STRESS INDICES FOR BRANCH CONNECTIONS WITH ARBITRARY BRANCH TO RUN ANGLES

Transcription

1 STRESS INDICES FOR BRANCH CONNECTIONS WITH ARBITRARY BRANCH TO RUN ANGLES L. Mkrtchyan 1, H. Schau 1, D. Hofer 2 1 TÜV SÜD Energietechnik GmbH Baden-Würtenberg, Mannheim, Germany 2 Westinghouse Electric Germany GmbH, Mannheim, Germany of corresponding author: lilit.mkrtchyan@tuev-sued.de ABSTRACT Branch connections and tees are among the most sensitive piping components in nuclear power plants and need to be carefully analyzed to provide their structural integrity. In modern nuclear codes such as the German KTA or American ASME Code different stress indices for primary stress evaluation are defined. The stress indices are applied to modify nominal stress equations for straight pipes so that the behavior of other piping components such as branch connections or elbows can be controlled using the same basic stress limits as those for straight pipes. The codes provide also formulae for calculation of the stress indices for many piping components. However, along with standard components there are also those outside the scope of nuclear codes. For such components as branch connections with non-standard branch to run angles no stress indices are available. However, accurate assessment of stress indices for mentioned nonstandard piping components is necessary to prevent their plastic collapse or excessive deformation. In present paper a new procedure for computing the stress indices, corresponding to the run and the branch pipes for arbitrary branch connections is proposed. The study is performed with geometrically nonlinear FE-analyses. The stress index for the branch connection is determined using the ratio of the stress index for the component to the corresponding stress index for a straight pipe with similar dimensions. This method has an advantage of guaranteeing that the index will be always 1.0 for a straight pipe. The procedure is based on the margin consistent definition of the stress index, developed in [10]. Two nonstandard branch connections, having different branch-to-run angles are considered to demonstrate the proposed method. Detailed nonlinear finite element analyses are performed for each junction, subjected to different loadings and boundary conditions. The effects of the cross sectional ovalization are taken into account. The stress indices for the branch or the run pipes are determined to be the maximum values of corresponding indices for different loading cases. It is shown that the stress index depends on the value of the branch-to-run angle. INTRODUCTION Structural integrity assurance of piping systems is essential for safe operation of nuclear power plants (NPPs). Modern nuclear codes, among them American ASME Code [3] or German KTA [1] and KTA [2] provide rules for the design of piping components in NPPs to prevent their plastic collapse or excessive deformation. Protection against plastic collapse is ensured by simplified analysis, evaluating the effects of internal pressure and external moments due to mechanical loads. The shape effects are accounted for with the help of stress indices, which are defined as:. Here, is the stress magnitude corresponding to the limit load of the component and the nominal stress due to the limit load. The stress indices are used to modify nominal stress equations for straight pipes (see [1-3]) so that the behavior of other piping components such as branch connections, tees or elbows can be controlled, using the same basic stress limits as those for the straight pipe. Modern nuclear codes provide formulae for calculation of the stress indices for many standard piping components in NPPs. However, along with these standard components there are also those outside the scope of nuclear codes. For components such as branch connections with non-standard branch to run angles or branch-to-run radius ratios no stress indices are available. Therefore, while calculating branch connections with arbitrary branch to run angles, the commercially available piping system programs (e.g. Rohr 2, Cesar, LV-pipe, etc.) usually perform calculations with the help of flexibility factors and stress indices for similar standard components. Further, an assumption is made, that the values of these factors for nonstandard components will be close to the ones calculated for standard components. In order to determine the stress indices accurately a rigorous approach is needed, involving finite element analysis of the piping component. Pipe tees and branch connections are very often the weakest components in piping systems. Due to their complex geometries the stresses occurring within branch connections and tees under certain loadings are much higher than 1

