1. Seismic Design Methodology for Precast Concrete Floor Diaphragms
Research to Practice Webinar
April 23, 2012
Dr. Ned M. Cleland, P.E Dr. Robert B. Fleischman Dr. S.K. Ghosh, P.E.
Blue Ridge Design, Inc University of Arizona SKG Associates
Sponsored by the Earthquake Engineering Research Institute (EERI) and the Network for Earthquake Engineering Simulation (NEES)

2. 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
The common practice of precast concrete construction in Chile is different from that of the United States.
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
NEES/EERI Webinar
April 2

3. 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
The common practice of precast concrete construction in Chile is different from that of the United States.
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
NEES/EERI Webinar
April 3

4. Diaphragm Action
Diaphragm action is intended to carry seismic forces horizontally in the floor slab to walls and frames…
NEES/EERI Webinar
April

5. Precast Diaphragm Details
Precast floors can be vulnerable due to the need to transfer forces at discrete locations across floor joints between precast panels
NEES/EERI Webinar
April

6. Precast Diaphragm Past Performance
NEES/EERI Webinar
April

7. DSDM Project Project Co-funders: CPF, PCI and NSF
Objective: Develop an industry endorsed seismic design methodology for precast concrete diaphragms.
Scope: Untopped and topped composite precast floor diaphragms.
NEES/EERI Webinar
April

8. DSDM Consortium DSDM Task Group Producer Members
University of California
San Diego
Jose’ Restrepo, PI
Lehigh University
Clay Naito, PI
Richard Sause, Co-PI
Industry Advisory Panel
Industry Liaison
S. K. Ghosh, Co-PI
University of Arizona
Robert Fleischman
Consortium Leader
DSDM Task Group
NEES/EERI Webinar
April

9. Industry Task Group DSDM Task Group S.K.Ghosh DSDM Task Group Chair
President, S. K. Ghosh Associates
R. Becker
Vice President
Spancrete Industries, Inc.
N. Cleland
President
Blue Ridge Design, Inc.
Tom D’Arcy
President
Consulting Engineers Group
N. Hawkins
Professor Emeritus
Univ. of Illinois
Doug Sutton
Professor
Purdue University
Paul Johal
Research Director
PCI
Joe Maffei
Engineering Consultant
Rutherford & Chekene
Engineers
Susie Nakaki
President
The Nakaki
Bashaw Group, Inc.
Harry Gleich
Vice President
Metromont Prestress
Dave Dieter
Vice-President
MidState Precasters
Chuck Magnesio
Vice-President
JVI, Inc
Dichuan Zhang, Ge Wan, Michael Mielke, Alicia Mullenbach, Univ. of Arizona
Liling Cao, Rui Ren, Wesley Peter, Lehigh Univ.
Matt Schoettler and Andrea Belleri, UCSD
Graduate Researchers
NEES/EERI Webinar
April 9

10. 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
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
NEES/EERI Webinar
April 10

11. Diaphragm Forces
An aspect of diaphragm behavior not elucidated in the codes is the relationship of the design forces used in equivalent lateral force (ELF) procedures to the inertial forces that may actually develop in floors during a seismic event.
Fleischman and Farrow, Eq. Eng & Struc. Dyn, 2001
Diaphragm peak inertial forces may significantly exceed current design values
NEES/EERI Webinar
April

12. Current Design Code
The presence of large inertial forces can be critical in precast floor systems:
In combination with complex load paths in floor systems, can lead to inelastic diaphragm action.
Inelastic deformation demands in precast diaphragms will tend to concentrate in the joints between precast units, and only at certain joints.
These demands can exceed the deformation capacity of reinforcing details developed without this consideration, leading to a nonductile diaphragm failure.
High diaphragm flexibility due to the inherently less stiff jointed system, in long floor spans where precast is used effectively, could lead to excessive drift of gravity system columns
NEES/EERI Webinar
April

13. Amplified design force
Diaphragm Design Approach
YeFpx
Elastic Design Option (EDO)
Diaphragm force
Maximum Force Demand
(MCE)
Amplified design force
Possible Nonductile Response
Current design force
Fpx
Diaphragm lateral displacement
NEES/EERI Webinar
April

14. Basic Design Option (BDO)
DSDM Design Philosophy
Basic Design Option (BDO)
Diaphragm force
Elastic design option
Shear Failure
WvYDFpx
Chord Failure
MCE ductility demand
Capacity Design
YDFpx
DBE force demand
Amplified design force
Current design
Fpx
force
Diaphragm lateral displacement
NEES/EERI Webinar
April

15. Reduced Design Option (RDO)
DSDM Design Philosophy
Reduced Design Option (RDO)
Diaphragm force
Elastic design option
Within allowable deformation limits in MCE
Yields in DBE
YrFpx
Current design force
Fpx
Diaphragm lateral displacement
NEES/EERI Webinar
April

16. Fpx DSDM Design Philosophy EDO BDO RDO Current design force LDE MDE
Diaphragm force
EDO
BDO
LDE
RDO
MDE
HDE
Current design force
Fpx
Connector Classification
Diaphragm lateral displacement
NEES/EERI Webinar
April

