Seismic Design of Precast Concrete Structures

Seismic Design of Precast Concrete Structures S. K. Ghosh S. K. Ghosh Associates Inc. Palatine, IL and Aliso Viejo, CA Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 1

2015 NEHRP Provisions Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 2

Two Diaphragm-Related Developments FEMA P-1050, the 2015 NEHRP Provisions includes two significant new items related to the seismic design of precast diaphragms. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 3

Two Aspects to Seismic Design Seismic design is an exercise in tradeoff between Strength and Inelastic deformability Inelastic deformability is directly related to design and detailing Inelastic Deformability Required Strength Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 4

New Items in the 2015 NEHRP Provisions Design Force Level Provision in Part 1 modifies ASCE 7-10 Section 12.10 Section 12.10.3 in ASCE 7-16 Design Force Level Provision in Part 3 modifies ASCE 7-10 Section 12.10 Precast Diaphragm Design Provision in Part 1 modifies ASCE 7-10 Section 14.2.4 Section 14.2.4 in ASCE 7-16 Resource Paper in Part 3 Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 5

Alternative ASCE 7-16 Force Level for Seismic Design of Diaphragms Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 6

Diaphragms, Chords, and Collectors 12.10.1.1 Diaphragm Design Forces. Floor and roof diaphragms shall be designed to resist design seismic forces from the structural analysis, but not less than the following forces: Where F px = the diaphragm design force F i = the design force applied to Level i w i = the weight tributary to Level i w px = the weight tributary to the diaphragm at Level x Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 7

Floor Level Diaphragm Design Forces 7 6 5 4 3 2 1 0 Fpx Fx 0 50 100 150 200 Force (kips) Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 8

Floor Accelerations for Diaphragm Design ASCE 7 Method F j w j F j F pj j j j j j SRSS F and n i j j, j i 1 Sa Ti f w gr PGA 0. 2 S I F / w 0. 4 S I but 0. 4S g PGA PGA 05. Ie F px / wpx Ie g g or 0. 5 I Acceleration "Magnification" 1. 0I DS e px px DS e DS e 2 Each mode s contribution is reduced by R e Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 9 p. 9 of Set 8

Floor magnification Floor Accelerations for Diaphragm Design ASCE 7 Method 0. 5 I Acceleration "Magnification" 1. 0I e e? 5 4 3 2 1 0 Northridge Northridge earthquake Earthquake and shaketable Datatest data ASCE 7 Range, I e =1 0 0.2 0.4 0.6 0.8 1 Peak ground acceleration (g) RC Frames n 5 RC Frames 5< n 10 RC Frames 10 < n 20 Walls 5 < n 10 Walls 10 < n 20 Steel Frames n 5 Steel Frames 5 < n 10 Steel Frames 10 < n 20 Steel Frames n > 20 Braced Frames n 5 Braced Frames 5 < n 10 Braced Frames 10 < n 20 Braced Frames n > 20 7-story building Repaired PCI building The upper and lower limits in ASCE7 do not seem to be rational The computation of floor acclerations based on the assumption that all modes are equally reduced by plasticity does not seem rational either Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 10 p. 10 of Set 8

Diaphragm Design In 2001 Rodriguez et al. noted that inelastic response in multi-story buildings tended to cause an important reduction in floor accelerations contributed by the first mode of response but had a much lesser effect on those contributed by the higher modes of response. They proposed the First Mode Reduced method, in which the roof acceleration could be determined by a square root sum of the squares combination in which the first mode contribution was reduced for inelasticity and the higher modes were left unreduced. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 11

Diaphragm Design F px = C px w px /R s 0.2S DS I e w px C px comes from C p0, C pi, and C pn Note: C pi is not used in the 2015 NEHRP Provisions Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 12

Diaphragm Design 2015 NEHRP Provisions Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 13

Diaphragm Design ASCE 7-16 Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 14

Diaphragm Design C p0 = 0.4 S DS I e Cpn= m1 0 C S 2 + m2 C S2 2 Cpi Note: The lower-bound limit on Cpn is in ASCE 7-16 only, not in the 2015 NEHRP Provisions. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 15

Diaphragm Design m1 = 1 + 0.5z S (1 1/N) m2 = 0.9z S (1 1/N) 2 where z S = modal contribution coefficient modifier dependent on seismic force-resisting system. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 16

Diaphragm Design Values of mode shape factor z s 0.3 for buildings designed with Buckling Restrained Braced Frame systems 0.7 for buildings designed with Moment-Resisting Frame systems 0.85 for buildings designed with Dual Systems with Special or Intermediate Moment Frames capable of resisting at least 25% of the prescribed seismic forces 1.0 for buildings designed with all other seismic forceresisting systems Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 17

