2k cold box structural analysis - jlab.org · seismic design category e asce 7 -10 ch. 11.6 ... 30%...

CSA Documentation-Calculations

Title: 2K Cold Box Pressure Safety and Structural Analysis

Note Number: 79222-P0002, Rev. A

Author(s): Fredrik Fors 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

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.






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







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







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.







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







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.







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

and acceptable. 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.






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







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.







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.







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.







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

Top Plate 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.






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,







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.







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







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).







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.







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.


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







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)



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.







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


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







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.


Figure 13. Contour plot of maximum equivalent stress the vacuum vessel support structure.







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.






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



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.







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

Membrane Stress 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.






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 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







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.







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


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


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







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.




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

Hollow Rod 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.



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
