1. 2K Cold Box Vacuum Vessel Structure Analysis
Fredrik Fors
LCLS-II 2K Cold Box FDR
March 28, 2018

2. Summary
This presentation concerns the analysis performed to assure the design of the LCLS II 2K Cold Box fulfills the pressure safety requirements of the ASME Boiler and Pressure Vessel Code and the structural requirements of (among others) the ASCE 7-10 seismic code.
To take seismic and other occasional loads into account, the cold box is analyzed according to the Design by Analysis section of the BPVC. FEA models for this analysis have been created and processed in ANSYS Workbench 18, with input loads from an internal piping model solved in Bentley AutoPIPE.
LCLS II 2K Cold Box – Structural Analysis

3. Analyzed Geometry
The scope of this analysis is the main vacuum vessel and its circumferential weld joints, central column, and bottom support skirt
Since the loads on the vessel structure are dominated by the vacuum pressure loads the mass loads from the valves and bayonets attached to the top plate can be neglected. These components are not included in the analysis model.
The main transfer line nozzle is analyzed separately (79222-P0004).
The analysis does not cover the bolts, anchor chairs and shear keys anchoring the baseplate to the ground. These are analyzed and presented in a separate report (79222-A00011)
The picture to the side shows the current state of the design
LCLS II 2K Cold Box – Structural Analysis

4. Main Finite Element Model
The model geometry is created with imported CAD data (assemblies and -0036), that is simplified into a workable model geometry.
The cold compressors and diffusion pump are included as rigid bodies with appropriate mass and inertial properties.
The mesh consists of 2nd order, 3D hexahedral elements in the vacuum vessel walls. Other thin- walled structure is meshed with 1st order hexahedral “solid shell” elements.
Material properties used are presented in the table below:
Property
Steel, SA-36
Steel, SA-516 Gr 70
SST, SA L
Density, ρ [lbm/in3]
0.28
0.30
0.29
Elastic Modulus, E [ksi]
28.3×106
28.1×106
27.0×106
Poisson’s Ratio, ν [-]
0.31
Yield Strength, Sy [ksi] 36 38 25
Ultimate Strength, Su [ksi] 58 70
Stress Limit, S [ksi]
21.2
22.4
16.7
Stress Limit, SPL [ksi]
31.8 (1.5S)
33.6 (1.5S)
25.1 (1.5S)
LCLS II 2K Cold Box – Structural Analysis

5. Main FE Model – Loads & Boundary Conditions
The loads on the 2K cold box consists of:
D, Dead loads, gravity acceleration loads
P, Vacuum and internal pressure loads, 14.7 psi on vessel walls
E, Earthquake loads, seismic acceleration loads according to ASCE 7-10
L, Live loads, 100 lbf\ft2 on the top surface
These are applied as four load combinations yielding a total of 18 load cases that need to be solved for the model. The combinations are:
Pvac + D + L + T
Pint + D + L + T
0.9Pvac D + 0.7E L
0.9Pvac D + 0.7E L
Additionally, transportation loads are considered, but not analyzed since these loads are negligible in comparison to the load cases including vacuum loads. These load cases are defined as:
D g in lateral and longitudinal directions
D ± 3 g vertically
LCLS II 2K Cold Box – Structural Analysis

6. Main FE Model – Loads & Boundary Conditions
Seismic loads from the internal piping are imported from an external piping analysis and applied to the vacuum vessel nozzles.
The loads are BC reaction extracted from a version of Shirley Yang’s AutoPIPE model used for the internal pipe flexibility analysis (79222-P0003)
Boundary conditions are applied to the anchoring structure at the bottom skirt base.
Frictionless Constrain on the bottom surface of the base ring. No vertical movement allowed.
Surfaces of shear key holes are constrained in horizontal translation.
A closer analysis of the anchoring provisions is performed in a separate analysis (79222-A0001). Therefore, these linear BC’s are considered sufficient
LCLS II 2K Cold Box – Structural Analysis

7. Weld Joint FE Model
A finite element submodel is created for a detailed analysis of the circumferential weld joints of the vacuum vessel walls.
Cut-plane boundary deformations are imported from the solution of the main FE model and applied to the sub model cut surfaces.
The submodel is not solved for all 18 load cases, but only those that result in the highest stresses for each of the three weld joints.
Unlike the main model, the submodel uses nonlinear contact formulations between some surfaces.
½” bevel weld
⅜” bevel weld
Top Plate
Weld Joint
Top Skirt
LCLS II 2K Cold Box – Structural Analysis

8. Results – Stainless Steel Top Plate
For the vacuum vessel components of the cold box, the stresses and deformations have been evaluated for the 18 structural load cases for ASME BPVC verification.
For the stainless steel top plate, which has a somewhat lower allowable stress, the highest stress outside a weld fillet region is seen at the center column attachment area.
Equivalent stress and the sum of principal stresses have been checked, but they are at all points lower than the BPVC stress limits. No stress linearization is necessary to assure protection against Plastic Collapse or Local Failure.  
σeq,max = 10.8 ksi 67% of S CASE17
Σσp,max = 22.0 ksi 31% of 4S CASE17
LCLS II 2K Cold Box – Structural Analysis

9. Results – Main Vacuum Vessel
The main vacuum vessel structure (cylindrical shell and bottom head) also shows moderate stress levels. Outside the areas covered by the weld joint submodel and other weld connection regions, the highest stress levels are seen in the bottom head where the center column is attached.
Equivalent stress and the sum of principal stresses have been checked, but they are at all points lower than the BPVC stress limits. No stress linearization is necessary to assure protection against Plastic Collapse or Local Failure.
σeq,max = 5.1 ksi 23% of S CASE17
Σσp,max = 10.3 ksi 28% of 4S CASE17
LCLS II 2K Cold Box – Structural Analysis

