Deflections of Thin-Walled Storage Tanks with Roof due to ...

displacement in both the experiment and the computation, Figure 3.c, then the results are inreasonable agreement.The complete pattern of deflections computed using ABAQUS is shown in Figure 7, for u max= 1 mm. The deflected shape is very similar to what was obtained in the experiments, as shownin Figure 2.CONCLUSIONSThe simulations carried out in this research, as well as the tests performed on a small scalemodel, show that the deflection patterns in thin-walled cylindrical shells with a top flat roof dueto localized settlements of the foundation are associated to a geometrical behavior of the shellthat is highly non-linear. For the small-scale model of a cylindrical tank with a flat roof, thebehavior seems to be similar to a stable symmetric bifurcation. A linear fundamental equilibriumpath is seen to occur, until buckling develops into a new shape for the shell. In the new stableconfiguration, the shell can withstand further vertical displacements at the base with an increasein the amplitude of the post-buckling mode. Regarding the engineering importance of this effect,one has to look at the displacement amplitudes: the out-of-plane displacements computed usinga geometric non linear theory of shells are much larger than the linear values (as shown inFigure 5), so that it does not seem wise to establish tolerance criteria for settlements based ongeometrically linear shell models.ACKNOWLEDGEMENTSThis work was supported by the US National Science Foundation (grant NSF CMS-9907440), and by the US Federal Emergency Management Agency (grant FEMA PR-0060-A).Their contribution is gratefully acknowledged.REFERENCESD’Orazio, T., Ducan, J. M. and Bell, R. A. (1989), “Distortion of steel tank due to settlement oftheir walls”. Journal of the Geotechnical Engineering Division, ASCE, Vol. 115 (6), 871-890.Hibbitt, H. D., Karlsson, B. I. and Sorensen (1997), ABAQUS/ User’s Manual, Version 5.7,Hibbitt, Karlsson and Sorensen, Inc.Jonaidi, M. and Ansourian, P. (1998), “Harmonic settlement effects on uniform and tapered tankshells”. Thin-Walled Structures, Vol. 31, 237-255.Kamyab, H. and Palmer, S.C. (1989), “Analysis of displacements and stresses in oil storagetanks caused by differential settlement”, Proceedings of Institutional Mechanical Engineers,Part C: Journal of Mechanical Engineering Science, Vol. 203, 60-70.Malik, Z., Morton, J. and Ruiz, C. (1977), “Ovalization of cylindrical tanks as a result offoundation settlement”. Journal of Strain Analysis, Vol. 12, 339-348.Marr, A., Ramos, J. A. and Lambe, T.W. (1982), “Criteria for settlement of tanks”. Journal ofthe Geotechnical Engineering Division, ASCE, Vol. 108 (8), 1017-1039.Myers, P. (1997), Aboveground Storage Tanks, McGraw-Hill, New York, 519-562.