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CSA Documentation-Calculations
Title: 2K Cold Box Pressure Safety and Structural Analysis
Note Number: 79222-P0002, Rev. A
Author(s): Fredrik Fors Page 1 of 30
CSA Documentation – 2K Cold Box Structural Analysis Page 1
2K Cold Box
Vacuum Vessel Pressure Safety
and Structural Analysis
Revision History:
Revision Date Released Description of Change
- December 12, 2017 Original release, Issued for Project use
A February 23, 2018 Rewritten to include ASME BPVC requirements
Issued for Project Use
Fredrik Fors
Mechanical Engineer
Mechanical Engineering Group
Jefferson Lab
Shirley Yang
Mechanical Engineer
Cryogenic Engineering Group
Jefferson Lab
Nathaniel Laverdure
Mechanical Engineer
Cryogenic Engineering Group
Jefferson Lab
Joseph Matalevich
LCLSII Cold Systems Manager
Mechanical Engineering Group
Jefferson Lab
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CSA Documentation-Calculations
Title: 2K Cold Box Pressure Safety and Structural Analysis
Note Number: 79222-P0002, Rev. A
Author(s): Fredrik Fors Page 2 of 30
CSA Documentation – 2K Cold Box Structural Analysis Page 2
Table of Contents
Table of Contents ........................................................................................................................................ 2
1. Introduction ......................................................................................................................................... 3
2. Scope..................................................................................................................................................... 4
3. Design Parameters .............................................................................................................................. 4 Pressure Safety Analysis ....................................................................................................................... 4
Seismic Load Parameters ...................................................................................................................... 6
External Seismic Loads ........................................................................................................................ 7
Transportation Loads ............................................................................................................................ 8
Load Combinations ............................................................................................................................... 8
4. Analysis .............................................................................................................................................. 10 FE Model ............................................................................................................................................ 10
Weld Joint Submodel .......................................................................................................................... 11
Material Data ...................................................................................................................................... 13
Nozzles and Manhole.......................................................................................................................... 13
Thermal Load ...................................................................................................................................... 14
Boundary Conditions .......................................................................................................................... 15
Applied Loads ..................................................................................................................................... 15
5. Results ................................................................................................................................................ 17 Pressure Vessel Structural Evaluation ................................................................................................ 17
Nozzle Structural Evaluation .............................................................................................................. 20
Support Structure Evaluation .............................................................................................................. 21
Deformations ...................................................................................................................................... 22
Submodel Weld Analysis.................................................................................................................... 23
Analytical Weld Evaluation ................................................................................................................ 24
Buckling Analysis ............................................................................................................................... 26
6. Conclusions ........................................................................................................................................ 26
7. Associated Analysis Files & Documents .......................................................................................... 27
8. References .......................................................................................................................................... 28
Appendix A – Central Column Thermal Calculation ........................................................................... A1
Appendix B – Analysis of Weld between Bottom Head and Bottom Skirt ......................................... B1
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Title: 2K Cold Box Pressure Safety and Structural Analysis
Note Number: 79222-P0002, Rev. A
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1. Introduction
The purpose of this Engineering Note is to document the analysis that was performed to ensure
that the LCLS-II 2K Cold Boxes are suitable for all operating and occasional loads. The design of
the CP1 and CP2 cold boxes is identical so theanalysis presented in this report covers both cold
boxes.
Figure 1. View of the LCLS-II 2K Cold Box including pumps, piping and auxiliary components.
Transfer
Line Nozzle
CC2
CC4
CC5
CC3
Bayonet
Connections
CC1
Weka
Valves
Diffusion
Pump
CC6
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Title: 2K Cold Box Pressure Safety and Structural Analysis
Note Number: 79222-P0002, Rev. A
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2. Scope
The scope of this analysis is the main vacuum vessel and its circumferential weld joints, central
column, and bottom support skirt. The LCLS II 2K cold box design feature a large vacuum vessel
topped by a 2” thick flat plate, buttressed by a central column, which supports six cold compressors
and associated piping.
All piping and the vacuum vessel were designed to meet applicable ASME and ASCE codes for
operating, transportation and seismic conditions. 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-A0001, see Section 7). The analysis of the piping inside the vacuum
vessel is also analyzed and reported in a separate document (79222-P0003, see Section 7).
Table 1. Drawing information of components included in the analysis
Drawing Number
Drawing Title Drawing Revision
Drawing Type
79222-0028 Complete Manufactured Vessel - Assembly
79222-0036 Bottom Section Weldment A Assembly
79222-0031 Vessel Top Section Assembly - Assembly
3. Design Parameters
The 2K cold boxes are designed in accordance with local and national requirements. These local
requirements include the Cryogenic Plant Seismic Design Criteria [1], the 2013 California
Building Code (CBC) [2] and the national reference standards ASCE 7-10 [3], AISC 360-10 [4]
and AISC 341-10 [5]. In its capacity as a vacuum vessel, the cold boxes are analyzed for pressure
safety according to the Design by Analysis requirements in the ASME Boiler Pressure Vessel Code
(BPVC) 2015, Section VIII, Division 2 [6].
Pressure Safety Analysis
Section VIII of the BPVC offers two routes for validating a pressure vessel design – Design by
Rules (Part 4) where the main vessel components are checked for pressure safety by analytical
calculations, and Design by Analysis (Part 5) where code adherence is assured by comparing
linearized stress results obtained from a numerical analysis model with allowable values. Since the
analytical methods in Part 4 cannot easily accommodate other loads than pressure loads, the 2K
cold box is analyzed according to Part 5 to also take seismic and other occasional loads into
account.