2 those occurring in either a bend or in a straight run of a pipe. Hence assurance of the structural integrity of these piping components is essential for safe operation of the NPP. According to nuclear codes, the stress indices and for tees and branch connections must satisfy a modified equation, which governs the primary stresses for design loads and has the following form: Here is the allowable limit stress for which different values are specified at different service levels, and are the approximate section moduli for the branch and run pipes respectively. For determination of and certain equations are provided in the nuclear codes. Equation (1) intends to resist gross plastic deformation [7] or to place bounds on loading such that necessary conditions for a collapse load will not exist anywhere in the piping system [8]. In literature several limit load solutions for branch connections with straight branch to run angles are presented for in-plane bending loading, for example in [11, 13-15]. Lee [11] and Xuan [13] have studied limit load solutions for straight pipe junctions under internal pressure and in-plane bending moments. Berton [15] has implemented a full parametric study of straight pipe junctions for different loading cases, using the FE-method. Clark [16] has calculated the index for branch-to-run angle of 45 by matching the finite element model to the loads produced by the associated linear system model. In available studies finite element analyses of branch connections become increasingly popular due to complexity of the geometry and the loading of these components. However among numerous investigations for tees and connections with branch-to run straight angles, there are no studies suggesting methods on determining the stress indices for branch connections with arbitrary branch-to-run angles. Recently Matzen [9] and Tan [10] suggested a procedure for calculating the stress index for elbows subjected to bending moments. The resulting stress index equation, which is the ratio of the collapse moment of a straight pipe to the collapse moment of the component, gives a value of 1.00 when applied to the straight pipe and a safety margin for the component that is always the same as for the straight pipe. It is given below as: (1) (2) The mentioned authors used this definition for calculating the index for several pipe bends and straight pipes and verified the results with experiments. In the present study the definition (2) is used in a new procedure for computing the primary stress indices and, corresponding to the run and the branch pipes. The proposed procedure can be applied for nonstandard branch connections with arbitrary branch to run angles and pipe wall thicknesses. A LIMIT LOAD PROCEDURE FOR THE STRESS INDEX IN CASE OF BRANCH CONNECTIONS One of the ways to determine the stress indices and (primary indices for bending) for the run and the branch pipes in a branch connection with arbitrary branch-to-run angle is to determine the limit load, i.e. to obtain the loadcarrying capacity of the component. Generally two kinds of limit loads can be defined according to the nuclear codes: one is the TES plastic load, defined using the twice-elastic-slope method, and the other one is the instability load, defined by the maximum point in the load-deformation curve. The limit load can be determined using different methods, and finite element analysis is one of them. While performing geometrically linear finite element limit load analysis, it is easy to determine the limiting loads for the considered component. However, in difference to linear analysis, geometrically nonlinear finite element analysis does not result in distinct limit TES plastic loads. Especially for large radius-to-thickness ratios of a piping component the large geometry change effect is more pronounced. Due to ovalization of the cross section softening effects are observed and the TES load tends to be smaller than the plastic limit load (see Fig. 1). In order to determine the limit load, taking into account the influence of the cross sectional ovalization of the pipes on the limit load and hence, on the value of the stress index, in present study the instability moment is taken as a limit load. The instability load is determined by performing nonlinear finite element limit analysis (FEA) with a bilinear elastic-perfectly plastic material model. As a limit (collapse) load is then taken the load corresponding to the last iterated state in the FEM analysis. This definition of the TES load differs from the one in [10], where as a collapse load the TES plastic load is used. 2