Diaphragm Design 1.6 1.5 Γ m1 1.4 1.3 1.2 1.1 1.0 0 5 10 15 20 25 Number of levels, n e Number of levels, n Eq. 3.1 zs = 1 Eq. 3.1 zs = 0.7 Wall buildings Frame buildings Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 18

Diaphragm Design 1.0 Γ m2 0.8 0.6 0.4 0.2 0.0 Eq. 3.1 zs = 1 Eq. 3.1 zs = 0.7 Wall buildings Frame buildings 0 5 10 15 20 25 Number of levels, n e Number of levels, n Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 19

Diaphragm Design C pi is the greater of values given by: C pi = 0.8C p0 C pi = 0.9 m1 0 C S Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 20

Diaphragm Design C S = V/W or V t /W C S2 = minimum of: (0.15N + 0.25) I e S DS I e S DS I e S D1 /[0.03(N-1)] for N 2 or 0 for N = 1 Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 21

Consistent Look into the Design Spectra C s R For the Second mode, R = 1 C S (T 2 ) = min(0.15n+0.25, 1)I e S DS I e S D1 / [0.03(N-1)] N: number of levels above ground, N 2 Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 22

Diaphragm Capacity Why have we not been seeing inadequate performance of diaphragms in seismic events? Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 23

Inertial Forces in Diaphragms Existing diaphragms may carry seismic inertial forces through: (a) inherent overstrength in the floor system, including the floor plate and framing elements, that permit the transfer of higher than code design forces, Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 24

Inertial Forces in Diaphragms or (b) inherent ductility or plastic redistribution qualities within the diaphragm (or at the boundaries of the diaphragm) that limit the amount of inertial forces that can develop, without significant damage or failure. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 25

Diaphragm Force Reduction Factor, R s Elastic diaphragm design force level divided by a diaphragm force reduction factor, R s, to account for overstrength, ductility, or both. Reduction factors are different for flexurecontrolled and shear-controlled diaphragms. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 26

Diaphragm Design Flexure-controlled diaphragm: Diaphragm with a well-defined flexural yielding mechanism, which limits the force that develops in the diaphragm. The factored shear resistance shall be greater than the shear corresponding to flexural yielding. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 27

Diaphragm Design Shear-controlled diaphragm: Diaphragm that does not meet the requirements of a flexure-controlled diaphragm. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 28

Diaphragm Design (NEHRP Provisions) Diaphragm System Shear Control Flexure Control CIP Concrete 1.5 2 Precast concrete Untopped Steel Deck Topped Steel Deck EDO 1.0 0.7 BDO 1.0 1.0 RDO 1.0 1.3 Ductile 3.0 NA Low ductility 2.0 NA Reinforced topped Steel Deck with shear stud connection to framing Other topped Steel Deck with structural concrete fill 2.0 2.5 1.5 2.0 Wood Typical 3.0 NA When R s is greater than 1, such a diaphragm should have a well-defined, ductile shear yielding mechanism which limits the force that develops in the diaphragm. F = px C R px s w px Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 29

Diaphragm Design (ASCE 7-16) Diaphragm System Shear- Controlled Flexure- Controlled Cast-in-place concrete designed in accordance with Section 14.2 and ACI 318-1.5 2 EDO 1 0.7 0.7 Precast concrete designed in accordance with Section 14.2.4 and ACI 318 BDO 2 1.0 1.0 RDO 3 1.4 1.4 Wood sheathed designed in accordance with Section 14.5 and AF&PA (now AWC) Special Design Provisions for Wind and Seismic - 3.0 NA 1. EDO is precast concrete diaphragm Elastic Design Option. 2. BDO is precast concrete diaphragm Basic Design Option. 3. RDO is precast concrete diaphragm Reduced Design Option. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 30

Transfer Diaphragms ASCE 7-10 Section 12.10.1.1, 4th paragraph Where the diaphragm is required to transfer design seismic forces from the vertical resisting elements above the diaphragm to other vertical resisting elements below the diaphragm due to offsets in the placement of the elements or changes in relative lateral stiffness in the vertical elements, these forces shall be added to those determined from Eq. 12.10-1. The redundancy factor, ρ, applies to the design of diaphragms in structures assigned to Seismic Design Category D, E, or F. For inertial forces calculated in accordance with Eq. 12.10-1, the redundancy factor shall equal 1.0. For transfer forces, the redundancy factor, ρ, shall be the same as that used for the structure. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 31

Transfer Diaphragms Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 32

Transfer Diaphragms ASCE 7-16 Section 12.10.1.1, 4th paragraph All diaphragms shall be designed for the inertial forces determined from Eq. 12.10-1 through 12.10-3 and for all applicable transfer forces. For structures having a horizontal structural irregularity of Type 4 in Table 12.3-1, the transfer forces from the vertical seismic force-resisting elements above the diaphragm to other vertical seismic force-resisting elements below the diaphragm shall be increased by the overstrength factor of Section 12.4.3 prior to being added to the diaphragm inertial forces. For structures having other horizontal or vertical structural irregularities of the types indicated in Section 12.3.3.4, the requirements of that section shall apply. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 33

