IR hall deflection study

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IR hall deflection study

• October 31, 2006
• John Amann, Andrei Seryi

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Motivation and content

• To understand deformation of the floor in case of
  push-pull operation of detector
• Displacement of the floor during push-pull
  operation is an important consideration that may
  affect design of the detector support and
  alignment system
• A simplified estimation is discussed below
• Thank Gordon Bowden for a lot of help and
  comments
• Thanks to all colleagues who were involved in
  discussion

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Air-pads at CMS
Single air-pad capacity 385tons (for the first
end-cap disk which weighs 1400 tons). Each of
air-pads equipped with hydraulic jack for fine
adjustment in height, also allowing exchange of
air pad if needed. Lift is 8mm for 385t units.
Cracks in the floor should be avoided, to prevent
damage of the floor by compressed air (up to
50bars) use steel plates (4cm thick).
Inclination of 1 of LHC hall floor is not a
problem. Last 10cm of motion in CMS is performed
on grease pads to avoid any vertical movements.
Alain Herve, et al.
Photo from the talk by Y.Sugimoto,
http//ilcphys.kek.jp/meeting/lcdds/archives/2006-
10-03/
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Displacement of collider hall

• Disclaimer
• The estimations shown below are intended for very
  rough estimation of the variation of deformation
  under the detector, which affects design of its
  support and alignment system
• Simplified elastic model is assumed, and
  essential effects such as long term settlement,
  inelastic motion, non-homogeneity of rock, IR
  hall shape, etc, were not taken into account
• Early investigations (drilling, etc) of the site
  in the location of IR hall and careful
  engineering are crucial, independent of push-pull
  scheme

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Displacements of collider hall

• Modeling it now with ANSYS, first results below
• Also use approximate analytical model
• displacement of elastic half-space under load of
  circular load or radius R and mass M
• where E-Youngs modulus, n-Poisson ratio
• and displacement outside falls as 1/r
• express via Elliptical integrals
• approximate analytically as show on next page

) 1) Gordon Bowden, private communication
2) FORMULAS FOR STRESS AND STRAIN, 5th EDITION,
Roark Young, Table 33, p.519.
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Deformation its approximation
Example of theoretical deformation for infinite
half space under circular load and approximation
used in the Matlab model
Theory 1 Theor_coeff4M/(pi2r0E)(1-nu2)
1000 mm if x(i) lt r0 em(x(i)/r0)2
Kell,Eellellipke(em) Ztheory(i)
Theor_coeff Eell else em(r0/x(i))2
Kell,Eellellipke(em) Ztheory(i)
Theor_coeff x(i)/r0(Eell-(1-em)Kell) end 1
Theory of elasticity, Timoshenko Goodier, 1951
Approximation Z0 (2M/(pi E r0))(1-nu2)
1000 in mm ee2 aaee0.25 ccee1
bb(1aa)(pi/2)2-1-cc Zapprox Z0
(( 1aa(x/r0).2 )./ (1 bb(x/r0).2
cc(x/r0).4)).0.5
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Assumptions for strength

• Typical values of Youngs modulus
• Granite, Dolomite 50-70 GPa (Japan FNAL ILC
  sites)
• Sandstone 20 GPa (CERN ILC site)
• Concrete 30 GPa
• Soil (varies a lot) 0.1 GPa
• Will assume 30GPa (3e9 kg/m2) which is
  conservative for deep site, and assume that
  sufficient amount of concrete is used for shallow
  sites to make its strength close to this value

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Note the comparison

• IR hall 1102535m
• volume 100 000 m3
• amount of removed rock 250 kton
• two detectors 30 kton
• the structural stability of the hall that need to
  be provided by careful design, does not depend
  much on the need to move the detector
• If the IR hall built in water table, will have to
  solve engineering issues of buoyancy anyway.
  Detector moving along the longer dimension of the
  hall (and not along shorter dimension), which
  helps.

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Displacement, Matlab model
Parameters M14000 ton R0.75m (radius of
air-pad) E3e9 kg/m2, n0.15 (as for
concrete) Number of air-pads36
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Displacement, Matlab model
Parameters M14000 ton R0.375m (radius of
air-pad) E3e9 kg/m2, n0.15 (as for
concrete) Number of air-pads36
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Displacement . . ANSYS Results

• Same Youngs Modulus and Poissons Ratio as
  MATLAB Model
• Finite Slab - 25m x 25m x 3m
• Air Caster Modeled as Circular Indentation
• Slab Restrained in all DOF at Side and Bottom
  Areas
• Material Model - Linear Elastic Isotropic
• Mesh Element Type - SOLID92, 10 Node Tetrahedral
• Plotted Nodal Solution for Y Displacement

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Displacement . . . ANSYS Results
25m x 25m x3m Slab
.75m Air Casters x36, 14000 ton Load Evenly
Distributed
Y Max. Displacement .003391 or .086131mm
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Displacement . . . ANSYS Results
25m x 25m x3m Slab
.375m Air Casters x36, 14000 ton Load Evenly
Distributed
Y Max. Displacement .006956 or .176682mm
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Displacement . . . ANSYS Results
Analytical Model Predicts (Formulas for Stress
and Strain, Roark, 4th Ed. p.323 eq.13)
Y max .007646 Y edge .004868
Y max .003823 Y edge .002438
5m x 5m x 1m Slab .75m R Air Caster
5m x 5m x 1m Slab .375m R Air Caster
ANSYS Predicts
Y max .002789 Y edge .00092
Y max .005825 Y edge .003233
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Displacement . . . ANSYS Results
Displacement vs. Slab Thickness 5m x 5m
1m Thick Slab
.1m Thick Slab
Y max displacement .002879
Y max displacement .249e-3
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Displacement . . . ANSYS Results

• Want to Investigate Y Displacement 1/r Decay
• Model Changes to Cylinder on Block
• Eliminates Indentation
• Coarse Mesh Fast, Now Can Model Contact
• Cylinder/Slab Surface/Volume Interaction
• No Friction
• Vary Slab Thickness 1m, 5m, 10m

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Displacement . . . ANSYS Results
5m x 5m x 1m
5m x 5m x 5m
A36 Steel Cylinder .75m R x .75m H
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Displacement . . . ANSYS Results
Radial Growth of Y Displacement with Increasing
Slab Thickness
5m x 5m x 1m Slab
5m x 5m x 5m Slab
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Displacement . . . ANSYS Results
5m x 5m x 10m Slab
Y max displacement .002737 ???
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Displacement . . . ANSYS Results
5m x 5m x 10m Slab
Restrained Sides and Bottom All DOF
Restrained Bottom Only All DOF
Difference in Y Max .001373
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Displacement . . . ANSYS Results
25m x 25m x 3m Slab
Restrained Sides and Bottom All DOF
Restrained Bottom Only All DOF
Difference in Y max .0001
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Summary

• For typical ILC sites, expected detector
  displacements are about 0.5mm and local variation
  under supports around 0.1-0.2mm
• Displacement estimated for elastic half-space may
  not be a good model for collider hall, so
  accuracy of estimations may be not more than a
  factor of two
• Uniform distribution of support point is
  desirable (need to study its feasibility,
  assuming the need for maintenance of air-pads).
  More local distribution of air-pads closer to
  perimeter would increase variation of local
  deformations
• Steel plates on the floor may help. They were not
  yet included in the estimations