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PCI/NSF/CPF PART 2: 1 of 30 NEES/EERI Webinar April Outline Introduce PCI/NSF/CPF DSDM Research Effort Review Key Behaviors of Precast Diaphragms and Design Philosophy Adopted Summarize DSDM Research Project Findings Present Precast Diaphragm Design Procedure Cover Precast Diaphragm Design Example Discuss Codification Efforts

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PCI/NSF/CPF PART 2: 2 of 30 NEES/EERI Webinar April Precast Concrete Diaphragm Seismic Design Procedure

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PCI/NSF/CPF PART 2: 3 of 30 NEES/EERI Webinar April Design Procedure Applicability o Seismic design of precast concrete diaphragms with and without topping slabs Design Methodology Summary Objective o Provide adequate strength and deformability of connectors between precast diaphragm segments Method o Amplify code forces F p by a factor o Amplify shear forces by an overstrength factor o Select appropriate diaphragm reinforcing based on deformation capacity o Check gravity column drifts using factors C d,dia and C r,dia

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PCI/NSF/CPF PART 2: 4 of 30 NEES/EERI Webinar April Design Procedure Step 1: Determine the diaphragm seismic baseline design force as per ASCE 7-05 Design Steps Step 2: Determine diaphragm seismic demand level (Low, Moderate, and High). Step 3: Select diaphragm design option (Elastic, Basic and Reduced). Step 4: Determine the required diaphragm reinforcement classification (LDE, MDE and HDE). Step 9: Select specific diaphragm reinforcement type and determine properties. Step 10: Strength design of diaphragm reinforcement at joints between precast elements. Step 5: Determine the diaphragm force amplification factor ( ) Step 6: Determine the diaphragm shear overstrength factor ( ). Step 7: Determine the amplified diaphragm design force. Step 8: Determine the diaphragm internal forces (in-plane shear, axial and moment). Step 11: Determine the diaphragm stiffness: effective elastic (E eff ) and shear modulus (G eff ) Step 12: Check the diaphragm-induced gravity column drift

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PCI/NSF/CPF PART 2: 5 of 30 NEES/EERI Webinar April Design Procedure Step 1: Baseline design force Step 1: Determine the diaphragm seismic baseline design force as per ASCE 7-05 (1)Determine design spectral acceleration from hazard maps as per ASCE 7 Section 11.4 (2)Determine SDC from seismic use groups as per ASCE (3) Calculate the controlling seismic response coefficient C s as determined in accordance with ASCE Use structure fundamental period T as determined in accordance with ASCE (4) Calculate the vertical distribution factor C vc, at each floor level in accordance with ASCE (5) Calculate the lateral seismic design force F x at each floor level as per ASCE 7 Section (6)Calculate maximum diaphragm design acceleration, C dia, max C dia,max = max (F x / w x ) (Eqn.1)

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PCI/NSF/CPF PART 2: 6 of 30 NEES/EERI Webinar April Design Procedure Step 1: Baseline design force (con’t) Calculate Baseline Diaphragm Force at each level x, F Dx F Dx = x C dia,max w x (Eqn. 2) where w x = the portion of the total structure weight (w) located at Level x, x is the diaphragm force vertical distribution factor: Multistory buildings: x See Appendix 1 of PART 1. Parking garage : x =1.0 top floor, x =0.68 other floors Shear Wall x factor: Shear Walls # of stories xx Appendix 1: Diaphragm Force Vertical Distribution Shear Wall

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PCI/NSF/CPF PART 2: 7 of 30 NEES/EERI Webinar April Design Procedure Commentary Step 1: Baseline design force Comparison to Analytical Results: Maximum Diaphragm Force Profile (MCE) Taller Structures Low-rise and Parking Structures

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PCI/NSF/CPF PART 2: 8 of 30 NEES/EERI Webinar April If AR>2.5 and diaphragm seismic demand falls in Low, it shall be moved from Low to Moderate. Design Procedure Step 2: Demand Level Step 2: Determine diaphragm seismic demand level (1)Three diaphragm seismic demand levels are defined as: Low, Moderate, and High (2)Diaphragm demand level is based on seismic design category (SDC), number of stories and diaphragm span as follows: For SDC B and C: Low For SDC D and E: See Fig. 1 If AR<1.5 and diaphragm seismic demand falls in Low, it can be moved from High to Moderate