3 Fig. 1: The collapse loads resulting from linear and nonlinear finite-element analysis The stress indices and (primary indices for bending) for the run and the branch pipes in a branch connection are then determined using the ratio of the load-carrying capacity of the whole component, which is in this case the junction, to the load-carrying capacity of a straight pipe with dimensions of the run and the branch pipes respectively, with the help of the following equations: Here and denote the stress indices; and denote the plastic moments of the straight pipes having similar geometrical parameters as the run and branch pipes; and are the limit (collapse) moments of the whole component when loading it at the run pipe or the branch pipe respectively (for the loading. The procedure of calculation of the stress indices is described in the following with the help of two examples. CALCULATION OF THE STRESS INDICES FOR DIFFERENT BRANCH-TO-RUN ANGLES Two non-standard branch connections, having similar radius to thickness ratios ( and ) for the run and the branch pipes are considered. In the first component the branch segment extends outward from the run pipe at a 46 angle, in the other one - at a 65 angle, as shown in Fig. 2: (3) Fig. 2: Considered branch connections with different branch-to-run angles For determination of the stress indices for the considered branch connections, several detailed nonlinear finite element analyses are performed for each of them. The branch connections are modeled in Abaqus/Standard [17], 3

4 with 20 - node quadratic brick elements. In order to obtain accurate and stable results, three elements are taken in the thickness direction and the mesh size is optimized, particularly in the vicinity of the junction. In the finite element model the material and geometric nonlinearities are taken into account. To define the material nonlinearity, an elastic-perfectly plastic material model is defined. The following material properties are taken: ;. The components are subjected to bending moments in different directions. Regardless of the bending direction, a small internal pressure tends to stabilize the structure and increase its load-carrying capacity. Hence, the pure bending of the pipe component, without internal pressure seems to be more challenging in this case. In the following the stress indices and due to the internal pressure are assumed to be:. The stress indices and for the run pipe and the branch segment are obtained, performing calculations for single loading cases. As a stress index of the branch or the run pipe the maximum value of the obtained and indices for different loading cases is taken (see Eq. 3): In case of the considered elastic-perfectly plastic constitutive material model with the yield stress moment for straight pipes takes the following form:, the plastic where D is the outer diameter of the pipe. The considered branch segment is a DN400 pipe with an average wall thickness of 12,5-mm and a length of 8 m; the run pipe is a DN500 pipe with an average wall thickness of 11 mm and a length of 2 m. In the considered case not only the branch to run angle, but also the branch-to-run-radius ratio is outside the scope of standard components, prescribed in nuclear codes. If we consider straight pipes having similar geometrical parameters (radius, wall thickness, length) as the run segment and the branch segment of the branch connection, considered in the paper, the plastic moments for these straight pipes take the following values (see Table 1): Table 1: The plastic moments for straight pipes DN400 and DN500 Straight pipe Cross section [mm] Plastic moment [knm] DN 400 (DN 500) 406 x 12,4 (508 x 11,0) 466 (652) The presence of boundary conditions or ring stiffeners reduces significantly the cross-sectional ovalization, which affects the values of stress index. According to the analysis of Axelrad [19], end effects are considered to have no influence on the ovalization response of a cylinder when. In order for this relationship to be satisfied and the boundary conditions have no influence on the ovalization behavior of the pipes, the run and branch segments are modeled longer than in reality. For determination of the stress indices and, in-plane opening, in-plane closing and out-of-plane bending moments, acting on the branch and the run pipes are analyzed. All practically possible boundary conditions are considered. The boundary nodes of the cross-sections of the run and the branch pipes are coupled to master nodes. This forces each cross section to translate and rotate with the corresponding (master) node (see Fig. 3). In order to enable ovalization of the structure, the constraint in the radial direction is removed. In the first step in-plane opening, in-plane closing and out-of-plane moment loadings are applied to the master node 3 of the branch pipe, while fixing the master node 1 of the run pipe (see Fig. 4, 5). For the master node 2 of the run pipe different boundary conditions are analyzed: free, simply supported, fixed. The bending moments are applied about the positive and negative directions of the axis z in the local coordinate system of the branch pipe. The moment loading is increased incrementally till the structure s collapse. The collapse load is then the bending moment of the last iterated equilibrium state of the piping component. (4) 4

