1. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 1 Alexandre Riabov (IHEP, Protvino) Justin Greenhalgh (RAL) Finite Element Analysis of Dee with fixed reinforcing beam.

2. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 2 General Issues This work is based on the note “Request for calculation of effect of reinforcing beam on Dee backplates” (EE/358/RJSG/2004) by Justin Greenhalgh and preliminary results presented in the note “FE analysis of Dee with reinforcing beam” (EE/445/RJSG+AR/2005) Two Extreme variants which can be realized at SC assembly and Dee transportation stages have been considered. Along with the natural gravitation the Dee can be exposed to an additional acceleration of 0.35g in all directions which is equal to the static equivalent seismic load. Maximal braking accelerator allowed is 1g. The worst combined load cases are (X-axis is vertical, Z-axis is perpendicular to Dee plane, Y-axis is in a transportation direction - see pictures for explanation of the global coordinate system of the model) : E1: Accel=(1.35, 1, +0.35) g E2: Accel=(1.35, 1, -0.35) g At installation stage the worst combination of gravity and seismic loads is described by accelerating load vector (here Y-axis becomes vertical, and X-axis – horizontal): E3: Accel=(0.35, 1.35, 0.35) g Additional load case C7 without seismic loads is also have been considered: C7: Accel=(0, 1.35, 035) g

3. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 3 Questions. Displacements and Stresses in the aluminum of the backplate; Stresses in the steel of the brackets and reinforcing beam; Axial forces in all bolts; Shear forces in all dowels (pins); Reaction forces on the reinforcing beam and the brackets bolts from the direction of the OPAL frame; Loss of SC clearance. Where does the maximum loss occur?

4. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 4 The full FE Model Support ring (SR) Brackets (BR) Reinforcing Beam Backplate (BP) Supercrystals (SC) Global CS (X,Y,Z)

5. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 5 Backplate details

6. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 6 BR details and some definitions

7. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 7 SC Arrangements

8. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 8 Boundary conditions Beam ends fixed Brackets fixed Coupling between the model parts (bolts and pins) Loading: Acceleration vector A=(α x, α y, α z ) g g

9. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 9 E1: BP&SC displacements Result: The maximal displacements of BP are very low ~ 0.9 mm Assembly/Transp. A=(1.35, 1, 0.35) g Beam ends fixed Last BR removed

10. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 10 E1: Von Mises Stresses in BP Assembly/Transp. A=(1.35, 1, 0.35) g Beam ends fixed Last BR removed Result: The stress concentration is ~ 56 MPa. Overall stress is low

11. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 11 E1: Brackets displacements Assembly/Transp. A=(1.35, 1, 0.35) g Beam ends fixed Last BR removed Result: The maximal displacements are low ~ 0.2 mm (reached for -70ºBR)

12. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 12 E1: Von Mises Stresses in BRs Assembly/Transp. A=(1.35, 1, 0.35) g Beam ends fixed Last BR removed Result: The stress concentration is ~ 40 MPa. It’s very low for steel

13. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 13 E1: Reinforcing Beam Stresses L-Beam (LB) L-Section (LS) Assembly/Transp. A=(1.35, 1, 0.35) g Beam ends fixed Last BR removed Result: The stress concentration is ~ 170 MPa. It occurs near LS-LB bolts

14. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 14 E1: Stresses in Support Ring Assembly/Transp. A=(1.35, 1,0.35) g Beam ends fixed Last BR removed Result: The stress concentration is ~ 40 MPa. It occurs at SR-BP bolts

15. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 15 E2: BP&SC displacements Result: The maximal displacements of BP and SCs are very low ~ 0.55 mm Assembly/Transp. A=(1.35, 1,-0.35) g Beam ends fixed Last BR removed

16. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 16 E2: Von Mises Stresses in BP Result: The stress concentration is ~ 32 MPa. It occurs near BP-BR bolts Assembly/Transp. A=(1.35, 1,-0.35) g Beam ends fixed Last BR removed

17. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 17 E2: Von Mises Stresses in BRs Result: The stress concentration is ~ 98 MPa. It is not critical for the steel Assembly/Transp. A=(1.35, 1,-0.35) g Beam ends fixed Last BR removed

18. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 18 E2: Reinforcing Beam Stresses Result: The stress concentration is ~ 56 MPa. It occurs in L-section Assembly/Transp. A=(1.35, 1,-0.35) g Beam ends fixed Last BR removed

19. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 19 E3: BP&SC displacements Installation A=(0.35,1.35,0.35)g Beam removed Last BR removed Result: The maximal displacements of BP are rather large ~ 8.6 mm Large displacements are due to Z-direction seismic load. This may be dangerous from the point of view loss of SC clearance.

20. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 20 E3: Von Mises Stresses in BP Installation A=(0.35,1.35,0.35)g Beam removed Last BR removed Result: The stress concentration is ~ 103 MPa. It occurs near BP-BR bolts For the Aluminium σ yield = 270 MPa. The safety factor is 0.9*(270/103) = 2.4. Overall stress is small- it is not greater than 40MPa

21. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 21 E3: Bracket displacements Result: The maximal displacements is ~ 1.4 mm for the lower bracket. Installation A=(0.35,1.35,0.35)g Beam removed Last BR removed

22. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 22 E3: Von Mises Stresses in BRs Installation A=(0.35,1.35,0.35)g Beam removed Last BR removed Result: The stress concentration is ~ 330 MPa. The Steel of BRs should be good

23. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 23 C7: BP displacements Installation A=(0,1.35,0)g Beam removed Last BR removed No seismic Result: Without seismic the displacements are small: ~ 0.7 mm.

24. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 24 Loss of CS clearance in Dee Result: Variant E3 may be problematic It was suggested (RJSG) to consider the value of 0.18 mm as a worrying limit for loss of clearance between supercrystals in a Dee. From this one can conclude that a worrying limit for loss of clearance between SCs centers of masses is 0.18/(400/300) = 0.135 mm. Here: 400mm – length of the SCs, 300mm – the distance of the SCs mass centers from the BP Next table presents maximal loss of clearance, SC pair for which this maximum occurs, and the number of SCs pairs with Loss ≥ 0.135 mm. For detailed results see files Case_*.doc. Case : (accel)Maximal Loss of Clearance [mm] / SCs pair for which it’s reached Number of problematic SC pairs (Loss ≥ 0.135 mm) E1 : (1.35,1, 0.35)0.144 / (B2M, C2M)1 E2 : (1.35,1,-0.35)0.019 / (B2, B3)0 E3 : (0.35,1.35,0.35)0.353 / (C1, C2)46 C7 : (0,1.35,0)< 0.075 for all SCs0

25. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 25 Forces in BP-BR bolts and pins For bolts: positive value denotes tension, negative – compression. For pins shear forces are given. Result: For all cases forces are acceptable. Maximal axial force is ~ 9 kN, maximal shear force is ~ 15 kN

26. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 26 Forces in LS-BP bolts and pins Result: Maximal forces are due to braking and they occur at one of the L-beam ends. Maximal reaction force is about 4.5 tons. Result: The LS-BP bolts practically do not work. Maximal shear force is about 1.5 tons. It is due to Braking. Reaction forces [kN]Force Moments [kN∙m] CaseY-posRXRYRZMXMYMZ E11700-3.816.45-13.98-15.57-0.157.41 -1700-19.29-36.69-18.6921.93-0.31-29.78 E217002.53-9.79-1.19-1.470.03-3.15 -1700-12.95-20.45-5.907.83-0.13-19.21 This table presents reaction forces and moments on the beam ends from OPAL frame

27. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 27 E1&E2: BR-OPAL frame bolts

28. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 28 E3&C7: BR-OPAL frame bolts

29. ECAL End Cap Dee Assembly, Transport, InstallationCERN January 2006AR / RJSG – 29 Conclusions Fixing of the reinforcing beam ends to the OPAL frame fully solves all mechanical problems which can arise at stages of the Dee assembly and transportations. The deflections and stresses in all parts of the construction are small, the loss of the SC clearance lies within specified limits (0.18 mm). At the stage of installation seismic load acting in the direction perpendicular to the backplate plane produces rather large deflections (up to 8.6 mm) and consequently rather large stresses in the backplate (~ 100 MPa) and in the brackets (~ 330 MPa). It should be noted that it is the stress concentration which arises locally. Overall stresses are much less. Nevertheless the mechanical quality of materials of the backplate and the brackets should be good enough. The loss of SC clearance in the Dee can reach 0.47 mm. In case of seismic absence (Case C7) the stress concentrations do not exceed 60 MPa in the backplate and 85 MPa in the brackets. The losses of SC clearance in a Dee are negligible - for all SC pairs the losses do not exceed 0.1 mm. We can not make true conclusions about the loss of SC clearance between Dees without performing additional calculations. The question is that during the installation of one Dee which is supporting by the brackets the another Dee has already installed in operational position and it is supported by the support flange (on HE). So the Dees are under different boundary conditions and additional calculations should be done for the Dee in the operational mode. We can only present here the maximum displacements of the A-column SCs towards to another Dee: they are ~1.95 mm for the E3 load case and only 0.27 mm for the C7 load case.