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For Design by Analysis according to BPVC 2015 three main criteria need to be fulfilled.
1. Protection against Plastic Collapse (5.2)
2. Protection against Local Failure (5.3)
3. Protection against Collapse from Buckling (5.4)
4. Protection against Failure from Cyclic Loading (5.5)
Protection against Plastic Collapse:
Since the FE model is linear elastic, the Elastic Stress Analysis Method (5.2.2) is used. At each
location of interest, the equivalent (von Mises) stress is linearized and the following is checked:
General Membrane Stress PM does not exceed material stress limit S
Local Membrane Stress PL does not exceed material stress limit SPL
Local Membrane plus Bending Stress PL + PB does not exceed SPL
Special requirements for determining PM and PL in nozzle necks is provided in 5.6
Protection against Local Failure:
At each location of interest, the primary stresses are linearized through the thickness and the
requirement is that the sum of the maximum primary stresses (σ1 + σ2 + σ3) does not exceed four
times the stress limit, S. The “linearized maximum principal stress” is interpreted as the numerical
maximum value of the membrane + bending stress for each line.
Protection against Collapse from Buckling:
The code specifies that when a linear bifurcation buckling analysis is performed using an elastic
stress analysis without geometric nonlinearities (the case for the analysis presented here), the
required design factor is:
Minimum design factor, Φ𝐵 =2
𝛽𝑐𝑟
This design factor is to be calculated using the load cases specified for the structural analysis,
taking all possible buckling modes into account. The capacity reduction factor, βcr, depends on the
specific part of the structure:
Cylindrical vessel shell βcr = 0.8 => ΦB,cyl = 2.5
Center column βcr = 0.834 => ΦB,col = 2.4
Bottom head βcr = 0.124 => ΦB,head = 16.1
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Protection against Failure from Cyclic Loading:
An evaluation of the possibility for fatigue damage is first performed according to the screening
criteria in section (5.5.2). If none of the criteria are fulfilled, no fatigue analysis is required. Due
to the material of the 2K cold box vacuum vessel, Method A (5.5.2.3) is used. The relevant
requirement here is the sum of pressure and thermal cycles:
𝑁Δ𝐹𝑃 + 𝑁ΔP0 + 𝑁Δ𝑇𝐸 + 𝑁Δ𝑇𝛼 ≤ 400
The number of full and partial pressure cycles (NΔFP and NΔP0) are expected to be very low for the
vacuum vessel, 50 cycles for each parameter is a conservative estimate.
The thermal cycles are expected to be close to zero since no significant temperature differentials
between either adjacent points (NΔTE), or across the stainless to carbon steel weld joint (NΔTα) are
expected. Thus, since ΣNΔ < 400, no fatigue analysis is required for the vacuum vessel or associated
components.
Seismic Load Parameters
In addition to operating conditions, the cold boxes are designed for occasional seismic loads. The
applied seismic loads and load combinations are determined in accordance with the 2013 CBC and
ASCE 7-10. Since the cold boxes are installed inside a building, no wind loads are considered.
Per the ASCE 7-10 [3], LCLS-II Cryogenic Building Geotechnical Report [7] and the Cryogenic
Plant Seismic Design Criteria [1], the site seismic design parameters are determined:
Site Class C
Spectral Response Parameter S1 = 1.168 LCLSII-4.8-EN-0227-R2
Design Spectral Response Acc. SDS = 1.968 ASCE 7-10 Ch. 11.4
Seismic Importance Factor Ie = 1.0 ASCE 7-10 Table 1.5-2
Seismic Design Category E ASCE 7-10 Ch. 11.6
The substances used in the LCLS-II Cryoplant and these lines (inert cryogenics, gaseous helium)
are not hazardous (highly toxic, explosive or flammable). Thus, per ASCE 7-10 Table 1.5-1 and
the Cryogenic Plant Seismic Design Criteria, the Cryogenic Building and its associated
components are categorized as Risk Category II.
As the cold box is a self-supporting structure that carries gravity loads and is required to resist the
effects of an earthquake, it is classified as a non-building structure [3]. The cold box is considered
a welded steel skirt-supported vertical vessel (ASCE 7-10 Table 15.4-2), giving a Response
Modification Factor of R = 2. However, option 2 in the Cryogenic Plant Seismic Design Criteria
is applied, so the Response Modification Factor is reduced to R = 1 for design of the cold box and
its appurtenances. The component importance factor is taken as Ie = 1 as required by ASCE 7-10
15.4.1.1.
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The seismic response coefficient, Cs, is determined in accordance with ASCE 7-10 as:
• 𝐶𝑠 =𝑆𝐷𝑆
𝑅
𝐼𝑒
=1.968
1.0
1.0
= 1.968 (12.8-1, 2)
• 𝐶𝑠,𝑚𝑎𝑥 =𝑆𝐷𝑆
𝑇𝑅
𝐼𝑒
=1.968
0.071 1.0
1.0
= 27.72 (12.8-3)
• where 𝑇 = 𝑇𝑎~0.02 (65.5/12).75 = 0.071 (12.8.2, 12.8-7)
• 𝐶𝑠,𝑚𝑖𝑛 = 0.044 𝑆𝐷𝑆𝐼𝑒 = 0.044(1.968)(1.0) = 0.009 (15.4-1)
• 𝐶𝑠,𝑚𝑖𝑛 = 0.8 𝑆1/(𝑅
𝐼 𝑒) =
0.8 (1.168)
2.0
1.0
= 0.4672 (15.4-2)
• So, 𝐶𝑠 = 1.968
To meet the requirement that the seismic force is applied in the direction that produces the most
critical load effect, 100% of the seismic design force is applied in one horizontal direction and
30% of the seismic design force is applied in an orthogonal direction (ASCE 7-10 12.5.3.1). In
addition, a vertical seismic force of 0.2 SDS Wp is also simultaneously applied. All sixteen
directional combinations are applied (see Table 3f vacuum vessel (red surfaces).). The design load
combinations in which these forces are applied are discussed in in subsection Load Combinations
below.
