TR-110996

Stress Intensification Factors andFlexibility Factors for Unreinforced Branch Connections SED R I A L LICE N M AT E WARNING: Please read the Export Control and License Agreement on the back cover before removing the Wrapping Material. Technical Report Stress Intensification Factors and Flexibility Factors for Unreinforced Branch Connections TR-110996 Final Report November 1998 Prepared for EPRI 3412 Hillview Avenue Palo Alto, California 94304 EPRI Project Manager R. Carter DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES THIS REPORT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE. APPARATUS. INC. Inc. INCLUDING ANY PARTY'S INTELLECTUAL PROPERTY. EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOUR SELECTION OR USE OF THIS REPORT OR ANY INFORMATION. POWERING PROGRESS is a service mark of the Electric Power Research Institute. (EPRI). Pleasant Hill. 207 Coggins Drive. METHOD. NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM: (A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER. ORDERING INFORMATION Requests for copies of this report should be directed to the EPRI Distribution Center. All rights reserved. INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. . PROCESS. APPARATUS. OR (B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAMAGES. EXPRESS OR IMPLIED. ORGANIZATION(S) THAT PREPARED THIS REPORT Wais and Associates. ANY COSPONSOR. METHOD. OR SIMILAR ITEM DISCLOSED IN THIS REPORT. THE ORGANIZATION(S) NAMED BELOW. Box 23205. OR (III) THAT THIS REPORT IS SUITABLE TO ANY PARTICULAR USER'S CIRCUMSTANCE. NEITHER EPRI. Inc. PROCESS. (925) 934-4212. Copyright © 1998 Electric Power Research Institute.O. OR (II) THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS. Inc. EPRI. (I) WITH RESPECT TO THE USE OF ANY INFORMATION. Inc. OR SIMILAR ITEM DISCLOSED IN THIS REPORT. CA 94523. P. ANY MEMBER OF EPRI. Electric Power Research Institute and EPRI are registered service marks of the Electric Power Research Institute. EPRI Licensed Material CITATIONS This report was prepared by Wais and Associates. Palo Alto. Report Number TR-110996. Rodabaugh This report describes research sponsored by EPRI. iii . 3845 Holcomb Bridge Road. Inc. The report is a corporate document that should be cited in the literature in the following manner: Stress Intensification Factors and Flexibility Factors for Unreinforced Branch Connections. Georgia 30092 Wais Assoc@aol. Suite 300 Norcross. EPRI.com E. Wais E. CA: 1998. The report contains results of an investigation into the flexibility and stress intensification factors of unreinforced fabricated tees (and other similar configurations). Tests and analyses were performed on representative models and the results were compared to existing data. Results This report summarizes the experimental data and the test program in Section 2. experiments. Objectives • To derive expressions for stress intensification factors for branch connections • To derive expressions for flexibility factors for accurately modeling the behavior of branch connections in a piping analysis Approach A review of the present approach for evaluation of branch connections in accordance with the Code. the applicability of results in Section 5.REPORT SUMMARY This report provides equations. It provides flexibility equations for a more accurate evaluation of these configurations. the investigation of flexibility in Section 4. The ASME Section III Class 2&3. the combination of moments and stresses in Section 3. provided an understanding of the current methodology in the determination of the various factors. and the results of the investigation on branch connections in Section 6. for determining the stress intensification factors and flexibility factors for branch connections. Available data on studies. Equations were developed to more accurately calculate stress intensification factors and flexibility factors for branch connections. Background Fatigue is a major concern in the design and engineering of piping systems. v . based on analyses and test data. and B31 piping design codes use factors such as stress indices and stress intensification factors to account for fatigue effects produced by reversing loads. and testing were collected and reviewed. and moderate-energy line break locations and reduction of snubber testing. TR-110996 Interest Categories Piping. The results of this program can provide a basis to reduce the scope of ongoing pressure boundary component testing and inspection programs in operating nuclear power plants.EPRI Perspective Design for fatigue is a major concern for any power or process facility. reactor vessel & internals Keywords ASME Code Fatigue Piping design and analysis Stress intensity factors Stress indices vi . and for evaluating remaining fatigue life of plant designs. The work being done under EPRI’s SIF optimization program continues to establish the technical justification to allow for reductions in current Code stress intensification factors. Accurate methods of engineering for fatigue are important for cost-effective design. Examples include reductions in the inspection scope of postulated high. for root cause failures. Also. The report reviews existing test data and develops expressions for estimating the stress intensification factor. i. flexibility factors for accurately modeling the behavior of a tee connection in a piping analysis are presented. Branch connections are a major consideration in the design and evaluation of piping systems. vii . for each direction of moment loading.EPRI Licensed Material ABSTRACT This report was prepared under the auspices of the EPRI (Electric Power Research Institute) project on Stress Intensification Factor Optimization. The expressions presented in this report significantly improve evaluation of these connections. This report presents the results of an investigation into the flexibility and stress intensification factors of unreinforced fabricated tees (and other similar configurations). ................................................... 2-14 2....................7 FEA Results Validation ............................................................................................................................................................................................................3 Project Test Program .....1 In-plane bending of the branch ...................1 Nomenclature ..................2 Current Code Factors ..................................................................................................................................................9............................................................. 2-6 2...9..................................9................................4 Design of Test Specimens .. 2-15 2......................................4 In-plane bending of the run ................................. 2-20 ix .........8..............2 Out-of-plane bending of the branch .......... 2-15 2.............................................................3 Torsion of the branch .......................... 2-1 2.............................. 2-14 2.............................5 Out-of-plane bending of the run .......................... 1-1 1........... 2-1 2......................................... 2-19 2...........................................8....................................... 2-19 2............. 1-3 2 EXPERIMENTAL AND FINITE ELEMENT ANALYSIS .........................................6 Torsion of the run ...............................................................................5 Out-of-plane bending of the run .................................... 2-14 2....................................9........................................................9...........................9.............................................................. 2-4 2........................................................................................................................................................... 2-1 2.....9 Comparison of Test Data to FEA Results ..... 2-10 2......................8........................... 2-19 2................................................................................1 In-plane bending of the branch ...................... 2-14 2.6 Finite Element Analysis.................................................................... 1-1 1.....................2 Experimental Data ....................8............................................................ 2-4 2....................................8......... 2-12 2.... 2-16 2....2 Out-of-plane bending of the branch ............................................................... 2-4 2......................3 Torsion of the branch ...6 Torsion of the run ..............................................................8 Curve Fit Expressions......................1 Introduction ....................................................... 2-20 2.................EPRI Licensed Material CONTENTS 1 INTRODUCTION ....................................................................5 Testing Performance.......... 2-19 2..........8............4 In-plane bending of the run ........................ .............................................2 Branch Connection Configurations ........................................ 4-19 4.........................................5 FEA ResultsFlexibility of Run Pipe ...................................................................5 B Indices ....................................................................................... 4-15 4......................................................................... 4-18 4..................................6 Review of the Run Pipe Flexibilities . 6-1 6............................................................. 4-20 4..............2 Out-of-Plane Bending of the Run Pipe.................................... 4-1 4..5........................1 Introduction ..............................1 Stress Intensification Factors........................................................................................................................................................................................................................................................... 4-21 5 APPLICABILITY OF RESULTS ...........8 Comparison to Test Data ...................... 6-1 6....... 5-1 5...7 Sensitivity of Results to Accuracy of FEA .....................3 Flexibility Factors .. 3-1 4 INVESTIGATION OF FLEXIBILITY OF BRANCH CONNECTIONS ...............................................................................................................................................................................................................................5.......................1 Discussion ..............................................2 General Discussion.............................................................. 5-4 5...................................... 6-4 6...... 7-1 x ...4..... 4-6 4................................................................................................................................................. 4-17 4..... 6-4 7 REFERENCES ...................3 Torsion of the Run Pipe ........... 5-1 5..................................................1 Introduction ..1 In-Plane Bending of the Branch ...................................................................................... 5-1 5..4....................................... 4-19 4.......... 6-3 6......4...................6 Comparison to Present Code...............................2 Out-of-Plane Bending of the Branch ....................................EPRI Licensed Material 3 COMBINATION OF MOMENTS AND STRESSES........................5......................................................... 4-3 4............................................................................................................................................................................................................................................................... 4-1 4..................4 Applicability of Results .......................................................2 Combination Of Moments .......................................... 4-14 4......................... 6-1 6.................... 6-2 6......................................................3 Requirements for Applicability of SIF and Flexibility Expressions ....... 4-16 4............................................................................................................ 3-1 3..................................3 Torsion of the Branch.................. 4-13 4....... 5-6 6 CONCLUSIONS .............4 Limitations of Equations................... 4-1 4........................................................4 FEA ResultsFlexibility of Branch Pipe .........1 In-Plane Bending of the Run Pipe........................................3 Finite Element Analysis................................. .......................A-1 B CALIBRATION RECORD ..............................EPRI Licensed Material A MATERIAL CERTIFICATIONS ...............................................................................................................................................C-1 Overview of Appendix C ..................................................................................................B-1 C TEST DATA AND RESULTS .......C-1 xi ..................................................................................... ............................................................................................... 5-3 Figure 5-2 Flexibility and Stress Intensification Factors (Do/tn ≤ 100) Figure NC-3673.................................................................................................... 4-3 Figure 4-3 Loading Conditions......................2(b)-1 .............................................................................................................. 2-9 Figure 2-5 FEA Element Configuration ................... 2-10 Figure 4-1 Beam Model for Branch Loading ..........Figure NC-3673... 2-3 Figure 2-2 Test Configuration ...................................................................................... 2-5 Figure 2-3 Finite Element Mesh................................... 2-8 Figure 2-4 Loading Conditions....................................................................................EPRI Licensed Material LIST OF FIGURES Figure 1-1 Unreinforced Fabricated Tee Connection........................................................ 4-6 Figure 4-4 Beam Model for Run Pipe Loads................................................ 5-4 xiii ..................................................... 4-17 Figure 5-1 Branch Dimensions ...................................... 1-2 Figure 2-1 Markl Fatigue Test Configurations.......................................................... 4-2 Figure 4-2 Boundary Conditions ..................................................................................................2(b)-2............................................................................ .......................................... 2-19 Table 4-1 FEA Models .......................................................................................................................................................... 2-2 Table 2-2 Summary of Test Results... 5-8 Table 5-2 Comparison of FEA and Regression Equations for Flexibility Factors ......................................EPRI Licensed Material LIST OF TABLES Table 1-1 Experimental Stress Data for the Determination of C2 branch.............................................................................................................. 2-6 Table 2-3 FEA Models .............................................................................. 1-5 Table 2-1 Test/Experimental Results—Unreinforced Fabricated Tees ...........Unreinforced Fabricated Tees ................... r/R <0............ 2-17 Table 2-7 Test/Regression Analysis ResultsUnreinforced Fabricated Tees............... 2-18 Table 2-8 Comparison of Stresses to Experimental Data ......................... 4-7 Table 5-1 Comparison of FEA and Regression Equations for Stress Indices .......... 2-11 Table 2-5 Finite Element Analysis Results....................................... 2-13 Table 2-6 Test/FEA Results ....... 4-5 Table 4-2 Flexibility Factors ...........................................................................7........................................................................ 5-9 xv ............... 2-7 Table 2-4 Comparison of Stress Intensity Results to Studies by Others......... . 