Structural Consequences of Natural Hazards on Metal Storage Tanks

LACCET’2005 – Engineering Infrastructure Track – Paper No. 31 1

Third LACCEI International Latin American and Caribbean Conference for Engineering and Technology (LACCEI’2005) “Advances in Engineering and Technology: A Global Perspective”, 8-10 June 2005, Cartagena de Indias, Colombia.

Structural Consequences of Natural Hazards on Metal Storage Tanks

Luis A. Godoy, Ph. D. Civil Infrastructure Research Center and Department of Civil Engineering and Surveying, University of

Puerto Rico at Mayagüez, Mayagüez, Puerto Rico 00681-9041, [email protected]

Rossana Jaca Constructions Department, Engineering School, National University of Comahue, Buenos Aires 1400,

Neuquén, Argentina, [email protected]

Genock Portela, Ph. D. Department of General Engineering, University of Puerto Rico at Mayagüez, Mayagüez, Puerto Rico

00681-9044. [email protected]

Eduardo M. Sosa Department of Civil Engineering and Surveying, University of Puerto Rico at Mayagüez, Mayagüez,

Puerto Rico 00681-9041. [email protected]

Juan C. Virella, Ph. D. Civil Infrastructure Research Center, Department of Civil Engineering and Surveying, University of Puerto

Rico at Mayagüez, Mayagüez, Puerto Rico 00681-9041. [email protected] Abstract Aboveground metal storage tanks are used in the Caribbean islands and the United States as part of the infrastructure supporting the storage and distribution of oil and fuel. To assure the continuing supply of such products, this infrastructure should be in service following major natural hazards, including earthquakes, hurricanes, and floods. This paper reports results from a five-year research program on the structural consequences of natural hazards on thin-walled metal tanks with large diameter and low aspect ratio (short tanks). The tanks considered have several roof configurations, including conical, shallow spherical cap, flat, and floating roofs. Most tanks have rafters and columns to support the roof. The emphasis of the study is on the computational modeling of the structural response to predict buckling of the shell due to external loads. In the case of wind loads, two studies were carried out to estimate pressures on the shell: First, wind tunnel experiments on small scale models; and second, computational fluid dynamics simulations. For earthquake loads, the liquid stored plays an important role in the evaluation of loads, and both hydrostatic and sloshing actions have been considered in the analysis. Keywords Buckling, earthquake, foundation settlement, tanks, winds. 1. Introduction This paper summarizes the main conclusions of a research carried out at the University of Puerto Rico at


Mayagüez, together with collaborators from other institutions in Argentina, on the structural behavior of thin-walled metal tanks. Specifically, steel aboveground storage tanks are considered, such as those used to store oil and fuel in the oil industry; however, applications also extend to water tanks and those employed in the production of chemicals and alcoholic drinks. The structural response of interest is the buckling of tanks, i.e. a change in the shape of the shell due to external loads, because this is a crucial design factor in all tanks (Godoy 2000). The loads are the consequence of natural hazards, such as winds, hurricanes (Godoy, 1998) and earthquakes, and support settlements. Significant research efforts have been devoted to the study of the structural response of tanks; however, much of this assumes a tank without any roof. No effort is made here to summarize all research done in this field, because that would require a much more extensive work, and only the contributions emerging from this research program are reported. Emphasis is given in this paper to the structural behavior rather than to the methodology of analysis. A theme structure was chosen for most computations, and the geometric characteristics are shown in Figure 1. The tanks were here assumed to have clamped boundary conditions at the base and various configurations at the top: open-top, self-supported roofs, and roofs supported by rafters. The self-supported roof geometries have dome, cone, shallow cone, and flat roofs; whereas the rafter-supported roofs include cone, shallow cone, and flat roofs. Tanks with cylinder height to diameter ratios H/D = 0.24 to 0.95 were studied, in order to identify the effect of the H/D ratio and the roof configuration on the response. Whenever necessary, the density ρ = 983 Kg/m3 and bulk modulus Κ = 2.07 GPa for the liquid, were assumed in the computations.