External Seismic Loads
In addition to imposing the seismic accelerations on the vacuum vessel structure itself, reactions
from application of the analogous seismic force on the internal piping are simultaneously imposed
at pipe support locations. These reaction forces are calculated separately, using a modified version
of the model used in the analysis of the internal piping system of the cold box. This analysis is
performed in Bentley AutoPIPE and the original analysis is presented in a separate report (79222-
P0003, see Section 0).
The reaction loads from the AutoPIPE model presented in Figure 2 does not reflect the revision of
the piping system to include flex hoses on some of the pipe spools. Given that the loads from the
stiffer piping system are expected to be higher, and that the seismic loading from the internal piping
is only a very minor part of the total load on the vacuum vessel, this is considered conservative
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Figure 2. AutoPIPE model of the internal piping of the cold box. All pipes are modeled as rigidly anchored at interfaces to compressors, valves and bayonet installations.
Transportation Loads
There are two load cases defined to cover the loads induced in ther structure during trans-portation
to the installation site. The first case is a 1.5g acceleration in two lateral directions plus the self-
weight load; the second case is a ±3g vertical acceleration plus the self-weight [8]. There is no
pressure differential during transportation and the no significant temperature loads.
Since the vacuum pressure is the completely dominant load component in the seismic load cases
(as seen by the FEA results presented in Section 5), and since the transportation accerelation are
in the same order of magnitude as the seismic accelerations, the vacuum vessesl is considered to
withstand the transportation loads without the need for further analysis.
Load Combinations
The general design load combinations are specified in ASCE 7-10 2.3.2, and the included
occasional seismic loads are calculated using the design parameters presented in Section 3 of this
report. The relevant load combinations for this analysis are:
ASD 5(E) (1.0 + 0.14 SDS) D + 0.7Ω0 QE
ASD 8(E) (0.6 - 0.14 SDS) D + 0.7Ω0 QE
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Specifically for a pressure vessel following the BPVC 2015 Design by Analysis requirements, the
design loading conditions are defined in section 5.1.3 of BPVC Section VIII, Div. 2 [6] and the
load combinations are defined in Table 5.3 of the same document. For the analysis of the 2K cold
box vacuum vessel, the applicable load combinations are:
(3) P + PS + D + L + T
(6) 0.9P + D + (0.7E or 0.6W)
(8) 0.9P + D + 0.75(0.7E or 0.6W) + 0.75L + 0.75SS
The load type definitions in the above combinations are:
D Dead Loads, gravity acceleration. In this case applied both as (1.0 + 0.14SDS)*g and
(0.6 - 0.14SDS)*g to cover both combinations 5 and 8 from ASCE 7-10
E Seismic loading defined as Ω0QE. Note that the overstrength factor is Ω0 = 1, as
described in ASCE 7-10 Ch. 15.7.3.
W Wind loads. Not applicable
P Pressure Loads. For the vacuum vessel defined as an external pressure of Pvac =
1.0 atm, or in a special case an internal pressure of Pint = 5 psi
PS Static pressure from liquid, not applicable for vacuum vessel
T Temperature loads. See Section 4
L Live load. The live loads on the top plate are taken to be the same as for the adjacent
platform – a uniform load of 100 lbf/ft2 or a concentrated force of 500 lbf.
SS Snow Loads. Not applicable
To simplify the analysis and minimize the number of load cases for solving, BPVC combinations
(6) and (8) above, are combined by conservatively adding the 0.75L live load factor to the load
cases produced by combination (6). When seismic loads are applied, to assure compliance to both
ASCE 7-10 and BPVC 2015, the dead load coefficients case applied both as (1.0 + 0.14SDS)*g and
(0.6 - 0.14SDS)*g to cover both combinations 5 and 8 from ASCE 7-10. Thus, the combinations
used in the analysis of the vacuum vessel model are:
(3a) Pvac + D + L + T
(3b) Pint + D + L + T
(6a) 0.9Pvac + 1.28D + 0.7Ev + 0.75L
(6b) 0.9Pvac + 0.32D + 0.7Ev + 0.75L
The resulting load cases that are applied to the ANSYS FE model are presented in subsection
Applied Loads below.
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4. Analysis
FE Model
The cold box weldment structures are analyzed using the Finite Element Analysis (FEA) tool
ANSYS Workbench 18.2. The model geometry is created with imported CAD data (assemblies
79222-0031 and -0036), that is simplified into a workable model geometry. Since the loads on the
vessel structure are dominated by the vacuum pressure loads, the mass loads from the valve
components attached to the top plate can be neglected. For the diffusion pump assembly and the
six cold compressors (CC), only the mass loads are included in the model. These components are
represented as rigid bodies that can be scoped with loads and boundary conditions, but are
converted to mass elements and rigid constraints when solving the model.
The internal piping is completely excluded from the model. The effects of the piping during
seismic events is included by applying the reaction forces from a separate piping analysis to the
piping attachment point at the transfer line connection, cold compressors and bayonet valves.
