4.5k lower cold box shear key calculations - jefferson lab · 7.0 cover plate to baseplate...

Engineering Calculation

Document Title: 4.5K Lower Cold Box Shear Key Calculations

Document Number: 79221-A0001 R- of 21

4.5K Lower Cold Box

Shear Key Calculations

Document Approval: Date Approved

Originator: Scott Kaminski, Mechanical Engineer LCLS-II 02/01/17

Checker: Chase Dubbe, JLab Mechanical Design Engineer 02/01/17

Approver: Michael Bevins, JLab Cryogenics Plant Deputy Control Account Manager 02/01/17

Issued for Project Use

History

Revision Date Released Description of Change

- February 01, 2017 Original release, Issued for Project Use

Approved: 2/1/2017; E-Sign ID : 336974; signed by: DCG: T. Fuell; Re. 1: C. Dubbe; Re. 2: M. Bevins |




1.0 Introduction .................................................................................................................................. 3

2.0 Shear Key Design ......................................................................................................................... 4

3.0 Design Basis ................................................................................................................................. 7

4.0 Concrete Bearing ........................................................................................................................ 10

5.0 Shear Key ................................................................................................................................... 11

6.0 Pipe to Cover Plate Attachment Weld ........................................................................................ 13

7.0 Cover Plate to Baseplate Attachment Weld ............................................................................... 14

8.0 Summary / Conclusions .............................................................................................................. 16

9.0 References .................................................................................................................................. 16

Appendix A – LCB Reaction Shear Forces ....................................................................................... 17





1.0 Introduction

The purpose of this Engineering Note is to document the analysis that was performed to ensure the

shear key design for the LCLS-II Cryoplant 4.5K Lower Cold Box (LCB) is suitable for the

maximum design shear force. Figure 1 provides a graphical representation of the LCB.

A separate analysis by HDR verifies the LCB anchor bolt design is suitable for the maximum

design uplift and overturning moments. Separate analyses also verify that the LCB baseplates are

suitable for the anchor bolt / shear key reaction forces and the LCB itself is suitable for all normal

operating conditions as well as the occasional seismic loads.

This report discusses the shear key design (Section 2), the basis of the analysis that was performed

(Section 3), the calculations (Sections 4 through 7) and the summary / conclusion (Section 8).

Figure 1: LCLS-II 4.5K Lower Cold Box (LCB)





2.0 Shear Key Design

The shear key design for the LCB is reflected in Figures 2 through 6 (the first two sketches are

modified from the SLAC CRYO Lower Cold Box Final Calcs [1]). Namely, two 6” Sch 160 A106

Grade B pipes per 29” x 44” x 2.5” thick baseplate. The pipes are 10.5” long, such that they extend

6” into the concrete slab, centered on a 10” x 1/2” thick diameter cover plate that is used to attach

the shear key to the baseplate. The shear key pipes include two 1.5” diameter holes to facilitate the

flow of grout to the inside of the pipe. The 1.5” holes are oriented parallel to the long dimension of

the LCB baseplates (i.e. holes face plant east-west). The shear keys are attached to the cover plates

by a full penetration groove weld and a 3/8” fillet weld. The shear keys are attached to the LCB

baseplates by a 1/2” fillet weld between the shear key cover plate and the baseplate.

Figure 2: LCB Baseplate Arrangement (Top View)





Figure 3: LCB Baseplate Arrangement (Side View)

Figure 4: LCB Shear Key Design





Figure 5: Shear Key Hole Alignment

Figure 6: Shear Key in Concrete Section View





3.0 Design Basis

The applied seismic loads and load combinations are specified in the 2013 California Building

Code (CBC) [2] and its reference standard ASCE 7-10 [3].

Per the LCLS-II Cryogenic Building Geotechnical Report [4] and the Cryogenic Plant Seismic

Design Criteria [5], the site seismic design parameters include Site Class C, SD1 = 1.012 and SDS =

1.968.