Transfer Diaphragms 12.10.3.3 Transfer Forces in Diaphragms All diaphragms shall be designed for the inertial forces determined from Eq. 12.10.3-1 and 12.10.3-2 and for all applicable transfer forces. For structures having a horizontal structural irregularity of Type 4 in Table 12.3-1, the transfer forces from the vertical seismic force-resisting elements above the diaphragm to other vertical seismic force-resisting elements below the diaphragm shall be increased by the overstrength factor of Section 12.4.3 prior to being added to the diaphragm inertial forces. For structures having other horizontal or vertical structural irregularities of the types indicated in Section 12.3.3.4, the requirements of that section shall apply. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 34

Transfer Diaphragms ASCE 7-16 Section 12.10.1.1, 4th paragraph ASCE 7-16 Section 12.10.3.3, Exception: One- and two-family dwellings of light frame construction shall be permitted to use Ω 0 = 1.0. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 35

Collectors 12.10.3.4 Collectors - Seismic Design Categories C through F In structures assigned to Seismic Design Category C, D, E, or F, collectors and their connections including connections to vertical elements shall be designed to resist 1.5 times the diaphragm inertial forces from Section 12.10.3.2 plus 1.5 times the design transfer forces. EXCEPTION: 1. Any transfer force increased by the overstrength factor of Section 12.4.3 need not be further amplified by 1.5. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 36

Diaphragm Design Force Level Comparisons Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 37

4-Story Perimeter Wall Precast Concrete Parking Structure (SDC C, Knoxville) 10'-6" 10'-6" 47'-6" 10'-6" 16' 204' Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 38

4-Story Perimeter Wall Precast Concrete Parking Structure (SDC C, Knoxville) Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 39

4-Story Interior Wall Precast Concrete Parking Structure (SDC D, Seattle) Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 40

4-Story Interior Wall Precast Concrete Parking Structure (SDC D, Seattle) Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 41

8-Story Precast Concrete Moment Frame Office Building Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 42

8-Story Precast Concrete Moment Frame Office Building Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 43

8-Story Precast Concrete Shear Wall Office Building Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 44

8-Story Precast Concrete Shear Wall Office Building Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 45

Precast Concrete Diaphragm Design Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 46

Diaphragm Design Options Elastic Design Option (EDO) Basic Design Option (BDO) Reduced Design Option (RDO) Diaphragm remains elastic in DBE and MCE Highest diaphragm design force Connections can include LDE, MDE and HDE Diaphragm remains elastic in DBE but Not Necessarily in MCE Lower diaphragm design force than EDO Connections can include MDE and HDE Some Diaphragm yielding in DBE, significant in MCE Lowest diaphragm design force Connections must be High Deformation Elements (HDE) No shear overstrength needed since elastic design Shear overstrength factor is needed Shear overstrength factor is needed Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 47

Tension FORCE Deformation Category LDE MDE HDE 7.5 mm (0.3 in.) 15 mm (0.6 in.) OPENING DISPLACEMENT LDE Low Deformability Element MDE Moderate Deformability Element HDE High Deformability Element SEAOH 2015 (C. Naito) 48

Number of Stories, n Diaphragm Seismic Design Level (DSDL) Step 1B: Determine Diaphragm Seismic Design Level (DSDL) Diaphragm Seismic Design Level: LOW B or C NO Seismic Design Category D, E or F Diaphragm Seismic Design Level: MODERATE YES YES IS DSDL LOW & AR>2.5? DSDL Moderate 8 7 6 5 4 3 2 1 DSDL: Low DSDL: High DSDL: Moderate Diaphragm Seismic Design Level: HIGH SEAOH 2015 (C. Naito) NO IS DSDL HIGH & AR<1.5? 0 0 50 100 150 200 Diaphragm Span, L [ft] 49

Seismic Design Option Step 2A: Determine Diaphragm Design Option Diaphragm Seismic Design Level: LOW Diaphragm Seismic Design Level: MODERATE Diaphragm Seismic Design Level: HIGH Design Option Diaphragm Seismic Demand level Low Moderate High Elastic Recommended With Penalty* Not Allowed Basic Alternative Recommended With Penalty* Reduced Alternative Alternative Recommended Penalty* = Diaphragm design force shall be increased by 15%. Choose Design Option: Elastic / Basic / Reduced SEAOH 2015 (C. Naito) 50