1-1 . reinforced or unreinforced. The lengths of run and branch pipe segments that form the fabricated tee are sufficiently long to preclude interaction effects between the tee junction weld and the welds that join the fabricated tee to other piping segments. the ratios of the branch pipe mean radii to the run pipe mean radii. or different. vary from slightly greater than one-tenth to a maximum value of one. there is no fillet radius to reduce stress concentration effects at the intersection of the run and branch segments of the tee and the weld joint is left aswelded. These uniform wall thickness tee connections satisfy piping design code rules for pressure reinforcement. This study investigates stress intensification factors and flexibility factors for unreinforced fabricated tees and other types of branch connections. These connections are termed “fabricated” because they are made by joining run and branch pipe segments with a full penetration weld at the junction of the segment surfaces. The nomenclature includes terminology used in the body of this report and the associated appendices. and the three outlets of the tee connection may be of equal.EPRI Licensed Material 1 INTRODUCTION Tee or branch connections are among the most complex of piping components to evaluate. For this study. They can be fabricated or forged.1 Nomenclature Figure 1-1 shows the configuration and applied moments for evaluation of stress intensification factors for unreinforced tee connections. diameters and wall thickness. Typically. The unreinforced connections are termed “unreinforced” because the pipe walls are not locally thickened or otherwise reinforced to provide additional resistance to moment loads. r/R. The two run segment outlets of the tee connection are of equal diameter and wall thickness. Stress concentration effects occur at or near the intersection of the branch and run pipe segments of a tee connection. 1. in3. inches R = mean radius of the run pipe. in-lb. in-lb. in-lb. in-lb. inches T = wall thickness of the run pipe. inches do = outside diameter of the branch pipe. at the intersection of the branch and run segments rp = outside radius of the branch pipe. if any. r = (do -t)/2. Cxx = stress intensity index at the juncture of the branch and run Cib = maximum stress intensity/(Mib/z) Cob = maximum stress intensity/(Mob/z) Ctb = maximum stress intensity/(Mtb/z) Cir = maximum stress intensity/(Mir/Z) Cor = maximum stress intensity/(Mor/Z) 1-2 . inches r2= correlation factor squared R/T = characteristic of the run pipe r/t = characteristic of the branch pipe r/R = characteristic of the connection t/T = characteristic of the connection 3 2 Z = approximate section modulus of the run pipe. inches d = mean diameter of the branch pipe. =πR T z = approximate section modulus of the branch pipe. Mtr1. Do/2. inches Mir1. Mtb = torsion moment on the branch. in-lb. Mor2 = out-of-plane bending moments on the run. R = (D o -T)/2. in . Mib = in-plane bending moment on the branch. Mtr2 = torsion moments on the run. inches r = mean radius of the branch pipe.EPRI Licensed Material Introduction Figure 1-1 Unreinforced Fabricated Tee Connection Do = outside diameter of the run pipe. inches t = wall thickness of the branch pipe. Mor1. =πr2t r2 = outside fillet radius. in-lb. Mir2 = in-plane bending moments on the run. inches D= mean diameter of the run pipe. Mob = out-of-plane bending moment on the branch. n3 = exponents for the SIF and Flexibility equations 1. = Stress resulting from in-plane moments So. Markl in 1952 [1]. out-of-plane bending moments on the run pipe itr = Stress Intensification Factor for through-run torsion moments on the run pipe kib = Flexibility Factor for in-plane bending moments on the branch pipe kob = Flexibility Factor for out-of-plane bending moments on the branch pipe ktb = Flexibility Factor for torsion moments on the branch pipe kir = Flexibility Factor for through-run in-plane bending moments on the run pipe kor = Flexibility Factor for through-run.4) A0 = constant for SIF equations B0 = constant for Flexibility equations n1. in the pipe (in.0. = Stress resulting from out-of-plane moments St.) Mb = Moment used in the FEA based on a nominal bending stress of 10 ksi. 1-1) 1-3 . = Stress resulting from torsion moments Ma = Moment used in the FEA based on a nominal bending stress of 10 ksi. radians Mi = In-plane moment on the branch or run end Mo = Out-of-plane moment on the branch or run end Si.C.) Ip = Moment of Inertia of the pipe (in. R/T>50 (eq. in the branch (in. n2.4) Ib = Moment of Inertia of the branch (in. out-of-plane bending moments on the run pipe ktr = Flexibility Factor for through-run.9(R/T)2/3 ≥1.R. lb.2 Current Code Factors Understanding the fatigue behavior of unreinforced fabricated tee connections begins with the work of A. lb. torsion moments on the run pipe φi-j = Rotation of point i with respect to point j. Markl fatigue-tested four equal size outlet unreinforced fabricated tee configurations and proposed the following expression for the Stress Intensification Factor for equal size outlet unreinforced fabricated tees: i = 0.EPRI Licensed Material Introduction Ctr = maximum stress intensity/(Mtr/Z) ii = Stress Intensification Factor for in-plane bending moments on the branch or run pipe io = Stress Intensification Factor for out-of-plane bending moments on the branch or run pipe iib = Stress Intensification Factor for in-plane bending moments on the branch pipe iob = Stress Intensification Factor for out-of-plane bending moments on the branch pipe itb = Stress Intensification Factor for torsion moments on the branch pipe iir = Stress Intensification Factor for through-run in-plane bending moments on the run pipe ior = Stress Intensification Factor for through-run. R/T>50 r/R ≤ 0.0. 1-5) C2(run) = 0. and Equation 1-3 is used with z=πr2t to evaluate the resultant moment on the branch side of the tee connection. R/T>50 (eq.9(R/T)2/3 ≥1. Later. In 1965. The Code Case is now incorporated in the sections of the Code on determination of moments and section modulus of tee connections.0. These rules use z=πr2ts. and Equation 1-5 is used with Z=πR2T to evaluate the resultant moments on the run sides of the tee connection. He derived the following expressions for C2 factors to be used in ASME Section III [3] Class 1 analyses: C2(branch)= 3(R/T)2/3(r/R)1/2(t/T)(r/rp) ≥1.5.5 (eq. it was noted by Schneider and others that the Code might not be conservative in determining SIFs for branch connections [12].8(R/T)2/3(r/R) Equation 1-4 is used with z=πr2t to evaluate the resultant moment on the branch side of the tee connection. instead of z=πr2t for evaluation of the branch side resultant moment. where ts is the lesser of T or i*t. although the data that validates the equation is primarily from tests of in-plane bending of the branch side of a tee.5 were developed by Rodabaugh in 1970 [2]. ANSI Code Case 53 [16] gave rules for evaluation of reduced branch outlet tee connections. R/T>50 r/R ≤ 0. The effect of the Code Case is to change Equation 1-1 to the following two equations: = 0. 1-2) ibranch = 0. but might not be conservative when applied to out-of-plane branch moments on a tee [1]. Markl noted that Equation 1-1 is conservative when applied to run moments. which Markl found to reasonably match the test results for equal size outlet unreinforced fabricated tees.EPRI Licensed Material Introduction This equation is for the stress intensification factor for in-plane bending.9(R/T)2/3(t/T) ≥1. 1-3) irun Equation 1-2 is used with Z=πR2T to evaluate the resultant moments on the run sides of the tee connection. 1-4 .5.5 (eq. Equation 1-4 was derived by conservatively curve-fitting the experimental stress data shown in Table 1-1. 1-4) ≥1. R/T>50 (eq. Stress indices for evaluation of reduced branch outlet tee connections with r/R≤0. Equation 1-1 is applied to the resultant moment on each of the three sides of the tee connection. 39 102% Reinforced Average = 26% The data shown in Table 1-1 was obtained by various researchers with strain gauges applied to various tee configurations.95 4.76 0.90 -24% Uniform wall 38 0.5 1.75 0.474 0.95 10 10.96 4.4 5. and bounds strain gauge data for a variety of reinforcement designs.8 0.69 0.18 2.51 8 10.19 3.93 2.35 61% Uniform wall 46. unlike Equation 1-1.97 2.37 22% Uniform wall 9.54 1.35 0.32 0.63 0.53 0.32 0.8 0.73 1.53 7 10.65 0.44 4 4.51 42% Pad 38 0. 1-5 .96 10.14 1.5 0.45 0. r/R <0.01 20% Pad 38 0.99 3.8 0.2 6.19 0.18 0.5 0.43 0.13 0.07 26% Pad 39 0.13 0.95 8.19 0.64 10% Reinforced 9.3 3.5 5.43 0.5 0.00 61% Uniform wall 9.93 6.69 0.5 11.18 0.49 1.55 7.76 0.85 13% Uniform wall 39 0.43 0.70 10% Saddle 38 0.8 2.45 0.5 0.67 0.81 20% Saddle 38 0.53 6 8.36 -22% Pad 9.25 0.5 0.8 0.28 -18% Weldolet 21.6 4.12 0.42 0.5 0.EPRI Licensed Material Introduction Table 1-1 Experimental Stress Data for the Determination of C2 branch.43 0.93 3.39 4% Uniform wall 38 0.96 3.35 0.8 0.00 -18% Uniform wall 38 0.53 0.32 0.04 39% Uniform wall 9.00 72% Uniform wall 9.5 0.18 0.32 0.42 0.76 0. The equation applies to tees with an outside radius at the juncture of the branch and run segments.33 4.53 0.42 55% Uniform wall 46.38 0.55 5 6. It is seen from Table 1-1 that the expression for C2(branch) is conservative by amounts that vary between two and one-hundred percent.63 0.18 0.5 0.47 50% Saddle 38 0. The data is for out-of-plane bending moments on the branch. which is primarily based on in-plane bending moment tests on the branch.48 7 7.7 R/T r/R t/T r/rp σ/(M/z) C2 branch Difference Type 12.73 3.36 7.77 55% Reinforced 9.5 0.30 2% Uniform wall 13.35 0.5 0.98 12 19.5 0. R/T>50 r/R ≤ 0. 1-6) based on later work by Rodabaugh and Moore [15] in which the C2(run) factor was correlated to finite element analysis results for twenty-five tee configurations. for example.4] for reduced branch outlet tees with r/R≤0.EPRI Licensed Material Introduction Equation 1-5 is based on one test point.5 (also referred to as branch connections) are one-half the Equation 1-4 and 1-5 C2 factors.5 (eq.5: i(branch)= 3(R/T)2/3(r/R)1/2(t/T)(r/rp) ≥ 2. and 1-8. R/T>50 r/R ≤ 0. for unreinforced fabricated tees with r/R≤0. Thus. The run i-factor has not been updated to reflect Equation 1-6. 1-8) In summary. Because Equations 1-4 and 1-5 are derived for tees with an outside radius of a minimum dimension at the junction of the branch and run segments.8(R/T) (r/R) ≥ 2. the current Code i-factors for branch connections are given by Equations 1-2.1. 1-7. The i-factors in the piping design codes [3.15(r/t)1/4 ≥1.5 (eq. 1-6 . 1-7) 2/3 i(run) = 0.1. 1-3. the Code requires that the ifactor values be doubled when such a radius is not provided.2(b). This expression has since been changed in the ASME Section III Class 1 Code to: C2(run) = 1.5.5 (eq. This requirement is contained in Note (6) item (h) in ASME Section III Figure NC-3673. R/T>50 r/R ≤ 0. 1 Introduction The experimental data and the results of the finite element analysis form the basis of this investigation. 2-1 . which were performed as a part of this study). 2.211 < t/T < 9 0.EPRI Licensed Material 2 EXPERIMENTAL AND FINITE ELEMENT ANALYSIS 2. The presentation in the tables of a certain number of significant figures is arbitrary. as for most of the tables in this report. Consequently. The tested tee connections have the following characteristics: 8.0 0.2 Experimental Data Table 2-1 lists unreinforced fabricated tee connection tests performed by various investigators to determine stress intensification factors (i-factors).5 < r/t < 50 0. This section discusses the available test data and describes the finite element analysis performed as part of the project. the number of significant figures used in the calculations is greater than indicated in the tables.125 < r/R ≤ 1.5 ≤ r/rp < 1. within r/R.0 < R/T < 50 0. The data in the table is sorted by increasing r/R and.0 Note that Table 2-1. by increasing R/T (except for the tests identified as “W/EPRI”. is from an Excel spread sheet. 95 2.237 0.132 2.42 0.146 4.193 4.99 8.213 2.99 8.132 2.50 4.99 8.88 3.95 3.06 1.00 1.020 2.500 6.365 0.50 20.97 1.23 14.00 10.99 10.00 12.188 0.237 0.96 3.05 1.100 0.132 2.40 41.00 8.15 0.750 10.625 10.252 0.00 1.000 1.50 4.23 1.100 0.138 20.50 0.50 4.99 8.99 10.661 0.132 2.237 0.00 0.053 0.801 4.98 4.00 1.00 1.50 22.237 0.224 2.00 1.15 49.00 1.450 0.203 0.95 2.058 0.79 7.50 18.375 1.00 1.265 0.50 0.239 0.500 4.950 4.237 0.00 1.00 1.44 22.416 0.87 0.032 6.50 35.99 8.58 12.200 2.84 0.00 1.613 0.132 2.625 10.50 4.04 0.50 4.34 8.93 7.73 18.00 1.132 2.79 7.237 0.132 2.99 8.239 0.95 2.199 0.5 2. ORNL-3 and ORNL-4 [17] indicate special test specimens.90 0.5 t 0.132 2.05 1.056 0.29 0.33 24.237 0.223 2.00 1.203 0.99 8.25 1.95 2.84 8.58 10.40 0.661 0.398 0.200 0.57 0.00 1.43 0.44 22.219 4.218 R/T 24.237 0.149 2.188 0.99 0.149 2.100 0.50 0.00 1.60 49.99 8.60 0.20 0.97 0.203 0.7 4.200 9.50 4.00 1.90 0.881 2.168 0.50 4.00 1.49 0.28 0.100 0.99 8.100 1.98 8.23 5.000 4.687 0.70 0. These 2-2 .500 4.064 0.173 5.12 0.250 0.132 2.75 --2.000 1.00 1.50 4.132 2.00 1. forged and machined to achieve.99 8.925 5.87 0.203 0.58 1.50 24.50 4.44 r/t 3.14 4.750 14.142 5.000 4.70 0.239 0.98 3.43 0.500 4. The tests identified as ORNL-1.99 14.69 0.881 2.132 2.237 0.99 8.219 r 0.89 16.188 4.00 1.043 2.50 10.132 2.23 0.99 8.00 1.18 0.00 1.132 2.50 4.132 2.73 1.375 0.142 5.00 8.500 4.188 6.000 8.200 0.625 8.75 0.79 41.237 0.237 0.625 T 0.950 9.32 0.99 8.188 do 1.219 4.149 3.79 49.00 1.15 3.152 6.05 1.00 4.50 1.92 0.132 2.50 4.132 2.99 34.99 8. ORNL-2.500 9.365 0. as closely as possible.99 8.50 9.00 1.00 12.180 5.34 3.50 4.375 0.11 36.67 0.99 8.50 4.290 1.237 0.00 41.82 1.50 4.97 1.375 0.7 10.45 3.500 4.35 0.5 2.950 1.132 9.99 8.053 0.50 9.00 1.900 2.00 1.946 0.7 4.35 r/rp Test iib 0.060 0.100 0.239 0.58 10.87 0.95 0.99 8.132 2.280 0.59 8.00 1.63 0.70 10.73 22.93 1.97 0.50 4.237 0.5 2.45 24.33 14.00 1.50 8.70 10.84 If several tests were conducted on a specific configuration.000 0.00 4.132 2.237 0.00 1.96 1.30 0.95 2.73 r/R 0.500 4.100 0.90 0.95 2.223 4.500 4.73 18.801 4.625 8.32 1.34 0.99 8.223 4.29 t/T 0.00 1.13 0.74 1.00 1.95 2.60 12.237 0.053 0.50 4. the individual test results are listed.200 2.00 1.142 10.223 2.EPRI Licensed Material Experimental and Finite Element Analysis Table 2-1 Test/Experimental Results—Unreinforced Fabricated Tees Test ORNL-3 ECR/EAW ORNL-4 Roarty Roarty Decock Roarty Roarty ECR/EAW ECR/EAW Decock ORNL-1 Pickett Decock Khan Khan Khan Moffat 4 Moffat 3 Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Blair Moffat 2 Moffat 1 Markl Markl Decock Markl Markl ORNL-2 W/EPRI-A W/EPRI-B W/EPRI-C W/EPRI-D Do 10.36 20.100 0.64 0.880 3.75 0.21 0.22 0.500 4.500 4.237 0.00 1.00 1.62 0.00 0.500 4.50 16.99 8.50 21.36 20.237 0.50 0.59 8.76 0.000 12.00 1.132 2.96 0.97 0.00 20.00 1.237 0.500 4.000 6.00 1.67 0.132 2.47 0.50 20.149 3.07 0.252 0.00 1.97 0.84 8.00 0.50 4. There are forty-nine entries in Table 2-1 for twenty-seven different unreinforced fabricated tee configurations.97 0.900 2.95 0.625 5.188 0.416 0.000 1.89 0.218 1.50 4.132 2.97 Test iob Test itb Test iir Test ior 0.65 0.85 0.00 1.07 R 4.35 0.63 10.100 0.84 1.237 0.000 2.218 1.00 1.99 8.132 2.18 0.00 1.73 22.35 0.132 2.42 1.95 2.07 0.94 2.99 6.132 2.500 20.041 9.881 2.94 0.97 0.75 12.38 0.50 8.7 10.50 5.625 12.50 4.70 4.99 8.500 10.90 0.132 2.100 0.239 0.03 0.99 8.00 1.237 0.290 1.73 18.250 0.44 22.07 0.13 0.99 0.000 1.50 4.95 2.00 1.70 4.500 4.00 22.053 0.40 41.05 0.29 0.237 0.51 3.00 1.851 0.99 8.500 4.250 0.237 0.95 2.625 8.224 2.750 10.398 0.219 4.95 0.50 9.042 4.50 4.237 0.132 2.03 0.00 1.99 8.193 5.500 4.58 12.475 6.00 4.237 0.98 2.237 0.00 1.00 1.95 2.75 0.00 22.322 0.500 0.78 28.925 5.79 41.130 1.561 0.020 2.050 0.851 0.99 8.69 2.237 0.218 1.95 2.00 4.73 2.237 0.75 10.34 0.50 6.53 0.500 4.180 5.450 0.00 1.050 0.500 4.99 41.50 8.40 0.99 8.00 1.11 0.237 0.90 5.21 0.265 0.237 0.000 1.00 20.450 0.78 11. the ninety degree intersection of two cylinders.95 2.00 1.00 41.237 0.95 2.69 2.00 1.132 2.29 0.132 2.79 49.98 0.132 2.475 4.200 9. Moffat 2. F. F. The tests identified as Moffat 1. An in-plane force. An out-of-plane force. branch nominal moment stress at the juncture equal to FL/z. They will be discussed in more detail later in this section. on a run end applies an inplane bending. Moffat 3 and Moffat 4 are equal size outlet unreinforced fabricated tees that were tested to determine their flexibility factors. An in-plane force. The specimens were instrumented with strain gages and are useful for validating analytical models. on the free run end applies an out-of-plane bending. one end of the run is fixed.25] contain additional studies that were not included in the forty-nine entries but were reviewed in the preparation of this report. References [22 . F. through-run nominal moment stress at the juncture equal to FL/Z. An in-plane force. An outof-plane force. In Position C. through-run nominal moment stress at the juncture equal to FL/Z. Figure 2-1 illustrates the end conditions and applied load directions used by Markl to experimentally determine i-factors. In Position B. As can be seen from the table. Markl performed many of the tests. one end of the run is fixed. F. F. Figure 2-1 Markl Fatigue Test Configurations In Position A. The test labeled Moffat 2 was instrumented with strain gages and analyzed with Finite Element Analysis (FEA) by others. on the free run end applies an in-plane bending.EPRI Licensed Material Experimental and Finite Element Analysis specimens did not have a weld at the intersection of the run and branch side segments. on the branch applies an in-plane bending. 