1. Warm cryostat mechanical calculations A.Catinaccio PH-DT Engineering Office, CERN Page 1 CERN, May 27th 2015

2. Calculation models available Several models have been implemented and results compared (ref. chap 6) Analytical preliminary model of an insulated main vertical member (to benchmark the FEA ANSYS and SCIAeng models, assess the range of expected deflections and moments depending on the members and connections selected) FEA models (full beam, beam-shell) of the entire 3D cryostat (to assess global effects, contribution by the grid/warm membrane, equivalence of a 3D main portal frame model) FEA models (beam, shell) of a simpler 3D equivalent portal frame (equivalent loading of a unit representative cell) FEA shell to solid sub-modelling techniques to analyse in details the connections Analytical (EC3 code driven) analyses of main beams and connections FEA/analytical verification according to Eurocode 3 by SCIAengineer software. Page 2

3. Calculation models available The analyses have covered: Static stress-deflection behaviour Evaluation against plastic collapse, by linear and non linear analyses (ANSYS, SCIAeng) Local failure criteria: stresses, stability (global and lateral buckling), on main members, connections, welds, bolts. Load combination as for 6.1 (1): full P+D Page 3

4. Calculation model: 3D and “2D” portal models The structure can be seen as a long box with relatively compact "short side walls" at its ends. At regular intervals along, "standard cells" will form the repetitive unit. This basic skeleton is the "portal". It takes the principal load -- fluid pressure and weight The standard cell is then completed by a grid of much-lighter beams- The majority of these standard cells are far away from the short side walls, and do not benefit from noticeable stiffening from these remote walls. Page 4

5. Calculation models geometry Page 5

6. Calculation models description Page 6 Filling ratio up to 98% of liquid (rounded in the following models at 100%) Top pressure: working pressure between 50 to 120 mbar. Safety valve opening pressure set at 350 mbar, which becomes the design nominal pressure value. Static head of Lar (14 m). Density taken as 1400 kg/m3 Self-weight of composing members. Main beam members: HL1100-607 (607 kg/m) The weight of the insulation with the stainless steel, level1 to 3 membranes is estimated in 170kg/m2. The small outer grid beam have been computed by the CAD system, for a unit cell of 1.6 m pitch and 16.42 m length, at 2300 kg. See for details Annex A: Total Mass of the cryostat structure, for estimates of the entire structure and unit cell (pitch of 1.6 m)

7. Calculation models loading Page 7

8. Calculation model: preliminary design Some analytical equations on simply supported beam under distributed side load from the fluid pressure and simple FEA benchmarks for larger models. Page 8

9. Calculations model: global “box” beam Page 9

10. Calculation model: portal beam Page 10 Model loading and boundary conditions Max long stress on beams [Pa] Total displacement [m]

11. Model: beam model EC3 verification Page 11 Model loading and boundary conditions Bending moment of the main vertical beam Example of conclusions from Eurocode 3 semi- analytical verification, ref annex E of report:

12. Calculations model: shell portal Page 12 Shell model well suited to analyse buckling, identify optimum position of splice connection and sub-model connections for ASME FEA verification.

13. Calculations models: main connections Welded and bolted connections sub-modelling Page 13

14. Calculations model: main connections Semi-Analytical Eurocode 3 verification: Page 14 Example of conclusions for main splice from Eurocode 3 verification, ref annex H of report:

15. Calculations model: 3D beam (Scia eng) Scia engineer full verification according to Eurocode 3 Page 15 Dedicated Eurocode 3 software verifications (AISC next step)

16. Steel Grades Steel S355 (EC properties for t>40mm) –σ y =335 MPa → σ y /1.5=223 MPa –UTS=470 MPa → UTS/3.5=134 MPa → UTS/2.4=195 MPa Baseline material S460ML (properties for t>40mm): –σ y =430 MPa → σ y /1.5=286 MPa –UTS=530 MPa → UTS/3.5=151 MPa → UTS/2.4 =220 MPa Page 16 24/04/2015