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PCI/NSF/CPF PART 2: 9 of 30 NEES/EERI Webinar April Design Procedure Commentary Step 2: Demand Level (con’t) BDO Max Joint Opening Demands in MCE Effect of Diaphragm Aspect Ratio LowModerateHigh

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PCI/NSF/CPF PART 2: 10 of 30 NEES/EERI Webinar April Design Procedure Step 2: Demand Level (con’t) (1)Diaphragm span on a floor level is defined as the larger value of: - maximum interior distance between two LFRS elements - twice the exterior distance between the outer LFRS element and the building free edge (2)Diaphragm aspect ratio (AR) is calculated using the floor diaphragm dimension perpendicular to (sub)diaphragm span associated with the pair of adjacent chord lines. Commentary Step 2

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PCI/NSF/CPF PART 2: 11 of 30 NEES/EERI Webinar April Comments: The Elastic Design Option (EDO): targets elastic diaphragm behavior in the MCE. uses a diaphragm force amplification factor E. allows the use of low deformability reinforcement (LDE). Design Procedure Step 3: Design Option Step 3: Select diaphragm design option Three diaphragm design options are defined as: Elastic, Basic and Reduced Comments: The Elastic Design Option (EDO): targets elastic diaphragm behavior in the MCE. uses a diaphragm force amplification factor E. allows the use of low deformability reinforcement (LDE). The Basic Design Option (BDO): targets elastic diaphragm design in the DBE. uses a diaphragm force amplification factor D. requires the use of moderate deformability reinforcement (MDE). Comments: The Elastic Design Option (EDO): targets elastic diaphragm behavior in the MCE. uses a diaphragm force amplification factor E. allows the use of low deformability reinforcement (LDE). The Basic Design Option (BDO): targets elastic diaphragm design in the DBE. uses a diaphragm force amplification factor D. requires the use of moderate deformability reinforcement (MDE). A Reduced (Force) Design Option (RDO): permits diaphragm yielding in the DBE uses a diaphragm force amplification factor R. requires the use of high deformability reinforcement (HDE). targets MCE deformation demands within allowable HDE deformation limits. Increased Deformation Capacity but Lower Design Force

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PCI/NSF/CPF PART 2: 12 of 30 NEES/EERI Webinar April Design Option Diaphragm Seismic Demand Level LowModerateHigh ElasticRecommendedWith Penalty*Not Allowed BasicAlternativeRecommendedWith Penalty* ReducedAlternative Recommended Design Procedure Table 1. Diaphragm design option Step 3: Design Option (con’t) Diaphragm design option is based on diaphragm seismic demand level *15% Design Force Increase

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PCI/NSF/CPF PART 2: 13 of 30 NEES/EERI Webinar April Design Procedure Commentary Step 3: Design Option Design Force Penalty determined through analytical results (MCE response): BDO Designs for High Diaphragm Seismic Demand

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PCI/NSF/CPF PART 2: 14 of 30 NEES/EERI Webinar April Design Procedure Step 4: Reinforcement Classification High deformability element (HDE): Moderate deformability element (MDE): Low deformability element (LDE): Step 4: Determine required Diaphragm Reinforcement Classification Three Classifications: Comments: Classification of diaphragm reinforcement determined through cyclic testing protocols in the Precast Diaphragm Reinforcement Qualification Procedure (See PART 2) In meeting the required maximum deformation capacity using the above testing protocols, the required cumulative inelastic deformation capacity is also met. An element demonstrating a reliable and stable maximum joint opening deformation capacity: of greater than 0.6 ” of between 0.3 ” and 0.6 ” not meeting others (< 0.3 ” )

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PCI/NSF/CPF PART 2: 15 of 30 NEES/EERI Webinar April Design Option Diaphragm Reinforcement Classification LowModerateHigh ElasticRecommendedAllowable BasicNot allowedRecommendedAllowable ReducedNot allowed Recommended Design Procedure The required diaphragm reinforcement classification is based on diaphragm design option, see Table 2 Step 4: Reinforcement Classification (con’t) Table 2. Required diaphragm reinforcement classification

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PCI/NSF/CPF PART 2: 16 of 30 NEES/EERI Webinar April Design Procedure Step 5: Force Amplification Factor Step 5: Determine diaphragm force amplification factor ( ) where n is the total number of stories in building, L is diaphragm span in ft as defined in Step 2 AR is diaphragm aspect ratio (0.25 ≤ AR ≤ 4.0). (L/60-AR) not to be taken larger than 2.0 nor less than -2.0.

