The purpose of this study is to determine limit loads for pipe elbows subjected to in-plane bending moments that tend to close the elbow (i.e., decrease 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 or 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. The limit load was found to increase and then decrease with increasing pressure for all the elbow geometries studied.

1.
ABAQUS, 1995, ABAQUS/Standard Version 5.5, User’s Manual Vol. I, 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,” ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY Paper No. 71-PVP-37, pp. 1–12.
3.
Boyle, J. T., and Spence, J., 1977, “The Nonlinear Analysis of Pressurized Pipe Bends,” Proceedings, 3rd International Conference on Pressure Vessel Technology, Tokyo, Japan, pp. 121–131.
4.
Brashel, R. A., et al., 1983, “Calculation of the Load Carrying Capacity of Pipe Elbows With the Help of the Method of Approximation,” Proceedings, 7th SMiRT Conference, Chicago, IL, G/F5/8, pp. 373–380.
5.
Brouard, d., et al., 1981, “In-Plane and-Out-of-Plane Bending Tests on Carbon Steel Pipe Bends,” Proceedings, 6th SMiRT Conference, Paris, France, F3/2.
6.
Calladine
C. R.
,
1974
, “
Limit Analysis of Curved Tubes
,”
Journal of Mechanical Engineering Sciences, Institute of Mechanical Engineers
, Vol.
16
, No.
2
, pp.
85
87
.
7.
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, 275–285.
8.
Dhalla, A. K., 1980, “Plastic Collapse of a Piping Elbow: Effect of Finite Element Convergence and Residual Stresses,” Proceedings, 4th International Conference on Pressure Vessel Technology, Vol. 11, The Institution of Mechanical Engineers, London, U.K., pp. 243–249.
9.
Dhalla
A. K.
,
1987
, “
Collapse Characteristics of a Thin Walled Elbow: Validation of Analytical Procedure
,”
ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Vol.
109
,
394
401
.
10.
Goodall, I. W., 1978a, “Large Deformations in Plastically Deforming Curved Tubes Subjected to In-Plane Bending,” Research Division Report RD/B/N4312, Central Electricity Generating Board, England.
11.
Goodall, I. W., 1978b, “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.
12.
Hibbitt, H. D., and Leung, E. K., 1985, “Verification and Application of an Inelastic Analysis Methods for LMFBR Piping System,” Welding Research Council Bulletin, No. 308, pp. 1–28.
13.
Hilsenkpf
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
.
14.
Kitching
R.
, et al.,
1979
, “
Limit Moment for a Smooth Pipe Bend Under In-Plane Bending
,”
International Journal of Mechanical Sciences
, Vol.
21
, pp.
731
738
.
15.
Kussmaul
K.
, et al.,
1987
, “
Investigation of the Plastic Behaviour of Pipe Bends
,”
ASME PVP
-Vol.
127
, pp.
55
66
.
16.
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
.
17.
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.
18.
Sobel, L. H., and Newman, S. Z., 1977, “Instability Analysis of Elbows in the Plastic Range,” Proceedings, 4th SMiRT Conference, San Francisco, CA, Vol. L, Paper No. L 3/2, pp. 1–11.
19.
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
.
20.
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
.
21.
Spence, J., and Findlay, G. E., 1973, “Limit Loads for Pipe Bends Under In-Plane Bending,” Proceedings, 2nd International Conference on Pressure Vessels Technology, San Antonio, TX, Vol. 1-28, pp. 393–399.
22.
Whatham
J. F.
, and
Thompson
J. J.
,
1979
, “
The Bending and Pressurizing of Pipe Bends With Flanged Tangents
,”
Nuclear Engineering and Design
, Vol.
54
, pp.
17
28
.
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