The substances used in the LCLS-II Cryoplant and the LCB (namely inert cryogenics, gaseous /

liquid helium and gaseous / liquid nitrogen) are not hazardous (highly toxic or explosive /

flammable) in accordance with CBC Table 307.1 and the Cryogenic Plant Seismic Design Criteria.

Thus, per ASCE 7-10 Table 1.5-1 and the Cryogenic Plant Seismic Design Criteria, the Risk

Category for the Cryogenic Building and its associated components is II. Per ASCE 7-10 Table

1.5-2 and the Cryogenic Plant Seismic Design Criteria, the Seismic Importance Factor for the

Cryogenic Building and its associated components is Ie = 1.0. Per ASCE 7-10 11.6 and the site

seismic design parameters (S1 = 1.168), the Seismic Design Category for the Cryogenic Building

and its associated components is E.

As the LCB 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 in ASCE 7-10. The LCB is

considered an elevated vessel on unbraced legs in accordance with ASCE 7-10 Table 15.4-2. This

classification is more conservative that the other possible classification (Steel Ordinary Moment

Frame in accordance with Table 15.4-1). Since Option 2 in the Cryogenic Plant Seismic Design

Criteria applies to the LCB, the Response Modification Factor in ASCE 7-10 is reduced by a factor

two. Thus R = 2 / 2 = 1.0 for design of the LCB shear keys.

The seismic base shear applied to the LCB shear keys is determined in accordance with ASCE 7-10

12.8 and 15.4.1 as demonstrated below.

• 𝑉 =𝑆𝐷𝑆

𝑅

𝐼𝑒

𝑊 =1.968

1.0

1

𝑊 = 1.968 𝑊 (12.8-1, 2)

• 𝑉𝑚𝑎𝑥 =𝑆𝐷𝑆

𝑇𝑅

𝐼𝑒

𝑊 =1.968

0.13 1.0

1

𝑊 = 14.66 𝑊 (12.8-3)

• where 𝑇 = 𝑇𝑎~0.02 (152/12).75 = .13 (12.8.2, 12.8-7)

• 𝑉𝑚𝑖𝑛 = 0.044 𝑆𝐷𝑆𝐼𝑒 𝑊 = .044(1.968)(1)𝑊 = .087 𝑊 (15.4-1)

• 𝑉𝑚𝑖𝑛 = 0.8 𝑆1/(𝑅/𝐼𝑒) 𝑊 = 0.8 (1.168)

1.0

1

𝑊 = .935 𝑊 (15.4-2)

• So, 𝑉 = 1.968 𝑊





The structural height of the LCB, hn = 152” in 12.8-7 above, is in accordance with the FEA analysis

of the LCB itself [6]. This report also includes the reaction shear forces at the columns of the LCB

for the seismic, dead and live loads (see Appendix A). To accurately reflect the influence of the

attached platforms and cryoduct, the LCB design shear force is based on these reaction forces.

These seismic reaction forces are based on a seismic base shear of V = 1.968 W as calculated

above. These dead reaction forces include all operating fluid loads.

A free body diagram of the baseplate (see Figure 6) is used to determine the forces on the shear

keys from these column reaction forces. With the sum of the forces and moments about various

points set equal to zero, the maximum shear key forces are determined to be

• 𝐹𝑆𝑎𝑥 =1

2𝐹𝐶𝑥

• 𝐹𝑆𝑎𝑧 =1

2𝐹𝐶𝑧 +

𝑀𝑦

𝐿1+

(𝐹𝐶𝑥)𝐿2

𝐿1

Figure 6: Baseplate Free Body Diagram





First, the shear key seismic force is determined. Column reactions are considered for both 100% x /