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PCI/NSF/CPF PART 2: 17 of 30 NEES/EERI Webinar April Local E – Diaphragm force amplification factor used in the EDO. Calibrated to produce elastic diaphragm response in the MCE. Design Procedure Global LDE MDE HDE Commentary Step 5: Force Amplification E – Diaphragm force amplification factor used in the EDO. Calibrated to produce elastic diaphragm response in the MCE. E – Diaphragm force amplification factor used in the EDO. Calibrated to produce elastic diaphragm response in the MCE. D – Diaphragm force amplification factor used in the BDO. Calibrated to produce elastic diaphragm response in the DBE. D produces MCE deformation demand not exceeding MDE allowable, 0.2 ” E – Diaphragm force amplification factor used in the EDO. Calibrated to produce elastic diaphragm response in the MCE. D – Diaphragm force amplification factor used in the BDO. Calibrated to produce elastic diaphragm response in the DBE. D produces MCE deformation demand not exceeding MDE allowable, 0.2 ” R – Diaphragm force amplification factor used in the RDO. Calibrated to produce MCE deformation not exceeding HDE allowable, 0.4 ” HDE Test Req. MDE Test Req. Mean response from suite of spectrum compatible earthquakes SDC E n=6 SW L= 240’

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PCI/NSF/CPF PART 2: 18 of 30 NEES/EERI Webinar April Design Procedure Commentary Step 5: Force Amplification Comments: Design equation is greater than or equal to 90% of mean data. The data is the mean of the maximum response from 5 ground motions. The design equations (design procedure Eqns. 3-5) are curve fits of the analytical results (e.g. those shown on the pushover curves).

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PCI/NSF/CPF PART 2: 19 of 30 NEES/EERI Webinar April Design Procedure Step 6: Shear Overstrength Factor Step 6: Determine diaphragm shear overstrength factor ( v ): where AR is diaphragm aspect ratio: 0.25 ≤ AR ≤ 4.0 Commentary Step 6: The overstrength factors equations are similarly based on the statistical data from the analytical earthquake simulations.

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PCI/NSF/CPF PART 2: 20 of 30 NEES/EERI Webinar April Design Procedure Step 7: Diaphragm Design Force Berkeley (SDC E) It should be noted that other rationally-based expressions are being proposed for design force increase for all diaphragms in general. FMR Method (Restrepo and Rodriguez 2007) Amplify the baseline diaphragm force obtained from Eqn. 2 by the diaphragm force amplification factor obtained from Eqn. 3-5: Step 7: Determine diaphragm design force F Dia,x = F Dx (Eqn. 9) The precast diaphragm design procedure presented here can be aligned to work with these factors.

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PCI/NSF/CPF PART 2: 21 of 30 NEES/EERI Webinar April Design Procedure Step 8: Diaphragm Internal Forces The internal force demands (N u, V u, M u ) at all potential critical joints in the diaphragm must be determined based on application the amplified diaphragm design force. Step 8: Determine diaphragm internal forces 1. Semi-rigid diaphragm model: The internal forces at critical sections can be extracted from a structural analysis model of the building incorporating semi-rigid modeling of the floor and roof diaphragms. Comments: The diaphragm is to be evaluated for the effects of seismic loading in each orthogonal direction individually. The diaphragm effective elastic moduli, E eff and G eff, can be estimated as 25%~35% of the uncracked concrete E and G for the semi-rigid diaphragm model. These estimated values shall be verified in Step 12 after sizing the diaphragm reinforcement.

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PCI/NSF/CPF PART 2: 22 of 30 NEES/EERI Webinar April Diaphragm Design Example Parking flat under transverse loading Step 8: Diaphragm Internal Forces (con’t) 2. Analysis using free-body diagrams: Determine internal forces at all potential critical sections in the diaphragm by taking the applied amplified diaphragm forces and reactions on the diaphragm and evaluate appropriate free-bodies at each critical section using the principles of statics. N V M

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PCI/NSF/CPF PART 2: 23 of 30 NEES/EERI Webinar April Design Procedure Commentary Step 8: Internal Forces Rational Methods: As an alternative to the two options, rational methods such as the strut-and-tie method or the panel and stringer method can be used. Strut-and-Tie Panel and Stringer

