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International CAE Conference 2014 27-28 October. 2014

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Seismic analysis of a liquid storage tank used

in wine industry: a FEM-based approach

Denis Benasciuttia, Luciano Moro

a, Nicola Cimenti

b

aUniversit di Udine, Dip. Ingegneria Elettrica Gestionale e Meccanica (DIEGM), Udine, Italy

bGortani s.r.l., Amaro (Udine), Italy

Email: [email protected]

Web:www.diegm.uniud.it

Summary

This paper illustrates an example of seismic analysis of a thin wall cylindrical tank used in the wine

industry. A FEM-based approach, based on response spectrum analysis, is used to simulate the

seismic response of the tank/liquid system to horizontal earthquake action. The tank/liquid system is

modeled by shell elements and displacement-based fluid elements, respectively. Simulations results

are compared with estimations given by Eurocode 8 (Part 4), according to two different approaches: a

simplified lumped dynamic model by Malhotra, a FEM-based static analysis with the hydrodynamic

pressure computed by Eurocode 8. The different approaches are shown to provide a general

agreement for the shear and overtuning moment at the tank base. Elastic and elasto-plastic buckling of

the tank wall is finally assessed with the stress values calculated by the previous approaches.

Keywords

liquid tank, seismic analysis, ANSYS, Eurocode 8

Introduction

Thin wall metallic tanks are used in the wine industry for wine fermentation and conservation.

Typical damage of the tank wall during an earthquake is due to elastic ("diamond shape") or elasto-

plastic ("elephant foot") buckling. In Italy, the seismic assessment of liquid tank has become more

important after some recent earthquakes, as those in the Emilia region in 2012 (see Fig. 1(a)).

The European standard for tank seismic design is EN 1998-4:2006 Eurocode 8 (Part 4) [1], which is

supported by other codes defining the seismic ground actions (for example, the Italian reference is the

Ministerial Decree January 14th2008 "Technical rules for constructions" [2]). In this work, the results

by Eurocode 8 are compared with FEM-based simulations with ANSYS software, which applies a

response spectrum analysis to a liquid/tank finite element model. The different approaches are

compared by considering the shear and overtuning moment at the tank base. The tank structural

integrity against elastic and elastic-plastic buckling is also assessed. The main goal of this study is to


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evaluate the applicability of the FEM-based approach as a possible substitute of Eurocode 8,

especially for those configurations that are outside the range of applicability of the design code.

(a) (b)

Figure 1: (a) "elephant foot" damage after earthquake in Emilia region (Italy), May 2012; (b)

geometry of the liquid tank analysed in this study

The case study of a cylindrical tank subjected to horizontal earthquake action is discussed [3]. The

tank is fully anchored at its base, it has diameter 2R=8 m, height H=7.3 m and three courses of

thickness 3, 2.5, 2 mm (from bottom), see Fig. 1(b). The material is AISI 304 stainless steel. The tank

is located in the city of Corropoli (TE), Italy, classified as seismic zone 2.

Seismic analysis by FEM: response spectrum analysis

Figure 2(a) shows the finite element model used in the seismic analysis. The tank is modeled by 4-

nodes shell elements and the liquid is represented by 8-nodes fluid elements (called FLUID80 inANSYS [4]). The fluid element has a displacement-based formulation, where the fluid is

characterized by a "fluid elastic (bulk) modulus" Ef(the value Ef=2240 MPa used in simulations is

calibrated based on the values of static pressure computed in a preliminary static analysis). This

element is particularly suited to model fluid/structure interaction and fluid sloshing. The fluid

elements are not directly attached to the shell elements at the tank wall. Instead, they have separate

and coincident nodes that are coupled only along the direction normal to the interface, so to allow

relative movements in the tangential and vertical directions. Similarly, fluid element nodes at tank

base are constrained only along the vertical direction, while they can slip in the horizontal direction.

Due to symmetry, only one half of the tank is necessary. On the other hand, for a tank subjected to

horizontal excitation in one direction only, the seismic behaviour is symmetric about a vertical plane

containing the diameter parallel to the excitation direction ("cos-type" vibration modes). Preliminary

simulations have confirmed the correctness of this assumption, which means that no vibration modes

are lost due to symmetry.

