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Seismic  reliability  analysis  methods  for  elevated spherical  tanks

Stanford California Earthquake Engineering Center (06-1989).
Tung, Albert T. Y.- Kiremidjian, Anne S.-John A. Blume

Elevated spherical tanks, a unique type of structure commonly used  inmajor industrial facilities to store extremely toxic and/or flammable material under pressure, are included in the group of critical structures whose reliability against failure under seismic load is of critical concern.

In this study, three different systematic approaches are developed, from different perspectives and at different levels of complexity, for evaluating the seismic performance (reliability) of elevated spherical tanks.

A discretized-mass mechanical system with masses and stiffnesses as functions of liquid fill height is constructed to model the dynamic effects of liquid sloshing.
The component reliability analysis, the first of the three methods developed, computes the annual failure probabilities of the structural components at intact state using only the hazard curve of the region and the site-dependent dynamic amplification factor spectrum as the seismic load input.
Using the same input as the component reliability analysis but taking progressive failure and load redistribution into account, the system reliability analysis, the second method developed, identifies the most likely component failure sequences and obtains the overall system failure probability.
The third method, the random vibration analysis, uses the nonstationary ground motion in the frequency domain as the seismic load input and a hysteretic restoring force model to include the nonlinear behavior of the elevated spherical tank supporting frame in the analysis.
It evaluates the maximum horizontal displacement statistics at various ductility ratio levels. A liquid-containing elevated spherical tank located in the San Francisco Bay Area is analyzed using all three methods as an illustrative example.
This invention relates to elevated tanks for the storage of fluids, and and relates particu- larly to a spherical tank supported on circumferentially spaced columns.

It has been found in the past that elevated tanks,and especially spherical tanks, are sub- jected to expansion and contraction caused by the heart of the sun,changes in tempera- ture caused by the weather,variations in pressure,and the like.
These expansions and contractions sometimes tear the tank loose from its supporting legs or columns and thus many of these tanks require frequent and expensive repairs.

They are especially bothersome with spherical tanks as it is difficult to attach supporting columns to the tank,this being usually done by welding the columns to the sides of the tank at points below the horisontal equator.

As the columns are welded to the tank at an angle,any loosening of the welding by expansion or contraction immediately brings the weight of the tank to bear on the weakened portion  and tends to tear the whole column loose.

A reservoir of this supporting documentation tends to oscillate back and forth and this fact makes it very vulnerable to earthquake tectonic instability of the ground wave andso increases the problem of providing adequate support for the spherical tank to avoid disaster imaginable.


Pacific Eartquake Engineering Research ( PEER ) Center

Life assessment of a Structural Engineer
The applicability of the proposed simulation-based approach to life-intended in this section with a practice-relevant engineering structure shown.lt comes mounted on a cylindershaped columns of spherical Gas pressure vessels are used, what a seismic load is suspended.

Spherical tanl<s on cylindrical supports

The previously for the material 20 Mn Mo Ni 55 calibrated and validated micropores injury
tion model is described for determining the life of a practice-relevant Engineering
structure,the ethylene tank B 101 of the lCl-Wilhelmshaven GmbH & CO,is used. This
cylinder-shaped supports mounted to 12 spherical gas tank (Figure 8.1 ) a seismic load is
suspended as a result of uplift and Reduction of the bearing on short-term fatigue of the
container out. The load is assumed to be unfavorable,that is,two adjacent columns always


Perform a opposite movement(Figure 8.2 ).The main geometric data and the applied finite element discretization are the following Figures see gene. lt will be the symmetry oft he structure and Antimetrie and properties of the structure exploited used and only a shell region of i.5" as shown in Figure 8.2 (b) models,to reduce the numerical effort. The discretization oft he modeled part the structure takes place with 72 element.For more graphic representation of numerical results of this segment is as shown in Figure 8.2 (C) mirrored.

Figure 8.2 (a) spherical tanks of lCl-Wilhelmshaven, (b)geometric data of the container and (c) finite element discretization of the structure.
Note: The simulation of this structure requires the use of a specific parameterization of the shell director in the finite element shell formulation,becouse it is a composite shell structure (Appendix c).
As stress is the El Centro earthquake of 18 May 1940 at California-take. The earthquake measuring 6.9 on the Richter scala was a long time in the field civil engineering as a design-relevant
earthquake. Figure 8.3 shows the vertical Earth movement of the first 32 seconds of the quake,which as the relevant exposure set ( Berg & Housner 1961) is'


Spherical tanks on cylindrical support

The results of numerical simulation in ( Figure 8.4 ) shows the strain after 32 seconds,a significant
accumulation of damage in the area of transition support container.



The maximum pore volume fraction lf,characterized by the dark areas occurs while at the highest point of transition to. The (Figure 8.5 Xb)shows the damage-evolution for this decisive point of the structure overthe entire duration of the load earthquake in Figure 8.5 (a)

An increase of the maximum pore volume fraction for the strain fields of Subsidence-train the rest clearly observed,whereas for the relief erd survey or close to a constant state damage is visible.The rate,maximum pore volume fraction only,f =0.015,far away from the value the critical pore coalescence(f crit = 61:0.09). The damage influences the behavior of the overall design is very low and therefore a global failure of the high-pressure gas tank is in the loading case of the ElCentro Earthquake,not to worry.

Determination of Lifetime Structural Engineer.

The applicability of the developed numerical model for work in the short show termüdungs simulations,i use the life cycle analysis of a shell-shaped in design engineer in the fiel of container contruction.

Here,the gas high-pressure vessel of the lCl-Wilhelmshaven GmbH & CO is subjected to earthquake loading, which corresponds to the EL Centro, California earthquake of 1940.

The numerical study allows the following assessment :
The occurrence of significant damage accumulationin the transition Brace containers can be seen.

The modeled structure would have the simulated El Centro earthquake almost without prejudice det over, since the maximum occurring pore volume fraction outside the critical range.


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