10. Results – Center Column Structure
Although not part of the pressure boundary, it is analyzed by the same criteria as the rest of the vacuum vessel.
Outside areas covered by separate weld analyses, the center column shows highest stresses around the top and central flanges.
Equivalent stress and the sum of principal stresses have been checked, but they are at all points lower than the BPVC stress limits. No stress linearization is necessary to assure protection against Plastic Collapse or Local Failure.
σeq,max = 13.8 ksi 65% of S CASE17
Σσp,max = 21.7 ksi 26% of 4S CASE17
LCLS II 2K Cold Box – Structural Analysis

11. Results – Nozzle Stress
The nozzles are analyzed similarly to the vacuum vessel, but since they are meshed with “solid shell” elements the linearization is done directly for each element and no SCLs are needed.
The maximum stress values are for all nozzle walls are: 
PL,max = 9.1 ksi 54% of S CASE17
(PL+PB)max = 21.3 ksi 82% of 1.5S CASE17
Σσp,max = 9.2 ksi 26% of 4S CASE17
The vacuum break plate of the transfer line nozzle is analyzed for two vacuum loss load cases.
Neither vacuum loss in the cold box vacuum vessel or in the transfer line will cause any severe stress in the vacuum break plate.
PL,max = 2.2 ksi 13% of S Vacuum Loss in CB
(PL+PB)max = 8.2 ksi 33% of 1.5S Vacuum Loss in CB
Σσp,max = 11.0 ksi 16% of 4S Vacuum Loss in CB
LCLS II 2K Cold Box – Structural Analysis

12. Results – Deformations
Similar to the equivalent stresses, displacement magnitudes are evaluated for all analyzed load cases. It’s mainly the displacement of the top plate that is of interest, due to tolerance concerns for cold compressors.
The maximum displacement for any anchoring point of internal piping is:
Utot,max = in Cryo-valve 1 CASE17
LCLS II 2K Cold Box – Structural Analysis

13. Results – Buckling Analysis
In the vacuum vessel structure, the cylindrical walls, the bottom head and the center column are susceptible to buckling due to compressive loads from the vacuum pressure.
The results from the ANSYS eigenvalue buckling analysis shows that the first linear buckling mode is found in the cylindrical shell of the vacuum vessel at the full vacuum pressure load case (CASE17).
The loads factor for the cylindrical shell is:
Φ = 15.5
which higher than the minimum allowable:
ΦB,cyl = 2.5
LCLS II 2K Cold Box – Structural Analysis

14. Results – Weld Joint Calculations
Separate weld joint calculations are performed for all weld joints related to the center column assembly and the cold box nozzles. Minimum allowable weld sizes are calculated and compared against the weld size on the drawing.
The tables below show a summary of the analyzed weld joints and the resulting margins against the drawing weld size.
Weld Joint
Size
Margin
Upper Tube -Reinf. Plate
3/8”
1.30
Reinf. Plate -Top Plate
3/16”
1.51
Upper Tube -Flange
1.48
Floor Plate -Bottom Head
1/4" 4-7
4.42
Lower Tube -Reinf. Dish
1/4"
4.36
Gussets -Reinf. Dish
1/4" 1-3
1.18
Lower Tube -Floor Plate
3.54
Gussets -LowerTube
1.86
Lower Tube -Flange
Weld Joint
Size
Margin
Pump Nozzle
1/4"
20.9
Relief 1
1/8”
145.8
Vac. Break Plate
22.2
Relief 2
182.8
Manway
3/8”
30.3
Relief 3
CC1
0.12”
5.8
Relief 4
CC2
7.2
Relief 5
117.4
CC3
10.4
Relief 6
CC4
12.9
Instr. 1
59.7
CC5
13.8
Instr. 2
59.8
CC6
13.5
Electrical 1
88.5
Cryo Valve 1
9.2
Electrical 2
Cryo Valve 2
Electrical 3
Cryo Valve 3
11.8
Electrical 4
14.9
Cryo Valve 4
61.8
He Valve 1
Cryo Valve 5
74.3
He Valve 2
182.9
Bayonet 1
13.4
Vent
1/16”
479.9
Bayonet 2
Bayonet 3
12.4
Bayonet 4
9.0
Bayonet 5
15.7
LCLS II 2K Cold Box – Structural Analysis

15. Results – Weld Joint Submodel
The submodel has been evaluated for load cases CASE5, CASE17 and CASE18, which were determined to be the worst cases for the three circumferential weld joints of the vacuum vessel. The highest stress is seen at partially penetrating weld joint between the top plate and the upper skirt.
To verify the upper weld joint a stress classification line (SCL) is drawn up though the point of the highest equivalent stress
For the SCL at the upper weld joint the stress results at CASE 17 are:
PL,max = 2.3 ksi 14% of S
(PL+PB)max = 11.9 ksi 48% of 1.5S
Σσp,max = 30.8 ksi 46% of 4S
Membrane + Bending Stress
Membrane Stress
SCL
LCLS II 2K Cold Box – Structural Analysis

16. Conclusions
The material stresses in the vacuum vessel and the circumferential weld joints are below allowable for all operational and occasional design conditions.
The design weld sizes are large enough for any analyzed design conditions.
The buckling load factor is within the allowable range for all components
Thus, the 2K Cold Box design is acceptable
LCLS II 2K Cold Box Structural and Pressure Safety Analysis