Reaction loads of small diameter piping (< 2” OD) are considered negligible and not included.
Figure 3. Simplified cold box geometry for FE analysis purposes. Vessel walls are shown as transparent to show the interior structure. Rigidized components shown in grey.
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The FE model is mainly meshed with 2nd order, 3D hexahedral elements with two elements through
the thickness in the vacuum vessel walls (see Figure 4 below). The thin-walled structure of the
bottom skirt, center column and piping connections is meshed with 1st order hexahedral “solid
shell” elements. These essentially function as shell elements and give accurate results with just
one element through the thickness without the need for midsurfacing the 3D CAD model. The
typical element size is ¼” to 1”.
Figure 4. Cross section view of the FE mesh at the top plate to side wall connection. The rigidized CC is seen as an unmeshed geometric representation.
Weld Joint Submodel
To accurately analyze the long circumferential weld joints that join the different sections of the
vacuum vessel, a submodel approach is employed. A separate, detailed, model of the area around
the three main weld joints is created with enough detail to model the actual welds as separated
bodies, and mesh these with multiple elements through the thickness. Cut-plane boundary
deformations are imported from the solution of the main FE model and applied to the sub model
cut surfaces.
Unlike the main model, the submodel is non-linear and uses nonlinear contact formulations
between some surfaces. At the partially penetrating weld between the top plate and the top skirt
(see Figure 5) the mating surfaces not bonded by the weld have a frictionless contact applied.
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The submodel is not solved for all 16 seismic load cases, but only those that result in the highest
stresses for each of the three weld joints. This is determined by looking at the contact stresses of
the contact connections that represent the weld joint in the main model.
Table 2. Material data, steel
Property CS, SA-36 CS, SA-516 Gr 70 SST, SA-240 340L
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 0.30 0.31
Yield Strength, Sy [ksi] 36 38 25
Ultimate Strength, Su [ksi] 58 70 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)
½” bevel
weld
⅜” bevel
weld
⅜” bevel
weld
Weld Joint
Top Skirt
Figure 5. Geometry of the weld joint submodel with remaining vessel shown as transparent. (left). Cross section view of the partial penetration upper weld joint showing weld
body and FE mesh
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Material Data
The main vacuum vessel, except the top plate, is made from ASTM SA-516 Grade 70 pressure
vessel steel. The top plate and its accessories are made of 304/304L stainless steel. Other
components and brackets are considered to be ASTM SA-36 construction steel. For the welded
joints the weld filler metal is conservatively considered to have the same properties as the weaker
of the joined materials. The material properties in Table 2 are used in the FE model and are sourced
from the ASME BVPC, Section II 2015 [9]. All properties evaluated at room temperature (300 K).
Nozzles and Manhole
Vacuum vessel nozzles including the manhole opening are included in and covered by the general
structural analysis performed according to Part 5 of BPVC Sec. VIII, Div 2. This is in accordance
with section 4.5.15 of the same document, since the nozzles are subjected to external (seismic)
loads as well as pressure (vacuum) loads.
The detailed design of the transfer line is still in progress, so no seismic loads on the transfer line
nozzle are available. Instead a conservative estimate of maximum allowable loads on the transfer
line nozzle are calculated analytically in a separate analysis (79222-P0004, see Section 7) and
supplied to the external vendor responsible for the transfer line design and analysis. Since the
dominating load on the cold box is the vacuum load, the effects of seismic accelerations on the
transfer line are considered to be local around the nozzle. Therefore, detailed results of the transfer
line nozzle will not be presented in this report.
The exception is two load cases modeling loss of vacuum in either the transfer line or the vacuum
vessel. This puts a pressure load on the vacuum break plate, and since this component is not
included in the separate nozzle analysis, these load cases are included in this report. These cases
imply vacuum on one side, and a 5 psi overpressure on the other side of the vacuum break
In the FE analysis the general stress levels in the nozzle walls and surrounding material has been
checked and the weld joint has been analyzed further in a separate calculation. These welded
connections are modeled as a bonded linear contact between the two connecting surfaces, and
reaction moments and forces are extracted from each contact pair using individual coordinate
systems placed at the centroid of the contact surface.
The reaction forces and moments from the FE analysis are exported to a spreadsheet for weld
sizing calculations utilizing the methods for circular welds from Chapter 9.3-4 of Shigley’s
Mechanical Engineering Design [10]. The allowable weld stress is conservatively taken as 14,400
psi (“minimum acceptable material shear strength” [4]). This allowable stress is less than the
allowable weld filler material stress in the Structural Welding Code—Steel [11], which is 18,000
psi for an E60XX electrode.
For each weld joint, the minimum allowable weld throat dimension is calculated for each load
case, and the maximum value for all cases is used to verify the weld size. For these calculations,
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the nozzle loads are considered to be carried by a single circumferential fillet weld, which is very
conservative as most nozzles are set-in nozzles with an inner and an outer weld.
Only the external loads related to the cold box internal piping are applied on the nozzles (see
subsection Applied Loads below). In every load case, the vacuum pressure loads are completely
dominant, so the loads from external components such as bayonets, valves etc are considered
negligible and not included.
Thermal Load
The center column connects the bottom and top sections of the vacuum vessel. It is made of two
sections of 8” NPS Sch. 80S stainless steel pipe. The two sections are connected by tie rods and
nuts for alignment purposes. In order to reduce the thermal contraction, a copper shield is attached
to the outside surface of the center column. Four copper straps are used as a connection between
the upper and lower sections.