17. 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
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
NEES/EERI Webinar
April 17

18.  DSDM Research Flow Structure Level (UCSD) Diaphragm seismic force
MDOF Dynamic Analysis
Structure Level (UCSD)
Diaphragm seismic force
Diaphragm flexibility limits
Scaled Shake Table Test 
3D FE Dynamic Analysis
Diaphragm Level (UA)
Capacity Design Factors.
Internal Force Paths
FE Pushover Analysis
Hybrid Testing of Joints
Detail Level (LU)
Characteristics of diaphragm details
Connection classification
Full-Scale Detail Tests
NEES/EERI Webinar
April 18

19. Precast Diaphragm Connector Testing
Connection Details
Evaluation
Previous Test
Results Evaluation
Experimental
Analytical
Classify connectors:
Low Defo (LDE)
Mod Defo (MDE)
High Defo (HDE)
Lehigh’s test setup is innovative in that it allows applying shear, axial and moment at the same time
NEES/EERI Webinar
April 19

20. Modeling of Chord Connector
a=0.7
NEES/EERI Webinar
April

21. Modeling of JVI Connector
Cyclic response
NEES/EERI Webinar
April

22. Modeling of Ductile Mesh
NEES/EERI Webinar
April

23. Nonlinear coupled springs and contact elements
Diaphragm Analytical Modelling
Nonlinear coupled springs and contact elements
Discrete FE models
NEES/EERI Webinar
April

24. Prototype Structure #1: Parking Garage
Model
NEES/EERI Webinar
April 24

25. PDH Test
NEES/EERI Webinar
April 25

26. PDH Test Results: Flexure
CH Service
CH DBE
CH MCE
CH Bi-dir DBE
BK MCE
Joint Flexural Response M q
Minor Cracking
Major Cracking/Crushing
Weld Fracture
NEES/EERI Webinar
April 26

27. Shaking Table Structure
NEES/EERI Webinar
April 27

28. Test Comparison: Knoxvilleδ
Knoxville DBE
Diaphragm midspan roof drift
NEES/EERI Webinar
April

29. Phase III: Design Methodology Development
NEES/EERI Webinar
April

30. Modeling of Evaluation Structure
Precast units:
Plane stress element
Chord connector:
Nonlinear springs
Shear connector:
Symmetry
boundary
Column: 3D beam element
Spandrel: 2D beam element
Connector Elements
Moment frame
3D beam element
Shear wall
3D shell element
NEES/EERI Webinar
April

31. Suite of Ground Motions
SDC E
SDC C
NEES/EERI Webinar
April

32. Diaphragm Force Amplification Factor Y
Trial Design Factors
Diaphragm Force Amplification Factor Y T
T, δ
Chord connector δ
SDC E AR=3
NEES/EERI Webinar
April

33. Design Methodology Verification: Prototype Structures
4-Story Parking Structure
NEES/EERI Webinar
April

34. Design Methodology Verification: Prototype Structures
8-Story Office Building
NEES/EERI Webinar
April

35. 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
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
NEES/EERI Webinar
April 35

36. Precast Concrete Diaphragm Seismic Design Procedure
NEES/EERI Webinar
April

37. Design Procedure Design Methodology Summary Applicability
Seismic design of precast concrete diaphragms with and without topping slabs
Objective
Provide adequate strength and deformability of connectors between precast diaphragm segments
Method
Amplify code forces Fp by a factor Y
Amplify shear forces by an overstrength factor W
Select appropriate diaphragm reinforcing based on deformation capacity
Check gravity column drifts using factors Cd,dia and Cr,dia
NEES/EERI Webinar
April

38. Design Procedure Design Steps
Step 1: Determine the diaphragm seismic baseline design force as per ASCE 7-05
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 5: Determine the diaphragm force amplification factor (Y )
Step 6: Determine the diaphragm shear overstrength factor (W ).
Step 7: Determine the amplified diaphragm design force.
Step 8: Determine the diaphragm internal forces (in-plane shear, axial and moment).
Step 9: Select specific diaphragm reinforcement type and determine properties.
Step 10: Strength design of diaphragm reinforcement at joints between precast elements.
Step 11: Determine the diaphragm stiffness: effective elastic (Eeff ) and shear modulus (Geff)
Step 12: Check the diaphragm-induced gravity column drift
NEES/EERI Webinar
April

39. 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 Cs as determined in accordance with ASCE Use structure fundamental period T as determined in accordance with ASCE
(4) Calculate the vertical distribution factor Cvc, at each floor level in accordance with ASCE
(5) Calculate the lateral seismic design force Fx at each floor level as per ASCE 7 Section
Calculate maximum diaphragm design acceleration, Cdia, max
Cdia,max= max (Fx / wx) (Eqn.1)
NEES/EERI Webinar
April

