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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 14

Computing Hoop Strains in Out-of-Round Pipes under Internal Pressure

Z.W. Guan

Department of Engineering (Civil), The University of Liverpool, United Kingdom

Full Bibliographic Reference for this paper
Z.W. Guan, "Computing Hoop Strains in Out-of-Round Pipes under Internal Pressure", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 14, 2006. doi:10.4203/ccp.83.14
Keywords: composite, GRP, hoop strain, laminated, out-of-round, variable pressure.

Summary
Although there is limited information on the effect of non-circularity of cross-section on the strains (and hence stresses) in pressurised pipes, the importance of such effects has long been recognised. An early study of the effect of out-of-roundness dates back to the 1930s [1]. With the development of high strength, high stiffness, and low density composite materials, composite laminated structures have been used more and more widely in aerospace industry as well as in ground applications. Since the 1960s, a large number of papers have been published on laminated shells and cylinders. Researchers applied a theory of a thin laminated anisotropic shell, which may be considered as an extension of Reissner and Stavsky's work [2] on laminated anisotropic plates, to Donnell's shallow shell theory. Since then, a series of papers on the similar topics has appeared. To deal with pipes with a non-circular cross section, Gheorghiu and Blumenfeld [3] developed a circular section model, subjected to variable pressure, which is used to replace the ovalised cylindrical shell with variable wall thicknesses, subjected to a constant internal pressure.

On comparison with general composite cylindrical shells, laminated cylinders not only possess a relatively small radius-to-thickness ratio, but variable thickness and radius. Hence composite laminated cylinders are of more complicated mechanical behaviour in the way of load transferring through material layers. However, there is little information available that considers effects of variable radius and, or thickness on the hoop strains (and hence stresses) in pressurised pipes, especially in laminated composite pipes. Hose and Kitching [4] presented measured results using strain gauges for GRP laminated pipes subjected to internal pressure, of which wall constructions had glass provided in different combinations of CSM (Chop Strand Mats) and WR (Woven Roving). Experimental results showed that the hoop strains on the outer surface of the pipe were much lower than those on the inner surface. In spite of the analytical efforts to this phenomenon no satisfactory explanation was yet available. More recently, a computer aided design has been used to assist design of non-circular pipes [5].

In this paper, elastic solutions given by a special stress function are presented for GRP laminated pipes subjected to internal pressure, which include both the transverse shear deformations and the normal strains, as well as expansion strains. The effects of geometrical imperfections in the pressurised laminated pipe are taken into consideration by applying variable internal pressure, which was obtained by using the static equivalence between the practical pipe subjected to constant pressure with variable radii and the model pipe subjected to variable internal pressure but with a constant radius. Assuming elasticity applied, using static equivalence, a relationship between Fourier coefficients associated with the variable internal pressure and the geometrical imperfections is established. Using the developed theory, hoop strains for the GRP pipes were presented, in a form suitable for implementation in a computer. A test rig was also designed to measure variation of the radii for both GRP pipes in an interval of every 20. The corresponding Fourier coefficients of the variable radius were obtained based on the measurements. The theoretical calculations of the hoop strains for one-layer WR and three-layer WR pipes were then carried out by making a computer programme and solutions were compared with the experimental results. It is shown that the solutions can be used to explain, in some extent, a large proportion of experimental results, which cannot be explained by a simple elastic theory that can only deal with circular cross sections.

References
1
Haigh, B.P., "An estimate of the bending stresses induced by pressure in a tube that is not initially quite circular", 2nd Report to WRC, Appendix 9, 96-98, 1936.
2
Reissner, E. and Stavsky, Y., "Bending and stretching of certain types of heterogeneous anisotropic elastic plates", J. of Appl. Mech., 28, 402-408, 1961.
3
Gheorghiu, H. and Blumenfeld, M., "Hoop stresses in ovalized cylindrical tubes, with variable thickness walls", Mech. Appl, 30(5), 541-548, 1985.
4
Hose, D.R. and Kitching, R., "Glass reinforced composite of mixed wall construction", Int. J. Press. Ves. & Piping, l.27, 305-323, 1987.
5
Kiuchi, M., Moslemi, H. and Shintani, H., "Computer aided design of rolls for reshaping processes from round pipes to "channel-type" pipes", J. Mat. Proc.Tech., 111 (1-3), 193-197, 2001. doi:10.1016/S0924-0136(01)00511-8

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