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Figure 1: Section of a typical anchored tank with roof rafters. 2. Natural periods of empty steel tanks Most previous research on natural periods of vibrations of aboveground tanks concentrated on tanks which are open at the top. In contrast, this research looked at the influence of several roof configurations using computational (finite element) models. Virella et al. (2003) found that the vibration of empty tanks with a fixed roof is dictated either by purely cylinder modes or by roof modes (see Figure 2). For self-supported roofs, predominant roof modes resulted, whereas for tanks with roofs supported by rafters, cylinder modes dominate the dynamic behavior of the tank. Roof-dominated modes have natural periods that remain constant regardless of their H/D ratio. Cylinder modes, on the other hand (Figure 3), are characterized by natural periods that show a linear dependence on the H/D ratio of the tank. The periods do not change


when rafters are installed at the roof (Figure 3), but the dominant modes change. In the cases studied, the dominant modes changed from roof type for the self supported roof (i.e. cone, shallow cone, and flat roofs) to cylinder modes for the rafters-supported roof.

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Figure 2: First tank cylinder and roof vibration mode for self-supported cone roof tanks. (a) Mode 1, H/D = 0.63; (b) Mode 9, H/D = 0.63.

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Figure 3: First roof and cylinder modes natural periods for tanks with rafters-supported roofs. cone, cylinder-mode; shallow cone, cylinder- mode; flat, cylinder-mode;

cone, roof-mode; shallow cone, roof-mode; flat, roof-mode. 3. Natural periods due to impulsive action of the tank-liquid system Under horizontal motion, the fundamental impulsive modes of vibration of cylindrical tank-liquid systems anchored to the foundation are crucial to evaluate the seismic response of the structure. The hydrostatic pressure and the self-weight loads (which may be seen as a pre-stress state) have an influence on the natural periods and modes, and this influence has been evaluated for three tank-liquid systems with different H/D (0.40 to 0.95), with a level of liquid of 90% of the height of the cylinder. The numerical results presented by Virella et al. (2004a) show that the pre-stress state has a significant influence on the natural periods and mode shapes of tank-liquid systems with thinner walls; however, for


thicker shells, this effect is reduced (Figure 4). When the pre-stress state is either neglected or included, there is a small difference in natural periods, for modes characterized by small circumferential wave numbers. The steady-state response of a tank-liquid system to horizontal harmonic base accelerations showed large differences when the pre-stress state was neglected. A comparison of the Frequency Response Functions shows that the peak responses occur at quite different load periods and they have significantly different amplitudes. For the tank-liquid systems, the fundamental mode is a translational mode (n = 1), regardless of the cylinder height to tank diameter (H/D) considered (Virella et al. 2005). The highest natural periods are associated to cylinder modes, characterized with circumferential waves (n > 1) and axial half-waves (m = 1); however, those modes are not fundamental modes for predicting the response to a horizontal motion. For the range of shell dimensions of interest in the oil industry, the fundamental modes are not associated with circumferential wavy patterns. The fundamental modes of tanks with aspect ratios (H/D) larger than 0.63, are very similar to the first mode of a cantilever beam (Figure 5a and 6a). For the shortest tank, H/D = 0.40, the fundamental mode is a translational mode (n = 1), with an axial half-wave (m) characterized with a bulge formed near the mid-height of the cylinder (Figure 5b and 6b).

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Figure 4: Natural periods as a function of the circumferential wave number n for m = 1 for H/D = 0.40, including and neglecting the effect of the pre-stress state. (a) R/tavg =1660 and 553; (b) R/tavg =

332 and 237.

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Figure 5: Fundamental modes for tank-liquid systems. (a) H/D = 0.95, (b) H/D = 0.40.


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Figure 6: Fundamental modes for tank-liquid systems. (a) Deformed shape in meridian with maximum displacements for H/D = 0.95, (b) Deformed shape in meridian with maximum

displacements for H/D = 0.40. 4. Sloshing modes and pressures of tank-liquid systems The influence of non-linear wave theory on the sloshing natural periods and their modal pressure distributions were investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes were computed and compared for both, linear wave theory (LWT) and non-linear wave theory (NLWT). LWT was implemented in an acoustic model, while a plane strain problem with large displacements was used in NLWT. The computations were carried out for tank heights H to width B ratio (i.e. B = 2R) of 0.40 to 0.95, along with levels of liquid (HL/H) of 0.50 to 0.90. The first sloshing natural period for rectangular tanks considering LWT, decreases with HL/R, up to HL/R = 0.80, and then remains almost constant for larger ratios of HL/R (Figure 7a). The second and third anti-symmetric sloshing natural periods remain almost constant regardless of HL/R. It is found that non-linearity does not have significant effects on the natural sloshing periods, with differences smaller than 5% for all the tank-liquid systems considered (Virella et al. 2004b).