30% z and 100% z / 30% x seismic accelerations. To ensure the shear keys are designed for the

most critical load effect, the maximum absolute value for any node is used to determine FCxe, FCze

and Mye. For the 100% x / 30% z seismic acceleration FCx is the sum for Node N130 under a 100 -

x and 30% -z acceleration (Figures 4.4.19, 4.4.18), FCz is the sum for Node N127 under a 100 -x

and 30% +z acceleration (Figures 4.4.19, 4.4.20) and My is the sum for Node N127 under a 100 -x

and 30% -z acceleration (Figures 4.4.29, 4.4.18). For the 100% z / 30% x seismic acceleration FCx

is the sum for Node N128 under a 100 -z and 30% -x acceleration (Figures 4.4.18, 4.4.19), FCz is

the sum for Node N127 under a 100 +z and 30% -x acceleration (Figures 4.4.20, 4.4.19) and My is

the sum for Node N128 under a 100 +z and 30% +x acceleration (Figures 4.4.20, 4.4.21). Thus, the

potential critical loads are

• 𝐹𝐶𝑥𝑒 = 32.57𝑘, 𝐹𝐶𝑧𝑒 = 16.00𝑘, 𝑀𝑦𝑒 = 17.33 𝑘𝑖𝑛 100% x / 30% z

• 𝐹𝐶𝑥𝑒 = 13.00𝑘, 𝐹𝐶𝑧𝑒 = 37.33𝑘, 𝑀𝑦𝑒 = 52.37 𝑘𝑖𝑛 100% z / 30% x

Calculating the resultant (as indicated in the equation below) for the two seismic accelerations, the

maximum seismic acceleration occurs with a 100% x / 30% z seismic acceleration and is

determined to be

• 𝑄𝐸 = √(1

2𝐹𝐶𝑥𝑒)

2+ (

1

2𝐹𝐶𝑧𝑒 +

𝑀𝑦𝑒

𝐿1+

(𝐹𝐶𝑥𝑒)𝐿2

𝐿1)

2

• 𝑄𝐸 = 28,400 𝑙𝑏𝑠 Seismic Load

Conservatively, the dead and live loads are calculated from the maximum individual components.

• 𝐹𝐶𝑥𝑑 = 0.117𝑘, 𝐹𝐶𝑧𝑑 = 2.674𝑘, 𝑀𝑦𝑑 = 1.307 𝑘𝑖𝑛 Dead Load

• 𝐹𝐶𝑥𝑙 = 0.533𝑘, 𝐹𝐶𝑧𝑙 = 1.635𝑘, 𝑀𝑦𝑙 = 0.508 𝑘𝑖𝑛 Live Load

Calculating the resultants,

• 𝐷 = 1,500 𝑙𝑏𝑠 Dead Load

• 𝐿 = 1,200 𝑙𝑏𝑠 Live Load

The shear key embedment is in accordance with ACI 318-2011 [7] and, because this standard does

not address shear keys, ACI 349-13 [8]. While the maximum shear that can be transmitted to the

shear keys is limited by the development of a ductile yield mechanism, the shear keys are designed

using option (c) in D.3.3.5.3 of ACI 318-11. This option is used because of the relationship

between the ductile yield mechanism (i.e. yielding of the anchor bolts) and the maximum shear.

This relationship is indirect and complicated due to vessel asymmetries, the flexibility of the

internal support frame and because the maximum shear and maximum anchor tension likely do not

occur at the same column.





The design load combinations are specified in ASCE 7-10 2.3.2. Considering the shear loads

applied to the shear keys and design per option (c) in D.3.3.5.3, the two potential determining load

combinations are, in accordance with ASCE 7-10 12.4.3.2,

5. (1.2 + 0.2 SDS) D + Ω0QE + L + 0.2S

7. (0.9 - 0.2 SDS) D + Ω0QE

The snow load, S, is zero for the LCB and Ω0 = 2 per ASCE 7-10 Table 15.4-2. Since QE is the

same for both combinations, load combination 5 is the design combination for the shear keys.

5. (1.2 + 0.2 SDS) D + Ω0QE + L + 0.2S

5. (1.2 + 0.2 (1.968)) 1,500 + (2)28,400 + 1,200 + 0.2 (0)

5. V = 60,400 lbs

Consequently, the LCB shear key design shear force is

V = 60,400 lbs

To ensure the shear keys are suitable for the LCB design shear force,

- The resistance from friction to the applied seismic force is conservatively assumed to be

negligible (as required by ACI 349-13 D.4.6.1).

