The purpose of this study is to determine limit loads for pipe elbows subjected to inplane bending moments that tend to open the elbow (i.e., increase its radius of curvature), and the influence of internal pressure on the value of the limit load. Load-deflection curves were obtained, and from these curves plastic collapse and instability loads at various values of internal pressure were determined. This was done for different pipe bend factors (h = Rt/r2) using the nonlinear finite element analysis code (ABAQUS) with its special elbow element. A set of limit curves was generated from the results. These curves show the variation of collapse and instability loads with internal pressure for different elbows. Collapse loads were found to increase and then decrease with increasing pressure for all the elbow geometries studied. Instability loads were difficult to reach because of the large stiffening effect of the elbow cross-sectional deformation, and they were generally found to decrease with increasing pressure.

1.
ABAQUS, 1995, “ABAQUS/Standard Version 5.5,” User’s Manual, Example Problems Manual, Vol. I and Theory Manual, Hibbitt, Carlsson & Sorensen, Inc., RI.
2.
Bolt, S. E., and Greenstreet, W. L., 1972, “Experimental Determination of Plastic Collapse Loads for Pipe Elbows,” TRANS ASME, Paper No. 71-PVP-37, pp. 1–12.
3.
Braschel, R. A. et al., 1983, “Calculation of the Load Carrying Capacity of Pipe Elbows with the Help of the Method of Approximation,” 7th SMiRT Conference, Chicago, IL, G/F5/8, pp. 373–380.
4.
Brouard, D. et al., 1981, “In-Plane and Out-of-Plane Bending Tests on Carbon Steel Pipe Bends,” 6th SMiRT Conference, Paris, France F3/2.
5.
Calladine
C. R.
,
1974
, “
Limit Analysis of Curved Tubes
,”
Journal of Mechanical Engineering Science
, Institute of Mechanical Engineers, Vol.
16
, No.
2
, pp.
85
87
.
6.
Chain, K. L. C. et al., 1984, “Approximate Limit Loads for Pipe Bends with End Constraints,” Applied Solid Mechanics-1, eds., A. S. Tooth and J. T. Boyle, Elsevier, pp. 275–285.
7.
Dhalla, A. K., 1980, “Plastic Collapse of a Piping Elbow: Effect of Finite Element Convergence and Residual Stresses,” Proceedings, 4th International Conference on Pressure Vessels Technology, Vol. 11, The Institution of Mechanical Engineers, London, U.K., pp. 243–249.
8.
Gerdeen, J. C., 1979, “A Critical Evaluation of Plastic Behavior Data and a Unified Definition of Plastic Loads for Pressure Components,” Welding Research Council Bulletin, No. 254, pp. 1–63.
9.
Goodall, I. W., 1978, “Lower Bound Limit Analysis of Curved Tubes Loaded by Combined Internal Pressure and In-Plane Bending Moment,” Research Division Report RD/B/N4360, Central Electricity Generating Board, England, 14.
10.
Hilsenkopf
P.
et al.,
1988
, “
Experimental Study of Behavior and Functional Capability of Ferritic Steel Elbows and Austenitic Stainless Steel Thin-Walled Elbows
,”
International Journal of Pressure Vessels & Piping
, Vol.
33
, No.
2
, pp.
111
128
.
11.
Kitching
R.
et al.,
1979
, “
Limit Moment for a Smooth Pipe Bend under In-Plane Bending
,”
International Journal of Mechanical Science
, Vol.
21
, pp.
731
738
.
12.
Kussmaul
K.
et al.,
1987
, “
Investigation of The Plastic Behaviour of Pipe Bends
,”
ASME PVP
-Vol.
127
, pp.
55
66
.
13.
Marcal
P. V.
,
1967
, “
Elastic-Plastic Behavior of Pipe Bends with In-Plane Bending
,”
Journal of Strain Analysis
, Vol.
2
, No.
1
, pp.
84
90
.
14.
Prost, J. P., and Amzallag, C., 1981, “Experimental Study of Carbon Steel Straight Pipes and Elbows under Moment Loadings,” 6th SMiRT Conference, Paris, France, F2/9.
15.
Prost, J. P. et al., 1983, “Experimental Study of Stainless Steel Pipes and Elbows under Pressure and Moment Loadings,” 7th SMiRT Conference, G/F5/5, Chicago, IL.
16.
Rodabaugh, E. C., 1979, “Interpretive Report on Limit Load Analysis and Plastic Deformation of Piping Products,” Welding Research Council Bulletin, No. 254, pp. 65–82.
17.
Shalaby, M. A., 1996, “Elastic-Plastic Behavior and Limit Load Analysis of Pipe Elbows under In-Plane Bending and Internal Pressure,” M.Sc. thesis, The American University in Cairo, Cairo, Egypt.
18.
Shalaby
M. A.
, and
Younan
M. Y. A.
,
1997
, “
Limit Loads for Pipe Elbows with Internal Pressure under In-Plane Closing Bending Moments
,”
ASME PVP
-Vol.
347
, pp.
203
213
; also, 1998, ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY, Vol. 120.
19.
Sobel, L. H., and Newman, S. Z., 1977, “Instability Analysis of Elbows in the Plastic Range,” 4th SMiRT Conference, San Francisco, CA, Vol. L, Paper No. L 3/2, pp. 1–11.
20.
Sobel
L. H.
, and
Newman
S. Z.
,
1980
, “
Comparison of Experimental and Simplified Analytical Results for In-Plane Plastic Bending and Buckling of an Elbow
,”
ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Vol.
102
, pp.
400
409
.
21.
Sobel
L. H.
, and
Newman
S. Z.
,
1986
, “
Simplified, Detailed, and Isochronous Analysis and Test Results for the In-Plane Elastic Plastic and Creep Behavior of an Elbow
,”
ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Vol.
108
, pp.
297
304
.
22.
Spence, J., and Findlay, G. E., 1973, “Limit Loads for Pipe Bends under In-Plane Bending,” Proceedings, 2nd International Conference on Pressure Vessel Technology, San Antonio, TX, Vol. I-28, pp. 393–399.
This content is only available via PDF.
You do not currently have access to this content.