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.

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