Additional parameters used in analyzing the shear keys include

- The shear stiffness of each lug is the same

- The shear lug separation (28”) is sufficient for the shear lugs to be analyzed as single

lugs

- As the shear keys are located outside the anchor bolts, the resistance to the applied

seismic force due to confinement (see ACI 349-13 D.4.6.1 and D.11) is negligible

- The distance to the nearest edge (in excess of twenty five feet) is such that shear

concrete breakout is not a concern

- The grout compressive strength exceeds the concrete compressive strength

- The ASCE 7-10 load combinations are analogous to the ACI 349-13 9.2 load

combinations

- A shear key is suitable for the LCB design shear force if the bearing strength of the

concrete exceeds the applied bearing load, the reaction shear load does not yield the

shear key in shear, the resulting moment does not yield the shear key in bending and the

attachment welds are sufficient for the shear / moment applied at the connection

4.0 Concrete Bearing

First, it is determined if the bearing strength of the concrete exceeds the bearing load applied by the

shear keys.

Per ACI 349-13 RD11.1, the shear key “bearing area should be limited to the contact area below the

plane defined by the concrete surface.” Per ACI 349-13 D.4.6.2, the concrete design bearing





strength is 1.3 times the concrete compressive strength modified by the strength reduction factor

(1.3 φ fc’).

The concrete bearing strength is compared to the bearing load, where the Concrete Compressive

Strength is 4,000 PSI per Revision A0 of S-001 (ID-905-300-00) in HDR IFC Cryoplant Building

drawings [9].

• 𝜎𝐷𝐶 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝐶𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ

• 𝜎𝑆𝐶 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝐶𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝐴𝑆 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝐴𝑟𝑒𝑎

• 𝐷𝑆𝑂 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑂𝑢𝑡𝑒𝑟 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 6.625"

• 𝐻 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝐺𝑟𝑜𝑢𝑡 𝐻𝑜𝑙𝑒 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 1.5"

• 𝐿𝑆 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝐿𝑒𝑛𝑔𝑡ℎ = 8"

• 𝐺 = 𝐺𝑟𝑜𝑢𝑡 𝐻𝑒𝑖𝑔ℎ𝑡 = 2"

• 𝐴𝑆 = 𝐷𝑆𝑂(𝐿𝑆 − 𝐺) − 𝜋(

𝐻

2)

2

2= 6.625 (8 − 2) −

𝜋(1.5

2)

2

2

• 𝐴𝑆 = 38.86 𝑖𝑛2

• φ = 𝑆𝑡𝑟𝑒𝑔𝑛𝑡ℎ 𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 = 0.65 (D.4.4, RD.4.6.2)

• 𝑓𝑐′ = 𝐶𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 4,000 𝑝𝑠𝑖

• 𝜎𝐷𝐶 > 𝜎𝑆𝐶

• 1.3φ𝑓𝑐′ >

(𝑉)

𝐴𝑆

• 1.3 (0.65)4,000 >(60,400)

38.86

• 𝟑, 𝟑𝟖𝟎 𝒑𝒔𝒊 > 𝟏, 𝟓𝟓𝟓 𝒑𝒔𝒊

Thus, the design concrete bearing strength exceeds the bearing load applied by the shear keys.

5.0 Shear Key

Second, it is determined if the reaction load yields the shear keys in either shear or bending.

Combined shear and bending need not be considered as maximum shear and bending occur 90°

apart. This evaluation is in accordance with ACI 349-13 D.10 and the requirement that the design

strength of shear lugs shall be based on the specified yield strength instead of the specified tensile

strength.





The maximum shear stress in the pipe is compared to the design shear stress. The shear stress

varies around the circumference of the pipe in accordance with the sine of the angle from the

direction of force, (V sinθ)/(π Rm T) [10]. As such, the maximum stress occurs 90° from the

direction of force. As the hole in the shear key is not oriented at the point of maximum stress for

the design shear force, it is not included in the comparison.