The numerical simulation applies a response spectrum modal analysis with an acceleration spectrum

defined by the Italian regulation "Technical rules for constructions". The modal analysis adopts the

"matrix condensation" technique (based on Guyan method) the only one supported by the FLUID80

element of ANSYS where the finite element model is reduced to a specific set of Master Degrees of

Freedom (DOF), which are used to approximate the mass matrix [M]. The Master DOFs are selected

at the vertical Z direction on the free surface of the liquid and in X direction (the earthquake

direction), where the liquid/tank system is expected to vibrate. Fig. 2(b) shows an example of modal

response for the first impulsive mode atfn= 9.41 Hz (colour map refers to the vertical displacement).


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(a) (b)

Figure 2: (a) the fluid/tank finite element; (b) modal response at fn= 9.41 Hz

Seismic analysis by Eurocode 8The Eurocode 8 Part 4 (EC8-P4) suggests two different approaches to estimate the seismic response

of the liquid/tank system. The first is a simplified dynamic model (proposed by Malhotra [5]), which

provides analytical expressions to estimate the first natural periods Timpand Tconof the convective and

impulsive system responses, as well as the shear and overtuning moment at the tank base.

Alternatively, EC8-P4 gives analytical expressions to compute the hydrodynamic pressure for the

liquid, which can then be applied to a finite element model of the tank to perform a static structural

simulation. Base shear and moment are then calculated as output of finite element simulations.

Approach Method Shear (kN) Moment (kNm)

EC8-4 analytical (Malhotra) 1017 2853

EC8-4 hydrodynamic pressure applied to

FEM static analysis

1117 2222

FEM modal combination ("SRSS") rule 867 2567

Table1: Shear and overtuning moment at the tank base, calculated by different methods

A comparison of natural frequencies calculated by different methods (analytical and numerical) is

presented in [3]. Table 1 provides, instead, a comparison of the shear and overtuning moment at the

tank base, calculated by different approaches. A general agreement is observed.

Structural integrity: elastic and elasto-plastic buckling

The stress distribution calculated by the previous approaches are used to evaluate the stability of the

tank wall near and above the base for failure modes related to elastic and elasto-plastic buckling. The

analytical expressions for the buckling strength of anchored tanks can be found in [1] and [3]; they are

also summarized by the design chart in Fig. 3, taken from the literature [6].

Elastic buckling generally depends on the geometrical imperfections of the tank wall and on the

internal pressure (which has a stabilizing effect). Instead, elasto-plastic buckling normally occursclose to the tank base (see the "elephant foot" damage in Fig. 1(a)), due to a combination of vertical


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compressive stress and high hoop stress close to the yield limit. An empirical equation is available in

Eurocode 8 (based on Rotter's model [7]), where is shown that the buckling strength decreases with an

increasing internal pressure. The buckling strength of the tank wall is the lowest between elastic and

elasto-plastic strength, see Fig. 2. In the case study analysed in this paper, the buckling strength of the

tank wall was higher than the axial stress calculated by all the approaches examined.

Figure 2: Elastic and elasto-plastic buckling strength of anchored steel cylindrical tanks [6]

Conclusions

This work compared different approaches for the seismic analysis of liquid tanks used in wine

industry. All approaches provide comparable results in terms of base shear and overtuning moment,

although they differ in respect to advantages and disadvantages. The methods suggested by EC-P4 arerelatively simple; however their applicability is restricted to a specified range of geometries (e.g.

ratios H/R within the range 0.33). Instead, the proposed FEM-based approach that models explicitly

both tank and liquid is more flexible, as it can be applied to any type of liquid/tank configuration.

References

[1] EN 1998-4:2006 Eurocode 8 Design of structures for earthquake resistance Part 4: Silos, tanks

and pipelines.

[2] D.M. 14 gennaio 2008 - Nuove Norme Tecniche per le Costruzioni (NTC).[3] Bearzi D., Benasciutti D., Cimenti N., Moro L.: "Verifica sismica di serbatoi per l'industria

enologica: normativa tecnica e modellazione numerica", Proc. of 43 Conference of the "Italian

Association for Stress Analysis" (AIAS), September 9-12, 2014, Rimini (BO), Italy. (in Italian)

[4] ANSYS User Manual, Release 14.0

[5] Malhotra P.K., Wenk T., Wieland M.: "Simple procedure for seismic analysis of liquid-storage

tanks", Structural Engineering International, No. 3, 2000, pp. 197201.

[6] Hamdan F.H.: "Seismic behaviour of cylindrical steel liquid storage tanks", Journal of

Constructional Steel Research, No. 53, 2000, pp. 307333.

[7] Rotter J.M.: "Local collapse of axially compressed pressurized thin steel cylinders", Journal of

Structural Engineering, No. 116(7), 1990, pp. 1955-1970.

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