Even with the careful thermal design, the center column will experience a temperature gradient
between its center and the outer edges during operation, and this could have a structural
significance due to the thermal loads. A calculation of the temperature gradient was made by
Shirley Yang (See Appendix A), and the results are shown together with the column design in
Figure 6 below. Since the temperature gradient it so small, only about 4 K along the length of the
columns, this thermal load is not considered in the structural analysis load combinations.
Figure 6. Mechanical design of the center column (left) and the temperature loads as applied on the FE model representation.
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Boundary Conditions
The skid structure is constrained by a linear “frictionless” boundary condition (constrained in the
vertical direction, ±Y) at the bottom surfaces of the base ring, combined with translational
constraints (X and Z directions) at the holes for the shear keys. This represents the anchoring of
the structure by bolts to the underlying concrete slab. Since the entire structure will never
experience negative g’s, vertical constraints on the base ring are considered sufficient. No detailed
analysis of anchor bolts, anchor chairs or shear keys is performed in this analysis, as this is done
in a separate analysis (79222-A0001, see Section 7) using the Hilti PROFIS software.
Applied Loads
The loads for the FE analysis are applied in a total of 18 separate load steps, whereof sixteen are
required to produce all combinations of the dead loads and earthquake loads (as defined in Section
3 – Load Combinations). In each load step, acceleration loads are applied directly to all bodies of
the model. Table 3 below summarizes the directional accelerations for all load steps.
Table 3. Applied loads – Acceleration, pressure and live loads
ANSYS Acceleration Loads Pressure Live Loads
Load Case
BPVC Comb.
ASCE 7-10 Comb.
AX [in/s2]
AY [in/s2]
AZ [in/s2]
P [PSIG]
Load Factor [-]
CASE1 6 5(E) 532.1 492.6 159.6 -13.2 0.75
CASE2 6 5(E) 159.6 492.6 532.1 -13.2 0.75
CASE3 6 8 532.1 125.3 159.6 -13.2 0.75
CASE4 6 8 159.6 125.3 532.1 -13.2 0.75
CASE5 6 5(E) 532.1 492.6 -159.6 -13.2 0.75
CASE6 6 5(E) 159.6 492.6 -532.1 -13.2 0.75
CASE7 6 8 532.1 125.3 -159.6 -13.2 0.75
CASE8 6 8 159.6 125.3 -532.1 -13.2 0.75
CASE9 6 5(E) -532.1 492.6 159.6 -13.2 0.75
CASE10 6 5(E) -159.6 492.6 532.1 -13.2 0.75
CASE11 6 8 -532.1 125.3 159.6 -13.2 0.75
CASE12 6 8 -159.6 125.3 532.1 -13.2 0.75
CASE13 6 5(E) -532.1 492.6 -159.6 -13.2 0.75
CASE14 6 5(E) -159.6 492.6 -532.1 -13.2 0.75
CASE15 6 8 -532.1 125.3 -159.6 -13.2 0.75
CASE16 6 8 -159.6 125.3 -532.1 -13.2 0.75
CASE17 3 - 0 336 0 -14.7 1.0
CASE18 3 - 0 336 0 5 1.0
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The direct acceleration loads are combined with reaction loads from the previous piping analysis,
which are applied to the pipe attachment locations at the cold compressor inlets and outlets and
the nozzles for the transfer line, bayonet and control valves. All pipe reactions loads are determined
considering friction and other nonlinearities. The differences in how AutoPIPE and ANSYS define
acceleration loads and reaction forces requires special considerations. For example, the case with
a unit acceleration load in the +X direction on a fixed structure:
- AutoPIPE model deforms in the +X direction and the reaction force is in the +X direction
- ANSYS model deforms in the -X direction and the reaction force is in the +X direction
Therefore, to match the seismic load cases in the AutoPIPE analysis a factor -1 is applied to all
ANSYS acceleration loads.
The main pressure load is the internal vacuum, which is applied as a negative pressure load of 1
atm (14.7 psi) on all interior surfaces of the vacuum vessel (See Figure 7). A secondary pressure
load consisting of an internal pressure of 5 psig is also considered. The 2K cold box relief valve
report (79222-P0001, see Section 7) states the relief valve setting is 2 psi, with an additional
pressure drop in the relief valve header. This makes 5 psig a conservative estimate of the maximum
possible overpressure at the event of, for example, an internal helium leak.
In addition to the wall pressure the corresponding pressure thrust forces are added at the edges of
each nozzle and opening in the vessel. The thrust force is calculated as Fth = Aopening×P and is
directed in the normal direction of the opening.
Figure 7. Vacuum pressure loads applied to the inside of vacuum vessel (red surfaces).
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5. Results
Pressure Vessel Structural Evaluation
For the structural components of the cold box, the stresses and deformations have been evaluated
from the 18 load cases presented in Table 3. The equivalent (von Mises) stress is calculated and
evaluated for each load case and compared against the BPVC allowable stress values presented in
Table 2. Typically, the results at weld joint connections stress singularities can be disregarded
since the weld joint is analyzed separately. The max stress outside the weld fillet area is instead
considered for the structural stress evaluation.
For the stainless steel top plate (which has a somewhat lower allowable stress), the highest stress
results are seen around the cut-out for CC6 in the CASE1 load step (See Table 3). Even at the
worst load case the maximum equivalent stress does not exceed the allowable stress S. As seen in
the cross section in Figure 8 the maximum stress is concentrated to the surface and the average
value through the thickness will be much lower. For this reason, no further analysis using the
linearized stress methods of the ASME BPVC Section VIII is considered necessary to determine
Protection against Plastic Collapse.