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(a) (b) Figure 7: (a) Natural periods for first three sloshing modes. (b) Pressure distribution for first

sloshing mode, HL/R = 0.40 (Surface wave = 3.24 m). NLWT model, LWT model.


For the first three sloshing modes, the pressures on the walls computed using LWT led to conservative values in magnitude, while larger pressures resultant heights were obtained for NLWT (Figure 7b). The conclusion is that the non-linearity of the surface wave does not have major effects on the pressure distribution on the walls for rectangular tanks (Virella et al. 2004b). 5. Buckling of tanks subject to earthquake loadings Dynamic and static buckling loads were evaluated by considering individually, the impulsive action and the sloshing actions of the tank-liquid systems (H/D of 0.40 to 0.95, and HL/H = 0.50 to 0.90). The Budiansky-Roth criterion was proven to be adequate to evaluate dynamic stability, for seismic excitation. Elastic buckling was found for all the tank-liquid systems subjected to the impulsive action of the hydrodynamic response in which the dynamic buckling modes were characterized by circumferential waves. It was found that the dynamic critical loads due to the impulsive action decreased with the level of liquid, regardless of the aspect ratio considered. In all cases, plasticity was observed after buckling occurred. Static buckling from from bifurcation and step-by-step non-linear analyses showed that buckling due to sloshing alone does not occur for the models considered. The most critical action for dynamic instability is the impulsive action of the tank-liquid systems. Therefore, for anchored tanks, the effect of sloshing can be neglected, because sufficient freeboard is provided for the sloshing wave to form, without coming in contact with the roof. 6. Buckling of tanks under construction due to low intensity winds The collapse of a steel tank located in the North area of Patagonia in Argentina, which failed under wind during its construction, was investigated by Jaca and Godoy (2003). In its final design, the tank would have presented a conical roof; but the construction level had not reached the roof at the moment of failure. For this reason, only the cylindrical shell resisted the action of the wind. In the lower part, the metal sheets were welded to the bottom by means of weld stitches of 20 mm every 0.50 m of separation. The failure investigations identified that the causing action was wind, and the failure mode was buckling (loss of the original geometry). Wind gusts of 45 km/h were registered; this speed is certainly low for a tank which is supposed to resist gusts of over 150 km/h in its final configuration. Figure 10a shows the condition of the failure of the structure, seen from the windward part, where a raising of the bottom of the tank in the windward area can be observed. Figure 10b shows the deflected shape obtained with the computer simulation developed in the present study. To reproduce the failure mechanism, static studies were performed in different stages: First, a lineal eigenvalue analysis was carried out to evaluate critical loads. Second, the equilibrium paths were tracked assuming geometric non-linearity and including geometric imperfections, in order to reproduce the final deflected shape observed in the collapsed tank, relating in all cases the maximum loads found with the wind speeds. The structure was modeled using finite elements with a multiple-purpose program. The bottom of the tank was included in the modeling in order to evaluate the raising caused by the wind. The results obtained show that when the support conditions change, from a continuous support condition to a support that permits displacements in the areas of the shell with higher pressures, the failure load decreases and leads to instability of equilibrium. In this way, maximum load values compatible with wind speeds registered at the time of the collapse were obtained. The features of the construction process, by means of which weld stitches (allowed by API650) are used instead of continuous welds, and the posterior detachment of the shell in the weld stitches, have eroded and degraded the stiffness of the real shell with


respect to the as-designed complete shell. There are other reductions in strength with respect to the final version of the tank, which had not been built at the time of the collapse, such as the conical roof. The roof would have produced an increase in the maximum allowable wind. In the model of the perfect structure, the buckling loads were caused by wind speeds much higher than those recorded during the event; but an important reduction in the elastic critical load is produced when imperfections are included with an amplitude equal to twice the thickness of the shell wall. Considering imperfections in the shell, the effect of the lack of weld in the entire bottom and its possible flexibility still have to be represented. The results show that the inclusion of the bottom as part of the model is important to obtain a realistic representation of the failure process.

