Learn the New Method First | Inelastic Analysis—Design Methods for Load and Resistance Coefficients

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This article is from the ANSYS Analysis and Design Professionals WeChat account. Originality is respected; for more interesting content, follow this account: a platform dedicated to the exchange and learning related to pressure vessel analysis and design! With the convening in Nanjing in May 2018 of a kick-off meeting for the revision of the series of standards on the analysis and design of pressure vessels organized by the Boiler Capacity Standardization Committee, the planned content for these revisions underwent significant changes. An elastic-plastic analysis method was introduced in Part 5, making the revised standards more comprehensive compared to the original standards, which relied on a single stress classification method. As analysis and design engineers for pressure vessels, we should continuously learn new design methods, follow the guidance of relevant standards, strengthen our professional knowledge, and become qualified analysis and design engineers. 【1. Background】In ASME analysis and design standards, the approach is based on the following 4 failure modes: 1) Prevention of plastic collapse ； 2) Prevent local failure ； 3) Prevent instability ； 4) Prevent failure under cyclic loading. And in preventing plastic collapse of structures, this includes: elastic stress analysis (stress classification method) ； Inelastic stress analysis (limit load analysis and elastic-plastic analysis). The Load and Resistance Factor Design (LRFD) approach was introduced in the 2007 edition of ASME VIII-2, and it was applied to ultimate load and elastic-plastic analysis; the double elastic slope is no longer used as a criterion for ultimate load analysis. 【2. Pressure Vessel Design Methods】Before the release of the 2007 edition of ASME VIII-2, pressure vessel design relied on the allowable stress method. Its main design concept is to assign a overall safety factor to the material, thereby providing the necessary safety margin for the uncertainties present in the design. Load and resistance factor design (LRFD) has been applied in ultimate load and elastic-plastic analysis, and this method has been widely used for many years in fields such as steel structures and highway bridges. The LRFD method is another option for a precise calculation of the plastic collapse load. The main design principle of this method is to use different safety factors for various loads and resistances (strengths). The LRFD method is a general approach applicable to various fields, where the specific meanings of loads and resistances vary from one field to another; the same is true for the meanings of loads and resistances when the LRFD method is used in the design of pressure vessels. Loads: These include permanent loads, internal pressure, seismic loads, and wind loads. Permanent loads encompass the weight of the container itself, the weight of insulation materials, and the weight of the medium contained within. All loads are considered as random scalars. Resistance (strength): Including the yield limit and strength limit, both can be regarded as random variables. 【3. Reliability Theory of Structures】Load is the external factor that causes structural failure, while resistance is the internal capacity to resist such failure. Therefore, the relationship between load and resistance is one of the important factors determining whether a structure will fail. The randomness of loads and resistances determines the randomness of structural failure. The LRFD method is based on the theory of structural reliability, and its principles include the following 4 points: 1) The resistance of the structure is treated as a random variable or random process ； 2) Treat various loads acting on the structure as random variables or random processes, and consider the probability of their simultaneous occurrence ； 3) Assess the failure probability of the structure based on the stress-strength interference theory ； 4) Based on structural reliability theory. 【4.Load Combinations and Load Factors in ASME Standards】The 2007 edition of ASME VIII-2 specifies load factors appropriate for pressure vessels based on certain reliability criteria; these are shown in Tables 5.4 and 5.5, and are used respectively for ultimate load analysis and elastic-plastic analysis. The resistance coefficient corresponding to the material strength has already been incorporated into the load coefficient; that is, the resistance coefficient is equal to 1.0. Based on the load combinations and load coefficients from the ultimate load analysis in Table 5.4, they are classified into Load Condition Combination 1: overall criterion, Load Condition Combination 2: local criterion, and Load Condition Combination 3: hydraulic or pneumatic testing conditions. During analysis, it is necessary to consider the load combinations and coefficients for each combination of operating conditions; only when the solution for each condition converges can the limit load analysis of the structure be considered satisfactory. According to Table 5.5 of ASME VIII-2, the load condition combinations and load factors used for elastoplastic stress analysis include the overall criterion, local criterion, and hydraulic or pneumatic testing conditions that need to be taken into consideration. The structure is safe as long as the sum of the forming strains of all units and the total equivalent plastic strain is less than or equal to the triaxial strain limit. 【5. Comparison between traditional methods and LRFD method】The traditional allowable stress method uses a single overall safety factor to account for the uncertainties in design, which is too simplistic; it fails to consider the individual effects of various factors on the failure of pressure vessels, resulting in excessive safety margins and waste of material ； The LRFD method assigns different safety factors to various random design variables, taking into account the two fundamental aspects of pressure vessel design: safety, reliability, and economy. Based on the design philosophy of reliability theory, this method enables the establishment of more reasonable safety margins, thereby achieving structural lightweighting while ensuring safety. Pressure vessel design based on reliability theory is a relatively new field; although foreign standards have already incorporated this aspect, domestic standards have not yet been introduced, and it remains at the stage of research by experts and scholars. With the revision of the analysis and design standards, it is believed that the introduction of the LRFD method in the field of pressure vessel design represents a significant advancement in this area. It is possible that in the future, we will abandon stress classification methods, and elastic analysis will become the mainstream approach for analysis and design. The author has learned that there may be no more SAD examinations in the next two years. Firstly, the Standards Committee is busy working on the revision of new standards; Secondly, future SAD assessments will have to be conducted according to these new standards, as they introduce ASME’s new elastoplastic analysis methods. This means that those who have already obtained a SAD certificate may need to undergo retraining and assessment. These two years represent both challenges and opportunities for analysis and design professionals. Whether you can seize this opportunity to overtake others and become among the first to benefit from it depends entirely on you!