4.5K Lower Cold Box. Shear Key Calculations

Transcription

1 Document Number: A0001 R- Page 1 of K Lower Cold Box Shear Key Calculations Document Approval: Originator: Scott Kaminski, Mechanical Engineer LCLS-II Checker: Chase Dubbe, JLab Mechanical Design Engineer Approver: Michael Bevins, JLab Cryogenics Plant Deputy Control Account Manager Date Approved 02/01/17 02/01/17 02/01/17 Issued for Project Use History Revision Date Released Description of Change - February 01, 2017 Original release, Issued for Project Use

2 Document Number: A0001 R- Page 2 of Introduction Shear Key Design Design Basis Concrete Bearing Shear Key Pipe to Cover Plate Attachment Weld Cover Plate to Baseplate Attachment Weld Summary / Conclusions References Appendix A LCB Reaction Shear Forces... 17

3 Document Number: A0001 R- Page 3 of 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)

4 Document Number: A0001 R- Page 4 of 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)

5 Document Number: A0001 R- Page 5 of 21 Figure 3: LCB Baseplate Arrangement (Side View) Figure 4: LCB Shear Key Design

6 Document Number: A0001 R- Page 6 of 21 Figure 5: Shear Key Hole Alignment Figure 6: Shear Key in Concrete Section View

7 Document Number: A0001 R- Page 7 of 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, S D1 = and S DS = 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 and the Cryogenic Plant Seismic Design Criteria. Thus, per ASCE 7-10 Table 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 and the Cryogenic Plant Seismic Design Criteria, the Seismic Importance Factor for the Cryogenic Building and its associated components is I e = 1.0. Per ASCE and the site seismic design parameters (S 1 = 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 The LCB is considered an elevated vessel on unbraced legs in accordance with ASCE 7-10 Table This classification is more conservative that the other possible classification (Steel Ordinary Moment Frame in accordance with Table ). 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 and as demonstrated below. V = S DS R Ie V max = S DS T R Ie W = W = W = W (12.8-1, 2) W = W (12.8-3) where T = T a ~0.02 (152/12).75 =.13 (12.8.2, ) V min = S DS I e W =.044(1.968)(1)W =.087 W (15.4-1) V min = 0.8 S 1 /(R/I e ) W = 0.8 (1.168) 1.0 W =.935 W (15.4-2) 1 So, V = W

8 Document Number: A0001 R- Page 8 of 21 The structural height of the LCB, h n = 152 in 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 = 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 FS ax = 1 2 FC x FS az = 1 2 FC z + M y L 1 + (FC x )L 2 L 1 Figure 6: Baseplate Free Body Diagram

9 Document Number: A0001 R- Page 9 of 21 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 FC xe, FC ze and M ye. For the 100% x / 30% z seismic acceleration FC x is the sum for Node N130 under a x and 30% -z acceleration (Figures , ), FC z is the sum for Node N127 under a 100 -x and 30% +z acceleration (Figures , ) and M y is the sum for Node N127 under a 100 -x and 30% -z acceleration (Figures , ). For the 100% z / 30% x seismic acceleration FC x is the sum for Node N128 under a 100 -z and 30% -x acceleration (Figures , ), FC z is the sum for Node N127 under a 100 +z and 30% -x acceleration (Figures , ) and M y is the sum for Node N128 under a 100 +z and 30% +x acceleration (Figures , ). Thus, the potential critical loads are FC xe = 32.57k, FC ze = 16.00k, M ye = kin 100% x / 30% z FC xe = 13.00k, FC ze = 37.33k, M ye = 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 Q E = ( 1 FC 2 xe) 2 + ( 1 FC 2 ze + M ye + (FC xe )L 2 ) 2 L 1 L 1 Q E = 28,400 lbs Seismic Load Conservatively, the dead and live loads are calculated from the maximum individual components. FC xd = 0.117k, FC zd = 2.674k, M yd = kin Dead Load FC xl = 0.533k, FC zl = 1.635k, M yl = 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 [7] and, because this standard does not address shear keys, ACI [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 of ACI 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.

10 Document Number: A0001 R- Page 10 of 21 The design load combinations are specified in ASCE Considering the shear loads applied to the shear keys and design per option (c) in D , the two potential determining load combinations are, in accordance with ASCE , 5. ( S DS ) D + Ω 0 Q E + L + 0.2S 7. ( S DS ) D + Ω 0 Q E The snow load, S, is zero for the LCB and Ω 0 = 2 per ASCE 7-10 Table Since Q E is the same for both combinations, load combination 5 is the design combination for the shear keys. 5. ( S DS ) D + Ω 0 Q E + L + 0.2S 5. ( (1.968)) 1,500 + (2)28, , (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 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 D 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 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 RD11.1, the shear key bearing area should be limited to the contact area below the plane defined by the concrete surface. Per ACI D.4.6.2, the concrete design bearing

11 Document Number: A0001 R- Page 11 of 21 strength is 1.3 times the concrete compressive strength modified by the strength reduction factor (1.3 φ f c ). 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 ) in HDR IFC Cryoplant Building drawings [9]. σ DC = Design Concrete Bearing Strength σ SC = Shear Key Concrete Bearing Stress A S = Shear Key Bearing Area D SO = Shear Key Outer Diameter = 6.625" H = Shear Key Grout Hole Diameter = 1.5" L S = Shear Key Length = 8" G = Grout Height = 2" A S = D SO (L S G) π(h 2 )2 A S = in 2 2 = (8 2) π(1.5 2 )2 φ = Stregnth Reduction Factor = 0.65 (D.4.4, RD.4.6.2) f c = Concrete Compressive Strength = 4,000 psi 2 σ DC > σ SC 1.3φf c > (V) A S 1.3 (0.65)4,000 > (60,400) , 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 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.