2-3 . branch nominal moment stress at the juncture equal to FL/z. branch nominal moment stress equal to FL/z at the juncture. F. the branch end is fixed. on a run end applies a torsional branch nominal moment stress equal to FL/z. on the branch applies an out-of-plane bending. An out-ofplane force. The tests labeled W/EPRI are tests performed specifically for this project. EPRI Licensed Material Experimental and Finite Element Analysis In Positions B and C. results. The test specimens were labeled A. A summary is provided below. and other information are provided in Appendix C. 2. C.188 inches). The test specimens consisted of a run pipe of 8. which were not available in the literature. These tests corresponded to the test methodology followed by Markl. Each specimen was first tested to determine the load deflection curve for that particular specimen. of Decatur. etc. GA. See reference [26] for a description of the test equipment and methodology. The welds at the interface of the branch and pipe were normal full penetration in an as-welded condition. 2. The tests followed the standard approach corresponding to Markl type tests [13] [21]. These test configurations do not provide for the determination of i-factors for through-run torsional moments. and D. The tests are identified as W/EPRI-A. B. which appears later in this section. out-of-plane ( Position B) fatigue tests were performed on four specimens made of carbon steel. with a branch pipe OD of 2.5 inches (t = 0. These positions are used to determine branch side i-factors. The purpose of this test program was to obtain some specific data for out-of-plane bending for values of d/D. The measured distance that is dependent on the installation is included in the test data. 2.5 Testing Performance The testing was performed at the Ohio State University. The test distance from the load point to the surface of the pipe (~46 inches) varies slightly for each test specimen. For an equal size outlet tee (Z=z). In Position A the load path is solely through the run. The branch was located at the center of the run pipe and had a length of 30 inches.. and D in Table 2-6. d/t. positions B and C are equivalent.4 Design of Test Specimens Four specimens were manufactured by Wilson Welding Service. The test methodology is described in detail in reference [26]. B. C.3 Project Test Program As part of this project.065 inch). The test data. The load deflection curve was used to determine the stiffness of each specimen and the load applied to the specimen by a given amount of displacement. The tests were displacement controlled cantilever bending tests. The length of run pipe was 32 inches.. The load deflection curves were determined for loading in both positive and negative loading directions (down and 2-4 . This position is used to determine i-factors for through-run moments. the load path is through the branch.625 inches outside diameter (OD) (T = 0. Inc. The cycles to failure were counted to determine the fatigue life. Table 2-2 provides a summary of the test data. Failure was detected when throughwall cracks formed and water leaked through the cracks.EPRI Licensed Material Experimental and Finite Element Analysis up). Each specimen was then fatigue tested by cycling the deflection in both directions of loading by a controlled amount. Figure 2-2 Test Configuration 2-5 . Figure 2-2 shows the basic test configuration. EPRI Licensed Material Experimental and Finite Element Analysis Table 2-2 Summary of Test Results Test L N Nominal Stress.000 N-0.5 459 22. 2. S i (inches) (cycles to failure) (+/.0 0. and S = M/z.2 3.94 ≤ r/rp < 1.8 3.88 D 46.6 Finite Element Analysis A finite element investigation of tee intersections was performed for the purposes of investigating the: • differences in stress intensities for each direction of loading • relationship between stress intensity and the various geometric parameters • relationship between experimentally determined i-factors and stress intensities Finite element analyses were performed for the thirty-six tee configurations listed in Table 2-3.0 0. where N = cycles to failure.) (note 1) A 46.2/S.0 < r/t < 75 0. z is based on nominal dimensions of the branch.5 923 16.ksi. The tee connections selected for analysis include the configurations of Table 2-1 with the following characteristics: 8.9 3.875 754 18.2 < t/T ≤ 2.1 < r/R ≤ 1.84 (note 1) The value of i is calculated from i = 245.0 < R/T < 50 8.45 C 46.15 B 45.5 1816 14.1 3.0 2-6 . 900 2.473 9.485 24.0 100.186 0.050 0.706 9.05 1.0 16 Decock 10.211 0.286 0.00 Configurations from Table 2-1 with r/t < 8 were not selected for finite element analysis because of r/t limitations of shell models.01 1.22 6.420 7.00 1.00 0.500 0.945 2.0 19 Wais 10.063 0.749 92.2 25.71 0.0 8 Decock 10.000 1.0 83.17 1.07 99.25 99.0 34.375 99.900 9.0 2 Decock 3 Wais(Roarty 10.346 0.000 24.0 9 Wais 10.31 5.43 9.222 0.509 17.213 4.843 0.860 4.98 0.294 0.000 1.75 t (in.294 0.00 33.81 33.01 44.0 34 Wais34 10.250 0.000 1.527 0.700 0.0 87.000 1.000 17.00 5.129 0.549 9.) 9.0 29 Wais 10.706 9.839 28.900 9.00 6.865 9.0 50.7 100.100 0.0 23.025 0.0 20.00 99.25 8.145 8.750 0.29 2.088 do/Do t/T Do/T do/t 0.600 9.871 0.0 43.000 0.075 0.) 0.199 0.1 84.353 0.000 1.0 28 Wais 10.100 0.325 0.882 9.973 0.000 1.0 31 Markl 10.00 10.00 0.942 5.0 30 Decock 10.17 24.075 0.527 0.345 17.18 1.222 0.02 0.0 15 Pickett 10.178 0.050 0.3 100.800 9.031 6.00 17.00 1.000 0.473 9.500 9.0 22.0 25 Blair 10.038 0.07 1.527 0.0 19.000 1.900 9.50 2.1 25.500 0.000 33.633 0.01 99.750 0.200 0.599 85.750 0.683 0.100 0.000 1.503 2.00 0.3 100.98 21.0 19.0 100.118 0. The configurations labeled Moffat 1 and Moffat 2 were not analyzed because of their geometric similarity to cases titled Blair and Markl.0 13 OSU2 10.250 99.900 99.1 84.900 9.00 25.00 44.00 10.120 0.750 99.03 1.00 10.0 100.0 84.100 0.0 100.0 11 Wais 10.603 0.900 9.0 74.05 55.0 20.800 4.50 7.500 99.294 0.00 0.865 9.000 73.0 26.101 0. Wais or W/EPRI.899 9.00 10.0 45.96 0.822 9.064 0.1 100.00 10.0 23 Markl 10.68 8.290 0.500 0.0 26 Wais 10.881 9.000 0.0 24 Markl 10.910 9.9 100.778 9.000 1.00 99.900 9.0 10 Wais 10.900 1.00 0.000 1.000 83.500 0.344 4.00 0.0 36 Wais36 T (in.663 D/T d/D d/t 49.451 0.000 1.900 9.0 10.) 0.0 150.0 12 ORNL-1 10.2 74.400 0.431 0.100 0.881 9.900 9.226 1.050 0.0 100.0 100.491 34.000 1.33 0.2 25.0 4 ECR/EAW 10.100 0.03 83.100 0.900 d (in.0 100.0 6 Wais 10.375 0.50 3.900 1.000 99.178 0.500 0.) 1.764 22.6 29.948 0.0 84.778 9.0 19.522 0.0 20 Khan 10.100 0.33 17.2 20.900 9.90 3.0 22.0 27 Markl 10.500 0.0 100.200 0.5 99.0 5 Wais 10.0 17 Wais 10.223 19.00 0.3 19.706 9.01 49.625 0.00 5.233 18.07 83.451 0.00 82.199 0.475 3.5 58.702 57.00 49.0 50.0 21 Khan 10.0 35 Wais35 10.EPRI Licensed Material Experimental and Finite Element Analysis Table 2-3 FEA Models Model Do (in.75 99.473 9.250 0.706 9.00 0.600 9.242 0.5 100.00 0.01 19.0 34.801 9.688 0.625 99.7 100.00 10.53 0.120 0.875 50.0 100.823 3.0 1 ORNL-4 10.000 1.97 0.880 7.0 20.0 100.880 9.00 0.344 0.080 0.13 0.18 73.294 0.782 9.98 73.119 0.0 34.375 0.900 9.0 50.135 0.00 99.356 8.00 5.00 7.) 10.16 0.111 2.865 9.896 0.135 0.801 9.100 0.000 83. The configurations selected from Table 2-1 were supplemented with additional configurations titled OSU1.2 74.875 0.75 0.931 6.7 66.100 0.100 do (in.38 7.00 99.00 10.400 0.450 2.069 0.497 65.950 4.50 7.295 2.0 100.48 0.100 0.00 10.600 0.67 0.500 0.000 1.140 0.121 0.100 0.00 33.88 99.2 17.0 38.8 100.218 0.000 1.000 21.882 9.25 99.00 99.0 45.090 0.100 0.120 0.97 0.7 100. OSU2.000 1.289 37.53 4.75 1.0 18.000 55.373 0.710 9.635 17.46 0.400 0.549 9.48 98.250 0.000 1.822 9.118 0.0 32 ORNL-2 10.50 7.430 42.0 D (in.00 10.000 1.000 44.63 0.207 0.0 56.00 2.125 19.0 7 OSU1 10.753 149.875 99.0 18 Wais 10.0 22 Wais 10.) 1.00 33.22 2.188 8.0 100.627 9.197 16.290 0.925 4.00 99.713 6.275 0.320 1.750 0.100 0.42 2.0 34.00 99.3 93.450 7.638 0.800 0.0 45.222 0.21 0.425 7.98 1.0 35.900 9.0 56.500 0.768 0.5 100.135 0.00 10.900 9.075 0.625 0.00 5.75 6.0 33 W/EPRI 10.119 0.100 0.8 34. Configurations OSU1 and OSU2 were tested for reinforcement and elbow effects under other research efforts 2-7 .0 14 Wais 10.750 0.07 2.000 1.111 0.0 19.247 49.900 9.00 99. 5 inches from the centerline of the run to the end of the branch. quadrilateral shell elements composed of four triangular elements to achieve good symmetry of results. In the vicinity of the juncture.000 elements and the element aspect ratios are all less than four. The finite element models used four node. d/t. or about four times OD. etc. Finite element analyses were conducted with COSMOS version 1. Figure 2-3 shows a representative finite element mesh. The configuration labeled W/EPRI corresponds to the test specimen used in the tests associated with this investigation. Figure 2-3 Finite Element Mesh The total run segment length was set at 39 inches. 3 and 4 experimental models. 2-8 . the FEA models were standardized on an OD of ten inches. The other parameters were calculated based on the ratios of Table 2-1.EPRI Licensed Material Experimental and Finite Element Analysis for this EPRI program. This was done to match the ORNL-1. 2. d/D. most of the element aspect ratios are close to two and all are less than three. The branch segment length was set at 19. For simplicity.75 [10]. as the test specimens. The models typically consist of over 5. The dimensions were selected to yield the same values of D/T. or about two times OD. Configurations titled Wais were included to enhance the scatter of the data. T/2. and moments in the three orthogonal directions were applied at the branch or other run end (Figure 2-4). special care must be made when specifying the elements at the branch-pipe intersections. For branch moments this represents the upper bound for the stresses resulting in the connection. t/2. are neglected. E. 2-9 . such as A in Figure 25. The nodal stresses used are either at the outside nodes on the element in the branch and the run at points Bo and Ro or are on the inside of the element in the branch and the run at points Bi or Ri. The stresses at the node at the intersection of the branch and pipe are unreliable according to studies performed by G. Similarly the elements in the branch near the intersection are sized such that they have a length 1/2 the thickness of the run (pipe).EPRI Licensed Material Experimental and Finite Element Analysis The models were fixed at one run end. The element length in the run pipe is equal to one half the thickness of the branch. Since shell elements are used. The methodology accepted by the PVRC is to size the elements in the run (pipe) near the intersection with a length of 1/2 the thickness of the branch. The element length in the branch is equal to one half the thickness of the run pipe. The stresses at other points. Figure 2-4 Loading Conditions When modeling branch connections using shell elements. Widera at Marquette University for the Pressure Vessel Research Council (PVRC) on nozzle/vessel intersections. O. the nodes represent the midsection of the branch or the pipe. This is shown in Figure 2-5. EPRI Licensed Material Experimental and Finite Element Analysis Figure 2-5 FEA Element Configuration 2. Table 2-4 compares the stress intensity results of this study to the results obtained by others for these configurations. 2-10 . These configurations were experimentally tested with strain gauges and FEA analyzed by others [11]. ORNL-2 and ORNL-4 are configurations carefully manufactured to replicate the ninety degree intersection of two cylinders.7 FEA Results Validation The cases titled ORNL-1. 5 6.r/R=0.r/rp=0.r/R=1.0 15.8 0.7 out-of-plane run 1.0 run torsion 1.5.9 10.95) 2-11 .2 branch torsion 2.5.8 branch torsion 15.5.r/R=0.6 18.1 out-of-plane run 3.1 10.r/rp=0.0 10.1 1.6 2.t/T=0.5 FEA Strain Gauge FEA in-plane branch 12.1 18.5 15.3 2.2 out-of-plane branch 4.5 5.8 5.5 2.3 37.6 branch torsion 1.5 7.5 ORNL-1 (R/T=49.8 6.EPRI Licensed Material Experimental and Finite Element Analysis Table 2-4 Comparison of Stress Intensity Results to Studies by Others This Study ORNL Study FEA Strain Gauge FEA in-plane branch 11.8 5.9 out-of-plane branch 37.32.9 run torsion 12.99) ORNL-2 (R/T=49.6 in-plane run 5.9 12.t/T=0.8 8.4 3.5 in-plane run 2.7 4.2 35.5.8 17.2 out-of-plane branch 16.3 1.13.t/T=1.6 15.1 0.1 7.1 out-of-plane run 1.5.5 2.99) (R/T=49.r/rp=0.8 ORNL-4 FEA Strain Gauge FEA in-plane branch 3.1 14.8 11.7 4.8 in-plane run 8.0 6.0 3.2 2.7 run torsion 7. 0.EPRI Licensed Material Experimental and Finite Element Analysis 2. It should be noted that the equations from the regression analysis all have a lower limit of 1. Also included in this table is the percentage difference between the regression analysis and the FEA analysis.8 Curve Fit Expressions Table 2-5 lists the FEA stress intensities and the results from equations developed from regression analysis for the six loading conditions. The results are summarized following the table. 2-12 . 94 0.89 -26 4.85 -13 1.65 3.49 7.32 6.61 -16 3.84 0 10.7 49.56 8.00 1.76 -10 51.50 24.52 15 34.99 0.66 10.12 1.5 49.12 0 10.928 .75 0.97 -2 7.98 0.49 4.10 1 2.= 12 r2 = 0.99 0.96 0.55 6.15 1.14 1.99 -25 7.15 15.58 8.85 1 1.73 49.10 8 2.20 -14 1.53 -25 4.23 1 11.00 1.84 2.99 42.68 5.35 7.98 0.99 21.83 4.49 0 6.06 7.13 0.91 6.75 0.04 5 5.10 -3 1.79 -3 6.00 -11 2.00 -29 2.70 0.85 -17 13.00 -18 15.54 9.49 -8 1.48 0.05 -13 20.51 0.42 6.29 0.40 18 1.50 21.56 -3 3.87 18 Maximum = 19 Minimum = -19 Average = 0 Std Dev.EPRI Licensed Material Table 2-5 Finite Element Analysis Results Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Configuration ORNL-4 Decock Wais ('Roarty ECR/EAW Wais Wais OSU1 Decock Wais Wais Wais ORNL-1 OSU2 Wais Pickett Decock Wais Wais Wais Khan Khan Wais Markl Markl Blair Wais Markl Wais Wais Decock Markl ORNL-2 W/EPRI WAIS WAIS WAIS R/T 24.50 11.10 8 3.99 0.92 6.59 33.93 0 8.00 -26 2.04 1.94 -17 10.931 Load Case 3 Load Case 4 Load Case 5 Load Case 6 Torsion In-Plane Moment Out-of Plane Torsion on Branch on Run Pipe on Run Pipe on Run Pipe C-fea C-Regr % DIF C-fea C-Regr % DIF C-fea C-Regr % DIF C-fea C-Regr % DIF 1.50 r/R 0.50 -18 11.99 0.29 65.63 0.31 -1 34.77 2 12.10 6 2.34 0.04 5 8. r 2 = "goodness of fit" r/rp 0.15 12.93 5.10 9 3.68 2.99 0.66 -18 14.5 49.97 -7 6.01 1.13 11.00 -20 4.5 22.90 42.27 37.69 0 1.03 1.37 2.43 38.995 r2 = 0.98 6.29 2.74 7 5.50 32.60 1.33 5.91 11.25 -7 11.75 -18 9.67 3.02 10 6.00 1.95 0.5 r/t 9.88 9.61 7.32 14.6 36.74 -1 8.28 0 1.80 49.87 -28 38.99 0.12 -1 12.5 22.07 9.4 49.04 -6 1.4 49.78 46.25 0.95 -18 14.62 6.20 5.19 16 5.6 12.75 0.64 12.89 12.67 6.= 18 Std Dev.81 3.35 1.94 10 10.00 1.00 0.82 3. Std Dev = Standard Deviation 2.68 4.5 24.45 6.24 49.00 -13 2.93 1.68 1.93 3.98 8.50 2.38 -16 3.99 0.85 12.59 11.02 1.95 -18 13.43 0.50 8.10 -22 4.46 13 7.69 4.96 10.84 3.63 7.3 9.5 24.62 2 5.50 8.98 0.51 2.5 9.45 1 2.5 16.03 4.73 10.19 -12 1.40 5.08 1.44 3.5 41.76 2.63 -14 2.25 0.24 15 10.39 2.26 25 27.50 5 9.5 12.99 0.89 11.85 12 26.95 0.43 -19 6.30 18 3.57 6 37.83 7.82 6.97 -1 9.9 16.32 4.91 7 1.21 -3 4.42 6 9.38 4.5 16.18 1.28 3 12.91 -28 5.20 0.5 49.66 18 5.94 -14 12.83 7.50 0.86 3.95 0.99 10.02 1.68 12.74 4.54 14 4.64 9.99 0.00 1.26 6 36.86 22 13.03 5.00 -16 12.98 8.79 13.14 -6 3.32 -2 11.41 -7 7.58 1 13.56 2 4.73 3.33 -33 8.39 19 2.83 49.14 9.75 0.8 49.00 1.46 5.00 27.75 39.04 4.99 0.59 9.95 0.60 10.50 0.16 10 16.10 8 3.37 3 10.71 10.10 4.42 3.68 10.30 21 3.22 -6 6.81 20 10.52 8.85 2.12 -9 1.92 3.00 16.50 5.43 17 1.55 3.99 5.89 0.18 0 10.00 1.62 20.40 1 6.97 -27 6.97 3.68 0.13 -2 5.50 49.14 19 1.6 49.02 1.29 -15 1.10 10 2.61 -29 17.96 -23 8.45 6.04 18.74 -14 10.98 0.95 6.44 5 11.00 17.30 18 1.62 15.96 0.33 -14 3.12 4 8.97 0.0 9.80 9.24 2.93 -32 10.51 5.77 5.5 49.69 34 37.36 16.30 5 15.97 5.32 5.80 0.79 11 5.44 16 11.08 19 7.87 0.98 0.95 0.39 19 5.42 1.50 18.69 0.889 Load Case 2 Out-of Plane Moment on Branch C-fea C-Regr % DIF 4.54 3.92 -2 10.01 2.03 20 35.97 0.00 0.37 6.01 1.52 1 6.10 14 3.99 0.22 0.84 0 1.32 35.97 0.64 -1 2.09 -18 7.51 9.29 2 5.03 5 Maximum = 27 Maximum = 18 Maximum = 10 Maximum = 19 Minimum = -29 Minimum = -16 Minimum = -7 Minimum = -19 Average = -7 Average = -5 Average = 3 Average = -2 Std Dev.37 4.52 6.39 11.50 0.96 -7 1.12 6.00 -22 2.29 12.01 7 1.96 0.57 -6 3.71 27 6.77 4.50 0.88 10.86 -1 29.52 5.02 -6 9.88 t/T 0.56 2.