Application of Limit Analysis to Seismic Evaluation of Steam Generator Tube Bundles - Part 2: Verification of Reproduction of SG Tube Elastic-Plastic Behavior and Application of Limit Analysis by Nonlinear Model

Abstract Ensuring the structural integrity of Steam Generator (SG) U-bend tube arrays during out-of-plane earthquakes is crucial. The current primary stress evaluation method requires that tubes with the highest stress satisfy the primary stress criterion. However, even if one tube exceeded the criterion, the tube arrays is not supposed to easily collapse due to mechanism by which the tube shares the load between surrounding tubes through Anti-Vibration Bars (AVBs). Therefore, the current evaluation method seems to be conservative, and the rationalization of the design code is desired considering the increasing trend of design earthquake level. As one of the rationalization methods, the construction of a nonlinear model which can precisely the load sharing mechanism of the tubes by modeling all tubes and AVBs was investigated. In addition, a limit analysis by the nonlinear model was applied to obtain the collapse load and calculate the primary stress criterion as a tube bundle. In order to construct a nonlinear model applicable to the elastic-plastic analysis which includes a limit analysis, it is necessary to consider the elastic-plastic contact characteristics between the tube and TSP (Tube Support Plate) by the spring element, and to simulate the elastic-plastic behavior of the tube by the beam element. Furthermore, since the buckling behavior cannot be evaluated in the beam element, it is necessary to evaluate the buckling criterion by another analytical model and to limit the application range of the nonlinear model. Therefore, in this project, in order to obtain and verify the elastic-plastic behavior including the buckling of the tubes, an element test using a single straight tube and TSP and an analysis reproducing the element test were carried out. In this simulation, two types of analysis were carried out: (1) the shell element model (Single tube is shell elements; TSP is solid elements) to evaluate the buckling criterion and the contact characteristics between the tubes and TSP, and (2) the beam element model (Single tube is beam elements; TSP is spring elements) which is the base of the nonlinear model used for the evaluation of the SG. The results of the simulation analysis revealed that, both (1) the shell element model and (2) the beam element model were well consistent with the moment displacement curve of the single straight tube tip obtained in the element test, and this finding confirmed that the elastic-plastic behavior could be reproduced. Using the verified beam element model, the limit analysis by the nonlinear model under the actual condition was carried out, and the applicability of the limit analysis to the primary stress evaluation of the tube bundle was confirmed. The moment Mcr generated at the collapse load Pcr of the tube bundle, which was obtained from the limit analysis by the nonlinear model, was compared with the collapse moment (buckling moment) Mcr’ obtained from the limit analysis by the shell element model of a single tube. When Mcr was lower than Mcr’, it was estimated that the tube did not buckle under the collapse load Pcr of the tube bundle. Based on the comparison result, it was confirmed that Mcr is lower than Mcr’, and that the collapse load Pcr obtained from the limit analysis by the nonlinear model was applicable as an allowable load for the primary stress evaluation of the tube bundle.