Precast Concrete Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 51

FEMA P-1051 Chapter 6 Overview Introduction Alternative ASCE 7-16 Force Level for Seismic Design of Diaphragms Step-by-Step Determination of Traditional Diaphragm Seismic Design Force Step-by-Step Determination of Alternative Diaphragm Seismic Design Force Diaphragm Design Force Level Comparisons Connector Qualification Protocol Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 52

Precast Concrete Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 53

Requirements for Precast Concrete Systems: Design Examples The examples in Section 11.1 illustrate the design of untopped and topped precast concrete floor and roof diaphragms of three five-story masonry buildings (SDC B, C, D) The example in Section 11.2 illustrates the design of an intermediate precast concrete shear wall building in a region of low or moderate seismicity. The precast concrete walls in this example resist the seismic forces for a three-story office building. The example in Section 11.3 illustrates the design of a special precast concrete shear wall for a single-story industrial warehouse building. The example in Section 11.4 is a partial example for the design of a special moment frame constructed using precast concrete per ACI 318 Section 18.9. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 54

FEMA P-1051 Chapter 11 Overview 11.1 HORIZONTAL DIAPHRAGMS 11.1.1 Untopped Precast Concrete Units for Five-Story Masonry Buildings Assigned to Seismic Design Categories B and C 11.1.2 Topped Precast Concrete Units for Five-Story Masonry Building Assigned to Seismic Design Category D Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 55

11.1.1 Untopped Precast Concrete Units for Five-Story Masonry Buldings Assigned to SDC B and C This example illustrates floor and roof diaphragm design for five-story masonry buildings in SDC B and in SDC C on soft rock. The example in Section 13.2 provides design parameters used. The floors and roofs of these buildings are made of untopped 8-inch-thick hollow-core precast, prestressed concrete plank. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 56

24'-0" 24'-0" 24'-0" 14'-0" 72'-0" 6'-8" 11.1 Horizontal Diaphragms A B C D E F 40'-0" 24'-0" 24'-0" 24'-0" 40'-0" 4'-0" 4 3 8" concrete masonry wall 2 6'-0" Prestressed hollow core slabs 1 152'-0" Hollow core plank floor plan for diaphragm examples Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 57

11.1 Horizontal Diaphragms Building Elevation Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 58

11.1.2 Topped Precast Concrete Units for Five-Story Masonry Building Assigned to SDC D This example illustrates floor and roof diaphragm design using topped precast units in the five-story masonry building when it is assigned to SDC D. The topping thickness exceeds the minimum of 2 in. The topping is lightweight (115 pcf) concrete with f' c of 4,000 psi and is to act compositely with the 8-in.-thick hollow-core precast, prestressed concrete plank. Design parameters are provided in Section 13.2. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 59

FEMA P-1051 Chapter 11 Overview 11.2 THREE-STORY OFFICE BUILDING WITH INTERMEDIATE PRECAST CONCRETE SHEAR WALLS 11.3 ONE-STORY PRECAST SHEAR WALL BUILDING Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 60

11.2 Three-story Office Building with Intermediate Concrete Shear Walls This example illustrates the seismic design of intermediate precast concrete shear walls. These walls can be used up to any height in SDCs B and C but are limited to 40 ft for SDCs D, E, and F. An increase in structural height to 45 ft is permitted for single story storage warehouse facilities. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 61

40'-0" 8'-0" 120'-0" 40'-0" 15'-0" 40'-0" 11.2 Three-Story Office Building with Intermediate Precast Concrete Shear Walls 150'-0" 25'-0" 25'-0" 25'-0" 25'-0" 25'-0" 25'-0" 26 IT 28 precast beams 8'-0" 18" DT roof and floor slabs (10 DT 18) 8" precast shear walls Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 62

11.3 One-Story Precast Shear Wall Building This example illustrates the design of a precast concrete shear wall for a single-story building assigned to a high seismic design category. The precast concrete building is a single-story industrial warehouse building (Risk Category II) on Site Class C soils. The precast wall panels used in this building are typical DT wall panels. Walls are designed using intermediate precast structural walls. Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 63

48'-0" 48'-0" 24LH03 at 4'-0" o.c. 12 DT at 8'-0" = 96'-0" 24LH03 at 4'-0" o.c. 11.3 One-Story Precast Shear Wall Building 15 DT at 8'-0" = 120'-0" Steel tube columns Joist girder (typical) 3 DT at 8'-0" = 24'-0" 16'-0" O.H. door 5 DT at 8'-0" = 40'-0" 16'-0" 3 DT at 8'-0" = O.H. door 24'-0" Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 64

FEMA P-1051 Chapter 11 Overview 11.4 SPECIAL MOMENT FRAMES CONSTRUCTED USING PRECAST CONCRETE Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 65

Precast Concrete Instructional Slides developed by S. K. Ghosh, PhD Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 66

Precast Concrete Instructional Slides developed by S. K. Ghosh, PhD, Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 67

Questions Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 68