(a) (b)

Figure 10: (a) Photograph of the collapsed tank. (b) Deflected shape in the final stages of the simulation.

7. Wind pressures on short tanks The American code ASCE 7-02 in the chapter on wind-load provisions, presents recommendations to use uniform distributions of pressure around the circumference in cylindrical tanks. This pressure distribution is clearly inadequate for tank structures, in which changes in magnitude and in the direction of the pressures around the circumference have been observed by many authors. In the present research, the wind tunnel experiments on short tanks with conical and dome roofs showed positive pressures on the windward region of the cylinder (Figure 11), and negative pressures about 90° from the windward meridian (Portela et al., 2002). Negative pressures were also detected on the leeward region of the tanks. It seems that the wind pressure distributions in isolated tanks strongly depend on the geometry of the tank (aspect ratio H/D) and on the type of roof (either conical, shallow-dome or deep-dome configurations). Comparison between the experimental results obtained by Portela and Godoy (2005a) and other researchers, show that the associated angle of inclination of the meridian of the conical roof is responsible for an increase in pressures on the central part of a roof, at least up to an angle of about 30˚. Furthermore, the details of the transition between the cylindrical body and the roof are crucial in the evaluation of pressures on the roof, since this transition changes the main features of the flow separation. Smooth transitions, such as in deep-dome configurations, lead to lower pressure levels than abrupt transitions, such as in shallow conical roofs. Therefore, results from one case cannot be freely applied to another case with a different transition. In terms of shielding effects, it is intuitive to assume that a tank in front of another tank would block the flow and thus reduce the pressures on the second tank. This is implicit in ASCE 7-02 recommendations. However, this is not necessarily true, and depends on the relative geometric features of both tanks, and on


the separation between the tanks. If the front tank is shorter than the second tank, then there is an increase in pressures and a change in distributions on the windward meridian with respect to the isolated tank (Portela and Godoy, 2004). It is also commonly assumed in the literature that a group of tanks surrounding a specific tank could prevent wind damage to the surrounded tank. However, what occurs is a change in the pattern of pressures, with a decrease in positive pressures and an increase in negative pressures, especially in regions of the cylinder close to the windward meridian. Furthermore, group effects are usually responsible for asymmetric distributions of pressures on the cylinder walls and also on the roof. For close two-tank configurations (i.e. separation S = 0.5 D) with the same H/D ratio, the largest positive pressures are not coincident with the windward meridian, but are displaced by an angle depending on the group configuration (Portela et al., 2003).

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Figure 11: Wind pressure distributions around the cylinder of tanks with conical, shallow-dome and deep-dome roofs.

8. Buckling of tanks due to high intensity winds Isolated tanks described by a bifurcation behavior, seem to be marginally affected by the negative pressure distributions around the tank and the distribution of pressures along the height of the cylinder (Figure 12). At least for the cases of isolated tanks with conical roof, buckling may be caused by local effects due to positive wind pressures in a localized region. This behavior was observed in the isolated tank with conical roof, for which with only localized positive wind pressures in the windward region, the bifurcation loads were similar to the case in which the pressures were distributed around the circumference. The roof of a tank provides additional stiffness to the structure, so that the buckling capacity of the tank with a conical roof is increased by a factor of two with respect to a tank without the roof. Geometric imperfections are important in a somewhat surprising way: A tank with conical roof has a larger buckling load than a similar tank without a roof; however, the reduction in buckling load due to small geometric imperfections is higher in tanks with a conical roof (Portela and Godoy, 2005b). Tanks with levels of imperfections larger than 0.5t (where t = shell thickness) have a very flexible behavior, with large displacements at low load levels, driving the structure rapidly to reach its maximum load. Therefore, sustained winds instead of three-second gusts, begin to be of concern based on the lower load capacity observed in the nonlinear path of tanks with large imperfections (25% reduction of the


buckling load computed). In addition, the sensitivity to imperfections of an isolated tank with conical roof is not affected by whether the imperfection is located only in the windward region or around the circumference. The loss of shell thickness reduces dramatically the buckling capacity of a tank. With a thickness reduction in the order of 1.6 mm in a tank with conical roof and H/D = 0.43, the wind velocity associated to the first buckling point corresponds to 49 m/s, a value that has been exceeded by hurricanes affecting the Caribbean Region. On the contrary, tanks with self-supported dome roofs with height to diameter ratios H/D = 0.48 seem to sustain the wind loads experienced by tanks in the Caribbean even when reductions (in the order of 20%) in the thickness of the shell are considered. This conclusion agrees with the undamaged physical aspect of these tanks after hurricane events.