5 Fig. 3: Coupling of the branch connection with master nodes In the second step moment loadings are applied to the master node 2 of the run pipe, leaving the free the node 3 of the branch pipe. Similar approach is applied, fixing all the degrees of freedom of the master node 2 and applying the bending moments to the branch and to the run pipes. The boundary and loading conditions for the run pipe are shown in Fig. 4, and for the branch pipe - in Fig. 5: a) b) c) d) e) Fig. 4: Boundary conditions for the run pipe: a) clamped-free; b) clamped-simply supported; c) clamped - clamped; d) simply supported clamped; e) free- clamped From the non-linear limit load analyses the collapse moments for above mentioned loading cases are obtained and compared with the collapse moments of straight pipes with corresponding dimensions. 5

6 Fig. 5: Boundary condition for the run pipe while the branch pipe is free The values of the collapse moments for different analyzed cases for the branch pipe are given in Table 2 and for the run pipe in Table 3, where and denote the plastic moments (for the loading of the run and branch pipes respectively. Table 2: Collapse moments of the component for different loading cases of the run pipe Moment at node 1 BC at node 2 BC at node 3 [-] in-plane closing mode clamped free 1,46 1,23 in-plane opening mode clamped free 1,12 1,19 out-of-plane mode clamped free 1,12 1,39 Table 3: Collapse moments of the component for different loading cases of the branch pipe Moment at node 1 BC at node 2 BC at node Free clamped 1,65 2,17 Free clamped 1,77 2,36 Free clamped 2,97 4,02 Clamped supported 2,16 2,59 Clamped supported 1,62 2,26 clamped supported 2,82 4,09 Clamped free 2,14 2,57 Clamped free 1,56 2,18 Clamped free 2,81 4,07 Supported supported 1,56 2,06 Supported supported 1,64 2,19 supported supported 2,91 3,95 [-] As a stress index of the branch or the run pipe the maximum value of the obtained cases is taken: indices for different loading 6

7 The described procedure is valid for arbitrary run to branch angles and branch-to-run-radius ratios. The calculations show that the stress indices depend on the values of the branch to run angle. The most critical loading mode is the out-of-plane loading mode of the branch pipe, when one of the ends of the run pipe is clamped and the other end is free. The resulting stress index has a value of 4.1 for the branch pipe. In Fig. 6 the equivalent stresses corresponding to the last iterated state are given for the component with branch-to run angle of 65. Fig. 6: Von-Mises equivalent stress at the last iterated state in case of out-of-plane loading of the branch The calculated stress indices for the run and the branch pipes in case of the considered different branch to run angles are presented in Table 4. Table 4: The stress indices of the components Stress index ,5 1, ,1 The obtained results are compared with those obtained with the formulae, suggested in the American ASME Section III NB and German KTA section 8. A direct comparison with the values calculated from the formulae in nuclear codes is not possible since the suggested formulae are given for branch connections with branch-to-run straight angles and. However, since the formulae are used in the modern commercial piping calculation programs, the stress indices of the present study are compared with those values and are summarized in Table 5: Table 5: Comparison of the stress indices for branch and run with those suggested in nuclear codes Stress index Nonlinear FE-analyses ASME Section III, KTA Branch-to-run angle 46 (65 ) Branch-to-run angle 46 (65 ) 1,5 (1,4) 1,72 1,72 3,0 (4,1) 5,9 11,8 Comparison of the results suggests, that the stress index for the branch pipe, given in German KTA is reducible, depending on the angle between the branch and the run, by a factor of up to 3. The values, calculated according to the formula in ASME Code [3] result in a factor of up to 1,5. SUMMARY The present paper presents a method for calculating the stress index used in nuclear codes KTA and ASME for branch connections with arbitrary branch to run angles. The method is based on the definition of the stress index proposed in [10] and [11]. 7