The sum of the principal stresses is extracted for all elements and the maximum value is found to
be significantly lower than the allowable 4S. No stress linearization is necessary to determine
Protection against Local Failure.
σeq,max = 10.8 ksi 67% of S CASE17
Σσp,max = 22.0 ksi 31% of 4S CASE17
Figure 8. Top plate stress results. Contour plot of the equivalent stress at the worst load case (CASE1). Detail shows the stress level around the maximum in cross section.
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The main vacuum vessel structure (cylindrical shell and bottom head) also show moderate stress
levels, with the highest stress seen around the weld joint of the top skirt to the top plate and the
welds joints at the manway and nozzles. The circumferential weld area is analyzed separately in a
submodel analysis below. The weld joints around the manway and other nozzles are also analyzed
analytically separately (see Table 5). Apart from around weld joint connections, moderate stresses
are seen in the bottom vessel head around the attachment point for the center column. Since not
even the local maximum stress exceeds the allowable stress, S, no linearization through the
thickness is necessary to determine Protection against Plastic Collapse.
σeq,max = 5.1 ksi 23% of S CASE17
Σσp,max = 10.3ksi 28% of 4S CASE17
Figure 9. Contour plot of the equivalent stress in the main vacuum vessel structure. Close-up shows local stress around the manway opening
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Outside areas covered by separate weld analyses, the center column shows highest stresses around
the top and central flanges. The levels of the equivalent stress and the principal stress sum are
moderate, and do not exceed the local material stress limits. Therefore, as for the vacuum vessel
shell, no linearization through the thickness is necessary to confirm code compliance. The weld
joints around the flanges and bottom gussets are analyzed separately (see Table 6)
σeq,max = 13.8 ksi 65% of S CASE17
Σσp,max = 21.7 ksi 26% of 4S CASE17
Figure 10. Contour plot of the equivalent stress in central column structure. Close-up shows local stress around the upper plate connecting to the vacuum vessel.
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Nozzle Structural Evaluation
The nozzles are analyzed similarly to the vacuum vessel, with linearized stress components being
compared against material allowable stresses according to Part 5.6 of the BVPC Section VIII.
Since the nozzle walls are meshed with “solid shell” elements the linearization can be done directly
for each element and no separate Stress Classification Lines need to be added. No “strain related”
loads, such as thermal conditions, are present. This puts the secondary equivalent stress
component, Q, to zero. The maximum stress values are for all nozzle walls are:
PL,max = 9.1 ksi 54% of S CASE17
(PL+PB+Q)max = 20.5 ksi 82% of 1.5S CASE17
Σσp,max = 9.2 ksi 26% of 4S CASE17
Figure 11. Contour plot of the bending plus membrane stresses (PL+PB) in the top plate nozzle walls.
The vacuum break plate of the transfer line nozzle is analyzed here for two vacuum loss load cases.
As is shown in the results below 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+Q)max = 8.2 ksi 33% of 1.5S Vacuum Loss in CB
Σσp,max = 11.0 ksi 16% of 4S Vacuum Loss in CB
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Figure 12. Contour plot of the equivalent membrane stress around the vacuum break plate at loss of vacuum in the cold box.
Support Structure Evaluation
The support structure of the Vacuum vessel consists of a support skirt with a base ring attached at
the bottom. The anchoring provisions (anchor chairs/bolt and shear keys) are not part of this
analysis. As can be seen in Figure 13 below, the stress levels are very low for all parts of the
support structure.
σeq,max = 4.9 ksi 23% of S CASE14
Figure 13. Contour plot of maximum equivalent stress the vacuum vessel support structure.
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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
the cold compressor installations. A summary of the maximum total deformation for each cold
compressor location is provided in Table 4 below. A plot of the top plate deformation is shown in
Figure 14. The maximum displacement for any anchoring point of internal piping is:
Utot,max = 0.099 in @ Cryo-valve 1, CASE17
Table 4. Top plate deformation magnitudes at cold compressors
Load case
CC1 Utot [in]
CC2 Utot [in]
CC3 Utot [in]
CC4 Utot [in]
CC5 Utot [in]
CC6 Utot [in]
1 0.0777 0.0636 0.0631 0.0719 0.0730 0.0953
2 0.0695 0.0582 0.0628 0.0736 0.0762 0.0947
3 0.0700 0.0567 0.0568 0.0651 0.0664 0.0872
4 0.0616 0.0512 0.0565 0.0668 0.0695 0.0866
5 0.0815 0.0693 0.0653 0.0721 0.0716 0.0952
6 0.0819 0.0770 0.0697 0.0741 0.0714 0.0944
7 0.0738 0.0625 0.0590 0.0652 0.0649 0.0872
8 0.0743 0.0701 0.0634 0.0672 0.0647 0.0864
9 0.0655 0.0680 0.0689 0.0769 0.0772 0.0934
10 0.0658 0.0596 0.0646 0.0751 0.0774 0.0942
11 0.0578 0.0610 0.0627 0.0701 0.0705 0.0854
12 0.0579 0.0526 0.0584 0.0683 0.0707 0.0861
13 0.0693 0.0734 0.0709 0.0770 0.0758 0.0933
14 0.0783 0.0781 0.0713 0.0755 0.0727 0.0938
15 0.0617 0.0665 0.0647 0.0702 0.0691 0.0853
16 0.0708 0.0712 0.0651 0.0687 0.0660 0.0858
17 0.0785 0.0745 0.0742 0.0823 0.0826 0.1052
18 0.0120 0.0126 0.0138 0.0159 0.0165 0.0205 Approved: 2/26/2018; E-Sign ID : 360561; signed by: DCG: T. Fuell; O.: F. Fors; Re. 1: S. Yang; Re. 2: N. Laverdure; Re. 3: J.
