Seismic Analysis of Large-Scale Piping Systems for the JNES ... - NRC

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development of the parameters (except for γ3) for the Chaboche model in this study. The curve from the test was presented in terms of engineering stress-strain and was first converted into a true stress-strain curve for consistency with the multi-linear kinematic hardening material models and for compatibility with large deformation analysis option utilized in this study. The elastic strain was then removed from the total stress-strain curve by subtracting the elastic strain (stress / Young’s modulus). As shown in Figure 4-11, the initial values of C1 and C3 are determined by fitting the elastic portion and the very end of the linear portion of the forward loading curve. The initial values of C2, γ1, and γ2 were taken from the previous report [DeGrassi and Hofmayer 2005]. Utilizing the initial values of C1, C2, γ1, and γ2, a least-square minimization of the difference between the test and the developed forward loading curve (Eq. 4-1) can yield an optimal set of values for these parameters. C3 does not participate in this least-square minimization in order to maintain the linear portion of the plastic stress-strain curve. The excellent match between the test curve and the Chaboche curve with the optimal parameters can be clearly seen in Figure 4-12. Also demonstrated in Figure 4-12, the change of the parameters during the minimization process does not change the original intention of the three rules proposed by Chaboche [1986]; the three rules α1, α2, and α3 still represent the initial high plastic modulus portion, the transient nonlinear portion, and the linear portion of the plastic stress-strain curve, respectively. Using the same approach as the one in the previous report, the parameter γ3 was determined by performing a parametric study of γ3 using the strain-controlled cyclic test (SE-4) of an elbow component [DeGrassi and Hofmayer 2005]. By varying γ3 while maintaining other parameters, a series of trial-and-error runs of an ANSYS shell model (see Figure 4-13) developed for the SE-4 test were carried out, and a value of γ3 was then found to achieve the best prediction of the strain ratcheting behavior of the elbow component. Figure 4-14 shows a comparison of the final hoop and axial strain ratcheting behaviors between the test and the analysis, with γ3 =2.2. In summary, the revised Chaboche nonlinear kinematic hardening material model used in the analyses is defined by the follow parameters: σy=275.92 MPa, E =203000 MPa, C1 =65191.29 MPa, C2 =14909.91 MPa, C3 =1653.90 MPa, γ1 =1044.83, γ2 =177.06, and γ3 =2.2. 4.2.3 Finite Element Models and Analyses DeGrassi and Hofmayer have shown that the curved plastic pipe element in ANSYS is not adequate to simulate the elbow strain ratcheting behavior [2005]. Therefore, a shell representation of the elbow is necessary to predict its strain ratcheting behavior. In line with the analysis strategy as indicated in the beginning of this report, two FE models were developed to obtain the analytical responses. One model uses simple pipe elements (beams) to represent the whole piping system, while the other uses nonlinear shell elements to represent one of the nine elbows in the test. This modeling strategy is necessitated primarily by the high computational demand of a nonlinear transient analysis of the whole piping system. Such an analysis can be computationally very expensive if the piping system is modeled entirely with shell elements. Even a hybrid model involving pipe elements (beam elements) for straight pipe segments and shell elements for elbows has been shown to be prohibitive for a nonlinear transient analysis. In deed, even a nonlinear transient analysis of a shell model of a single elbow was found to be an intolerably lengthy calculation in a preliminary study. Some analysis options are shared by all models and analyses. Together with the true stress-strain curves, the large deformation option in ANSYS is set for both the piping system model and the elbow model, since responses due to both small and large input motions should be predicted well with this option. Automatic time stepping in ANSYS is used for all analyses with the upper bound equal to the time step of the input motions (0.005 sec) and with the lower bound so small 57
so as not to prevent ANSYS from finding an efficient and converged solution. Occasionally, the solution stabilization option has also been turned on to overcome convergence problems for large input motions. All outputs of interest are requested at exactly every 0.005 sec by utilizing appropriate output specification arrays, in order to make the analytical results easy to be compared with the test results. This subsection describes the relevant modeling and analyses for the piping system model and the elbow model. 4.2.3.1 Piping System Model Using Pipe Elements Figure 4-15 shows the ANSYS FE model of the piping system, overlaid with various major dimensions and symbols for boundary conditions. The entire piping system for the large-scale design method confirmation test is modeled with pipe elements, with the straight pipe segments discretized by PIPE20 elements that are mostly 500 mm long and with elbows discretized by four PIPE60 elements. In ANSYS, PIPE20 is a plastic straight pipe element while PIPE60 is a plastic curved (elbow) thin-walled pipe element. Both element types can handle large plastic deformation, and have tension-compression, bending, and torsion capabilities. These pipe elements do not allow the use of the Chaboche nonlinear kinematic hardening material model, and therefore the multi-linear kinematic hardening models described previously are used in the piping system analysis. The averaged as-built diameter and the averaged as-built thickness of the piping system are used for the FE model, with values of 219.2 mm and 10.38 mm, respectively. The mass of the water is considered in the analyses indirectly by increasing the mass density of the pipe material, with a resultant mass density of 12,388 kg/m 3 . The added weight of 1000 kg in the specimen was