The history of the primary stress design equations for Class 1 and 2 elbows in the ASME Boiler and Pressure Vessel Code (Section III, Division 1, Subsections NB and NC) is reviewed. The review includes the early analytical solutions for elbow bending, Markl’s stress-intensification factor, the development of Code equation (9), the relationship between SIFs and the and stress indices, development of equations that are functions of internal pressure and bend angle, and a suggested definition of the index which is based on nonlinear finite element analysis.
Issue Section:
Technical Papers
1.
ASME, 2001, Boiler and Pressure Vessel Code, Section III, Division 1. American Society of Mechanical Engineers, New York, NY.
2.
ASME, 2001, Section NB-3213.8.
3.
Dodge
, W. G.
, and Moore
, S. E.
, 1972
, “Stress Indices and Flexibility Factors for Moment Loadings on Elbows and Curved Pipe
,” Weld. Res. Counc. Bull.
, 179
, p. 2
2
.4.
Rodabaugh, E. C., and Moore, S. E. 1978, “Evaluation of the Plastic Characteristics of Piping Products in Relation to ASME Code Criteria,”’ NUREG/CR-0261, p. 5.
5.
Moore
, S. E.
, and Rodabaugh
, E. C.
, 1982
, “Pressure Vessel and Piping Codes—Background for Changes in the 1981 Edition of the ASME Nuclear Power Plant Components Code for Controlling Primary Loads in Piping Systems
,” ASME J. Pressure Vessel Technol.
104
, p. 351
351
.6.
ASME, 2001, Subsection NC, Class 2 Components.
7.
ASME, 2001, Subsection ND, Class 3 Components.
8.
ASME, 1969, Foreword to B31.7, Nuclear Power Piping.
9.
ASME, 2001, Paragraph NB-3681 (d).
10.
ASME, 2001, Section III, Division 1, Appendix II, Experimental Stress Analysis, Section II-1800, Experimental Determination of Stress Indices for Piping.
11.
ASME, 2001, Section III, Division 1, Appendix II, Experimental Stress Analysis, Section II-1430, Criterion of Collapse Load.
12.
ASME, 2001, Subparagraph NB- 3213.25.
13.
Gerdeen, J. C., 1979, “A Critical Evaluation of Plastic Behavior Data and a Unified Definition of Plastic Loads for Pressure Components,” Weld. Res. Counc. Bull., 254.
14.
von Karman
, T.
, 1911
, “U¨ber die Forma¨nderung du¨nnwandiger Rohre, insbesondere federnder Ausgleichrohre
,” Zeitschrift des Vereines deutscher Ingenieure
,55
, pp. 1889
–1895
.15.
Bantlin
, A.
, 1910
, “Forma¨nderung and Beanspruchung federnder Ausgliechrohre
,” Zeitschrift des Vereines deutscher Ingenieure
,54
, pp. 43
–49
.16.
Markl, A. R. C. 1955, “Piping Flexibility Analysis,” ASME Transactions; Reprinted in Pressure Vessel and Piping Design; Collected Papers (1927–1959), ASME, pp. 402-418.
17.
Rodabaugh
, E. C.
, and George
, H. H.
, 1957
, “Effect of Internal Pressure on Flexibility and Stress-Intensification Factors of Curved Pipe or Welding Elbows
,” Trans. ASME
, 79
, pp. 939
–948
.18.
Yu, L., 1999, “Elbow Stress Indices Using Finite Element Analysis,” Ph.D. dissertation, North Carolina State University; Report Number C-NPP-SEP 27/99, Center for Nuclear Power Plant Structures, Equipment, and Piping.
19.
Markl
, A. R. C.
, and George
, H. H.
, 1950
, “Fatigue Tests on Flanged Assemblies
,” Trans. ASME
, 72
, pp. 77
77
.20.
Markl
, A. R. C.
, 1952
, “Fatigue Tests of Piping Components
, Trans. ASME
, 74
, pp. 287
–303
.21.
Markl, 1952, p. 292.
22.
Beskin
, L.
, 1945
, “Bending of Thin Curved Tubes
,” ASME J. Appl. Mech.
, 67
, p. A-1
A-1
.23.
Pardue, T. E., and Vigness, I. Discussion of Markl’s paper, Trans. ASME, 74, p. 301.
24.
ASME, Foreword to B31.7, 1969, Para. 3.
25.
Markl, 1952, p. 407.
26.
Rodabaugh, and George, 1957, p. 939.
27.
Vigness
, I.
, 1943
, “Elastic Properties of Curved Tubes
,” Trans. ASME
, 65
, p. 105
–120
.28.
Turner
, E. E.
, and Ford
, H.
, 1957
, “Examination of the Theories for alculating the Stresses in Pipe Bends Subjected to In-Plane Bending
,” Proc. Inst. Mech. Eng.
, 171
, pp. 513
–515
.29.
Gross
, N.
, 1952
–1953, “Experiments on Short Radius Pipe Bends
,” Proc. Inst. Mech. Eng.
, 1
, p. 465
465
.30.
Gross, ibid., 1952–1953, p. 480.
31.
ASME, 1969, Foreword to B31.7, p. xiii.
32.
Dodge and Moore, 1972, p. 11.
33.
Mello, R. M., and Griffin, D. S., 1974, “Plastic Collapse Loads for Pipe Elbows Using Inelastic Analysis,” ASME J. Pressure Vessel Technol., pp. 177–183.
34.
Greenstreet, W. L., 1978, “Experimental Study of Plastic Responses of Pipe Elbows,” ORNL/NUREG-24.
35.