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PCI/NSF/CPF PART 2: 24 of 30 NEES/EERI Webinar April Design Procedure Step 9: Diaphragm Reinforcement See Prequalified Precast Diaphragm Reinforcement in PART 2 to determine the classification and look up the properties of commonly-used existing diaphragm reinforcement. 2) Establish diaphragm reinforcement properties required for design including: (a) Elastic stiffness in tension and shear: k t, k v (b) Yield strength in tension and shear: t n, v n 1) Select diaphragm reinforcement type based on required Diaphragm Reinforcement Classification. Prequalified to a Classification Level Needed properties in tension and shear for design

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PCI/NSF/CPF PART 2: 25 of 30 NEES/EERI Webinar April Design Procedure Step 9: Diaphragm Reinforcement (con’t) Use the cyclic testing protocols and qualification backbones in the Precast Diaphragm Reinforcement Qualification Procedure to classify and determine properties of new diaphragm reinforcement. Comments: The Precast Diaphragm Reinforcement Qualification Procedure is found in PART 2.

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PCI/NSF/CPF PART 2: 26 of 30 NEES/EERI Webinar April Design Procedure Diaphragm reinforcement must possess sufficient strength (N n, V n, M n ) at joints between precast elements to resist the diaphragm internal forces. Step 10: Design the diaphragm reinforcement to resist the diaphragm internal forces. Step 10: Diaphragm Strength Design Comments: The interpretation of nominal flexural strength (M n ) depends on the design option selected. The following interaction formula is used for diaphragm reinforcement design: where f = 0.9 and v = 0.85

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PCI/NSF/CPF PART 2: 27 of 30 NEES/EERI Webinar April Design Procedure Commentary Step 10: Strength Design Comments: A rational method has been developed for the diaphragm strength calculation. This method is embedded in a design aid program in PART 3 of the Seismic Design Methodology Document for Precast Concrete Diaphragms.

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PCI/NSF/CPF PART 2: 28 of 30 NEES/EERI Webinar April Design Procedure Step 11: Diaphragm Stiffness Step 11: Determine the diaphragm effective elastic modulus (E eff ) and shear modulus (G eff ) Comments: The rational method used to estimate diaphragm strength also produces effective stiffness parameters E eff and G eff (See PART 3). The average value produced for the differently reinforced diaphragm joints can be used. If using a semi-rigid diaphragm structural analysis model, the calculated E eff and G eff shall be checked with respect to the values estimated in Step 8, and the analysis repeated if necessary.

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PCI/NSF/CPF PART 2: 29 of 30 NEES/EERI Webinar April Design Procedure Step 12: Drift Check Step 12: Check the diaphragm induced gravity column drift (1) Determine the diaphragm elastic deformation ( dia, el ) under design force (F Dia ): -Semi-rigid diaphragm model: Extract the maximum diaphragm deformation from the static analysis performed in Step 8 using the calculated E eff and G eff -Free-body Method: Obtain the maximum diaphragm deformation based on classical methods using the M, V diagrams obtained in Step 8 using the calculated E eff and G eff (2) Determine the diaphragm inelastic deformation by applying the deformation amplifier (C d,dia ) to elastic diaphragm deformation ( dia, el ): dia = C d,dia dia, el (Eqn. 11) where for EDO: C d,dia = 1.0 C C 1 = 0.05 for BDO: C d,dia = 1.5 C C 1 = 0.08 for RDO: C d,dia = 2.9 C C 1 = 0.10 and C is the diaphragm drift P- multiplier, where C 1 is a the design option factor shown above

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PCI/NSF/CPF PART 2: 30 of 30 NEES/EERI Webinar April Design Procedure Step 12: Drift Check (con’t) (3)Determine the diaphragm induced gravity column drift by introducing a diaphragm drift reduction factor (C r,dia ) to the diaphragm inelastic deformation ( dia ) dia = dia C r,dia h (Eqn. 12) where h is the floor-to-floor height and C r,dia is calculated from: (4)Check the diaphragm induced gravity column drift with design limit: - If dia ≤ OK - If dia > then check dia + LFRS where LFRS is the LFRS story drift determined per ASCE 7, : If dia + LFRS ≤ 0.04 OK For EDO: 0.4 ≤ C r,dia = 1.1 1– 0.13AR ≤ 1.0 (Eqn. 13) For BDO: 0.4 ≤ C r,dia = 1.08 – 0.11AR ≤ 1.0 (Eqn. 14) For RDO: 0.4 ≤ C r,dia = 1.00 – 0.11AR ≤ 1.0 (Eqn. 15) and AR is diaphragm aspect ratio as limited by Step 6. If dia + LFRS > 0.04, then redesign the diaphragm to increase diaphragm stiffness (via diaphragm reinforcement or span)

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