• 𝜎𝐷𝑆 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝜎𝑆𝑆 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝑅𝑚 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑀𝑒𝑑𝑖𝑎𝑛 𝑅𝑎𝑑𝑖𝑢𝑠 = (𝐷𝑆𝑂 − 𝑇)/2


• 𝑇 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 0.719”

• 𝐹𝑌 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑀𝑖𝑛 𝑌𝑖𝑒𝑙𝑑 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 35,000 𝑝𝑠𝑖

• φ = 𝑆𝑡𝑟𝑒𝑔𝑛𝑡ℎ 𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 = 0.55 (D.4.4, RD.10)

• 𝜎𝐷𝑆 > 𝜎𝑆𝑆

• φ𝐹𝑌 >(𝑉) sin(90°)

𝜋𝑅𝑚𝑇

• (0.55)35,000 >(60,400)(1)

𝜋((6.625−0.719)/2)0.719

• 𝟏𝟗, 𝟐𝟓𝟎 𝒑𝒔𝒊 > 𝟒, 𝟓𝟐𝟖 𝒑𝒔𝒊

The maximum bending stress in the pipe is compared to the design bending stress. The maximum

stress occurs in line with the direction of force at the connection to the LCB baseplate. As the hole

in the shear key is away from the point of maximum stress (in orientation and, primarily, elevation),

it is not included in the comparison.

• 𝜎𝐷𝐵 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝜎𝑆𝐵 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝑆𝑆 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝑀𝑜𝑑𝑢𝑙𝑢𝑠


• 𝑇 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 0.719"

• 𝑆𝑆 =𝜋

32

(𝐷𝑆𝑂4−(𝐷𝑆𝑂−2𝑇)4)

𝐷𝑆𝑂= 17.81 𝑖𝑛3







• 𝑇𝐵 = 𝐵𝑎𝑠𝑒𝑝𝑙𝑎𝑡𝑒 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 2.5"



• 𝜎𝐷𝐵 > 𝜎𝑆𝐵

• φ𝐹𝑌 >(𝑉)(𝐺+𝑇𝐵+

𝐿𝑆−𝐺

2)

𝑆𝑆

• (0.9)35,000 >(60,400)(2+2.5+(8−2)/2)

12.22

• 𝟑𝟏, 𝟓𝟎𝟎 𝒑𝒔𝒊 > 𝟐𝟓, 𝟒𝟐𝟐 𝒑𝒔𝒊

Thus, the design shear key strength exceeds the reaction load applied on the shear keys.

6.0 Pipe to Cover Plate Attachment Weld

Third, it is determined if the reaction load yields the shear key pipe-cover plate weld in either shear

or bending. To simplify evaluation, the full penetration weld is assumed to resist bending and the

backing fillet weld is assumed to resist shear.

The weld stress is calculated by treating the weld as a line as detailed in Section 7.4 of the Design

of Welded Structures [11]. The pipe median diameter is used for the full penetration weld diameter.

As required by AWS D1.1 [12], the weld filler material shall match the base metal in accordance

with Table 3.1.

Per AWS D1.1 Table 2.6, the allowable weld stress for tension welds in tubular connection welds is

the same as the base metal (φFY = (0.9) 35,000 = 31,500 psi).

• 𝜎𝑊𝐷𝑇 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝑊𝑒𝑙𝑑 𝑇𝑒𝑛𝑠𝑖𝑜𝑛 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝜎𝑊𝐵 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑊𝑒𝑙𝑑 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝑆𝑊𝐵 = 𝐹𝑢𝑙𝑙 𝑃𝑒𝑛 𝑊𝑒𝑙𝑑 𝑎𝑠 𝑎 𝐿𝑖𝑛𝑒 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝑀𝑜𝑑𝑢𝑙𝑢𝑠


• 𝑇 = 𝑆ℎ𝑒𝑎𝑟 𝐾𝑒𝑦 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 0.719"