= 19 r2 = 0.97 0.17 2 3.19 -9 3.97 11.36 40.92 -13 9.69 1 7.53 13 3.41 17.88 Notes: 1.33 2.15 -13 5.10 7 3.63 0.20 4 2.= 13 r2 = 0.84 0.00 -14 3.28 3.0 27.00 1.03 1.00 1.96 4.59 4.76 19.32 54.78 -12 5.21 3 11.95 0.00 1.55 10.99 1 1.10 6 2.48 16 2.79 6.01 1.00 8.83 12 20.10 2 6.47 17 8.38 0.41 4.36 -18 7.87 11.59 1 13.28 -26 7.06 -10 2.59 -4 8.41 41.00 1.95 9.35 1.77 28.23 0.17 -1 3.54 41.75 8.49 0.38 49.5 41.99 0.33 16 6.11 19 10.58 12.90 1.78 -25 11.24 -3 11.10 9 4.51 4.82 11.25 0.50 8.0 36.45 0 12.83 -1 2.79 7.77 2.59 36.99 0.16 5.19 17.36 32.12 -6 3.90 2.83 6.13 -5 7.5 49.13 9.69 5.35 0.32 5.63 0.05 4.93 4.00 0.57 -10 7.59 17.64 -34 7.89 -6 1.15 3.95 2.54 11.26 -8 1.99 7.62 22 7.51 1.28 5.00 1.71 -1 4.32 8.867 r2 = 0.= 4 Std Dev.17 2.49 2.99 0.47 20 16.15 1.4 41.0 10.21 8 1.50 74.72 -9 3.76 0.00 -8 5.93 -19 6.95 0.90 1.74 13 7.42 7.84 -8 2.10 8 2.94 -26 7.78 22 Maximum = 34 Minimum = -34 Average = -1 Std Dev.13 3.21 0.24 30.38 2.00 1.68 7 5.25 -5 1.56 -14 73.00 1.25 8.81 8.74 -17 30.93 3.51 3.52 -6 16.18 -6 2.5 49.61 10 1.90 12.11 5 1.80 4.50 49.17 3.81 -1 18.24 5.98 2 8.76 -10 1.97 0.11 9.81 3.63 0.28 1.75 -26 10.75 2.35 10.55 5.63 -14 8.00 1.13 13.50 49.89 14.02 1.97 -12 5.97 -11 1.08 1.53 5.42 16 5.54 10 7.68 -19 1.32 1.0 16.95 0.08 10.34 3.= 8 Std Dev.42 2 1.38 0.6 49.93 -26 6.07 1.00 1.17 1.910 r2 = 0.97 12.59 1.03 16.52 19.50 1.84 18.05 17 5.00 1.00 1.5 49.60 0.99 Load Case 1 In-Plane Moment on Branch C-fea C-Regr % DIF 3.85 -10 5.5 49.82 -7 3.29 -19 14.60 0.40 0.31 -4 2.51 22.35 13.00 1.05 2.22 17 11.02 10 15.51 -2 1.53 -2 10.5 49.58 2 3.43 -11 1.25 8 2.95 0.25 1.05 -5 14.51 8.50 0.82 3.00 1.09 1.51 -9 1.81 6.75 0.70 3. 70 (R/T) (r/t)-0.EPRI Licensed Material Experimental and Finite Element Analysis 2.8.137 (r/t)0.0 (eq.482 (r/R).5 (r/R)2.8.558 (r/R)0.1 In-plane bending of the branch ≥ 1.49 (eq.97 (R/T)-0.867 2.28 (r/R)-(r/R)4) (R/T)1.05 (r/t)-0.0 (eq.387 (r/R)0.241 2-14 ≥ 1.8. 2-2) Average difference between the FEA and Equation 2-2: -1% Maximum difference between the FEA and Equation 2-2: 34% Standard deviation of difference between the FEA and Equation 2-2: 19% Goodness of fit: r2 : 0.931 2. 2-1) Average difference between the FEA and Equation 2-1: 0% Maximum difference between the FEA and Equation 2-1: 19% Standard deviation of difference between the FEA and Equation 2-1: 13% Goodness of fit: r2 : 0. 2-4) .8.889 2.56 (1.03 (R/T)1.0 Cib = 1.409 (r/t)-0.1 ≥ 1.0 (eq.4057 ≥ 1.2 Out-of-plane bending of the branch Cob = 2. 2-3) Average difference between the FEA and Equation 2-3: -7% Maximum difference between the FEA and Equation 2-3: 29% Standard deviation of difference between the FEA and Equation 2-3: 18% Goodness of fit: r2 : 0.4 In-plane bending of the run Cir = 1.3 Torsion of the branch Ctb = 1. 6 Torsion of the run Ctr = 1.73 (R/T)-0.910 2.528 (r/R)1. 2-6) Average difference between the FEA and Equation 2-6: -2% Maximum difference between the FEA and Equation 2-6: 19% Standard deviation of difference between the FEA and Equation 2-6: 12% Goodness of fit: r2 : 1.8.28 (r/R)-(r/R)4). the stress intensity increases.42 ≥ 1. peaks at a value of about 0. These terms were developed by examining the data for those cases where the parameters are held constant (R/T = r/t = 49.5 Out-of-plane bending of the run Cor = 1. for out-of-plane bending. and then decreases.0 (eq.5). This equation includes the terms: (1. The expression (1.8%.6093 ≥ 1.0 (eq.28 (r/R)-(r/R)4) was developed by curve-fitting these data.6. Equation 22.995 2.6%.21 (R/T)-0.237 (r/t)0. 2-5) Average difference between the FEA and Equation 2-5: 3% Maximum difference between the FEA and Equation 2-5: 10% Standard deviation of difference between the FEA and Equation 2-5: 4% 2 Goodness of fit: r : 0. The percentage difference between the data points and the curve fit was 2. 2-15 .0473 (r/t)0.EPRI Licensed Material Experimental and Finite Element Analysis Average difference between the FEA and Equation 2-4: -5% Maximum difference between the FEA and Equation 2-4: 18% Standard deviation of difference between the FEA and Equation 2-4: 8% 2 Goodness of fit: r : 0. The reason for this is that. differs from the other equations. and a standard deviation of 2.8. while all of the other stress intensities monotonically increase as r/R increases.8% on the average with a maximum difference of 10.000 The form of the regression equation for out-of-plane bending of the branch.5433 (r/R)0. 2-16 . (Note that “torsion of the run” is not included because there is no test data available. Table 2-8 summarizes the results that were obtained.) The ratios of i/FEA results and i/regression equation results are also provided. and regression equation results for the various tests listed in Table 2-1.9 Comparison of Test Data to FEA Results Tables 2-6 and 2-7 list the experimental.EPRI Licensed Material Experimental and Finite Element Analysis 2. FEA. 42 0.69 0. Note 3.29 t/T 0.95 2.35 0.44 22.05 1.49 0.49 0.50 9.00 1.99 0.99 8.00 12.00 1.75 11.99 14.99 8.99 8.15 5.33 0.93 7.84 10.25 1.97 0.95 0.97 3.55 1.56 10.56 Average = 0.95 0.90 0.00 1.43 5.05 7.44 22.50 0.34 5.84 1.23 0.97 0.32 1.95 2.50 24.99 8.94 2.82 4.30 0.68 1.00 1.98 8.38 8.99 8.00 1.44 22.05 6.99 8.41 2.50 18.50 4.44 0.04 5.73 r/R 0.0.00 1.49 0.00 1.50 35.21 0.50 8.04 0.50 9.99 8.98 0.47 0.95 0.42 0.21 0.18 0.42 0.00 1.00 1.84 8.90 11.21 0.00 1.99 8.32 5.99 8.50 0.67 8.50 9.95 2.00 1.58 10.40 41.99 36.79 41.99 8.00 41.00 1.00 1.73 18.87 6.00 1.62 6.96 3.95 2.60 12.00 1.12 0.C.96 0.00 1. Out of Plane Bending of the Branch Test iob FEA Cob Testob/Cob Torsion In-plane Bending of the Branch of the Run Test itb FEA Ctb Testtb /Ctb Test iir FEA Cir Testir/Cir Out of Plane Bending of the Run FEA Cor Testor/Cor Test ior 0.62 0.00 1.85 0.38 0.47 6.23 5.45 3.58 12.41 0.59 8.00 1.50 0.71 0.73 6.29 0.00 1.43 0.49 0.95 2.50 8.22 0.88 3.00 1.69 0.99 8.46 0.24 2.00 1.00 12.99 0.13 0.50 9.29 0.03 13.21 0.00 1.00 22.51 2.73 22.49 0.99 8.43 0.00 1.37 0.82 0.49 0.73 18.50 8.73 0.58 10.92 0.95 2.76 0.87 0.85 4.50 16.58 0.00 1.50 4.49 0.49 0.47 0.74 1.42 Average = 0.47 0.28 5.97 Average = 0.64 11.98 3.49 0.06 1.50 22.53 5.69 2.60 0.98 2.37 0.35 0.42 0.00 1.50 0.84 0.00 1.00 1.99 8.95 2.65 0.90 20.00 1.00 1.44 0.50 5.00 1.93 1.43 0.42 1.79 41.79 7.95 3.98 0.95 2.99 8.99 8.78 11.00 0.75 0.36 0.99 6.99 8.54 1.23 14.79 49.63 0.45 0.94 0.51 0.13 0.50 9.57 5.03 11.99 8.00 1.29 0.03 5.49 0. Average values are only from data with r/t>8.84 8.35 In-plane Bending of the Branch r/rp Test iib FEA Cib Testib/Cib 0.00 1.58 12.79 7.22 0.99 8.97 1.59 8.00 1.Unreinforced Fabricated Tees Ref.00 1.51 Note 1: W/EPRI-A.95 2.60 49.00 41.42 1.33 14.EPRI Licensed Material Table 2-6 Test/FEA Results .73 18.30 5.78 28.95 2.99 8.70 8.00 1.52 0.11 0.50 21.34 0.00 1.99 8.99 8.24 0.04 4.05 1.49 0.15 3.00 1.34 2.99 8.90 0.31 0.00 1.39 0.56 10.70 0.00 1.99 10.33 24.99 10.75 0.99 8.56 10.54 .97 0.95 0.03 0.22 0. Corresponding references can be found in Section 7.44 0.19 5.00 0.99 8.99 8.49 0.55 0.98 4.55 0.67 0.11 8.99 34.89 0.99 8.00 1.15 49.73 22.18 0.44 r/t 3.23 1.10 0.00 1. 11 18 11 19 19 7 19 19 18 19 19 18 7 11 6 7 8 8 8 21 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 21 21 1 1 7 1 1 11 Note 1 Note 1 Note 1 Note 1 Test ORNL-3 ECR/EAW ORNL-4 Roarty Roarty Decock Roarty Roarty ECR/EAW Roarty Roarty ECR/EAW Decock ORNL-1 Pickett Decock Khan Khan Khan Moffat 4 Moffat 3 Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Markl Blair Moffat 2 Moffat 1 Markl Markl Decock Markl Markl ORNL-2 W/EPRI-A W/EPRI-B W/EPRI-C W/EPRI-D R/T 24.75 6.40 0.20 0.00 1.50 0.79 49.73 7. and D correspond to the test configurations used for this report.B.96 1.60 Average = 0.45 Average = 0.52 6.00 1.00 1.55 0.00 1.45 0.99 8.95 2.49 0.35 0.51 0.50 1.00 1.90 0.95 2.35 13.45 24.05 1.51 0.00 1.42 0.69 2.90 0.59 2.00 22. Note 2.34 8.97 0.97 0.40 5.95 2.87 0.97 0.00 1.05 0.89 16.10 0.39 3.76 0.51 0.99 8.49 5.00 1.14 4.99 41.58 1.18 0.40 41.00 1.36 20.37 0.48 1.00 0.95 2.36 20.40 5.90 1.95 0.95 0. 07 1.0.13 0.00 1.12 0.65 4.17 0.90 0.29 Average 0.96 0.75 8.34 2.33 14.58 0.58 10.99 8.99 8.69 2.EPRI Licensed Material Table 2-7 Test/Regression Analysis ResultsUnreinforced Fabricated Tees Ref. Test 11 ORNL-3 18 ECR/EAW 11 ORNL-4 19 Roarty 19 Roarty 7 Decock 19 Roarty 19 Roarty 18 ECR/EAW 18 ECR/EAW 7 Decock 11 ORNL-1 6 Pickett 7 Decock 8 Khan 8 Khan 8 Khan 21 Moffat 4 21 Moffat 3 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 1 Markl 5 Blair 21 Moffat 2 21 Moffat 1 1 Markl 1 Markl 7 Decock 1 Markl 1 Markl 11 ORNL-2 Note 1W/EPRI-A Note 1W/EPRI-B Note 1W/EPRI-C Note 1W/EPRI-D R/T 24.95 0.40 2.24 0.59 0.46 0.23 5.00 1.75 Average Average = 0.00 1.10 Average 0.00 1.50 18.35 0.29 0.60 0.28 2.532 Average = 0.00 1.54 0.75 8.40 41.96 0.57 0.58 10.00 1.35 0.99 8.42 4.23 1.16 12.42 4.52 0.10 5.99 0.73 5.34 0.15 2.45 24.58 12.50 0.48 1.43 2.99 8.00 1.00 1.05 3.42 4.00 1.00 22.34 8.99 0.00 1.97 0.97 0.50 0.69 2.84 8.50 9.84 1.00 1.55 0.99 8.17 1.00 41.00 1.79 49.99 8.50 24.46 3.32 1.00 1.60 1.00 1.00 1.69 0.99 34.29 t/T 0.99 8.50 8.00 1.42 4.95 0.42 4.50 4.13 0.23 0.42 0.00 1.23 14.00 1.50 9.528 0.28 Out of plane Bending Torsion In-plane Bending Out of plane Bending of the Branch of the Branch of the Run of the Run Test i ob Cob Testob /Cob Test i tb Ctb Testtb/Ctb Test i ir Cir Testir/Cir Test i or Cor Testor/Cor 0.89 0.99 8.94 0.C. 0.33 24.38 6.92 0.00 1.99 8.97 1.95 0.00 8.535 0.98 0.89 16.00 1.00 1.73 4.93 0.60 0.27 0.53 0.44 22.95 0.20 0.00 1.07 2.97 0.95 0.99 8.00 1.59 1.21 0.34 2.56 0.00 1.53 2.50 35.99 8.18 0.59 3.79 41.78 28.98 0.99 8.35 0.20 0.29 0.95 0.22 0.58 1.97 0.75 8.95 0.99 8.50 8.99 8.74 1.79 49.00 1.92 5.00 0.00 1.50 16.42 4.67 0.99 8.79 7.99 8.71 1.68 4.05 1.00 1.51 2.29 0.59 8.43 0.17 0.65 0.84 0.60 0.03 8.90 9.87 0.95 0.00 1.15 3.73 18.50 22.00 1.00 1.11 36.00 1.50 21.87 0. Corresponding references can be found in Section 7.44 22.50 4.84 8.00 1.95 0.51 0.00 1.47 1.41 0.90 0.39 0.74 2.54 0.96 0.00 1.03 2.73 r/R 0.98 0.94 0.36 20.42 4.50 8.00 12.49 0.46 0.84 16.87 3.75 0.43 0. Note 1: W/EPRI-A.42 0.58 12.78 11.58 0.75 --- 13.95 0.29 2.20 4.73 22.35 r/rp 0.00 1.75 6.99 0.53 0.40 2.95 0.40 41.00 1.05 1.58 0.57 0.00 1.57 Average values are only from data with r/t> 8.52 .35 0.73 18.95 0.14 4.00 1.15 3.05 1.50 5.52 0.30 2.99 8.98 0.81 5.85 6.51 0.58 0.78 1.84 8.06 1.18 0.00 1.95 0.83 1.75 0.40 5.04 2.48 2.46 2.50 0.95 0.00 1. Note 2.98 0.42 4.52 1.00 0.60 12.25 1.00 1.44 0.42 4.42 4.88 3.93 7.64 14.82 0.24 12.42 1.36 0.49 2.99 10.00 1.00 22.99 8.00 1.00 12.99 8.70 8.73 18.55 0.82 4.44 0.95 0.60 49.99 8.67 10.62 0.95 0.99 0.00 1.26 2.65 0.99 8.73 22.00 41.79 7.92 4.44 22.46 0.99 41.42 4.21 0.99 0.95 0.99 8.00 1.00 1.99 8.97 0.99 8.97 In-plane Bending of the Branch Test i ib Cib Testib/Cib 2.B.70 0.62 4.57 2.05 0.50 1.59 8.15 49.79 41.11 0.00 1.44 r/t 3.36 20.99 10.00 12. and D correspond to the test configurations used in this report.90 8.90 0.42 4.36 2.50 0.45 3.99 8.04 0.99 8.32 2.00 0.00 1.27 16.97 0.76 0.97 1.00 1.42 4.95 0.63 0.50 9.00 1.97 0. 2-8) 2.05 (r/t)-0.465 Torsion of the branch: 0. The product C2 K2 corresponds to the maximum stress.4057 where iob ≥ 1.0 (eq.476 (Note 1) 0. ASME Section III uses the expression i = C2 K2/2 as a method for determining stress intensification factors where C2 and K2 are respectively the secondary stress indice and the local stress indice.535 0. 2-9) 2.0.1 where itb ≥ 1. The regression equations.483 (Note 1) 0. 2-10) 2-19 .0 (eq.558 (r/R)0.85 (R/T) (r/t)-0. In addition.523 In-plane bending of the run: Out-of-plane bending of the run: (Note 1) The average values are calculated only for the test data where r/t > 8.482 (r/R)0.9. correspond to equations for secondary stress indices.EPRI Licensed Material Experimental and Finite Element Analysis Table 2-8 Comparison of Stresses to Experimental Data Test Condition Average itest/C(FEA) Average i/C(Regression) In-plane bending of the branch: 0.4 In-plane bending of the run iir = 0.411 0. 2-7) 2. 2-1 to 2-6.28(r/R)-(r/R)4) (R/T)1.0 (eq.0. This then leads to the following expressions for the stress intensification factors: 2.4 (r/t)-0.985 (R/T)-0.575 Out-of-plane bending of the branch: 0.0 since the FEA covers only those configurations.0 (eq.28(1.508 0.515 (R/T)1.432 0. Consequently.387 (r/R)0.5 (r/R)2.137 (r/t)0.2 Out-of-plane bending of the branch iob = 1. there is a lower limit to the stress intensification factor of 1.416 0.9.3 Torsion of the branch itb = 0.9.1 In-plane bending of the branch iib = 0.49 where iib ≥ 1.241 where iir ≥ 1.9. Table 2-8 supports the expression i = C2 K2/2. assuming that K2 ≅ 1. 0 (eq.EPRI Licensed Material Experimental and Finite Element Analysis 2.42 where ior ≥ 1.6093 where itr ≥ 1.0 (eq. 2-11) 2.9.864 (R/T)-0.0473 (r/t)0. 2-20 .543 (r/R)0.528 (r/R)1. Applicability of Results.605 (R/T)-0.237(r/t)0. 2-12) The applicability of these expressions will be discussed in more detail in Section 5.9.6 Torsion of the run itr = 0.5 Out-of-plane bending of the run ior = 0. The value of i as presently specified by Section III and B31.1 [4] prescribe methodologies for checking branch ends and run ends. This methodology results in the calculation of a stress by the use of the following general expression: S = i(M i2 + M o2 + M t2 )1/2 (eq.1 Discussion ASME Section III [3] (for Class 2 or Class 3 piping) and ANSI B31. Mo. or it where these are the corresponding SIFs to the in-plane. and torsional moment loading at the point of interest (branch or run point). out-of-plane. The expression for Z i for the branch connection is: z = πr2t (eq.1 is the maximum of io. depending upon which is being evaluated. WRC Bulletin 329 [9] suggests that the “combined fatigue-effective stress” could be represented by: 3-1 . 3-2) The expression for the run pipe is: Z = πR2T (eq. ii. and Mt are respectively the in-plane. The value of Zi used is the one corresponding to the branch or run.EPRI Licensed Material 3 COMBINATION OF MOMENTS AND STRESSES 3. modifications for the values of z (branch) will be discussed for configurations with local reinforcement). out-of-plane. 3-1) Zi Where Mi. The branch and each of the run ends are evaluated separately. and torsional moment acting on the branch or run end. 3-3) (In Section 5. Equation 3-5.EPRI Licensed Material Combination of Moments and Stresses S = ii M i + io M o + it M t (eq. It should also be noted that there are inconsistencies among the various B31 Codes. no intensification is applied to the torsional stress. as applied to branch connections. 3-6) where [ S b = ( i i M i )2 + ( i o M o ) 2 ] 1/2 (eq. 3-5) Zi As discussed in [9] Equation 3-4 represents an upper bound since it assumes that the stress contribution of each moment acts in the same direction and occurs at the same point in the component. 3-4) Zi or by: [ S = ( i i M i )2 + ( i o M o ) 2 + ( i t M t )2 ] 1/2 (eq. Equation 3-1 is more conservative than Equation 3-5 because the value of i in Equation 3-1 is the maximum. The Section III Class 1 approach of combining moments represents an additional approach. Hence the stresses are added algebraically.3 combines stress using: S= (Sb2 + 4 St2)1/2 (eq. Because of the inconsistencies between the various B31 codes regarding this matter. 3-8) While there are different i factors for the in-plane and out-of-plane bending. there was a joint meeting in October 1996 on the subject where it was agreed to 3-2 . 3-7) Zi and St = 1/2 M/Zi (eq. “represents a judgmental evaluation of the effect of the three combined moments” [9]. B31. Reference [14] discusses this approach in great detail. Equation 3-1 is still required to satisfy the Code (Section III)-specific requirements. Conversely. 