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Title: 2K Cold Box Pressure Safety and Structural Analysis
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Figure 14. Contour of the deformation of the cold box top plate.
Submodel Weld Analysis
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 equivalent stress has been evaluated in the bodies representing the weld seam. The highest
stress is seen at weld between the top plate and the upper skirt, where local stress concentrations
are formed in the seismic load cases. At the lower weld joints the stress levels are much lower and
does not approach near the stress limit, S, for the weakest of the joined materials. Therefore no
further analysis is performed at these locations.
The maximum stress values for the analyzed welds are:
σmax,weld1 = 16.5 ksi 99% of S304
σmax,weld2 = 1.8 ksi 11% of S516
σmax,weld3 = 0.7 ksi 4% of S516
To verify the upper weld joint a stress classification line (SCL) is drawn up though the point of the
highest equivalent stress, as shown in Figure 15 below. This is done according to the guidelines in
Annex 5-A of BPVC, Section VIII [6]. The stress is linearized along the line and the resulting
stresses are compared to the allowable stress values presented in Section 3.
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Figure 15. Contour plot of the equivalent stress in the partially penetrating weld seam between the top plate and the upper skirt. LHS plot shows stress components along SCL.
For the SCL at the upper weld joint the stress results at CASE 1 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
All stress components are below the allowable values. Thus the weld joint design is validated.
Analytical Weld Evaluation
As mentioned above, a separate weld joint analysis is performed where minimum allowable weld
sizes have been calculated for all weld joints related to the center column assembly and the various
nozzles of the vacuum vessel. Table 5 summarizes the weld joint analysis for the nozzles and Table
6 contains the results for the Center Column welds. Further details about the calculations and the
weld joint nomenclature can be found in the respective calculation spreadsheets (See Table 7). As
can be seen in the weld result data, the weld sizes specified on the drawings are sufficient for all
joints. It should be noted that the low margins on the Center Column welds are due to the fact that,
in this analysis, the welds are considered to cary all compressive loads in the vacuum load cases.
This is very conservative for a column structure designed to carry the compression directly through
its members.
SCL
Membrane + Bending Stress
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The circumferential skip weld between the bottom head of the vacuum vessel and the bottom
support skirt has been analyzed analytically in a separate calculation performed by S. Yang. This
is presented in Appendix B. The Margin of Safety on the sizing of this weld joint is 2.03.
Table 5. Summary of the analytically evaluated nozzle weld joints
Weld Joint Dwg. Size Margin Weld Joint Dwg. Size Margin
Pump Nozzle 1/4" 20.9 Relief 1 1/8” 145.8
TL Vacuum Break 1/4" 22.2 Relief 2 1/8” 182.8
Manway 3/8” 30.3 Relief 3 1/8” 182.8
CC1 0.12” 5.8 Relief 4 1/8” 145.8
CC2 0.12” 7.2 Relief 5 1/8” 117.4
CC3 0.12” 10.4 Relief 6 1/8” 182.8
CC4 0.12” 12.9 Instrumentation 1 1/8” 59.7
CC5 0.12” 13.8 Instrumentation 2 1/8” 59.8
CC6 0.12” 13.5 Electrical 1 1/8” 88.5
Cryo Valve 1 1/8” 9.2 Electrical 2 1/8” 88.5
Cryo Valve 2 1/8” 9.2 Electrical 3 1/8” 88.5
Cryo Valve 3 1/8” 11.8 Electrical 4 1/8” 14.9
Cryo Valve 4 1/8” 61.8 He Valve 1 1/8” 182.8
Cryo Valve 5 1/8” 74.3 He Valve 2 1/8” 182.9
Bayonet 1 1/8” 13.4 Vent 1/16” 479.9
Bayonet 2 1/8” 10.4
Bayonet 3 1/8” 12.4
Bayonet 4 1/8” 9.0
Bayonet 5 1/8” 15.7
Table 6. Summary of center column weld joint analysis
Weld Joint Dwg. Size Margin Weld Joint Dwg. Size Margin
UpperTube-Reinf.Plate 3/8” 1.30 Reinf.Plate-TopPlate 3/16” 1.51
UpperTube-Flange 3/8” 1.48 FloorPlate-BottomHead 1/4" 4-7 4.42
LowerTube-Reinf.Dish 1/4" 4.36 Gussets-Reinf.Dish 1/4" 1-3 1.18
LowerTube-FloorPlate 3/8” 3.54 Gussets-LowerTube 1/4" 1.86
LowerTube-Flange 3/8” 1.48
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CSA Documentation – 2K Cold Box Structural Analysis Page 26
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 (see Figure 16), which is higher than the minimum
allowable for the shell, ΦB,cyl = 2.5. No further buckling modes are detected below the allowable
for the bottom vessel head, ΦB,head = 16.1, so all components are considered to pass the buckling
analysis
Figure 16. Deformation plot for the first buckling mode of the cylindrical shell.
6. 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 do not exceed the specified weld sizes 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.
