This paper is based on work done to establish the validity of a simple engineering approach to assess plastic collapse for a vessel with a local thin area (LTA). The approach is based on a recently developed p-M (internal pressure ratio and external bending moment ratio) diagram, which is an easy way to visualize the status of a vessel with a LTA simultaneously subjected to internal pressure, p and external bending moment, M due to earthquake, etc. If the assessment point (Mr,pr) lies inside the p-M line, the vessel with the LTA is judged to be safe. Numerous experiments and finite element analyses for a cylinder with an external flaw were conducted under (1) pure internal pressure, (2) pure external bending moment, and (3) subjected simultaneously to both internal pressure and external bending moment, in order to determine the plastic initiation load and plastic collapse load by applying the twice-elastic slope (TES) as recommended by ASME. It has been clarified that the collapse (TES) loads are similar to those calculated under the proposed p-M line based on the measured yield stress. The p-M line adopted in the Ibaraki fitness for service (FFS) rule based on the specified minimum yield stress with a safety factor of 1.5 indicates that the safety margin for the plastic initiation loads at LTA is about 1.0–3.0, about 1.5–4.0 for the TES loads at LTA, and 2.5–6.5 for the plastic instability (break) loads.
General components such as pressure vessels, piping, storage tanks, and so on are designed in accordance with the construction codes based on the assumption that there are no flaws in such components. There are, however, numerous instances in which in-service single or multiple volumetric flaws such as local thin areas are found in the equipment concerned. Therefore, it is necessary to establish a fitness for service rule, which is capable of evaluating these flaws. The procedure for a single flaw or multiple flaws has recently been proposed for assessing the flaws in the p-M (pressure-moment) diagram, which is an easy way to visualize the status of the component with flaws simultaneously subjected to internal pressure p and external bending moment M due to earthquake, etc. If the assessment point (Mr,pr) lies inside the p-M line, the component with flaws is judged to be safe. In this paper, numerous experiments and finite element analysis for a cylinder with external multiple volumetric flaws were conducted under (1) pure internal pressure, (2) pure external bending moment, and (3) subjected simultaneously to both internal pressure and external bending moment, in order to determine the plastic collapse load at volumetric flaws by applying the twice-elastic slope (TES) as recommended by ASME. It has been clarified that the collapse (TES) loads are much the same as those calculated under the proposed p-M line based on the measured yield stress.
With regard to piping systems of industrial facilities, sometimes they are subject to large deformation with high local plasticity. This results mainly from the detrimental ground movement due to possible liquefaction near seaside when a strong earthquake occurs. Especially the high local plasticity concentrates on elbows (bends) in piping systems. In this paper, the elbow behaviors of in-plane (closing: deflection to decrease elbow radius of curvature and opening: deflection to increase its radius of curvature) and out-of-plane bending are analyzed in a large plastic range using Nonlinear Finite Element Method (FEM) with the shell elements of material and geometrical nonlinear characteristics. The flexibility factor of elbows depends on flexibility characteristics, angular distortion and yield stress of material. Thus, in order to estimate the behaviors of piping systems with large plasticity at elbow by a simplified method, the modified flexibility factor method is introduced from results of FEM. Calculation results obtained using the simplified method are compared with experimental results, and this method gives an index to assess behaviors of piping systems subject to extremely large movement of supports. It is also possible to estimate local plasticity at elbows in piping systems by this conventional analysis.
Assessment of the local thin area should be undertaken for both tension and compression bending. In this paper, simplified reference stresses for a flaw in a cylinder are proposed. By using these results, a newly developed p-M (internal pressure ratio and external bending moment ratio) diagram which can evaluate the collapse condition for pressure equipment such as vessels, piping, and storage tanks with a local thin area simultaneously subjected to internal pressure p and external bending moment M due to earthquake, etc., is proposed. The p-M line is verified by comparison with the finite element analysis results and the numerous results of experiment for a cylinder with a volumetric flaw obtained through the reference literatures. It was clarified that the differences in collapse limit between the p-M line and DNV guideline under both internal pressure and compression moment became evident where the outer diameter/wall thickness of a cylinder is large and the yield ratio of the material is small.
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