Demir, H. H. and Drucker, D. C., 1963, “An Experimental Study of Cylindrical Shells Under Ring Loading,” 205-20 in Progress in Applied Mechanics (The Prager Anniversary Volume), MacMillan, New York, NY.
36.
Rodabaugh, and Moore, 1978, p. 5.
37.
Rodabaugh, and Moore, 1978, p. 9.
38.
Larson, L. D., Stokey, W. F., and Panarelli, J. E., 1974, “Limit Analysis of a Thin-Walled Tube Under Internal Pressure, Bending Moment, Axial Force, and Torsion,” ASME J. Appl. Mech., pp. 831–832.
39.
Rodabaugh, E. C., and Moore, S. E., 1982, “End Effects on Elbows Subjected to Moment Loadings,” Pressure Vessel and Piping Conference and Exhibition, Orlando, FL, ASME PVP-Vol. 56.
40.
Rodabaugh, and Moore, 1978, p. 23.
41.
Spence, J., and Findlay, G. E., 1973, “Limit Loads for Pipe Bends Under In-Plane Bending,” Proc. 2nd International Conference on Pressure Vessel Technology, Part I: Design and Analysis, Paper I-28, pp. 393–399.
42.
Rodabaugh, and Moore, 1978, p. 25.
43.
Moore, and Rodabaugh, 1982, p. 353.
44.
Rodabaugh, and Moore, 1982, p. 104.
45.
Case N-319, Cases of the ASME Boiler and Pressure Vessel Code, Approved by Council July 13, 1981, ASME, New York.
46.
Case N-319-3, Cases of the ASME Boiler and Pressure Vessel Code, Approved by Council August 14, 1990, ASME, New York.
47.
ASME, 2001, Subparagraph ND- 3673.2(h).
48.
Rodabough (sic), E. C. and Moore, S. E., 1983, “Stress Indices and Flexibility Factors for Concentric Nozzles,” Welding Research Council Bulletin 285.
49.
Avent, R. R., Sadd, M. H., and Rodabough (sic), E. E., 1983, “Finite Element Analysis of Eccentric Reducers and Comparisons with Concentric Reducers,” Weld. Res. Counc. Bull., 285.
50.
Williams, D. K, and Lewis, G. D., 1983, “Development of B1 and C1 Stress Indices for a Trunion Elbow Support,” ASME 83-PVP- 20.
51.
Touboul
, F.
, Ben Djedidia
, M.
, and Acker
, D.
, 1988
, “Stress Index Method of Design: Application to In-plane Closing Collapse of Elbows
,” Int. J. Pressure Vessels Piping
, 33
, pp. 153
–164
.52.
Spence, J. S. and Findlay, G. F., 1973, “Limit Loads for Pipe Bends Under in-plane Bending,” Proc. 2nd Int. Conf. Pres. Ves. Technol., Paper 1-28, ASME, New York, NY.
53.
Touboul
, F.
, and Acker
, D.
, 1991
, “Excessive Deformation and Failure of Straight parts and Elbows
,” SMiRT 11, E02/2
11
, pp. 19
–24
.54.
Rodabaugh, E. C., Gwaltney, R. C., and Moore, S. E., 1993, “Review of ASME Code Criteria for Control of Primary Loads on Nuclear Piping System Branch Connections and Recommendations for Additional Development Work,” NUREG/CR-5358.
55.
Kanninen, M. F., et al., 1976, “Mechanical Fracture Predictions for Sensitized Stainless Steel Piping with Circumferential Cracks,” EPRI NP-192, Sept.
56.
Wais, E. A., 1995, “Recent Changes to ASME Section III Welded Attachments (Lugs) Code Cases,” ASME PVP-Vol. 313-2, International Pressure Vessels and Piping Codes and Standards: Volume 2—Current Perspectives, pp. 29–31.
57.
Rawls, G. B., Wais, E. A. and Rodabaugh, E. C., 1992, “Evaluation of the Capacity of Welded Attachments to Elbows as Compared to the Methodology of ASME Code Case N-318,” ASME PVP-Vol. 237-2, Seismic Engineering, Vol. 2.
58.
Wais, E. A., 2001, private communication.
59.
Liu, T., Kumar, R., Saleem, M. A., and Usmani, S. A., 1999, “Stress Indices for Feeder Pipe Bends Based on Finite Element Analysis,” ASME PVP-Vol. 388, Fracture, Design Analysis of Pressure Vessels, Heat Exchangers, Piping Components, and Fitness for Service, pp. 343–352.
60.
Yu, L., Tan, Y., and Matzen, V. C., 1999, “B2 Stress Indices for Elbows and Straight Pipes Using Finite Element Analysis,” Transactions of the 15th International Conference on Structural Mechanics in Reactor Technology, Aug. Vol. IV, Paper F01/6, pp. IV:41- 48.
61.
Tan, Y., 2001, “Experimental and Nonlinear FEA Investigation of Elbow Leading to a New Definition of the B2 Stress Index,” Ph.D. dissertation, North Carolina State University, Raleigh, NC.
62.
Matzen, V. C., and Tan, Y., 2000, “The History of the B2 Stress Index and a New Margin-Consistent Procedure for its Calculation,” ASME PVP-Vol. 399, Design and Analysis of Pressure Vessels and Piping, pp. 251–258.
63.
McCabe, J., 2000, private communication.
64.
Tan, Y., Matzen, V. C., and Yuan, X., 2001, “A Margin—Consistent Procedure for Calculating the B2 Stress Index and a Proposed New Design Equation,” Trans. SMiRT-16
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