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7. Associated Analysis Files & Documents
The report defining the 2K cold box relief valves, as related to this analysis is:
79222-P0001 LCLS-II 2K Cold Box Relief Valves
The analysis report for the internal piping of the 2K cold box, related to this analysis is:
79222-P0003 LCLSII 2K Cold Box Internal Piping Flexibility Analysis
The report defining the allowable loads on the MTL nozzle, related to this analysis is:
79222-P0004 LCLS-II 2K Cold Box Transfer Line Nozzle Analysis and
Allowable Loads
The anchoring analysis report for the 2K cold box is found in document:
79222-A0001 LCLSII 2K Cold Box Anchor-Shear Key Calculations
The calculation documents and model files listed in Table 7 below are on file at JLab and can be
provided upon request. The files are located in the folder path on the JLab network indicated
below:
\\JLABSGRP\\cryo\LCLS II ANALYSIS FOLDER\2K\STRUCTURAL&ANCHORAGE\
Table 7. Additional documentation relating to the analysis.
File Name File Type Description
2K_Coldbox_-_Nozzle_Weld_ Calc.xlsx
Microsoft Excel 2016 spreadsheet
Calculation of nozzle weld sizes, tables of reaction loads from ANSYS analysis.
2K_Coldbox_-_CenterColumn_ Weld_Calc.xlsx
Microsoft Excel 2016 spreadsheet
Calculation of center column weld sizes, tables of reaction loads from ANSYS analysis
2K_ColdBox_Seismic.wbpz ANSYS Workbench 18 archived project
2K CB FE model and analysis setup, result databases not included
2K_ColdBox_AutoPIPE_Analysis S_Data.xlsx
Microsoft Excel 2016 spreadsheet
Calculations of applied seismic loads. Reaction loads from AutoPIPE analysis
2K_Coldbox_AutoPIPE_for_ Structural.zip
Compressed AutoPIPE Project
Modified version of the piping analysis for the 2K CB. Including result and input databases
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Note Number: 79222-P0002, Rev. A
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8. References
[1] Cryogenic Plan Seismic Criteria, LCLSII-4.8-EN-0227-R2.
[2] California Building Standards Commission, California Building Code, 2013.
[3] American Society for Civil Engineers, ASCE/SEI 7-10 Minimum Design Loads Buildings and
Other Structures, 2013.
[4] American Institute of Steel Construction, ANSI/AISC 360-10 Specification for Structural Steel
Buildings, Chicago, IL, 2010.
[5] American Institure of Steel Construction, ANSI/AISC 341-10 Seismic Provisions for Structural
Steel Buidlings, Chicago, IL, 2010.
[6] American Society of Mechanical Engineers, "Boiler and Pressure Vessel Code, Section VIII,
Division 2," 2015.
[7] Rutherford and Chekene, Final Report Geotechnical Investigation LCLS II Cryogenic Building
and Infrastructure, SLAC National Accelerator Laboratory, 2014.
[8] "Shipping Load for 2K coldbox", E-mail conversation between Shirley Yang (JLab) and Hongyu
Bai (SLAC), 12/6/2017.
[9] American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section II -
Materials, 2015.
[10] R. G. Budynas and J. K. Nisbett, Shigley's Mechanical Engineering Design, 8th ed., McGraw-
Hill Education, 2016.
[11] American Welding Society, ANSI/AWS D1.1 Structural Welding Code - Steel, Miami, FL,
2010.
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CSA Documentation-Calculations
Title: 2K Cold Box Pressure Safety and Structural Analysis
Note Number: 79222-P0002, Rev A
Author(s): Fredrik Fors
CSA Documentation – 2K Cold Box Structural Analysis Page A1
Appendix A – Central Column Thermal Calculation
Calculation by Shirley Yang, JLab
275.0
280.0
285.0
290.0
295.0
300.0
0.00 2.00 4.00 6.00
Tem
per
ature
[K
]
Distance from edge [ft]
Temperature Distribution along the axis of
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Title: 2K Cold Box Pressure Safety and Structural Analysis
Note Number: 79222-P0002, Rev A
Author(s): Fredrik Fors
CSA Documentation – 2K Cold Box Structural Analysis Page B1
Appendix B – Analysis of Weld between Bottom Head and Bottom Skirt
Calculation by Shirley Yang, JLab
A skip weld with a weld leg of 0.25” was used for the joint between the CB bottom head and
bottom skirt. It was assumed that the overall weight above the bottom skirt would be 33,000 lbm.
Acceleration loads of 1.38 g and 0.41 g in two perpendicular horizontal directions and -0.28 g in
vertical direction were applied as the worst case scenario.
Skip weld leg, ho 0.25
Skip weld length, Lw 2
Skip weld pitch, p 4
Nozzle OD 144.00
Nozzle outer perimeter, Lp=π*OD 452.39
Number of skip welds, N=Lp/p 113
Actual weld length, L=N*Lw 226.00
Skip weld throat area, At=0.707*ho*L 39.95
Equivalent continuous weld from skip weld, heq=At /
(0.707*π*OD) 0.12
Weld inner radius, i.e. port tube outer radius, ro 72.00
Throat area A=1.414h ro 12.72
Moment of Inertia 103,539
Allowable shear stress per AWS Sa, psi 18,000
Total weight above the bottom Skirt, lbf 33,000
Vertical force Fy, with Seismic effect, lbf 42,240
Lateral Resultant Force, with Seismic effect, lbf 47,507.39
Moment caused by Seismic load, in-lbf 5,570,242
Shear stress due to forces, =F/A, psi 4,999.60
Shear stress due to bending, = Mz*r/I, psi 3,873.50
Combined shear stress, τ, psi 8,873.10
Safety factor = Sa / τ 2.03
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