3-9) where F is the axial force. Equation 3-1. if would equal unity. As an example. if Section III is the applicable Code of record. Clearly there are conditions where the Section III approach (for Class 2 or 3 piping). One methodology under consideration uses the following expression for calculating stresses: [ S = {i f F/A + [(ii M i /Z i )2 + (io M o /Z i )2 ] 1/2 } 2 + (it M t /Z i )2 ] 1/2 (eq. This would be of particular concern for configurations with large values of R/T. until these changes are made. A designer is free to specify more rigid requirements as he feels they may be justified. It appears that the approach suggested by Equation 3-5 is more reasonable. and still satisfy the basic intent of the Code. The force term is included as a “warning to the designer” that the design layout might have a potential problem such as a long riser with a resulting high axial load due to dead weight or thermal expansion.1 is the applicable Code of record. corresponding to the plane with a small SIF. a designer who is capable of a more rigorous analysis than is specified in the Code may justify a less conservative design. It is anticipated that there will be modifications to the present methodology in the future. It should be noted that the B31. However. and if is a stress intensification factor associated with the axial force. using the maximum loading would be very conservative. A is the pipe cross-sectional area.EPRI Licensed Material Combination of Moments and Stresses consider using the same equations for stress calculations. Until the applicable Code committees implement the expected changes. this option is not available at this time.” If B31. 3-3 . if the moment loading was only in one plane. then the Foreward might serve as a mechanism for using one of the approaches suggested above. it is suggested that Equation 3-3 be utilized if the individual SIFs are to be used. In general. would be very conservative.1 Foreword states that: “The Code never intentionally puts a ceiling limit on conservatism. However. the rotation of one end. 4. φ.3/EI ∫oL M dx (eq. For bending of a straight pipe of length L. the rotation is given by: φ = (1/GJ) ∫oL M dx = 1. For a torsional moment. 4-1) where M is the bending moment.1 Introduction The flexibility of branch connections is directly related to the size and thickness of the run pipe and the branch connection. 4-1 . This flexibility study is based on the results from FEA. flexibility factors are used. with respect to the other is: φ = 1/EI ∫oL M dx (eq.EPRI Licensed Material 4 INVESTIGATION OF FLEXIBILITY OF BRANCH CONNECTIONS 4. This is based on the relationship between J and I in addition to G= E/(2(1+µ)). This is important because branch connections affect the stresses and flexibility of all piping systems. Thirty six FEA analyses were performed including a wide range of run/branch configurations. 4-2) where M is the torsional moment. In order to accurately represent the load displacement (flexibility) action of the components.2 General Discussion In piping analysis the various components are modeled as one dimensional beam elements. 4-3) where Ib is the moment of inertia of the branch. A rigid link is used to connect point 2 to 3.φb)/(Mdo/Ib) (eq.EPRI Licensed Material Investigation of Flexibility of Branch Connections There are several possible ways to model the run/branch connection. Figure 4-1 indicates one possible model that is provided in the Code (Figure NB-3686-1). The flexibility factor for the spring will be calculated by: k =(φfea . Then k is equivalent to the number of branch pipe diameters that would be added to represent the local flexibility. 4-4) where φfea is the rotation from the FEA and φb is the rotation from the beam model. 4-2 . At point 3. Figure 4-1 Beam Model for Branch Loading It is convenient to define the flexibility of the spring by: φ = k M do/EIb (eq. a point spring is used to represent the local flexibility of the connection. two sets of boundary conditions were used in the evaluation. of course. G = 12E6 psi. COSMOS version 1.75 from Structural Research and Analysis Corporation [10] was used in the analyses.3. This difference is considered insignificant. The beam equations (Equations 4-2.28. Figure 4-2). Figure 4-2 Boundary Conditions It is important to recognize that.3 Finite Element Analysis The same models that were discussed earlier were used in the flexibility analysis. be a function of the layout. and µ = 0. as is depicted in Figure 4-2. Figure 4-2) was fixed and the upper end (point C) was free. In the second case. The flexibility equations are valid for other values of E.. there is no “conservative” value that would be applicable for all piping layouts.EPRI Licensed Material Investigation of Flexibility of Branch Connections 4. both ends were fixed and the loads were applied at the end of the branch. in evaluating flexibility factors. The local rotation at the juncture of the run pipe and the branch is somewhat dependent on the boundary conditions at the ends of the run pipe (points A and C. The material properties used in the analyses are E = 30E6 psi. 4-3 . Consequently the “best” value to use is the one that is most representative of the actual value. As an example. This will. The flexibility factors are based on the average of the results. The first was where the lower end of the model (point A. This is complicated because the flexibility is a function of the end conditions at the ends of the attached run pipe. The loads were applied at the end of the branch (point B).) assumed a value of µ = 0.. etc. As a result of this. a high value might mean that the loads are lower in some components in a piping system than the “true” values. Torsion on the branch (point B). points A and C fixed. Load Case 2 .In-plane moment on the branch (point B). Load Case 3 . 4-4 . point A fixed. point C free.In-plane moment on the run (point C). point C free. Load Case 4 . points A and C fixed.In-plane moment on the branch (point B). Other pertinent data is also included. point C free.Out-of-plane moment on the branch (point B). point A fixed. was fixed and moments were applied to the upper end. point A fixed. in the pipe or branch. The 36 models are listed in Table 4-1 along with the dimensions.Out-of-plane moment on the run (point C). point A fixed. Table 4-1 includes the moments used in the FEA. Load Case 5 . point A (Figure 4-2).Out-of-plane moment on the branch (point B).Torsion on the run (point C). point C free. Load Case 7 .EPRI Licensed Material Investigation of Flexibility of Branch Connections For evaluation of the flexibility of the run pipe. one end of the model (the lower end). point A fixed. Load Case 9 . Analysis was performed for the same load cases that were discussed earlier (see Figure 4-2 for definition of loads): Load Case 1 . points A and C fixed. Load Case 6 . point C. Load Case 8 . which are based on a nominal bending stress of 10 ksi. The branch end (point B) was free.Torsion on the branch (point B). point A fixed. point C free. point C free. 29 0.8 9.0 9.75 0.100 5.78 2.00 74.0 0.197 0.900 0.6 38.522 0.576 0.1 38. The number of significant figures is D d D/T (in.050 0.90 4.0 0.71 9.064 0.509 0.1 106 73.47 9.00 1.046 0.0 0.2 28 Wais 10.0 0.750 0.625 0.0630 0.0 44.0 18.12 50.9 60.0 9.0880 0.00 56.100 1.1 38.3 58.0 0.2 2 Decock 10.0 9.9 45.71 3.0 9.8 99.0 0.0 26 Wais 10.625 100 100 35 Wais35 10.119 1.7 9.0 9.3 92.) 150859 91999 371428 103185 76977 76977 217529 150135 76977 76977 76977 76977 214746 77731 354411 150135 76977 76977 76977 271507 217529 76977 371428 322985 289529 217529 166703 134868 103185 91251 90503 76977 163811 76977 76977 76977 (in.8 12.2 56.348 0.71 4.100 5.500 0.0 99.075 0.2 24.140 0.0 42.3 9.00 1.0 9.5 177 50.0 9 Wais 10.125 0.90 2.00 1.00 19.93 98.290 0.1 177 155 139 106 81.0 0.875 d/t Ma Mb Ip Ib 19.3 9.9 45.101 6.0 20.0 99.0 45.07 0.90 3.00 1.0380 0.3 16 Decock 10.90 4.100 9.222 1.7 15.5 99.00 84.222 0.0 3 Roarty 10.75 0.0 9.871 26.0 86.750 100 100 18 Wais 10.00 0.00 1.55 21.6 28.66 29.375 100 100 34 Wais34 10.0 27 Markl 10.1 5.00 1.973 34.EPRI Licensed Material Table 4-1 FEA Models Model Do T do t do/Do t/T Do/T do/t (in.63 7.78 9.233 0.121 0.250 0.2 73.289 0.95 99.0 55.800 100 93.500 100 100 12 ORNL-1 10.1 9.411 0.03 19.0 9.0 9.74 2.0 0.0 9.603 50.375 0.100 7.0 0.7 99.1 38.2 19.2 22.00 0.42 0.100 2.0 0.0 9.88 1.1 38.0 0.344 0.0 34.688 20.250 0.135 2.32 3.8 17 Wais 10.100 0.0 9.0 177 155 139 106 81.0 0.22 0.0 0.00 100 100 32 ORNL-2 10.82 9.7 99.0 21.00 1.100 5.0 0.0 0.050 0.325 0.050 0.948 34.00 83.527 2.1 38.100 10.42 99.4 12.373 7.88 9.353 0.750 0.200 1.5 99.100 8.497 0.1 0.485 0.90 7.135 10.2 16.0 84.1 44.0 17.90 99.503 50.38 0.0 0.45 99.100 6.8 23.0 9.0 9.0 25 Blair 10.250 0.88 9.100 2.80 6.500 6.90 8.633 34.90 8.200 0.11 18.0 greater than indicated.2 1 ORNL-4 10.0 (in.00 1.1 8.00 1.0 25.1 9.0 0.00 1.90 9.3 .00 1.069 0.120 0.00 1.48 99.500 100 150 19 Wais 10.55 9.875 0.50 6.9 9.22 0.118 1.5 19.0 9.0 9.0 0.207 1.0 13 OSU2 10.71 99.6 38.82 55.0 19.0 0.0 0.0 23 Markl 10.0 30 Decock 10.5 169 73.0 29.) 10.1 29 Wais 10.218 2.0 7 OSU1 10.491 0.346 45.93 99.88 83.290 5.0 14 Wais 10.0 0.0 9.294 10.080 0.294 8.1 44.100 3.250 100 100 6 Wais 10. lbs.0 0.025 0.38 13.750 0.87 2.149 2.7 10 Wais 10.0 5 Wais 10.111 0.0 37.87 73.2 9.2 24 Markl 10.00 1.71 8.0 0.753 0.43 0.178 10.400 1.1 38.275 0.50 0.34 33.090 0. d/D 0.294 1.0 99.896 74.0 9.5 15 Pickett 10.90 4.60 24.80 1.00 0.31 0.7 11 Wais 10.0 0.0 0.0 0.0 0.30 73.82 22.0 0.1 (in4) 0.0 0.0 9.0 9.431 0.375 0.00 0.0 9.222 10.527 10. lbs.320 50.00 1.50 0.) (in.43 99.0 0.0 0.23 49.00 1.45 99.) 756 3565 3885 5005 2357 1203 16336 13940 36191 25971 14288 9622 52751 19063 98271 44612 34593 32475 21796 138120 149018 56116 371429 322985 289529 217529 166703 134868 103185 91251 90503 76977 4717 4059 18793 51568 (in4) 74.400 10.6 66.91 99.68 0.00 22.1 38.635 0.3 9.40 100 35.19 99.87 9.00 1.00 25.0 0.21 49.1 8 Decock 10.90 6.0 18.843 0.500 100 50.3 50.00 0.0 9.702 0.0 0.0 33.1 20.0 20.2 9.) (in.768 0.638 0.0 0.0 0.90 0.0 0.625 0.0 0.0 34.8 25.60 9.86 99.667 0.119 10.430 0.2 38.7 65.451 1.1 74.211 19.00 84.80 4.25 0.100 7.9 38.749 0.289 0.0 0.00 34.15 33.0 0.3 43.88 83.900 1.6 66.78 44.100 5.82 44.0 9.199 4.1 24.5 33 W/EPRI 10.0 9.0 0.839 0.1 83.135 1.247 0.00 1.754 5.9 38.00 0.0 0.0750 0.80 99.0 18.0 0.95 82.1 38.0 19.0 4 ECR/EAW 10.94 8.6 20 Khan 10.451 10.70 6.7 38.527 1.0 19.764 0.0 49.47 18.186 0.683 99.0 0.750 100 66.90 7.00 0.50 0.50 0.0 87.50 0.600 0.7 31 Markl 10.) (in.0 0.223 0.075 0.90 5.0 45.52 2.120 0.3 50.53 0.00 1.7 84.242 0.875 100 100 36 Wais36 Note 1.00 45.500 0.71 33.100 7.5 57.199 7.47 2.5 9.1 80.750 0.0 0. This table is produced on a spreadsheet using EXCEL.) (in.294 3.900 100 100 22 Wais 10.90 2.1 131 106 38.286 0.90 7.88 49.1 104 38.700 0.500 0.178 1.3 17.129 0.118 10.00 1.5 21 Khan 10.0 149 22.90 4.00 0.) 9.599 0.0 18.500 1.7 38.345 0.66 99.36 25.00 100 25.120 2.0 83.94 33.0 0.500 2. correspond to the same loading direction.EPRI Licensed Material Investigation of Flexibility of Branch Connections 4. The results are discussed in the following sections. Figure 4-3 Loading Conditions 4-6 . The flexibilities.4 FEA ResultsFlexibility of Branch Pipe Table 4-2 lists the rotations at the specified points for the various load cases as well as other data. These rotations were taken directly from the FEA output. The rotations that are listed in this table corresponds to the loadings as indicated in Figure 4-3. k. 60E-03 1.20 2.95E-03 5.7 38.2 -36.3 11.44E-03 3.57 7.34E-03 1.8 -16.2 9.84E-04 9.43E-05 6.20 -14.73E-03 6.2 39.87 5.91 4.00E-03 9.26E-02 6.22E-04 3.3 15.13E-03 5.330 0.49E-03 3.01E-03 1.4 8.04 8.75 7.43E-04 2.43 10.35 5.88E-03 2.92E-05 7.6 Note 1.86E-03 4.2 8.95E-03 9.31E-03 3.40E-03 7.5 39.9 15.72E-04 6.12 8.20E-03 3.14 1.96E-03 6.40 -3.01E-05 1.28E-02 9.90 5.29 5.89E-03 4.4 5.64E-04 3.0 4.78E-04 9.94E-03 3.36 6.14E-03 6.20 -2.92 10.19 7.99 4.95E-03 1.EPRI Licensed Material Table 4-2 Flexibility Factors Load Case .77 7.54E-03 5.7 -16.79 7.65E-06 4.31 7.68 4.02E-03 7.43 8.0 2.63E-03 1.210 0.40E-03 1.90E-03 2.37E-03 1.67E-03 5.8 13.62E-03 1.39E-05 4.83 7.8 39.1 11.64E-04 4.30E-03 6.57E-03 4.6 10.9 1.24E-02 1.56E-06 1.20E-04 1.1 -28.70E-04 1.31 13.95E-04 9.65 7.2 20.22 3.04E-03 6.88E-03 3.37 8.54E-05 7.690 1.21 6.58E-02 1.46E-03 7.50 8.31 10.7 In-Plane Moment on Branch Comparison LC1 to LC7 φ 5-4 φ 2-1 φ fea k φ 5-4 φ 2-1 φ fea k 7.6 15.0 13.75 19.8 15.92E-03 8.5 8.4 15.8 -11.90E-03 2.84E-04 9.3 -0.72 9.420 0.61 5.3 2.4 40.8 -33.17E-04 4.76 19.63E-03 1.2 8.20E-03 6.37 4.95E-03 4.31E-03 1.5 8.35 13.00 6.23E-02 9.78E-04 3.2 -4.580 0.95E-03 4.57 4.17E-02 1.62 k -Regr Eq.78 3.72 4.09 10.4 38.11E-05 4.7 11.11 9.3 -1.02E-03 1.6 12.7 12.7 12.32E-03 1.28E-04 3.11E-03 7.6 11.8 13.96E-03 1.4 38.71E-04 1.88E-03 2.66E-04 1.05E-03 7.01E-03 1.51E-03 9.99 4.09E-02 1.95 3.29E-03 2.66 3.64 2.73E-05 4.95 5.57E-03 4.92E-03 5.15E-04 1.0 30.63E-03 1.61E-03 6.88E-04 9.65E-04 1.3 29.42E-03 2.99E-03 1.16E-04 9.02E-06 2.8 41.3 0.02E-03 1.90E-03 7.99E-06 5.2 -36.20 6.29 8.4 9.480 0.05E-05 1.56E-03 1.60 STD= 17.6 1.45 4.32E-03 5.92E-05 3.80 2.23E-04 6.0 10.94E-04 5.87 9.7 13.30E-03 1.200 2.95E-03 1.270 0.86 4.7 38.98E-03 6.95E-03 1.74 19.32E-03 1.69 6.6 15.96E-03 1.39 19.59 2.5 -13.83 4.20 5.4 9.87 14.6 38.54E-05 3.2 9.1 10.95E-03 1.30E-07 6.35 13.42E-03 2.90 6.30E-03 1.30E-03 1.4 25.13E-03 4.33E-03 7.72 5.79 3. k ave 4. The number of s ignificant figures is greater than indicated.59E-03 4.92 5.60E-03 1.05E-05 4.8 12.85 4.42 22.48E-03 6.83 2.48E-03 7.76E-04 3.71E-03 3.5 3.11 10.36 13.96E-03 5.2 36. (4-11) 5.050 0.2 12.78E-04 9.95E-03 7.700 0.42E-03 6.460 0.97 4.3 37.10E-05 1.22E-03 1.3 5.92E-05 4.20E-04 8.64E-04 1.5 .42E-03 8.4 k % dif -0.31E-03 1.2 10.4 14.050 0.040 0.56E-03 4.000 0.67E-04 1.60E-03 1.92 9.99E-03 1.8 29.56E-03 1.24E-02 9.06E-03 5.29E-03 2.2 31.75 6.37E-06 1.73 5.88E-04 9.12E-03 6.34E-03 1.54E-03 3.10 6.90 6.33 7.72 2.12E-03 8.89 8.19E-03 1.78E-04 9.82E-05 6.70 17.23E-02 9.7 -30.86E-03 4.30E-03 1.9 23.65E-04 1.15 5.46 9.51 1.9 1.54 9.50 8.87 3.99 4.7 11.8 15.050 0.18 8.28 5.50 11.44E-04 1.50 11.45 3.70 20.63 3.33 5.16E-02 1.66 4.31E-03 1.94 5.19E-03 1.50E-03 6.10 -23. This table is produced on a spreadsheet us ing EXCEL.32E-03 1.93E-03 4.700 0.72 5.02E-05 2.33E-03 1.41 9.65E-05 8.28 5.42 8.9 20.09E-02 1.15 8.64E-06 5.3 13.11 9.08E-03 1.01E-03 1.11 9.7 40.9 33.35E-03 1.78E-06 8.74 4.68 4.00E-04 1.87E-03 6.64 3.67 10.57E-05 1.71E-05 5.40 7.02E-05 4.85 11.50E-03 1.55 7.95E-04 9.9 15.91E-03 7.230 0.79E-06 7.91E-03 3.05E-05 2.82 11.19E-03 5.48E-02 5.01E-03 1.30E-03 1.45 3.64E-04 1.60 6.78E-04 9.80 6.92 8.85 6.82 7.60E-03 1.6 12.62E-03 6.79E-04 9.25 3.08E-03 1.90E-04 5.36E-03 1.31E-03 8.1 In-Plane Moment on Branch Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ORNL-4 Decock Roarty ECR/EAW Wais Wais OSU1 Decock Wais Wais Wais ORNL-1 OSU2 Wais Pickett Decock Wais Wais Wais Khan Khan Wais Markl Markl Blair Wais Markl Wais Wais Decock Markl ORNL-2 W/EPRI Wais34 Wais35 Wais36 Load Case .78 11.5 -13.79E-04 1.4 MAX= MIN= AVER= % Dif % -22.40E-03 1.6 38.99 3.48E-02 5.37E-05 6.2 8.050 0.26 6.86E-04 9.90 8.7 12.210 1.2 31.08 7.7 -18.190 -0.9 1.69E-04 1.50 11.79E-04 9.54E-04 3.09E-02 1.28 6.26E-05 1.94E-03 3.7 40.41 8.64E-02 1.060 0.94 φ fea % dif 0.810 5.10E-04 1.17E-03 5.83E-03 4.7 8.00E-03 9.20E-03 3.76E-04 3.17 7.30E-03 1.57E-04 1.77 4.51 4.58E-03 7.6 35.0 -10.24E-02 1.22 16. 