposed reliability technique presented herein. The ultimate goal of the reliability type technique is to statistically predict the buckling load associated with the cylindrical pressure vessel within a defined confidence interval. The example cylindrical shell considered in this study is a fractionating tower for which calculations have been performed in accordance with the ASME B&PV Code. The maximum allowable external working pressure of this tower for the shell thickness of 0.3125 in. is calculated to be 15.1 psi when utilizing the prescribed ASME B&PV Code, Section VIII, Division 1 methods contained within example L-3.1. The Monte Carlo method as developed by the current authors and published in the literature is then used to calculate the maximum allowable external working pressure. Fifty simulated shells of geometry similar to the example tower are generated by the Monte Carlo method to calculate the nondeterministic buckling load. The representation of initial geometric imperfections in the cylindrical pressure vessel requires the determination of appropriate Fourier coefficients. The initial functional description of the imperfections consists of an axisymmetric portion and a deviant portion that appears in the form of a double Fourier series. Multi-mode analyses are expanded to evaluate a large number of potential buckling modes for both predefined geometries and the associated asymmetric imperfections as a function of position within a given cylindrical shell. The method and results described herein are in stark contrast to the dated “knockdown factor” approach currently utilized in ASME B&PV Code.