Dynamical and structural considerations about the third wall

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Dynamical and structural considerations about the
third wall

• C. Cattadori

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Report on the finite elemnt analysis performed by
Castellani on the GERDA (WT third wall
cryostat)

• The seismic excitation on the GERDA tanks system
  is computed according to BS EN 1473, and
  theoretical behaviour of water in between two
  containers is discussed. The finite element code
  Gosh-Wilson, in axial symmetry, is applied.
• The main loads are
• D dead load
• LT, thermal induced deformation, computed on the
  basis of a dilatation of the cryostat under a
  thermal excursion of - 210 C under the
  liquefaction of nitrogen
• p pressure in static conditions , computed on
  the basis of a density equal to 1 t/m3
• E earthquake excitation, as described below.

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Specification about the seismic loading
According to the Ordinanza 3274, Criteri per la
individuazione delle zone sismiche.
Individuazione formazione ed aggiornamento degli
elenchi nelle zone stesse", document dated
25/03/2003, the peak ground acceleration at the
site, corresponding to the reference return
period, is
on a rock type soil. The reference return period
is equal to 475 years.
ag depends on the seismic activity of the site
TB, TC, TD and S depend on the local soil
layering
the soil factor is S 1.0 and TB 0.15, TC
0.4, and TD 2 second. The quantity ? depends
on the damping ratio. It is 1 for a damping
ratio equal to 5 .
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Specification about the seismic loading

• The Gerda plant at Gran Sasso Laboratory, by
  specifications, is subject in addition to BS EN
  1473, 1997. In this document two seismic events
  are identified SSE (earthquake event for which
  the essential fail-safe functions and mechanisms
  are to be preserved ) , associated with a return
  period 10000 years, and OBE (the earthquake for
  which no damage is sustained, and restart and
  safe operation can continue.) associated with a
  return period 475 years.

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Specification about the seismic loading

• Loading combinations that involve SSE coincide to
  the ultimate limit state of Eurocode 8, and the
  loading combinations that involve OBE coincide
  with the serviceability limit state of Eurocode
  8. Since the Ordinanza has been derived directly
  from Eurocode 8, the same correspondence may be
  established between the SSE/OBE mentioned in BS
  EN 14731997, and the ultimate/serviceability
  limit state established in Ordinanza.
• Both events require that a behaviour factor be
  defined. According to EC8
• In the present design the behaviour factor q
  2.5 has been selected for the SSE, in agreement
  with Eurocode 8 Design of structures for
  earthquake resistance Part 4 Silos, tanks and
  pipelines, EN 1998, part 4, December 2004, 14.
  
• The event OBE requires a structural verification
  at the serviceability limit state. The behaviour
  factor q 1 shall be selected.
• The loading combinations are
• 1.35 (G LT p) (1)
• G p E10000 (2)
• 1.05 (G p) E475 (3)

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The SSE spectrum
The loading combinations (2), that involve SSE,
benefit of a q factor 2.5, except for the global
equilibrium conditions, against sliding and
overturnig. In these conditions, lacking a
deeper study for the possible consequences of
sliding or liftoff, a q factor equal to 1 is
selected.
SSE
OBE
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The finite element analysis

• A finite element model of the primary and
  secondary wall, connected by stiffening rings,
• has been implemented. The secondary wall is
  copper made
• By assumption, the structure, all items included,
  is symmetric with respect to
• a vertical axis.
• The boundary conditions are symmetric too.
• The actions or the imposed displacements may be
  arbitrarily distributed along the
• generic circumference.
• Each element is represented as a cylindrical
  frustrum, having a given thickness.
• Each material deserves its own density.
• The moduli of elasticity are those of copper, in
  the elastic range
• The adopted mathematical model is distributed by
  NISEE.
• S. Gosh, E. Wilson, Dynamic stress analysis of
  axisymmetric structures under arbitrary
• loading, Earthquake Engineering Research
  Center, University of California, Berkeley,
• report N EERC 69-10, revised September 1976

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The preliminary proposed solution in copper with
stiffening rings
For the cryostat thickness he Adopted 24 mm
everywhere.
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Items to be reviewed.

• After meeting with Castellani on the 4th november
  in Milano, I reviewed with him the inputs (es.
  Adopt proper shape and thickness for cryostat as
  we deliverd him on 28th september, adopt proper
  thickness and constructional details of WT and
  verify the proposed anchorages both for WT and
  cryostat dimensioned by the engineer that drawed
  the WT) and the boundary conditions of the GERDA
  setup, and the relevant issues for GERDA (es.
  Minimize the linear meters of copper soldering.
  In the actual proposed solution

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The possible 3rd wall configurations submitted to
Castellani
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The LEXAN cylindrical solution

• With reference to the sketch in the document 5
  by C. Cattadori, I have one objection. If the
  annulus between the two containers is filled with
  air or other gas, then the seismic actions on the
  primary containments are several times the
  analogous actions in a structure where the
  annulus is filled with water, all other
  parameters being the same. A similar concern
  applies to the secondary containment, but in this
  case the prevailing action on the wall is
  compression. In this case, the limit state of
  ovalization for cylinders that slender imposes to
  work on the basis of allowable stresses no more
  than 1/4 the yield stress. The Lexan
  polycarbonate, although very promising as already
  stated, offers a yield stress around 70 MPa, see
  appendix. If the earthquake induced actions are
  to be withstood at allowable stress around 70/4
  17.5 MPa, a wall thickness of a ten centimeters
  will be necessary.
• I thus suggest taking into account the
  possibility to relay on an annulus full of
  liquid, of a same density of water or if not
  possible structurally connect the secondary
  containment to the cryostat primary wall by
  stiffening rings
• As a general comment, the Lexan polycarbonate is
  a weak material with respect to steel and metals
  in general for which the yield stress may be one
  order of magnitude higher than that of Lexan.
• Besides, to reduce the amount of material as
  possible, the wall should be of orthotropic
  geometry, stiffened by IPE profiles, for
  instances 80 mm high, at a clear distance 1 m
  each to the other.

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The role of stiffening rings
WT wall
Secondary containment
Energy Equivalent by viscous dashpots.