76E-03 1.5 MAX= MIN= AVER= STD= % -172 -38.67E-05 1.42E-03 2.3 7.56 10.2 34.080 0.5 46.80 -35.200 19.19E-03 1.11 k % dif 0.EPRI Licensed Material Table 4-2 (cont.77E-03 1.28E-02 1.4 21.9 9.14E-03 1.12E-03 8.93 9.84E-02 6.00E-03 9.03E-02 8.71E-03 1. (4-17) 20.0 48.0516 0.33E-03 7.4 24.20 2.32E-06 3.6 35.160 0.22E-02 3.24E-03 1.22 11.08E-03 1.77 5.70E-04 8.53E-04 2.84 Note 1.76 6.00E-05 4.78E-02 Comparison LC2 to LC8 k 7.2 60.15 2.30 8.0 12.17E-02 3.04E-03 5.42E-03 2.84E-04 9.0 -17.4 21.96 44.42 5.25E-03 1.50 -33.2 13.67 18.5 36.29 5.55E-02 2.7 33.01E-03 1.19E-03 1.78E-04 9.1 35.8 13.6 1.8 -47.30E-06 4.95 11.4 7.63 13.8 7.0 24.66E-02 6.5 23.6 25.55E-02 1.244 5.61E-03 9.9 42.01E-04 2.96E-03 1.8 Out-of-Plane Moment on Branch φ 2-1 φ fea 7.60E-03 1.7 36.7 36. (4-18) 8.3 31.64E-02 5.0148 0.6 15.7 47.46E-03 9.0 28.88E-04 1.99E-03 1.17E-04 1.5 17.3 27.24E-02 1.39 39.9 32.66 9.24 17.18E-02 3.39E-02 2.9 14.5 24.33 39.5 34.76E-04 3.50 -39.7 20.80 -20.95E-03 1.0 24.30E-03 1.6 19.9 59.2 62.2 34.57E-03 4.71E-02 8.8 7.2 Out-of-Plane Moment on Branch φ 2-1 φ fea 7.0308 0.48E-02 1.3 43.2 10.56E-03 1.31E-03 1.790 4.0 15.12E-04 7.8 2.55E-04 8.47E-02 1.78E-04 8.8 25.490 0.95E-04 9.17 17.0 34.5 27.60 17.4 7.62 0.64E-02 1.02E-03 7.01E-03 1.55 7.1 7.9 MAX= MIN= AVER= STD= % -20.29E-03 2.5 12.30E-03 1.24E-02 1.4 -16.06E-02 1.88E-03 2.42E-04 4.71E-03 1.2 27.43 44.5 8.6 124 90.1 24.79E-04 9.13E-02 1.370 1.6 23.7 25.22E-04 8.2 31.6 124 90.56E-04 3.4 46.9 4.20E-03 3.150 0.24E-03 3.99E-03 1.7 47.98 5.78E-03 1.9 5.83E-04 8.40E-02 7.8 47.75 4.83E-02 6.95E-03 4.49E-02 4.81E-03 1.30 -6.4 -39.6 -70.0 48.0 3.4 -5.60E-03 1.88E-04 9.01E-03 1.5 53.58E-04 1.3 43.60 -20.7 124 90.84E-04 9.7 28.13 2.60 0.9 15.09 1.0677 0. This table is produced on a spreadsheet using EXCEL.71E-03 1.95E-03 1.1 10.040 0.9 40.20 45.31E-02 3.30E-03 1.3 24.3 12.1 28.96E-04 6.9 1.60E-04 2.5 27.2 34.60E-04 8.7 24.46E-02 1.94E-03 3.00 8.9 15.09E-04 2.65E-02 2.13E-04 4.59E-02 2.63 10.3 26.46E-04 5.94E-02 k 7.29E-03 2.91 9.89E-04 8.0 24.1 37.0715 0.1 30.63E-05 1.9 6.00E-05 4.4 40.8 14.500 0.0 19.0542 0.99 13.50E-05 2.41E-03 1.6 9.20 28.02E-03 1.3 43.31E-03 1.986 0.09E-02 1.64E-02 1.0218 0.8 34.6 37.8 17.07 1.92E-04 5.34E-02 3.71E-03 4.4 30.56E-04 8.0420 0.12E-02 1.7 4.87E-02 6.9 59.0 9.86E-03 4.9 5.11E-02 1.160 0.19E-04 4.72E-02 8.46E-02 3.39E-02 3.95E-04 9.25E-03 3.5 17.3 33.63E-06 6.57E-03 4.88E-04 9.5 19.7 13.78E-04 9.31E-05 5.07E-04 2.07E-02 9.6 20.7 25.26E-03 8.2 32.8 3.9 21.8 33.34E-02 3.40E-03 1.7 29.27E-04 4.1 28.4 16.92 6.92E-03 9.190 0.6 -0.58E-02 2.6 -9.080 0.76E-04 3.3 19.890 8.7 -71.9 33.2 22.56E-03 1.6 21.0 22.100 -6.0452 0.9 -36.43 44.55E-04 8.1 14.86 11.08E-04 5.8 2.67E-02 1.37E-02 6.30E-03 1.86E-05 8.1 3.94E-03 3.63E-03 1.95E-03 1.1 12.70 -16.20E-02 3.5 17.02E-03 1.15E-05 2.39 39.01E-03 1.31E-02 3.3 46.57E-03 6.00 11.62E-03 1.6 14.87 9.7 -16.1 -0.3 23.110 0.9 33.520 0.47 5.97E-05 9.0121 -0.17E-03 1.95E-03 4.5 27.5 28.95E-03 1.64E-04 8.83E-04 3.31E-05 9.60E-03 1.60 10.78E-04 9.0499 0.70 11.9 33.2 -57.86E-03 4.4 17.58E-02 2.8 17.20 17.3 Eq.9 28.63 46.1 30.40E-03 1.3 17.48E-02 3.6 0.88E-03 1.4 13.22 6.3 28.5 46.6 -91.109 0.33E-05 6.48 6. The number of significant figures is greater than indicated.2 21.2 25.73E-03 1.3 46.1 -20.72E-04 1.0490 0.65 2.3 -34.9 φ fea % dif 0.23E-05 2.30E-03 1.12E-03 4.) Flexibility Factors Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ORNL-4 Decock Roarty ECR/EAW Wais Wais OSU1 Decock Wais Wais Wais ORNL-1 OSU2 Wais Pickett Decock Wais Wais Wais Khan Khan Wais Markl Markl Blair Wais Markl Wais Wais Decock Markl ORNL-2 W/EPRI Wais Wais Wais φ 5-4 Load Case .10E-02 1.0 4.3 43.4 φ 5-4 Load Case .17E-04 2.8 77.00E-03 9.20E-04 4.78E-04 9.948 1.6 -7.8 13.3 46.1 34.213 0.53E-05 8.61E-05 1.4 21.8 26.30E-03 1.6 26.60E-04 8.5 46.4 13.14E-04 2.77 5.66E-02 6.5 17.6 34.7 -172 -7.90 -17.0 12.5 11.4 109 84.9 58.20 -13.13E-02 1.38E-02 3.2 .40 23.45 10.31E-04 1.3 12.49E-05 4.39 39.71 8.150 0.49E-02 2.10 5.44 44.08E-03 1.20E-03 3.6 1.83E-04 8.02E-04 5.72E-03 1.3 16.4 13.0 14.90E-03 2. k ave 7.7 0.79E-04 9.0 -0.2 32.55E-02 1.0161 0.1 11.0 13.02 6.4 13.5 28.4 13.9 21.46E-04 2.4 -52.1 30.90E-03 2.20 17.2 13.88E-03 2.67E-04 7.36E-02 2.76E-04 3.5 25.45E-02 4.64E-03 7.96E-03 1.60E-03 1.8 40.6 24.0 28.70 31.63E-03 1.430 0.4 17.19E-03 1.6 25.74E-03 1.9 48.1 20.560 0.91E-04 1.9 4.9 36.4 4.39 18.6 k -Regr % Dif W/factor k -Regr % Dif Eq.8 2.7 42.46 2.700 -7.19E-02 1.39 2.97 7. 967 11.29 30.0 89.20 6 Wais 5.9 27 Markl 1.41 30.27E-03 1.69E-03 4.55E-03 1.50 7 OSU1 3.08E-03 4.762 37.64E-06 1.74 53.463 -26.38 -40.64 12.29E-03 1.29E-03 2.92E-05 2.56 -3.67E-03 1.67E-03 2.49E-03 0.5 48.5 3 Roarty 5.1 8.16E-04 5.0 30 Decock 1.04E-02 0.83E-03 4.78E-03 2.40 0.70 2.55E-03 2.27E-03 1.40 4.04E-02 0.300 2 Decock 6.5 62.83E-03 3.85E-03 7.500 2.54E-05 3.43 1.14 4.30E-07 1.3 33 W/EPRI 4.45E-03 4.5 .97 63.25 74.63 4.70E-03 6.42E-03 0.63E-03 1.54E-03 2.00 0.27E-03 1.28E-03 1.1 1.88E-03 0.324 4.6 19 Wais 1.20 0.74E-03 1.80 0.9 6.76E-03 0.70 25 Blair 1.32E-03 1.15E-03 0.7 5.2 35 Wais35 2.0 0.05E-05 3.69E-03 3.0 11 Wais 2.55 -13.41E-03 9.17E-03 0.79E-04 8.72E-03 10.4 19.75E-03 1.28E-03 1.34E-03 9.64E-04 3.64 1.7 13.83E-03 3.6 6.5 45.64 30.5 1.40 80.32E-03 1.35E-02 15.28E-03 1.6 1.33E-03 8.58E-03 0.01 10.7 73.43 81.46E-03 7.43E-03 5.2 82.45E-03 8.03E-03 1.75E-03 1.0 4.3 85.86E-03 1.6 1.08E-03 2.17 37.7 88.200 0.0 22 Wais 1.42 2.2 2.3 11.7 1.95E-03 1.352 0.9 5.98E-03 1.27E-03 1.95E-03 1.43 81.17E-04 4.33E-03 1.71E-05 4.7 AVER= 8.552 -10.414 15.12E-03 4.64 2.00 k 0.71E-03 3.71E-02 20.72E-04 4.07 2.54E-03 9.69E-04 2.2 12.85E-03 10.7 1.94E-03 1.38E-03 8.306 0.6 4 ECR/EAW 5.92E-05 3.31 18.4 59.557 0.314 5.46E-03 6.99E-06 5.13E-03 5.78E-06 4.646 0.2 1.52E-03 5.86E-04 4.83 -49.965 49.7 34 Wais34 3.543 2.9 MIN= -63.47 1.44E-04 3.98 64.2 20 Khan 1.70E-02 20.92 15.631 0.23E-04 3.72 1.61E-03 7.16E-03 2.52 1.98E-03 1.28 4.14E-03 2.60 21.53E-03 4.7 18 Wais 1.26 2.26E-05 4.8 7.45E-03 3.5 31 Markl 1.03E-03 3.7 2.64E-04 3.311 0.27E-03 1.3 Load Case .5 5.1 29 Wais 1.22 2.9 67.0 1.310 0.66 5.28E-03 1.69E-03 7.70 4.70E-03 8.2 57.69E-03 6.582 3.20E-04 3.38E-03 6.67E-04 2.00E-04 4.6 78.08E-03 2.95E-03 2.00 26 Wais 1.10E-05 6.87E-03 1.96E-03 0.92E-05 2.90E-03 0.12E-03 0.86 -20.85E-03 1.04 -52.1 1.20 55.53E-03 3.612 1.50 13.21 4.40 0.02E-05 5.23E-03 6.12E-03 3.10 1.6 88.686 2.100 Model k Note 1.7 MAX= 61.32E-03 0.05E-05 5.622 5.75 61.65E-04 3.14 1.09 69.176 -43.45E-03 1.9 16 Decock 1.50 4.06 1.80 2.82 36.94E-04 3.74E-03 0.64E-04 3.82E-03 1.51 40.79 2.8 16.00 STD= 38.634 6.4 36 Wais36 1.24 53.1 1.12E-03 2.31E-03 1.2 11.41E-03 1.9 14 Wais 2.6 2.03E-03 4.2 1.3 28.358 0.87 38.8 k φ 5-4 φ 2-1 φ fea % dif 0.56E-06 5.33E-03 1.70E-03 0.69E-03 5.60 0.37E-05 2.37E-06 6.40 35.43E-05 6.28E-03 1.61E-03 6.25 3.65E-05 2.8 1.98 5.01E-05 2.28E-04 3.800 8.9 10 Wais 2.27E-03 1.528 2.02E-06 5.39E-05 5.32E-03 1.906 1.08E-03 2.6 76.41E-03 1.32E-03 1.58 40.617 0.58E-03 4.89 61.54E-04 4.29E-03 0.306 1.84 -49.8 37.627 0.458 0.22E-04 3.6 80.8 8 Decock 2.29E-03 1.50 11.71 1. k ave k -Regr % Dif % dif 2.61 3.45 5.66E-04 3.5 5 Wais 5.68 -47.27E-03 1.67E-03 1.31E-03 1.6 56.12 20.37E-03 6.46 83.61E-03 1.77E-03 1.65E-06 3.06 2.54E-05 3.50 9.91E-03 1.11E-05 3.01 2.31E-03 1.80 0.36E-03 7.5 4.10E-04 2.86E-03 0.83 -24.800 2.20E-04 2.6 17 Wais 1.4 16.8 1.25E-03 0.82E-05 4.78E-04 3.45E-03 0.452 0. This table is produced on a spreadsheet using EXCEL.05E-05 3.1 3.58 1. The number of significant figures is greater than indicated.14 -32.31E-03 1.313 5.3 3.54E-03 1.03 2.5 0.15E-04 2.79 57.46 2.468 2.4 2.3 15 Pickett 2.08E-03 3.14E-03 2.69E-03 5.6 24 Markl 1.31E-03 1.14 18.08 1.) Flexibility Factors Load Case .33 77.13E-03 4. (4-25) 0.4 10.312 0.64E-04 3.1 1.29 43.4 87.66E-03 1.6 32 ORNL-2 1.52 3.07 1.2 71.02E-02 6.12 27.86E-02 22.0 12 ORNL-1 2.571 3.70E-04 2.303 Eq.900 3.69E-03 1.03E-03 2.79 49.32E-03 1.25 2.60 2.65 55.29E-03 1.5 23 Markl 1.89 1.14 69.59E-02 19.65E-04 3.700 1.99E-03 2.40 54.57E-05 2.07E-03 2.57E-04 9.73E-05 2.02E-05 2.EPRI Licensed Material Table 4-2 (cont.4 9 Wais 2.71E-04 2.901 17.364 4.9 Torsion Torsion on Branch φ 5-4 φ 2-1 Comparison LC3 to LC9 on Branch φ fea φ fea 1 ORNL-4 1.79E-06 6.58E-03 5.5 6.43E-04 4.81E-03 1.110 % -63.31E-03 1.8 21 Khan 1.18E-02 13.53 1.0 1.35E-03 7.54E-03 1.717 28.90E-04 4.94E-03 1.3 13 OSU2 2.15 2.5 2.75E-03 0.93E-03 0.25E-03 0.6 33.02E-02 8.27E-03 1.55E-03 3.40 46.14E-03 0.607 4.75E-03 4.6 5.700 0.43E-03 6.555 0.463 5.9 28 Wais 1. 81 5.5 23.8 -19.9 -48.19 7.402 1.20 2.61 1.01 0.4 -36.4 -85.4 -12.7 -53. (4-31) 0.2 d/D>.30 12.30 -5.5 k -Regr % Dif Eq.90 3.33 3.96E-03 3.70E-03 2.11E-03 2.5 -94.6 16.17 6.69 -7.68E-03 2.75E-03 2.91E-03 7.78 -11.60 25.0 30.63E-03 2.601 0.52 MAX= MIN= AVER= STD= % -48.63E-03 2.3 23.23 MAX= MIN= AVER= STD= 6.7 3.68E-03 2.3 -35.63E-03 2.35 13.4 In-Plane Moment on Run k -Regr % Dif 0.EPRI Licensed Material Investigation of Flexibility of Branch Connections Table 4-2 (cont.70E-03 2.04E-03 2.10 20.1 9. This table is produced on a spreadsheet using EXCEL.39 2.8 1.97 5.01 -17.9 -49.4 -119 -142 -161 -184 -195 -196 -209 -3.63 5.55 6.014 0. The num ber of significant figures is greater than indicated.50 23.11E-03 5.63E-03 2.5 -15.442 0.63E-03 2.79E-03 2.40 1.63E-03 2.637 1.63E-03 2.357 0.71 3.7 32.993 1.80E-03 2.33 3.079 0.71E-03 2.65 4.511 0.3 -14.028 0.1 21.706 -1.63E-03 2.74E-03 2.30 4.94E-03 3.5 27.04 0.85E-03 6.00E-03 DIF -0.03 -2.11 4.969 0.84 4.6 2.09 4.89E-03 2.83 -17.05 -4.6 -104 -74.0 -30.5 k Load Case .35E-03 4.74E-03 2.3 -13.63E-03 2.7 .381 0.5 0.63E-03 2.77E-03 5.9 -35.2 -35.00 -10.36 2.05E-03 3.49E-03 7.76E-03 7.28 7.750 1.64 3.68E-03 2.65E-03 2.70E-03 2.69E-03 2.724 0.57 -9.35 2.045 0.178 0.127 0.16 1.112 0.0 25.53 Note 1.88E-03 2.53 7.54 3.6 11.73 2.5 -6.99 -2.93E-03 4.2 3.40 2.) Flexibility Factors Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ORNL-4 Decock Roarty ECR/EAW Wais Wais OSU1 Decock Wais Wais Wais ORNL-1 OSU2 Wais Pickett Decock Wais Wais Wais Khan Khan Wais Markl Markl Blair Wais Markl Wais Wais Decock Markl ORNL-2 W/EPRI Wais34 Wais35 Wais36 φ 6-1 2.7 23.90 13.63E-03 2.9 -14.34 4.533 0.44E-03 6.60E-03 3.63E-03 2.65E-03 2.63E-03 2.1 0.83E-03 3.65E-03 2.40 -15.32 2.63E-03 2.63E-03 2.5 39.04E-03 5.108 0.77E-03 8.5 20.63E-03 2. 4-10 Eq.12 3.67E-03 2.1 -8.35 4.7 30.078 0.465 0.05 2.4 -26.64 12.2 17.01 -3.10 6.26 -4.47 6.01E-03 3.83 4.0 -38.72E-03 2.66E-03 2.14 0.66E-03 2.45 3.9 -37.67E-03 2.809 0.19 4.43 3.73E-03 2.9 29.63E-03 2.31 2.5 4.60 7.63E-03 2.144 0.67E-03 2.80 25.150 0.112 39.92E-03 3.3 -14.66E-03 4.201 0.131 0.8 23.567 0.72 2.80 4.17 -9.40 3.8 -54.28E-03 3.0 -5.064 0. (4-41) % 0.619 0.63E-03 φ fea % 2.80 3.63 8.51 6.4 -17.63E-03 2.12 1.5 -4.7 -90.40 4.38E-03 5.68 4.48 2.25E-03 3.91 -28.3 20.380 1.9 29.9 -14.94 2.25E-03 5.26 0.92 1.43 -1.422 0.88 -3.30 3.60 7.9 -10.073 0.9 32.309 1.65E-03 2.2 -18.056 0.1 -17.561 1.8 -24.1 -49. 63E-03 2.68E-03 2.097 0.045 0.5 k -Regr % Dif Eq.00 -10.0 -23.71E-03 2.20 21.10 -3.031 0.7 4.63E-03 2.600 -0.372 0.6 -21.050 0.741 0.968 0.63E-03 2.7 -17.122 0.2 65.67E-03 2.63E-03 2.203 0.2 5.7 46.109 0.68E-03 2.64E-03 2.65E-03 2.63E-03 2.058 0.800 -0.3 -63.28E-03 2.5 Out-of-Plane Moment on Run k k -Regr % Dif φ fea % 2.8 43.5 -18.300 -0.352 0.3 95.63E-03 2.50 -1.70 -7.2 3.400 -0.025 0.76E-03 2.076 0.010 0.302 0.65E-03 2.63E-03 2.524 0.83E-03 -0.63E-03 2.64E-03 2.700 -1.726 0.63E-03 2.8 -0. (4-35) 0.20E-03 3.72E-03 2.68E-03 2.7 -10.047 0.015 0.016 0.00 -0.87E-03 2.0 38.67E-03 DIF -0.305 MAX= MIN= AVER= Note 1.8 d/D>=.6 -37.533 0.4 -47.599 0.98E-03 2.24E-03 3.807 -38.180 0.60 44.6 -25.4 -16.400 -0.6 84.63E-03 2.6 19.0 -38.900 0.367 0.331 0.20 -3.66E-03 2.170 0.6 -57. STD= The number of significant figures is greater than indicated.251 0.66E-03 2.50 -3.8 238 -98.65E-03 2.237 0.016 0.086 0.1 -24.63E-03 2.65E-03 2.079 0.189 0.051 0.074 0.76E-03 2.7 170 161 150 122 116 119 238 104 137 80.329 0.64E-03 2.467 MAX= MIN= AVER= STD= 8.237 0.165 0.411 0.67E-03 2.0 -38.63E-03 2.3 -62.212 0.96E-03 2.63E-03 2.001 0.442 0.7 43.7 -37.248 0.7 44.139 0.5 -13.74E-03 2.64E-03 2.700 -0.391 0.338 0.3 -12.3 -18.012 0.040 0.00 -2.4 -61.123 0.500 -0.019 0.042 0.158 0.0 28.0 -62.349 φ 6-1 Eq.524 0.900 -1.65E-03 2.084 0.50 -10.67E-03 2.7 0. (4-45) % 0.2 -32.63E-03 2.64E-03 2.63E-03 2.90 -2.099 0.400 -1.018 0.337 0.40 8.061 0.052 0.40 -8.60 24.9 -17.30 -9.72E-03 2.66E-03 2.300 0.1 -15.200 -0.73E-03 2.04E-03 3.66E-03 2.90 -9.1 -17.700 -0.738 0. This table is produced on a spreadsheet using EXCEL.09E-03 3.8 28.147 0.007 0.4 -22.634 0.9 28.9 -54.65E-03 2.258 0.129 0.63E-03 2.70E-03 2.14E-03 3.63E-03 2.30 -4.460 0.407 0.843 0.0 65.74E-03 2.057 0.3 9.165 0.251 0.3 -53.339 0.276 0.323 0.7 -16.64E-03 2.100 0. 34 Wais34 35 Wais35 36 Wais36 % -98.500 -0.019 0.897 0.039 2.74E-03 2.2 9.63E-03 2.40 -3.73E-03 2.9 -25.71E-03 2.059 0.70E-03 2.135 0.80 0.50 -1.258 0.99E-03 3.65E-03 2.7 59.038 0.294 0.69E-03 2.6 -23.63E-03 2.EPRI Licensed Material Investigation of Flexibility of Branch Connections Table 4-2 (cont.8 4-11 .090 0.242 0.309 0.90 -12.63E-03 2.167 0.24E-03 3.68E-03 2.314 0.118 0.40 33.691 0.78E-03 2.) Flexibility Factors Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 ORNL-4 Decock Roarty ECR/EAW Wais Wais OSU1 Decock Wais Wais Wais ORNL-1 OSU2 Wais Pickett Decock Wais Wais Wais Khan Khan Wais Markl Markl Blair Wais Markl Wais Wais Decock Markl ORNL-2 W/EPRI Load Case . 0 6.41E-03 5.40 -8.31 2.7 22.41E-03 1.024 ORNL-4 3.90 -17.92 Khan 3.50E-03 5.58E-03 0.72E-03 0.4 -28.6 -25.4 -43.216 Wais 3.80E-03 3.174 Wais 3.300 -7.451 0.2 29.6 -16.0 -66.41E-03 9.08 Markl 3.48E-03 0.08E-03 8.45E-03 5.42E-03 1.45E-02 16.35E-03 3.48E-03 9.70 -16.41E-03 6.41E-03 4.77 Wais36 MAX= MIN= AVER= STD= 1.41E-03 1.40 -1.4 6.04E-02 10.51E-03 7.08 7.70 -8.1 -6.91 4.41E-03 5.1 52.5 -68.95E-03 4.41E-03 3.9 -13.45 5.16 Khan 3.0 -24.48E-03 3.88 Markl 3.857 Wais 3.06 5.9 -25.20 ORNL-1 3.3 6.45 3.4 66.1 40.52E-03 0.2 44.501 1.41E-03 3.634 Decock 3.1 -14.10 -23.55E-02 17. (4-40) 3.9 -10.4 23.26 Wais 3.61 6.9 -75.0 -70.69 Wais 3.3 -11.48E-03 5.24E-02 13.90 27.742 0.44E-03 1.117 0.41E-03 3.41E-03 3.84E-03 0.5 k -Regr % Dif Eq.54E-03 0.187 0.73E-03 3.4 -5.37E-03 1.3 -25.78 2.30 -3.75E-03 0.750 Wais 3. 4-12 % Dif % -66.110 0.0 -24.6 Torsion on Run Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Notes: φ 6-1 φ fea % k k -Regr DIF -1.36 MAX= MIN= AVER= STD= 12.749 OSU2 3.10 -3.24E-03 4.9 -0.158 0.25 Blair 3.113 ECR/EAW 3.9 0.7 41.3 66.41 4.38 4.6 .45E-03 3.9 -25.095 0.80 17.1 -66.738 1. This table is produced on a spreadsheet using EXCEL.41E-03 3.2 5.6 -96. The num ber of significant figures is greater than indicated.7 -2.1 -20.69 0.528 0.4 5.09E-03 3.20 -2.) Flexibility Factors Load Case .16 4.48E-03 3.80 Wais 3.5 -14.68E-02 19.407 0.42E-03 1.99E-03 0.8 5.04E-03 2.81 2.41E-03 3.55 3.08E-02 10.96 4.600 27.69E-03 0.8 -65.52 Wais 3.0 -45.30 -8.3 -25.95 8.42E-03 3.286 OSU1 3.55E-02 18.90 -2.08 3.00 18.63E-03 0.9 -10.072 Decock 3.4 -3.097 Roarty 3.7 -42.63 ORNL-2 3.60 -4.9 -3.02E-03 2.20 3.56E-03 3.1 17.3 12.29 3.67 9.228 W/EPRI 3.184 0.93 10.01 1.28 Decock 3.20 Wais 3.40 10.9 27.0 14.45E-03 3.06 Wais 3.2 -63.50 39.6 -58.50 -3.9 6.5 20.72 4.9 6.45E-03 3.11 Wais 3.20 -12.221 0.3 -50.22 2.79E-03 0.2 d/D>.2 -64.00 -34.0 -166 Eq.26E-03 1.08E-03 8.5 -4.58E-03 1.26 Pickett 3.14 Markl 3.41E-03 3.2 43.452 0.48E-03 6.08 Wais35 3.45E-03 1.4 14.53E-03 6.80 -8.3 13.50E-03 0.42 1.90 -8.99 3.68 Wais 3.0 39.071 0. (4-46) % 0.7 -22.42E-03 1.73 2.90 -11.EPRI Licensed Material Investigation of Flexibility of Branch Connections Table 4-2 (cont.91E-03 0.588 Wais34 3.1 1.0 -82.55E-03 4.8 26.03 Wais 3.5 -52.50E-03 0.41E-03 4.0 20.3 13.755 1.63E-03 0.1 -204 -78.8 -43.7 -6.32 Decock 3.563 0.0 -25.30 -8.857 1.44 8.9 -113 -161 -214 -260 -323 -352 -354 -393 -3.56E-03 6.42E-03 3.29 Markl 3. 4-5) where φi-j is the rotation of point “i” with respect to point “j” 4. Calculated values of φ5-4 and φ2-1 as well as the results from the FEA. substituting and rearranging Equation 4-5 yields: kib = 1/(Mibdo/EIb) [φfea . the FEA was performed with two sets of boundary conditions. At that juncture. from Equation 4-3 (eq. 4-10) Table 4-2 lists the data for in-plane bending of the branch. The rotation at the end of the branch (point 5) with respect to the fixed end (point 1) is given by: φ = φ5-4 + φ4-3 + φ3-2 +φ2-1 (eq. 4-8) As discussed earlier. The model depicted in Figure 4-1 will be used as the basis for evaluating the FEA results and determining the flexibility of the branch connection. Equation 4-8 is modified (considering that L2= L1): φ2-1 = 1/8 Mib L2/(EIp) (eq. The 4-13 . A rigid link is included in the model from the center line of the run pipe to its surface. Load Cases 1 and 7. for in-plane moments.EPRI Licensed Material Investigation of Flexibility of Branch Connections Figure 4-1 shows the model for branch connections.1 In-Plane Bending of the Branch For in-plane bending (where Mib is the in-plane bending moment on the branch): φ5-4 = MibL3/EIb (eq. When fixed at both of the run pipe ends.4. 4-7) φ3-2 = 0. are provided. fixed at the run pipe bottom end and fixed at both ends. since this is the rotation over a rigid link and assuming only one end of the run pipe is fixed: φ2-1 = Mib L2/EIp (eq. 4-6) φ4-3 = kib Mib do/EIb point spring.φ5-4 .φ2-1] (eq. a point spring is used to represent the local flexibility of the connection. 4-9) Replacing φ with φfea . “MIN” is the minimum % difference. A comparison to the results from an equation developed from regression analysis (“kRegr” in Table 4-2) is also provided.2 Out-of-Plane Bending of the Branch For out-of-plane bending where Mob is the out-of-plane bending moment: φ5-4 = Mob L3/EIb (eq. 4-13) Again φ3-2 = 0.6%. The data in the column labeled “k % dif” is the percentage difference between the values of k for the two FEA load cases.5%.3 Mob L2/EIp 4-14 (eq. The column labeled “k ave” indicates the average of the two values of k. In Table 4-2.488 (D/T)1.391 (d/t)-0. since this is the rotation over a rigid link Since the segment of the beam model from point 1 to point 2 is in torsion for out-ofplane bending of the branch. and the column labeled “% dif” indicates the percentage difference between the average value of k from the FEA analysis and the value calculated using the regression equation. The equation is: kib = . the data in the column labeled “φfea % dif” is the percentage difference between the value of the rotation for the two FEA load cases.279 (d/D)0.EPRI Licensed Material Investigation of Flexibility of Branch Connections values of kib are listed and a comparison of Load Cases 1 and 7 is also provided. Equation 4-8 is replaced by: φ2-1 = 1. 