• 𝑆𝑊𝐵 =𝜋

4(𝐷𝑆𝑂 − 𝑇)2 = 27.39 𝑖𝑛2 [11], 7.4 Table 5










• 𝜎𝑊𝐷𝑇 > 𝜎𝑊𝐵

• φ𝐹𝑌 >(𝑉)(𝐺+𝑇𝐵+

𝐿𝑆−𝐺

2)

𝑆𝑊𝐵𝑇

• (0.9)35,000 >(60,400)(2+2.5+(8−2)/2)

27.39 (.719)

• 𝟑𝟏, 𝟓𝟎𝟎 𝒑𝒔𝒊 > 𝟐𝟐, 𝟗𝟗𝟗 𝒑𝒔𝒊

The centerline of the effective weld throat is used for the fillet weld diameter. Per AWS D1.1 Table

2.6, the allowable weld stress for fillet welds in tubular connection welds is 30% of the filler metal

tensile strength. Per Table 3.1, the filler metal is known to be at least E60XX (i.e. a tensile strength

of 60,000 psi).

• 𝜎𝑊𝐷𝑆 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝐹𝑖𝑙𝑙𝑒𝑡 𝑊𝑒𝑙𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 = 18,000 𝑝𝑠𝑖

• 𝜎𝑊𝑆 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑊𝑒𝑙𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠

• 𝐿𝑊𝐹 = 𝐹𝑖𝑙𝑙𝑒𝑡 𝑊𝑒𝑙𝑑 𝐿𝑒𝑛𝑔𝑡ℎ

• 𝑇𝑊𝐹 = 𝐹𝑖𝑙𝑙𝑒𝑡 𝑊𝑒𝑙𝑑 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑇ℎ𝑟𝑜𝑎𝑡 = .265"

• 𝐷𝑊𝐹 = 𝐹𝑖𝑙𝑙𝑒𝑡 𝑇ℎ𝑟𝑜𝑎𝑡 𝐶𝑒𝑛𝑡𝑒𝑟𝑙𝑖𝑛𝑒 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 6.8125"

• 𝐿𝑊𝐹 = 𝜋(𝐷𝑊𝐹) = 𝜋(6.8125) = 21.4 𝑖𝑛

• 𝜎𝑊𝐷𝑆 > 𝜎𝑊𝑆

• 18,000 >(𝑉)

𝐿𝑊𝐹𝑇𝑊𝐹

• 18,000 >(60,400)

21.4 (.265)

• 𝟏𝟖, 𝟎𝟎𝟎 𝒑𝒔𝒊 > 𝟏𝟎, 𝟔𝟓𝟏 𝒑𝒔𝒊

7.0 Cover Plate to Baseplate Attachment Weld





Fourth, it is determined if the reaction load yields the shear key cover plate to LCB baseplate fillet

weld.

The shear and bending weld stresses are calculated separately and combined using the square root

sum of the squares as the two stresses are 90° apart (equation 3 in Section 7.4) [11]. As indicated

previously, the filler metal is known to be at least E60XX.

• 𝜎𝑊𝐷𝑆 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝐹𝑖𝑙𝑙𝑒𝑡 𝑊𝑒𝑙𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 = 18,000 𝑝𝑠𝑖

• 𝜎𝑊𝐶𝐵 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐶𝑜𝑣𝑒𝑟 𝑃𝑙𝑎𝑡𝑒 𝑊𝑒𝑙𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 𝑓𝑟𝑜𝑚 𝐵𝑒𝑛𝑑𝑖𝑛𝑔

• 𝑇𝑊𝐶𝐹 = 𝐶𝑜𝑣𝑒𝑟 𝑃𝑙𝑎𝑡𝑒 𝐹𝑖𝑙𝑙𝑒𝑡 𝑊𝑒𝑙𝑑 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑇ℎ𝑟𝑜𝑎𝑡 = .35"