Figure 12: Buckling mode shape of a tank with conical roof subjected to wind forces. 9. Dynamic wind buckling of tanks Wind gusts induce transient vibrations in the shell during short times, and may eventually lead to dynamic buckling. In the design of tanks in the United States, wind gusts of 3 s duration at 10 m above ground surface are considered, with wind velocities of 64 m/s in the Eastern Coast and the Caribbean Islands. Preliminary results using wind pressures in the form of a rectangular impulse with 3 s duration indicate that the dynamic effects are not significant in terms of buckling (Flores and Godoy, 1999 and Sosa and Godoy, 2005a). At present, there are no extensive records regarding the values or the nature of pressure fluctuations for periods less than 3 s, and the question remains open if it is necessary to obtain such data because it may have a significant influence on stability of the shell. Sosa and Godoy (2005a) analyzed the influence of such fluctuations on the dynamic response of the shell through computer simulations, using geometrically nonlinear dynamic analysis under impulsive loads with fluctuations in the pressure. It is common to employ the dynamic buckling criterion due to Budiansky and Roth (see for example Flores and Godoy (1991), Flores and Godoy (1999), Godoy et al. (2004) and Sosa and Godoy (2005a)). This is a qualitative criterion and requires the computation of the transient geometrically nonlinear response of the shell for different levels of dynamic pressures. Dynamic buckling occurs if, for a small increment in the load, there is a large increment (at least one order of magnitude) in the transient displacements at a given time. This criterion requires expensive computations, i.e. the geometrically nonlinear transient response of a system with many degrees of freedom, and many trials are necessary to find the dynamic buckling load. The time domain results reported in Godoy et al. (2004) and Sosa and Godoy (2005), indicate that for a deterministic model of velocity and pressure variations, a change in the period of oscillations does not produce a significant change in the dynamic buckling load. For small periods of pressure fluctuations, the


dynamic buckling load is close to the value obtained with a rectangular impulse of the same duration, and for periods longer than the natural period of the structure the same situation occurs. The coincidence of the period of excitation with the natural period of the tank does not induce large changes in the buckling strength. The simpler pressure model based on a 3 s rectangular impulse yields dynamic buckling loads only 5% higher than the worst situation considering pressure fluctuations. Figure 13 shows the time response for the rectangular impulse and Figure 14 illustrates the deflected pattern at two different stages. The small changes in buckling load of short tanks due to a wide range of fluctuations seem to suggest that it would not be necessary to obtain a more refined record of wind velocities to account for wind changes at intervals less than 3 s for this class of structures.

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Figure 13: Nonlinear dynamic response for 3 sec wind gust assumed constant. Each curve is for different pressure amplitude. Instability occurs for λ = 2.515.

(a) (b) Figure 14: Nonlinear dynamic analysis. (a) Deflected pattern at the onset of instability; (b) deflected

shape in an advanced buckled state. The inclusion of Rayleigh damping in the model did not change the results by more than 1% with a damping ratio of 3%; however, imperfections were found to play an important role. For imperfections with