4. The maximum difference is 36% and the standard deviation is 17. 4-14) . The value “MAX” is the maximum percentage difference between “k-Regr” and “k ave”.4. “AVER” is the average % difference and “STD” is the standard deviation of the distribution of the percentage differences. The average values (column labeled “k ave” in Table 4-2) are used as the basis.602 (eq. in the columns labeled “Comparison LC1-LC7”. the average % difference between the regression analysis and the FEA data is 1. for the case where only one end of the run pipe is fixed. 4-11) For the 36 cases. 4-12) The value of φ4-3 is given by φ4-3 = kob Mob do/EIb (eq. 3. Eight models with R/T = r/t = 49. It was determined that the flexibility of these cases 2 3 varied as a function of a constant times f = 3(d/D) .72 (d/D)0. 4-15) As before. where Mtb is the torsional moment.2%.EPRI Licensed Material Investigation of Flexibility of Branch Connections For out-of-plane moments on the branch with both ends of the run pipe fixed.00 were investigated. This information is listed in Table 4-2 in the columns indicated as “W/factor” where the factor is “3(d/D) .158 (d/t)-0. and with d/D = t/T varying from 0. Because of the differences and the recognition that the flexibility was not always monotonically increasing as a function of d/D. 4-17) For the 36 cases. The model where the maximum difference was 172% was ORNL-4.3 Torsion of the Branch For torsion of the branch. The next highest maximum difference was 91%. Equation 4-9 is replaced by: φ2-1 = (1/2) *1.75(d/D)2 + (d/D)3”.25 to 1. substituting and rearranging Equation 4-5 yields: kob = 1/(Mob do/EIb) [φfea . 4. Equation 4-18 is an improvement over Equation 4-17.75(d/D)2 + (d/D)3) (D/T)1.75(d/D) + (d/D) . The factored equation is: kob= 0.2%. replacing φ with φfea . The equation is: kob = 0.φ2-1] (eq.828 (3(d/D) . The k ave data was normalized to this factor (f) and an equation was developed from regression analysis.717 (eq. Load Cases 2 and 8. the average percentage difference between the regression analysis and the FEA data is -7. 4-16) Table 4-2 also lists the FEA and other data for out-of-plane bending of the branch.5057 (d/t)-0. we have: 4-15 .4.φ5-4 .81 (d/D)0. 4-18) For the 36 cases.3 Mob L2/EIb (eq. The maximum difference is 39. the average percentage difference between Equation 4-18 and the FEA data is -. A comparison to the results from an equation developed from regression analysis (k-Regr) is also provided. This correlation provided results that were within about 10% of the data.169 (D/T) 1.3. the dependence on d/D was further investigated.5.3.6% and the standard deviation is 19.2%. The maximum difference is 172% and the standard deviation is 45%.654 (eq. The beam model for loading of the run pipe is similar to that of the loading of the branch (see Figure 4-4). point 8. 4-21) For one end of the run pipe fixed: φ2-1 = Mtb L2/EIp (eq. 4. a point spring is assumed.751(d/D)2.553 (eq. The equation is: ktb = 2. 4-19) φ4-3 = ktb Mtb do/EIb (eq. the effects of the branch connection on the flexibility of the run pipe was investigated. At the intersection of the centerlines of the run pipe and the branch.5%. A comparison to the results from an equation developed from regression analysis (k-Regr) is also provided.5 FEA ResultsFlexibility of Run Pipe As part of this study.3 Mtb L3/EIb (eq. 4-25) For the 36 cases.43 (D/T)0.7% and the standard deviation is 38.11 (d/t)-0. 4-24) Table 4-2 lists similar data for torsion of the branch. The results for the load cases where the run pipe is loaded are also presented in Table 4-2. substituting and rearranging Equation 4-5 yields: ktb = 1/(Mtb do/EIb) [φfea . The maximum difference is 63. 4-23) and: Replacing φ with φfea .φ5-4 . 4-22) For both ends fixed: φ2-1 = 1/8 Mtb L2/EIp (eq.φ2-1] (eq.EPRI Licensed Material Investigation of Flexibility of Branch Connections φ5-4 = 1. 4-20) φ3-2 = 0 (eq. the average percentage difference between Equation 4-25 and the FEA data is 8.0%. Load Cases 3 and 9. 4-16 . The rotation at point 6. is: φ = φ6-7 + φ7-2 + φ2-1 (eq. 4-26) Three loading conditions were considered and the results are given below: 4. φ.EPRI Licensed Material Investigation of Flexibility of Branch Connections Figure 4-4 Beam Model for Run Pipe Loads All moments are applied at point 6. substituting and rearranging Equation 4-26 yields: 4-17 . 4-28) φ2-1 = Mir L2/EIp (eq. 4-29) and: Replacing φ with φfea .5. (eq.1 In-Plane Bending of the Run Pipe For in-plane bending (where Mir is the in-plane bending moment on the run pipe): φ6-7 = MirL1/EIp (eq. 4-27) φ7-2 = kir Mir Do/EIp point spring. 4-34) For out-of-plane bending of the run pipe (LC-5).EPRI Licensed Material Investigation of Flexibility of Branch Connections kir = 1/(MirDo/EIp) [φfea .6% Maximum difference: 48% Standard deviation: 25% 4.008 (d/D)2.φ6-7 . 4-33) and: φ2-1 = Mor L2/EIp (eq.φ2-1] (eq. 4-32) φ7-2 = kor Mor Do/EIp point spring. 4-31) Average percentage difference between the regression analysis and the FEA data: 3. 4-35) Average percentage difference between the regression analysis and the FEA data: 28.5. 4-30) For in-plane bending of the run pipe (LC-4).128 (D/T)-1.9% Maximum difference: 238% Standard deviation: 85% 4-18 .φ6-7 .63 (d/t)0.2 Out-of-Plane Bending of the Run Pipe For out-of-plane bending (where Mor is the out-of-plane bending moment on the run pipe): φ6-7 = MorL1/EIp (eq. the regression equation is: kir = 1.305 (eq.φ2-1] (eq.085 (d/D)1.077 (d/t)1.627 (D/T)0. (eq. 4-33a) and: kor = 1/(MorDo/EIp) [φfea .2366 (eq. the regression equation is: kor = 0. The results are given below: For in-plane bending of the run pipe (LC-4).5.276 (eq. 4-40) Average percentage difference between the regression analysis and the FEA data: 6. regression analyses were performed to determine representative equations for these load cases when d/D ≥ 0. where Mtr is the torsional moment.675 (d/D)3. 4-38) ktr = 1/(Mtr Do/EIp) [φfea . 4-37) φ2-1 =1.5.56 (D/T)0.7% Standard deviation: 39. the regression equation is: ktr = 1.9% Maximum difference: 25% 4-19 . flexibility of this order can be neglected.3 Torsion of the Run Pipe For torsion of the run pipe.5% Maximum difference: 66.3 Mtr L2/EIp (eq.φ6-7 . In order to improve on the accuracy of the equations. we have: φ6-7 = 1.2% 4.5. the regression equation is: kir = 0.φ2-1] (eq. 4-39) For torsion of the run pipe (LC-6). Considering the accuracy of the overall design process.995 (D/T)0.25 where d/D ≥ 0.47 (d/t)0.78 (d/t)-0.039 (d/D)2.3 Mtb L1/EIp (eq.0 for d/D < 0. 4-36) φ7-2 = ktr MtrDo/EIp (eq.6 Review of the Run Pipe Flexibilities A review of the FEA data for all load cases for the run pipe loadings indicates that the value of k is on the order of or less than 1.EPRI Licensed Material Investigation of Flexibility of Branch Connections 4. 4-41) Average percentage difference between the regression analysis and the FEA data: 0.5 (eq. The maximum variation was 53.159 (d/D)4. where the original value of k was 1. the larger variations were associated with small values of k. The results were similar for out-of-plane bending of the branch (Load Cases 2 and 8) with an average variation of 13%.5 kor = 0.EPRI Licensed Material Investigation of Flexibility of Branch Connections Standard deviation: 13.8% Maximum difference: 27% Standard deviation: 17. For in-plane bending of the branch (Load Cases 1 and 7). the regression equation is: where d/D ≥ 0.7 Sensitivity of Results to Accuracy of FEA A brief study of the effects of the accuracy of the FEA on the determination of the flexibility factors was performed for loads on the branch connection. Again.0771 (D/T)-0. 4-45) Average percentage difference between the regression analysis and the FEA data: 3.5 (eq.2% Maximum difference: 44.67 (eq.49. 4-46) Average percentage difference between the regression analysis and the FEA data: 4. as it was also for model number 3.096 (d/t)0. A ± 10% variation was assumed in the FEA rotations and then flexibility factors were determined in the same manner as discussed earlier for all the models.8% For torsion of the run pipe (LC-6).0% Standard deviation: 21.5%.328 (d/t)-0.7. the larger variations 4-20 . The maximum variation was 37.813 (D/T)0.6% These equations represent an improvement over the other regression equations.5% for model number 3 “Roarty” which had an original flexibility of 0. Both the +10% and -10% results were very similar. the average variation in the calculated values of k was about 16%.349 where d/D ≥ 0.7% For out-of-plane bending of the run pipe (LC-5).982 (d/D)4. the regression equation is: ktr = 0. 4. In general. the calculated deflection was 0.63. When the FEA results were reduced by 10%.93. The large variations were for models 1 to 7 and 33.0. the results were somewhat different. for those cases where the flexibility is significant. In this case. The average deflection of the four tests at a load of 100 pounds was 0. 4. they can be used to evaluate one of the equations derived above.79 inches. however.5 inches. which had very small original values of k. The average variation was about 75% with a maximum of 503% for an assumed change of ±10% in the FEA. Considering that the calculation estimates the flexibility of the testing assembly. k > 1.5.63 (models 1 to 7 and 33). the dimensions of the test specimens and Equation 4-45 for out-of-plane bending. it is deemed that minor inaccuracies in the FEA will not significantly affect the results. for example. The variations were the same. the average variation was about 21%. Considering the variations in the values of k for the two sets of boundary conditions and the conservatism of the overall process.EPRI Licensed Material Investigation of Flexibility of Branch Connections were associated with the small values of k. 4-21 . and that Equation 4-45 was developed using average k data. In summary. Using an average branch length of 46. this is considered to be a confirmation of the methodology. the ± 10% results were very similar. the calculated values of k were negative for the models where the original values were less than about 0. for torsion of the branch.0. Likewise. The average magnitude of the negative values was less than 0. for those models with original values of k greater than 1. minor variations in the FEA results will yield only minor variations in the calculation of the values of k. For torsion of the branch (Load Cases 3 and 9). Loads and deflections at the loading point for in-plane bending were recorded and are included in Appendix C. less then 0. the greatest variation occurred when the values of k were small. the new values were positive.8 Comparison to Test Data The tests discussed previously were not specifically for determining flexibility factors. As for the other load cases. When the FEA results were increased by +10%. 2 Branch Connection Configurations Section III of the Code identifies several configurations for branch connections for Class 2 components in Figure NC-3673. Figure NC-3673. where x corresponds to in-plane.2(b)-1 and are included in this report as Figure 5-2. The applicability of the results covers two main areas: (1) configurations or geometries covered by the results and (2) limitations of the parameters of the equations. branch or run pipe end).1 Code and Section III Class 1 requirements have similar figures. Note 6 of NC-3673.EPRI Licensed Material 5 APPLICABILITY OF RESULTS 5.2(b)-2 (in this report as Figure 5-1). it might be that the original intent was to assume a rigid connection at the juncture of the run and the branch. for example. While not clear. It should be noted that Figure NC-3673.1 Introduction Section 2 discussed the results of the FEA and comparison to the available test data. This chapter discusses these results in more detail and also discusses the applicability limitations. These areas are discussed below: 5.2(b)-1 establishes the specific requirements for the applicability of the SIF equations in the Code for the configurations of Figure NC3673.2(b)-2 includes sketches showing four configurations that are applicable to various designs. This report provides a more accurate approach. It was determined that the relationship: i = Cxy/2 is reasonable for the configurations considered. In addition. the applicability of the flexibility factors is also discussed. 5-1 .2(b)-1 states that the flexibility factor is “1” for branch connections. As noted in WRC Bulletin 329.2(b)-2. this is misleading at best. outof-plane. The applicable notes regarding this figure are given in Figure NC-3673. The B31. The tests and FEA models used in the evaluation of stresses and flexibility in this report (Sections 2 and 4) are directly applicable to the configuration of sketch (d) of this figure. or torsional moment and y corresponds to the location. (Cxy is the secondary stress indice. that this area should be treated as a tapered transition joint. This is the value of thickness to be used in the determination of the section modulus of the branch. It must be noted that this approach might be used to qualify the area of the branch connection near the intersection of the branch and the run. This configuration is not in the scope of this study. the mean radius of the branch can be based on the thickness of the reinforced section. 5-2 . Under certain circumstances. it is 0.5 (see Figure 5-1 for the definition of the terms).EPRI Licensed Material Applicability of Results The results of this study can be extended to the configurations of sketches (a) and (b). if L1 equals or exceeds 0. Based on a review of the of the results of the ORNL studies [11] and other studies. However. depending upon the configuration.5 (r’mTb) and the requirements of θn of Figure NC3673.2(b)-2 are satisfied.) It might be. For the configurations of sketches (a) and (b). (This location is indicated in Figure NC-3673. the thickness of the branch can be represented by Tb (Figure NC-3673.5 reasonable to assume that. then Tb can be substituted for the branch thickness t subject to the requirements discussed below. Tb.5 (r’mTb)0.2(b)-2 indicates that. the results of this study cannot be readily extended to the configuration of sketch (c). the location where the branch pipe joins the reinforced section could be critical.2(b)-2) if the value of L1 is sufficiently long so that the branch will perform as a branch of thickness Tb. The note in Figure NC-3673.2(b)-2 just below the points indicated by the arrows labeled “Branch pipe”. if L1 ≥ 0. EPRI Licensed Material Applicability of Results Reprinted with the permission of The American Society of Mechanical Engineers from ASME BPVC.1995 Edition.Figure NC-3673.2(b)-2 5-3 . Figure 5-1 Branch Dimensions . Section XI . Each of these conditions is discussed below: 5-4 . These requirements have been revised following the discussion of WRC 329 [9].2(b)-1 5.Figure NC-3673.2(b)-1 will serve as the basis of the conditions of applicability of the expressions for SIFs and flexibility factors. Section XI .1995 Edition. Figure 5-2 Flexibility and Stress Intensification Factors (Do/tn ≤ 100) .3 Requirements for Applicability of SIF and Flexibility Expressions The requirements of Note (6) of Figure NC-3673.EPRI Licensed Material Applicability of Results Reprinted with the permission of The American Society of Mechanical Engineers from ASME BPVC. Axis of branch normal to pipe run: This requirement is applicable to the configurations covered by this study. Distance between branches: This requirement is applicable to the configurations covered by this study. Pending further investigation. Tr to T. It should be noted that the nomenclature of Figure NC-3673(b)-2 differs from that used in this study. this condition is redundant with other parts of the Code and as such is not required. this report does not recommend dividing the i-factors by two even if r 2 is provided and meets the minimum requirements of Note (6) of Figure NC-3673. r2: The configurations covering the analysis and testing correspond to sketch (d) in an “as welded” condition. there is no specification of r2 and the equations for SIFs are to be used directly. Requirements on the outer radius. The limitations on geometric parameters are specified below. 