• 𝐷𝑊𝐶𝐹 = 𝐶𝑜𝑣𝑒𝑟 𝑃𝑙𝑎𝑡𝑒 𝐹𝑖𝑙𝑙𝑒𝑡 𝑇ℎ𝑟𝑜𝑎𝑡 𝐶𝑒𝑛𝑡𝑒𝑟𝑙𝑖𝑛𝑒 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 10.25"

• 𝑆𝑊𝐶𝐵 =𝜋

4(𝐷𝑊𝐶𝐹)2 = 82.51 𝑖𝑛2 [11], 7.4 Table 5




• 𝜎𝑊𝐶𝐵 =(𝑉)(𝐺+𝑇𝐵+

𝐿𝑆−𝐺

2)

𝑆𝑊𝐶𝐵𝑇𝑊𝐶𝐹

• 𝜎𝑊𝐶𝐵 =(60,400)(2+2.5+(8−2)/2)

82.51 (.35)

• 𝜎𝑊𝐶𝐵 = 15,947 𝑝𝑠𝑖

• 𝜎𝑊𝐶𝑆 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐶𝑜𝑣𝑒𝑟 𝑃𝑙𝑎𝑡𝑒 𝑊𝑒𝑙𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 𝑓𝑟𝑜𝑚 𝑆ℎ𝑒𝑎𝑟

• 𝐿𝑊𝐶𝐹 = 𝐶𝑜𝑣𝑒𝑟 𝑃𝑙𝑎𝑡𝑒 𝐹𝑖𝑙𝑙𝑒𝑡 𝑊𝑒𝑙𝑑 𝐿𝑒𝑛𝑔𝑡ℎ

• 𝐿𝑊𝐶𝐹 = 𝜋(𝐷𝑊𝐶𝐹) = 𝜋(10.25) = 32.2 𝑖𝑛

• 𝜎𝑊𝐶𝑆 =(𝑉)

𝐿𝑊𝐶𝐹𝑇𝑊𝐶𝐹

• 𝜎𝑊𝐶𝑆 =(60,400)

32.2 (.35)

• 𝜎𝑊𝐶𝑆 = 5,360 𝑝𝑠𝑖

• 𝜎𝑊𝐷𝑆 > √𝜎𝑊𝐶𝐵2 + 𝜎𝑊𝐶𝑆

2

• 𝟏𝟖, 𝟎𝟎𝟎 𝒑𝒔𝒊 > 𝟏𝟔, 𝟖𝟐𝟒 𝒑𝒔𝒊





8.0 Summary / Conclusions

The bearing strength of the concrete exceeds the applied bearing load. The reaction shear load does

not yield the shear key in shear and the resulting moment does not yield the shear key in bending.

The attachment welds are sufficient for the shear / moment applied at the connection. Thus, the

LCB shear key design is acceptable.

9.0 References

[1] SLAC CRYO Lower Cold Box Final Calcs, Rutherford+Chekene LC1-LC19 1/4/2017

[2] California Building Code, 2013

[3] Minimum Design Loads for Buildings and Other Structures. ASCE/SEI 7-10, 2010

[4] Final Report Geotechnical Investigation LCLS II Cryogenic Building and Infrastructure

SLAC National Accelerator Laboratory, Rutherford+Chekene #2014-106G

[5] Cryogenic Plant Seismic Design Criteria, LCLSII-4.8-EN-0227-R2

[6] Hopper Report – Component Seismic Design (PHP001-C1), Air Liquide C1303-NT-300 Rev0

[7] Building Code Requirements for Structural Concrete, ACI 318-11

[8] Code Requirements for Nuclear Safety-Related Concrete Structures, ACI 349-13

[9] LCLS-II Cryogenic Building and Infrastructure IFC Submittal, ID-905-000-00

[10] Mechanics of Materials, Beer, Johnston Jr and DeWolf – 3rd

Ed, p. 400, 781

[11] Design of Welded Structures, Blodgett, 1966

[12] Structural Welding Code—Steel, AWS D1.1/D1.1M 2015





Appendix A – LCB Reaction Shear Forces


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