Node A Node A


the shape of the first buckling mode, the dynamic buckling load was reduced following a pattern similar to static buckling problems, with reductions of 30% for imperfections of the order of the thickness. This effect, however, is not due to the fluctuating load and is associated with the sensitivity of the shell itself, so that the same sensitivity is detected for tanks under pressure that is constant in time. Results for the frequency domain reported by Sosa and Godoy (2005) illustrate the close similarity between the FFT of the load and the response, for both rectangular impulse and fluctuating load. In all cases, the peaks in the FFT of load and response occur for frequency zero. For higher frequencies, within the range of the lowest natural frequencies of the tank, the peaks have small amplitudes so that resonance may be ruled out as a likely effect. The results discussed previously indicate that dynamic effects do not dominate the response for short tanks, so that static buckling models may provide a reasonable approximation to the buckling strength of the shell under deterministic wind simulations. Thus, inertia forces do not play an active role because the frequencies of excitation are far from the natural frequencies of the shell. A main lesson learned is that this is essentially a static problem. 10. Buckling due to support settlements Thin-walled metal tanks may be supported in various forms, including compact soil foundation, ring walls, slabs or pile-supported foundations. The support may be lost in some part of the base circumference affecting the cylindrical shell and the tank bottom. Non-homogeneous geometry or compressibility of the soil deposit, non-uniform distribution of the load applied to the foundation, or uniform stresses acting over a limited area of the soil stratum may be some of the causes of differential settlements. In many cases, heavy rains, such as those that happen during tropical storms and hurricanes, may aggravate the situation. The differential settlements in tanks may have several consequences. Some of them may include out-of-plane displacements induced in the shell in the form of buckling under a displacement-controlled mechanism or high stresses develop at the base of the shell and in the region of the settlement. There are many reasons to be concerned about such stresses and distortions: First, tanks are not isolated from other parts in an industrial plant, and have pipes and connections to other facilities that may be damaged due to the vertical displacements. Second, excessive displacements in the cylindrical shell affect the normal operation of a floating roof. Third, a geometric distortion greatly affects the buckling resistance of the shell under wind. Fourth, plasticity may occur in parts of the shell wall. Godoy and Sosa (2003) reported some results for an empty tank, fixed at the base, except for an arc where a settlement is imposed. The geometrical non-linear behavior of thin-walled tanks under localized settlements was considered and compared with classic bifurcation analysis. The computer analysis carried out by Godoy and Sosa (2003), as well as the tests performed on a small scale model reported previously (Godoy and Sosa, 2002), showed that the deflection patterns in thin-walled shells due to localized settlements of the foundation are due to a highly non-linear behavior of the shell. The patterns of displacements in the shell are identified, and they are different from those found in buckling of the same shells under wind load or internal vacuum: Compare for example the modes shown in Figures 12 or 14 and that of Figure 16. The equilibrium path displays a non-linear behavior with a plateau, which is a clear sign of instability. The tangent to the equilibrium path becomes zero for approximately umax / t = 0.5, and then it increases for higher values of radial displacements. Figure 15(a) shows this feature. The results suggest that the shell buckles for a small value of the control parameter, and then deflects into a post-buckling mode. Thus, it seems that one should question the results obtained by many authors in the past, which are restricted to a linear analysis and would thus reflect unstable states along a linear fundamental path.


Computational models analyzed by Godoy and Sosa (2003) showed that the critical bifurcation settlement depends on the central angle, with lower values computed for larger angles. The difference between bifurcation and nonlinear critical settlements is large for small angles and both curves tend to similar values for central angles larger than 40°. Figure 15(b) illustrates this behavior. The bifurcation buckling modes are in reasonable agreement with those obtained in the nonlinear analysis.

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Figure 16: Deflected shape for small angle base support settlement.

Bifurcation analysis gives a reasonable approximation to the problem. A linear fundamental equilibrium path is seen to occur, before buckling develops into a new shape for the shell. In the new stable configuration, the shell can withstand further vertical displacements with an increase in the amplitude of the post-buckling mode. Concerning the engineering importance of this effect, one has to look at the displacement amplitudes: the out-of-plane displacements computed using a geometric non linear theory of shells are much larger than the linear values, so that it does not seem wise to establish tolerance criteria for settlements based on linear shell models. 11. Conclusions This paper has summarized the main conclusion obtained from a five year research program on the structural response of thin walled, aboveground steel tanks subject to loads due to natural hazards. The