5-5 . r3: This requirement has been dropped per WRC 329 [9]. Requirements on the outer radius. Requirement on the outer radius.2(b)-1. As such. r2: This requirement has been dropped. r1: This requirement is not included since the inside corner radius is “not a critical consideration” for fatigue [9]. Requirement on inside radius.EPRI Licensed Material Applicability of Results Reinforcement requirements: As noted in [9]. Requirements on Rm/Tr and r’m/Rm: These requirements are not applicable to this study. and so on. Rm of Figure NC-3673(b)-2 corresponds to R. Tb to t. These expressions are based on FEA with the following range of parameters: 9. The results from the FEA and the regression equations are presented.5 8. An investigation of the equations at the lower limits of R/T and r/t was performed to determine if an extension of these limits was reasonable.125 ≤ r/R ≤ 1.0 ≤ R/T ≤ 49. the values from the regression equation were calculated. 5-1) 3. It should be noted that the exponents in the expressions for these parameters are less then 1.5. The expressions are presented as functions of the parameters R/T. and r/R. the effects of the combination of limits of the ranges of parameters of R/T. The values of Cxx have a lower limit of 1. 5-2) 0.0 These ranges were based upon the limitations of the FEA models and the availability of test data.0. In addition. Table 5-1 shows the values of the equations for Cxx (the stress intensity index ) and the FEA results. The results appeared to be reasonable. Table 5-2 shows the results of flexibility for the three models for loading of the branch. A review of this indicates that the equations yield reasonable results for these cases.1 ≤ r/t ≤ 99 0.4 Limitations of Equations Equations 2-1 to 2-6 provide expressions for the stress intensity indices.0 (eq. It is desirable to extend the limits to approximately: 3. 5-3) To investigate this. r/t. The d/D ratio for these additional models is such that the additional flexibility of the run is negligible. 5-6 .5 (eq.75 ≤ R/T ≤ 49. r/t and r/R were also investigated. three additional FEA models were developed and the stress intensities generated.EPRI Licensed Material Applicability of Results 5. which is considered in the comparison (see the note in Table 5-1). and provides a comparison. Using the various limits of the ranges of Equations 5-1 to 5-3.75 ≤ r/t ≤ 99 (eq.125 ≤ r/R ≤ 1. are valid for the range of parameters listed in Equations 5-1 to 5-3. 5-7 . Based on this review. this is considered acceptable. Consequently. it is concluded that the equations provided for the stress intensification factors. only one condition was considered here. however. and r/R of Equations 5-1 to 5-3.EPRI Licensed Material Applicability of Results It should be noted that the regression equations are based on the average of two sets of boundary conditions. Considering the range of flexibilities between the two boundary conditions. 2-7 to 2-12. it is concluded that regression equations are applicable to the range of parameters R/T. r/t. EPRI Licensed Material Applicability of Results Table 5-1 Comparison of FEA and Regression Equations for Stress Indices 5-8 . EPRI Licensed Material Applicability of Results Table 5-2 Comparison of FEA and Regression Equations for Flexibility Factors 5-9 . 237 0.985 n1 1. The conclusions derived from the tests and analysis described in this report are listed below.850 0. 6.2(a)-1 for an “as welded” configuration.387 0. for example. Figure NC3673.1 Stress Intensification Factors For the geometry indicated in Figure NC-3673.50 0.0473 -0.42 Torsion Branch Run itb itr 0. torsion.543 2. the evaluation of the stresses must be based on the maximum i factor for the branch and the maximum i 6-1 .609 In-plane bending Note 1: Replace A0 with 1. the various code committees are considering changes at this time.137 n2 -0.482 n3 0.28(r/R)-(r/R4)] 6. The extension to other configurations is discussed in Section 5 and summarized below.00 -0.558 0.528 1.241 Out-ofplane bending Branch iob Note 1 1. for individual loadings.406 Run ior 0.10 0.515 0.40 -0. in-plane and out-of-plane bending. This study focused on the configuration indicated as sketch (d). the stress intensification factors for the branch and run pipe ends are given by: ixy = A0 (R/T)n1(r/t)n2(r/R)n3 ≥ 1. Until these changes are finalized.49 0.2(b)-1 (included in Section 5 as Figure 5-1) indicates these configurations.EPRI Licensed Material 6 CONCLUSIONS There are several configurations that are categorized as branch connections.05 -0.605 -0.864 1.2 Combination Of Moments For combination of stresses due to different moments.0 Part Branch Run SIF iib iir A0 0.28[1. iob.3 Flexibility Factors For the geometry indicated in Figure NB-3643. ior. or itb. S = i(M i2 + M o2 + M t2 )1/2 (eq. the value of i is the maximum of iir. 6. the flexibility modeling of the branch connection should be based on Figures 4-1 and 4-4 for the branch and pipe run respectively: Figure 4-1 shows the model for branch loading where it is assumed there is a rigid link from the centerline of the run pipe to its outer surface. 3-3) For the branch. This is discussed in Section 3. 3-2) (See Section 5 for a definition of r and t for reinforced branches. For the run.) For the run pipe. it is assumed that a point spring exists. or itr. Equation 3-1 should be used for evaluating the branch connections. The values of the moments and section modulus are appropriate for the location. If B31. Zi is: Z = πR2T (eq.3(a)-1.1 is the Code of record. The value of Z i for the branch is given by Equation : z = πr t 2 (eq. the value of i is the maximum of iib. a less conservative approach is permitted. At this point.EPRI Licensed Material Conclusions factor of the run. 3-1) Zi where the branch and each end of the run pipe are evaluated. If Section III is the Code of record (for Class 2 or 3 piping). The flexibility factors of the point spring are given by: 6-2 . EPRI Licensed Material Conclusions kxy = B0 (D/T)n1(d/D)n2(d/t)n3 In-plane bending Out-ofplane bending Part Branch Run k kib kir B0 0.78 n3 -0.72 0.125 ≤ r/R ≤ 1.250 Branch kob Note 1 1.1 and 6.305 Torsion Branch ktb 2.488 0.391 3.982 4.75 ≤ R/T ≤ 49.5057 -0.11 -0.3 are applicable to the following range of parameters: 3. kor and ktr are valid only for d/D ≥ 0.4 Applicability of Results The equations specified above in Sections 6. sketch (d) (Figure 5-2 in Section 5).349 2 3 Note 1.159 4. As discussed in Section 5. 6. 5-2) 0.75 ≤ r/t ≤ 99 (eq. the transition at the end of the reinforced branch to the branch pipe might require additional qualification.828 (3.5. For d/D<0.096 1.813 0.0771 -0.553 Run ktr 0. 6-3 . values of k ir.3(d)-1 when the effective values of branch thickness and radius are used as specified in Section 5.0 (eq. 5-3) This report focused on the branch connection configuration depicted in Figure NC3673.717 Run kor 0. for configurations corresponding to sketches (a) and (b).751 2.2(b)-1. 5-1) 3.5 (eq. Replace Bo with 0.279 0. kor and ktr are small and should be set to zero.0 (d/D)-3.995 n1 1.43 0.675 n2 0.75(d/D) +(d/D) ) Note 2.5. The equations for kir.602 -0. The equations presented above are also applicable to the configurations of sketches (a) and (b) of Figure NB-3643.328 -0. 5 B Indices This report is focused on SIFs and flexibility factors for ASME Section III Class 2 or 3 and ANSI B31.374”) 10’ long. 6-4 . 6. the factor would change to 10. Assume the material is A106 Grade B. Assume there is an in-plane moment on the branch such that the rotation is 0. would be 19 times that calculated using the flexibilities defined in this report. it is suggested that the existing plant-specific Code of record be followed. In other words. As an example. with E = 30. t=0. consider a straight run of pipe (Do=24”.75”. The use of the expressions defined in this report will clearly result in a more realistic evaluation of branch connections. The use of the flexibility factors suggested herein will tend to offset this increase in the indices. The moment calculated to obtain this rotation. Reference [27] contains a discussion of the potential effects of including the flexibility of the branch connection.1 piping. T=0.000 ksi. The scope of this report did not address the B indices for the branch connections. fixed at both ends with a branch pipe (do= 12. ignoring this flexibility would result in over-estimating the stresses by a factor of 19.375”) 2’ long located 4’ from one end of the run pipe.6 Comparison to Present Code The present Code yields unconservative results for certain ranges of the parameters. If the lengths were doubled. This unconservatism has been documented in various studies previously. assuming no local flexibility of the branch. Many examples are given where inclusion of the appropriate flexibility will turn a not-Code-acceptable piping system into a Code-acceptable system.EPRI Licensed Material Conclusions 6.001 radians. This unconservatism has been addressed by the equations herein. If B indices are required in the qualification process. Certain editions of ASME Section III require the use of B indices for the qualification of Class 2 or 3 piping. E. Los Angeles. Power Piping.S. 5. Welding Research Council Bulletin 329. 6. Bryson. 4).. “Reinforcement of Branch Pieces”. 1995. Rodabaugh. Texas: May 1985.1 (2.. 8. 74.W. Engineering. Section III. ORNL-TM-3014. Corum. 7. American Society of Mechanical Engineers. A. Gwaltney. New York. (1947). COSMOS.. J. Markl. 9-12. 2. London. 11. S. A General Purpose Finite Element Analysis Computer Program. J.. 287-303). Accuracy of Stress Intensification Factors for Branch Connections.S. ASME Boiler and Pressure Vessel Code. July 1964-January 1965. Low Cycle Fatigue Testing of One-Half Scale Model Pressure Vessels. 9. Rodabaugh. December 1987. A Study of Fatigue Crack Initiation and Failure in Reinforced Shell to Shell Intersections. J. Transactions of the ASME.. August... Code for Pressure Piping. Progress Reports No. E..R.C.. 4 th International Conference on Pressure Vessel Technology.C. 4.EPRI Licensed Material 7 REFERENCES 1. Houston.G. Journal of Mechanical Engineering.C. 3. University of Oklahoma.. E. Theoretical and Experimental Stress Analysis of ORNL Thin-Shell Cylinder-to-Cylinder Model No. San Antonio. A. Decock. Structural Research and Analysis Corporation. Pickett. 1952. R. American National Standards Institute (ANSI). Fatigue Tests of Piping Components. (1980). Southwest Research Institute. Nuclear Power Plant Components. New York.M. Stress Indices for Small Branch Connections with External Loads. 1970. Texas. B31. A. 10. Report Prepared by WFI International. American Society of Mechanical Engineers. Blair. “External Loads on Nozzles in Cylindrical Shells”. England.C. CA. 3. ORNL7-1 . (pgs. Khan. J. Bolt.1. 3.5 Subjected to Through-Run Moments. Roarty.. Oak Ridge... E.. M. E..G. 18. I. “Finite Element Stress Analysis of An Equal Diameter Branch Pipe Intersection Subjected to Out-Of-Plane and Twisting Moments”. C5/85.E.. 15. 12.G..W.. respectively.A. and June 1975. and 4. and Gwaltney.D. NUREG/CR-3243. Pressure Vessels and Piping. May 1994.. Oak Ridge National Laboratory.. “Stress Indices and Flexibility Factors for Nozzles in Pressure Vessels and Piping”. 17.C. E. D. June 1979. and Moore. 20. October 1975.. Schneider. Experimental Stress Intensification Factors for Small Branch Connections. 1996. American Society of Mechanical Engineers.C. 14. and Kirkwood. American Society of Mechanical Engineers. October 1972. respectively. (1985). and Moore. R.E. June 1983. “Flexibility Factors for Fabricated Equal Diameter Branch Pipe Intersections”. Oak Ridge National Laboratory. S. June 1975. Volume 338. H.C.EPRI Licensed Material References TM-4553. “Comparisons of ASME Code Fatigue Evaluation Methods for Nuclear Class 1 Piping with Class 2 or 3 Piping”.. Evaluation of Branch Connections With r/R Less than 0. No. ORNL/Sub/82-22252/1. 1991.C.C. NUREG/CR-5359. Gwaltney R. Carmichael.. American Society of Mechanical Engineers. (1986). P. M. 2.Mech.. and Strauch. Wais. 1. Moore. ORNL-6339. Ellenberger. 5021. New York.Mech. ASA Code Case 53. TN. (Reop) June 1965.E. Oak Ridge National Laboratory. 21.C. Pressure Vessels and Piping. NUREG/CR-0778. L. E. 5020. D.T. Rodabaugh. and 5019 for Models 1. G. Rodabaugh. December 1987. E. NUREG/CR-4785.. D.G... Volume 218. “Review and Evaluation of Design Analysis Methods for Calculating Flexibility of Nozzles and Branch Connections”. Millman. Volume 21. Moffat. 1986. S. 13. I. 1981 (copy to Code Committee on Pressure Piping). Letter to J. P. London. E. E. Rodabaugh. R.E.. Rodabaugh. New York. S. Mokhtarian. Moffat.. Secretary of ASME III.G.C. April 21. Moore. 7-2 .. “Review of Elastic Stress and Fatigue-toFailure Data for Branch Connections and Tees in Relation to ASME Design Criteria for Nuclear Power Piping Systems”. S.E. 19. London. Rodabaugh. Kirkwood. ORNL/TM-11152.. 16. Journal of Strain Analysis. E. Bryson.E. (1987). November 1993.. EPRI. 1996. B. 26. E... Oak Ridge National Laboratory.3 Allowable Stresses”. S.. E.G. NUREG/CR-5358.C. “Review of ASME Code Criteria for Control of Primary Loads on Nuclear Piping System Branch Connections and Recommendations for Additional Development Work”.C.C. 25. and Wais. J. E. S. Elsevier Applied Science Publishers Ltd. W. ASME. 03080161/87.. CA: May. A.E.. Palo Alto.. ORNL/TM-11572.W. England. Pressure Vessels and Piping Conference. International Journal of Pressure Vessels and Piping. Johnson. ORNL/NUREG-52. Rodabaugh. Rodabaugh. Oak Ridge National Laboratory. Gwaltney. July 1978... 7-3 .. “Evaluation of the Plastic Characteristics in Relation to ASME Code Criteria”. “Flexibility of Branch Connections and B31. Oak Ridge National Laboratory. Stress Intensification Factors and Flexibility Modeling for Concentric and Eccentric Reducers. and Moore. C. NUREG/CR-0261. “Stresses in Reinforced Nozzle/Cylinder Attachments Under External Loadings Analyzed by the Finite Element Method”. A. 27. (1996). TR-106416. R.. Rodabaugh.S.. and Bass.EPRI Licensed Material References 22. 23.R. 24. Khan. and Moore. “A Study of Stress Intensification Factors of Integrally Reinforced Shell to Shell Intersections”. EPRI Licensed Material A MATERIAL CERTIFICATIONS A-1 . EPRI Licensed Material Material Certifications A-2 . EPRI Licensed Material Material Certifications A-3 . EPRI Licensed Material B CALIBRATION RECORD B-1 EPRI Licensed Material Calibration Record B-2 EPRI Licensed Material Calibration Record B-3 EPRI Licensed Material C TEST DATA AND RESULTS Overview of Appendix C The description of the testing is contained in Section 2. 2. The data includes loads. and so on.directions. such as resetting a dial gauge. The sheets are used to determine the linear slope of the loaddeflection curves for the four loading conditions. This plot indicates the reasonableness of the slope of the load-deflection curves. loading. Table 2-2 contains a summary of the results. A summary plot of the load-deflection curve and the four straight lines from the load displacement data (item 1 above). and unloading). The fatigue test data analysis. 3. The columns identified as “modified” are for the case where adjustments are required to the data collection. Each test report contains the following: 1. deflections. This appendix contains reports of the details regarding the test data for each of the four tests. C-1 . including the displacement amplitude and number of cycles at each displacement. Load-deflection data sheets for four conditions (=/. EPRI Licensed Material Test Data and Results Test Specimen A Test Report C-2 . EPRI Licensed Material Test Data and Results C-3 . EPRI Licensed Material Test Data and Results C-4 . EPRI Licensed Material Test Data and Results C-5 . EPRI Licensed Material Test Data and Results C-6 . EPRI Licensed Material Test Data and Results C-7 . EPRI Licensed Material Test Data and Results C-8 . EPRI Licensed Material Test Data and Results Test Specimen B Test Report C-9 . EPRI Licensed Material Test Data and Results C-10 . EPRI Licensed Material Test Data and Results C-11 . EPRI Licensed Material Test Data and Results C-12 . EPRI Licensed Material Test Data and Results C-13 . EPRI Licensed Material Test Data and Results C-14 . EPRI Licensed Material Test Data and Results C-15 . EPRI Licensed Material Test Data and Results Test Specimen C Test Report C-16 . EPRI Licensed Material Test Data and Results C-17 . EPRI Licensed Material Test Data and Results C-18 . EPRI Licensed Material Test Data and Results C-19 . EPRI Licensed Material Test Data and Results C-20 . EPRI Licensed Material Test Data and Results C-21 . EPRI Licensed Material Test Data and Results C-22 . EPRI Licensed Material Test Data and Results Test Specimen D Test Report C-23 . EPRI Licensed Material Test Data and Results C-24 . EPRI Licensed Material Test Data and Results C-25 . 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