Analysis of the impact of temperature load on the state of stress in a bolted flange connection Patryk Towarnicki, Rafał Grzejda West Pomeranian University of Technology, Szczecin Faculty of Mechanical Engineering and Mechatronics Szczecin, Poland patryk_towarnicki@zut.edu.pl, rafal.grzejda@zut.edu.pl Abstract—Modelling and calculations of a bolted flange connection located under elevated temperature conditions are presented. Analysis of forces acting on the bolt and the joined elements on the basis of analytical formulas and using the finite element method (FEM) is performed. In the case of theoretical calculations the recommendations given in books on the fundamentals of machine design are applied. For a case of numerical calculations a simplified model of the bolt is used. The obtained results of calculations are checked in terms of fulfilment of the adopted strength criterion associated with acceptable thermal stress in the bolt. Selected results of simulation studies of the connection FEM-model in the form of temperature distribution in the model are shown. On the basis of the comparison of the theoretical and numerical analyses results, the usefulness of the simplified bolt model for calculations of forces in the bolts in flange connections under elevated temperature conditions is determined. Keywords—thermal stress; bolt force; flange connection I. INTRODUCTION One of the applications of bolted flange connections is to join the flanges in the pipelines. Such structures are subjected during operation to various loads, including temperature loads [1-3]. The temperature of fluids transported inside the pipelines induces thermal stresses in both the joined elements and bolts [4]. Prolonged exposure of elevated temperatures on elements of the connection may lead to their time-dependent deformation called creep [5, 6]. Bolted flange connections are also used in pipelines in which fluids are transported at low temperatures [7]. Finally, bolted flange pipe connections are sometimes exposed to high external temperatures, especially under fire conditions [8]. Based on the above facts, it can be concluded that modelling and analysis of temperature-loaded bolted flange connections are justified and important. Depending on the aim of modelling, bolted flange connections may be calculated according to various methods. For engineering design of this type of connections the traditional theoretical methods of calculations [9, 10] are appropriable. In more complex analyses it is common to use the finite element method (FEM) and three-dimensional models of the connections. In these cases, the issues of both single-bolted flange connections separated from the full joint [1, 4, 5] and multi-bolted flange connections [3, 11, 12] are taken into account. Between the mentioned calculation methods, the FEM- modelling bolted flange connections using simplified bolt models can be positioned. These include, among others, such models as:  no bolt models [13, 14],  bolt models with a flexible shank and a rigid head [15, 16],  truss [17] or beam elements [18]. In the paper the theme of modelling bolted flange connections using the Midas NFX 2017 FEM program has been undertaken. The aim of the study is assessment and evaluation the usefulness of a simplified model of the bolt embedded in this program to static and thermal stress analysis of bolted flange connections. The results of numerical calculations are compared with the results of calculations under analytical methods [10]. II. MODEL OF THE BOLTED FLANGE CONNECTIOIN A. Description of the Connection and Load Conditions The subject of research is a fragment of a gasketed bolted flange connection shown in Fig. 1. The discussed connection is a joint of a pair of flanges of the EN 1092-1/11/B2/DN 150 x 7.1/PN 100/P245GH type, made according to the PN-EN 1092- 1 [19] standard, and assembled with twelve M30 bolts. The physical properties of materials used in the connection model is shown in Tab. 1. Fig. 1. 3D-model of the bolted flange connection [20].