1. October 31, 2006 Global Design Effort 1 IR hall deflection study October 31, 2006 John Amann, Andrei Seryi

2. 2 Oct 31, 06 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

3. 3 Oct 31, 06 Air-pads at CMS Photo from the talk by Y.Sugimoto, http://ilcphys.kek.jp/meeting/lcdds/archives/2006-10-03/ http://ilcphys.kek.jp/meeting/lcdds/archives/2006-10-03/ 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.]

4. 4 Oct 31, 06 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

5. 5 Oct 31, 06 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-Young’s modulus, -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.]

6. 6 Oct 31, 06 Deformation & its approximation Approximation: Z0= (2*M/(pi * E * r0))*(1-nu^2) * 1000; % in mm ee=2; aa=ee*0.25; cc=ee*1; bb=(1+aa)*(pi/2)^2-1-cc; Zapprox= Z0 * (( 1+aa*(x/r0).^2 )./ (1 + bb*(x/r0).^2 + cc*(x/r0).^4)).^0.5; Theory [1]: Theor_coeff=4*M/(pi^2*r0*E)*(1-nu^2) * 1000; % mm if x(i) <= r0 em=(x(i)/r0)^2; [Kell,Eell]=ellipke(em); Ztheory(i)= Theor_coeff* Eell; else em=(r0/x(i))^2; [Kell,Eell]=ellipke(em); Ztheory(i)= Theor_coeff* x(i)/r0*(Eell-(1-em)*Kell); end [1] Theory of elasticity, Timoshenko & Goodier, 1951 Example of theoretical deformation for infinite half space under circular load and approximation used in the Matlab model

7. 7 Oct 31, 06 Assumptions for strength Typical values of Young’s 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/m 2 ) 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

8. 8 Oct 31, 06 Note the comparison IR hall 110*25*35m –volume ~100 000 m 3 –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.

9. 9 Oct 31, 06 Displacement, Matlab model Parameters: M=14000 ton R=0.75m (radius of air-pad) E=3e9 kg/m^2, n=0.15 (as for concrete) Number of air-pads=36

10. 10 Oct 31, 06 Displacement, Matlab model Parameters: M=14000 ton R=0.375m (radius of air-pad) E=3e9 kg/m^2, n=0.15 (as for concrete) Number of air-pads=36

11. 11 Oct 31, 06 Displacement.. ANSYS Results Same Young’s Modulus and Poisson’s 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

12. 12 Oct 31, 06 Displacement... ANSYS Results.75m Air Casters x36, 14000 ton Load Evenly Distributed Y Max. Displacement =.003391” or.086131mm 25m x 25m x3m Slab

13. 13 Oct 31, 06 Displacement... ANSYS Results.375m Air Casters x36, 14000 ton Load Evenly Distributed Y Max. Displacement =.006956” or.176682mm 25m x 25m x3m Slab

14. 14 Oct 31, 06 Displacement... ANSYS Results Analytical Model Predicts (Formulas for Stress and Strain, Roark, 4 th Ed. p.323 eq.13) Y max =.003823” Y edge =.002438” Y max =.007646” Y edge =.004868” ANSYS Predicts Y max =.002789” Y edge = ~.00092”Y max =.005825” Y edge = ~.003233” 5m x 5m x 1m Slab.75m R Air Caster 5m x 5m x 1m Slab.375m R Air Caster

15. 15 Oct 31, 06 Displacement... ANSYS Results Displacement vs. Slab Thickness 5m x 5m Y max displacement =.002879”Y max displacement =.249e-3” 1m Thick Slab.1m Thick Slab

16. 16 Oct 31, 06 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

17. 17 Oct 31, 06 Displacement... ANSYS Results 5m x 5m x 1m5m x 5m x 5m A36 Steel Cylinder.75m R x.75m H

18. 18 Oct 31, 06 Displacement... ANSYS Results Radial Growth of Y Displacement with Increasing Slab Thickness 5m x 5m x 1m Slab5m x 5m x 5m Slab

19. 19 Oct 31, 06 Displacement... ANSYS Results 5m x 5m x 10m Slab Y max displacement =.002737” ???

20. 20 Oct 31, 06 Displacement... ANSYS Results Restrained Sides and Bottom All DOFRestrained Bottom Only All DOF Difference in Y Max =.001373” 5m x 5m x 10m Slab

21. 21 Oct 31, 06 Displacement... ANSYS Results Restrained Sides and Bottom All DOFRestrained Bottom Only All DOF Difference in Y max =.0001” 25m x 25m x 3m Slab

22. 22 Oct 31, 06 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