structural response in such extremely thin-walled shells is sensitive to changes in the geometry, so that buckling has been considered in detail. But this is by no means the end of the road, and further work is carried out at present in our group. The main new areas of work at present are: First, the development of lower bound techniques to compute buckling loads under wind in tank structures. This is an extension of the reduced energy lower bound approach originally develop by James G. A. Croll, from University College London, and which is here implemented for the first time for structures under wind, for which it seems that the buckling mode that would be obtained from an eigenvalue buckling analysis and the mode from a nonlinear analysis at the critical state are not similar to each other. Second, the evaluation of wind pressures on tanks is now considered using computational fluid dynamics instead of wind tunnel experiments. This is done for isolated tanks (Falcinelli et al. 2002), for tanks located on a hill (Falcinelli et al. 2003), and for tanks in locations that are not flat. It is expected that such results will improve our understanding of the conditions that the shell has to resist. Third, new simplified techniques for earthquake analysis of tanks are in the process of being completed. This would use techniques similar to what is done in buildings, but for shells for which the limiting conditions are quite different. Fourth, an inventory of tanks is under construction, to know the main features that are found in tanks. This is done using aerial photography in Puerto Rico, coupled with site visits. It is expected that this information can be used to understand the oil storage as a system and consider its vulnerability as such. Acknowledgements This work has been supported by grants from National Science Foundation (CMS-9907440), Federal Emergency Management Administration (PR-0060-A), and the Insurance Commissioner of Puerto Rico. J.C. Virella was supported by a post-doctoral fellowship grant PR-EPSCOR-0223152. R. Jaca was supported by a grant from the National University of Comahue. The authors thank the valuable contribution of several researchers who participated in various aspects of this research, including Fernando G. Flores, Julio C. Méndez, Carlos A. Prato, Luis E. Suárez and Raúl E. Zapata. References Falcinelli, O.A., Elaskar, S.A., Godoy, L.A. and Tamango, J. (2002), “Efecto de viento sobre tanques y silos mediante CFD”, Mecánica Computacional, vol. 21, pp. 256-273. Falcinelli, O.A., Elaskar, S.A. and Godoy, L.A. (2003), “Influencia de la topografía sobre presiones por viento en tanques usando CFD”, Mecánica Computacional, vol. 22, pp 110-123. Flores, F.G. and Godoy, L.A. (1991). “Instability of shells of revolution using ALREF: Studies for wind

loaded shells”, In: Buckling of Shells in Land, in the Sea and in the Air, Elsevier Applied Science, Oxford, pp 213-222.

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settlements, in: Structural Engineering and Mechanics, Editors C.-K. Choi and W. C. Schnobrich, Techno-Press, Seoul.

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conical roof under wind”, in: Thin-Walled Structures, Editor: J. Loughlan, Elsevier, Oxford. Jaca, R. and Godoy, L.A. (2003). “Colapso de un tanque metálico en construcción bajo la acción del

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dome roof”, Journal of Constructional Steel Research, Vol. 61, No. 6, pp 808-824. Portela, G., Godoy, L.A. and Zapata, R.E. (2002). “Distribuciones de presiones de vientos huracanados

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Biographic Information Dr. Luis A. GODOY is Professor and Associate Director for Research of the Civil Engineering and Surveying Department at UPRM, and is also the Director of the Civil Infrastructure Research Center at UPRM. He serves as editor of the LACCEI Journal and of the Journal “Revista Internacional de Desastres Naturales, Accidentes e Infraestructura Civil”. Rossana C. JACA is a doctoral candidate and also an Assistant Professor at the Constructions Department, National University of Comahue in Argentina. She is interested in computational mechanics and buckling of shells. Dr. Genock PORTELA GAUTIER received his Ph. D. from UPRM in 2004, and is Assistant Professor in the Department of General Engineering at UPRM. He is interested in wind analysis and design of structures. Eduardo M. SOSA is a doctoral candidate at the Department of Civil Engineering and Surveying at UPRM. He received his Civil Engineering degree from the National University of Córdoba in Argentina. He is interested in computational mechanics and buckling analysis. Dr. Juan Carlos VIRELLA CRESPO received his Ph. D. from UPRM in 2004, and at present is Post Doctoral Researcher in the Department of Civil Engineering and Surveying at UPRM. He is interested in earthquake analysis and design of structures. Authorization and Disclaimer Authors authorize LACCEI to publish the papers in the conference proceedings on CD and on the web. Neither LACCEI nor the editors will be responsible either for the content or for the implications of what is expressed in the paper.

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Structural Consequences of Natural Hazards on Metal Storage Tanks