8 The resulting equation for the stress index, which is the ratio of the collapse moment of a straight pipe to the collapse moment for any component, gives a value of 1.00 when applied to a straight pipe and a safety margin for the component that is always the same as for the straight pipe. As an example, calculations are done on two branch connections, consisting of a run pipe of DN400 and a branch pipe of DN500. with branch-to-run angles of 46 and 65. The analysis shows that the stress indices depend on the values of the branch to run angles. The results show also that the out-of-plane bending mode is the most critical loading mode for the branch connections. Comparison is made between the obtained values of the stress indices and and those, calculated with German KTA [1] and ASME Code [3]. The results show that the values suggested by the nuclear codes can be reduced by a factor of up to 3 in case of for the branch pipe and up to 1,2 in case of for the run pipe. REFERENCES [1] KTA Fassung , Komponenten des Primärkreises von Leichtwasserrektoren, Teil2: Auslegung, Konstruktion und Berechnung [2] KTA , 1992, Druck- und aktivitätsführende Komponenten von Systemen außerhalb des Primärkreises. Teil 2: Auslegung, Konstruktion und Berechnung. [3] 2007 ASME Boiler, Boiler & Pressure Vessel Code 2009b Addenda, Section III, Division 1 [4] Rodabaugh E. C., Gwaltney R. C., Moore S. E., 1993, Review of ASME Code criteria for control of primary loads on nuclear piping system for branch connections and recommendations for additional development work, Washington, DC. [5] Electric Power Research Institute (EPRI), 2005, Background of SIFs and stress indices for moment loadings of piping components, Technical Report , Palo Alto (California). [6] Markl, A. R. C., 1952, Fatigue tests of piping components, Transactions ASME 74 No. 3, pp [7] Moore, S. E.; Rodabaugh, E. C., 1981, Background for the ASME nuclear code simplified method for bounding primary loads in piping systems, in: Schneider, R. W.; Rodabaugh, E. C.: Stress indices and stress investigation factors of pressure vessel and piping components, ASME Publication PVP-50. [8] Mello, R. M.; Griffin, D. S., 1974, Plastic collapse loads for pipe elbows using inelastic analysis, Pressure vessels and piping-materials-nuclear conference, Miami Beach, Florida, USA. [9] Yu, L.; Matzen, V. C., 1999, B2 stress index for elbow analysis, Nuclear Engineering and Design 192, pp [10] Tan, Y., 2001, Experimental and nonlinear FEA investigation of elbow leading to a new definition of the B2 stress index, North Carolina State University, Ph.D. thesis. [11] Lee, K.-H.; Kim, Y.-J.; Park, C.-Y., 2006, Limit loads of piping branch junctions under internal pressure and in-plane bending, International Journal of Pressure Vessels and Piping 83, pp [12] Lee, K.-H.; Kim, Y.-J.; Park, C.-Y., 2008, Plastic loads of pipe bends under combined pressure and out-ofplane bending, International Journal of Fracture 149, No. 1, pp [13] Xuan FZ, Li P-N, TU S-T, 2006, Limit load analysis for the piping branch under in-plane moment, Int. J. Mech. Sci., 48, pp [14] Berton M.N., Michel B., 2003, Limit Analysis of pipe tee connection, Trans. of the 17 th Int. Conf. on Structural Mechanics in Reactor Technology (SMIRT17); Prague, Czech Republic. [15] Plancq, D. Berton M.N., 1998, Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading, Int. J. of Pres. Ves. &Piping, vol.75, pp [16] D. T. Clark, M. J. Russell, R. E. Spears, S. R. Jensen, 2009, Adaption of Nonstandard Piping Components Into Present Day seismic codes, ASME Pressure Vessels and Piping Division Conference. [17] Abaqus Version 6.9, SIMULIA (ABAQUS Inc., Providence, USA) [18] Murali, B; Munshi, D.; Vaze, K. K.; Kushwaha, H. S., 1993, Evaluation of primary stress indices for miter bends and possibility of extending to DO/T > 50, SMiRT-12 in Stuttgart, Germany. [19] Axelrad, E. L., 1965, Refinement of buckling-load analysis for tube flexure by way of considering precritical deformation [in Russian], Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, Mekhanika i Mashinostroenie, Vol. 4, pp