represented by a MASS21 element at node 35. The piping system for the design method confirmation test was subjected to an internal pressure of 10.7 MPa. Gravity load is considered in the transient analyses. The spring hanger is represented by a concentrated vertical force at node 35, which was determined as the reaction force to gravity assuming a vertical translational support at this location. At the beginning of the analysis, the two nozzles and one anchor are fixed for the six translational/rotational degrees of freedom and various translational restraints in the test are modeled by unidirectional displacement boundary conditions, as shown in Figure 4-15. Some of these restraints and the fixed boundary conditions are replaced by the acceleration time history in the transient analyses. The Rayleigh damping model is used for the transient analyses. The frequencies of the first two modes from the sine sweep tests, 6.3 Hz and 8.1 Hz, and the corresponding measured damping ratios, 2.1% and 4.8% respectively, were used to calculate the ALPHAD (mass term) and BETAD (stiffness) parameters for the Rayleigh damping model in ANSYS. However, these measured frequencies and damping ratios resulted in a negative ALPHAD; therefore, only the BETAD parameter was considered in analyses for the design method confirmation tests. The stiffness only damping parameter BETAD was calculated to be 1.061E-3 using the fundamental frequency and the corresponding measured damping ratio. JNES/NUPEC had also provided the fundamental frequencies and damping ratios for all tests, showing that frequency generally decreases while damping ratio increases as the piping system experiences the increasing levels of input excitations. These damping ratios were not used for the analyses because they are believed to include the energy dissipation effect from the hysteresis loops, which have already been directly taken into account by the multi-linear kinematic material models. In fact, a preliminary run of DM4-1 using the larger damping ratio measured in the test showed that the analytical responses became smaller than the test results and the result comparison became worse. 58
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NUREG/CR-6983 BNL-NUREG-81548-2008
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Seismic Analysis of Large-Scale Pip
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FOREWORD This report documents the
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Figure 2-7 Model B Simplified Pipin
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Figure 4-64 Acceleration A2 Compari
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In the final phase of the test prog
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Continued investigation of the subj
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1 INTRODUCTION Prior to the establi
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2 DESCRIPTION OF JNES/NUPEC TEST PR
Page 19 and 20: Photographs of the DM Test Piping a
Page 21 and 22: Design Method Confirmation Test Ult
Page 23 and 24: Stress (N/mm 2 ) Figure 2-1 Monoton
Page 25 and 26: Hoop Strain (%) 18 16 14 12 10 8 6
Page 27 and 28: φ76.3 7.8 1500 Variable Hanger Sma
Page 29 and 30: Figure 2-9 Overview of Design Metho
Page 31 and 32: Figure 2-11 DM Test Nozzle 17
Page 33 and 34: Figure 2-13 DM Test Spring Hanger 1
Page 35 and 36: Figure 2-15 DM Test Accelerometer L
Page 37 and 38: Figure 2-17 DM Test Strain Gage Loc
Page 39 and 40: Figure 2-19 US Test Piping System S
Page 41 and 42: Figure 2-21 US Test Elbow 2 and Add
Page 43 and 44: Figure 2-23 US Test Accelerometer L
Page 45 and 46: Figure 2-25 US Test Strain Gage Loc
Page 47 and 48: Displacem ent(m m ) S train(%) 100
Page 49 and 50: Figure 2-30 US Test Elbow 2 Fatigue
Page 51 and 52: 3 BNL LINEAR ANALYSES AND CODE EVAL
Page 53 and 54: where: PD 2t D + 0S m (3-4) 2I 0 0
Page 55 and 56: limits and specified that stresses
Page 57 and 58: Regulatory Guide 1.61 Revision 0 da
Page 59 and 60: Code Edition 1993 1993 Table 3-3 DM
Page 61 and 62: Figure 3-1 Design Method Confirmati
Page 63 and 64: Acceleration (g) Acceleration (g) 1
Page 65 and 66: Acceleration (g) 16 14 12 10 8 6 4
Page 67 and 68: g, and 0.471 g respectively in the
Page 69: A simple approach has been taken in
Page 73 and 74: are made with time histories and Fo
Page 75 and 76: DM4-2(2) (Restart): This analysis c
Page 77 and 78: The only responses obtained from th
Page 79 and 80: elements. The final hoop (plastic)
Page 81 and 82: are somewhat smaller than but in an
Page 83 and 84: difference in the residual displace
Page 85 and 86: esponse for the entire time histori
Page 87 and 88: Figure 4-1 Horizontal and Vertical
Page 93 and 94: Figure 4-7 Comparison of Baseline-c
Page 95 and 96: Stress(MPa) Stress (MPa) 600 500 40
Page 97 and 98: Hoop and Axial Strain (%) 17 16 15
Page 99 and 100: Figure 4-16 Displacement D2 Compari
Page 101 and 102: Figure 4-18 Acceleration A2 Compari
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Figure 4-39 Relative Deformation Hi
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Figure 4-47 Strain Ratcheting Compa
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Figure 4-60 Horizontal Input Motion
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Figure 4-62 Displacement D2 Compari
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Figure 4-64 Acceleration A2 Compari
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described in Sections 4 of this rep
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U.S. Nuclear Regulatory Commission,
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nominal dimensions for the straight
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Figure A-1 Original and Modified Re
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Figure A-5 Ratio of Reaction Forces
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Figure A-9 Ratio of Reaction Force
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Figure A-13 Ratio of Top Half Signi
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NRC FORM 335 U.S. NUCLEAR REGULATOR
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