12 Document Number: A0001 R- Page 12 of 21 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 R m 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. σ DS = Design Shear Key Shear Stress σ SS = Maximum Shear Key Shear Stress R m = Shear Key Median Radius = (D SO T)/2 D SO = Shear Key Outer Diameter = 6.625" T = Shear Key Wall Thickness = F Y = Shear Key Min Yield Strength = 35,000 psi φ = Stregnth Reduction Factor = 0.55 (D.4.4, RD.10) σ DS > σ SS φf Y > (V) sin(90 ) πr m T (0.55)35,000 > 19, 250 psi > 4, 528 psi (60,400)(1) π(( )/2)0.719 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. σ DB = Design Shear Key Bending Stress σ SB = Maximum Shear Key Bending Stress S S = Shear Key Section Modulus D SO = Shear Key Outer Diameter = 6.625" T = Shear Key Wall Thickness = 0.719" S S = π 32 (D SO 4 (D SO 2T) 4 ) D SO = in 3

13 L S = Shear Key Length = 8" G = Grout Height = 2" Engineering Calculation Document Number: A0001 R- Page 13 of 21 T B = Baseplate Thickness = 2.5" F Y = Shear Key Min Yield Strength = 35,000 psi φ = Stregnth Reduction Factor = 0.90 (D.4.4, RD.10) σ DB > σ SB φf Y > (V)(G+T LS G B+ 2 ) S S (0.9)35,000 > (60,400)(2+2.5+(8 2)/2) , 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 (φf Y = (0.9) 35,000 = 31,500 psi). σ WDT = Design Weld Tension Stress σ WB = Maximum Weld Bending Stress S WB = Full Pen Weld as a Line Section Modulus D SO = Shear Key Outer Diameter = 6.625" T = Shear Key Wall Thickness = 0.719" S WB = π 4 (D SO T) 2 = in 2 [11], 7.4 Table 5

14 L S = Shear Key Length = 8" G = Grout Height = 2" Engineering Calculation Document Number: A0001 R- Page 14 of 21 T B = Baseplate Thickness = 2.5" F Y = Shear Key Min Yield Strength = 35,000 psi φ = Stregnth Reduction Factor = 0.90 (D.4.4, RD.10) σ WDT > σ WB φf Y > (V)(G+T LS G B+ 2 ) S WB T (0.9)35,000 > (60,400)(2+2.5+(8 2)/2) (.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). σ WDS = Design Fillet Weld Shear Stress = 18,000 psi σ WS = Maximum Weld Shear Stress L WF = Fillet Weld Length T WF = Fillet Weld Effective Throat =.265" D WF = Fillet Throat Centerline Diameter = " L WF = π(d WF ) = π(6.8125) = 21.4 in σ WDS > σ WS 18,000 > (V) L WF T WF 18,000 > (60,400) 21.4 (.265) 18, 000 psi > 10, 651 psi 7.0 Cover Plate to Baseplate Attachment Weld

15 Document Number: A0001 R- Page 15 of 21 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. σ WDS = Design Fillet Weld Shear Stress = 18,000 psi σ WCB = Maximum Cover Plate Weld Shear Stress from Bending T WCF = Cover Plate Fillet Weld Effective Throat =.35" D WCF = Cover Plate Fillet Throat Centerline Diameter = 10.25" S WCB = π 4 (D WCF) 2 = in 2 [11], 7.4 Table 5 L S = Shear Key Length = 8" G = Grout Height = 2" T B = Baseplate Thickness = 2.5" σ WCB = (V)(G+T LS G B+ 2 ) S WCB T WCF σ WCB = (60,400)(2+2.5+(8 2)/2) (.35) σ WCB = 15,947 psi σ WCS = Maximum Cover Plate Weld Shear Stress from Shear L WCF = Cover Plate Fillet Weld Length L WCF = π(d WCF ) = π(10.25) = 32.2 in σ WCS = (V) L WCF T WCF σ WCS = (60,400) 32.2 (.35) σ WCS = 5,360 psi 2 2 σ WDS > σ WCB + σ WCS 18, 000 psi > 16, 824 psi

16 8.0 Summary / Conclusions Engineering Calculation Document Number: A0001 R- Page 16 of 21 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 # G [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 [8] Code Requirements for Nuclear Safety-Related Concrete Structures, ACI [9] LCLS-II Cryogenic Building and Infrastructure IFC Submittal, ID [10] Mechanics of Materials, Beer, Johnston Jr and DeWolf 3 rd Ed, p. 400, 781 [11] Design of Welded Structures, Blodgett, 1966 [12] Structural Welding Code Steel, AWS D1.1/D1.1M 2015

17 Document Number: A0001 R- Page 17 of 21 Appendix A LCB Reaction Shear Forces

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