40. Design Procedure Step 1: Baseline design force (con’t) Shear Wall
Calculate Baseline Diaphragm Force at each level x, FDx
FDx = ax Cdia,max wx (Eqn. 2)
where wx = the portion of the total structure weight (w) located at Level x,
ax is the diaphragm force vertical distribution factor:
Multistory buildings: ax See Appendix 1 of PART 1.
Parking garage : ax =1.0 top floor, ax =0.68 other floors
Shear Wall 1 2 3 4 5 6 7 8 9 10
0.2
0.4
0.6
0.8
1.2
ax factor: Shear Walls
# of stories ax
Appendix 1: Diaphragm Force Vertical Distribution
Shear Wall
NEES/EERI Webinar
April

41. Low-rise and Parking Structures
Design Procedure
Commentary Step 1: Baseline design force
Comparison to Analytical Results: Maximum Diaphragm Force Profile (MCE)
Taller Structures
Low-rise and Parking Structures
NEES/EERI Webinar
April

42. 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>2.5 and diaphragm seismic demand falls in Low, it shall be moved from Low to Moderate.
If AR<1.5 and diaphragm seismic demand falls in Low, it can be moved from High to Moderate
NEES/EERI Webinar
April

43. Effect of Diaphragm Aspect Ratio
Design Procedure
Commentary Step 2: Demand Level (con’t)
BDO Max Joint Opening Demands in MCE
Effect of Diaphragm Aspect Ratio
Low
Moderate
High
NEES/EERI Webinar
April

44. Design Procedure Step 2: Demand Level (con’t) Commentary Step 2
(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
NEES/EERI Webinar
April

45. 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 YE.
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 YD.
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 YR.
requires the use of high deformability reinforcement (HDE).
targets MCE deformation demands within allowable HDE deformation limits.
Comments:
The Elastic Design Option (EDO):
targets elastic diaphragm behavior in the MCE.
uses a diaphragm force amplification factor YE.
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 YD.
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 YE.
allows the use of low deformability reinforcement (LDE).
Increased Deformation Capacity but Lower Design Force
NEES/EERI Webinar
April

46. Diaphragm Seismic Demand Level
Design Procedure
Step 3: Design Option (con’t)
Diaphragm design option is based on diaphragm seismic demand level
Table 1. Diaphragm design option
Design Option
Diaphragm Seismic Demand Level
Low
Moderate
High
Elastic
Recommended
With Penalty*
Not Allowed
Basic
Alternative
Reduced
*15% Design Force Increase
NEES/EERI Webinar
April

47. Design Procedure Commentary Step 3: Design Option
Design Force Penalty determined through analytical results (MCE response):
BDO Designs for High Diaphragm Seismic Demand
NEES/EERI Webinar
April

48. Design Procedure Step 4: Reinforcement Classification
Step 4: Determine required Diaphragm Reinforcement Classification
Three Classifications:
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”)
High deformability element (HDE):
Moderate deformability element (MDE):
Low deformability element (LDE):
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.
NEES/EERI Webinar
April

49. Diaphragm Reinforcement Classification
Design Procedure
Step 4: Reinforcement Classification (con’t)
The required diaphragm reinforcement classification is based on diaphragm design option, see Table 2
Table 2. Required diaphragm reinforcement classification
Design Option
Diaphragm Reinforcement Classification
Low
Moderate
High
Elastic
Recommended
Allowable
Basic
Not allowed
Reduced
NEES/EERI Webinar
April

50. Design Procedure Step 5: Force Amplification Factor
Step 5: Determine diaphragm force amplification factor (Y )
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.
NEES/EERI Webinar
April

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

52. Design Procedure Commentary Step 5: Force Amplification
The Y design equations (design procedure Eqns. 3-5) are curve fits of the analytical results (e.g. those shown on the pushover curves).
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.
NEES/EERI Webinar
April

53. Design Procedure Step 6: Shear Overstrength Factor
Step 6: Determine diaphragm shear overstrength factor (Wv):
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.
NEES/EERI Webinar
April

54. Design Procedure FDia,x= Y FDx (Eqn. 9) Step 7: Diaphragm Design Force
Step 7: Determine diaphragm design force
Amplify the baseline diaphragm force obtained from Eqn. 2 by the diaphragm force amplification factor obtained from Eqn. 3-5:
FDia,x= Y FDx (Eqn. 9)
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)
The precast diaphragm design procedure presented here can be aligned to work with these factors.
NEES/EERI Webinar
April

55. Design Procedure Step 8: Diaphragm Internal Forces
Step 8: Determine diaphragm internal forces
The internal force demands (Nu, Vu, Mu) at all potential critical joints in the diaphragm must be determined based on application the amplified diaphragm design force.
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, Eeff and Geff , 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.
NEES/EERI Webinar
April

56. Diaphragm Design Example
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.
Parking flat under transverse loading N V M
NEES/EERI Webinar
April

57. 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
NEES/EERI Webinar
April

58. Design Procedure Step 9: Diaphragm Reinforcement
Select diaphragm reinforcement type based on required Diaphragm Reinforcement Classification.
Establish diaphragm reinforcement properties required for design including:
(a) Elastic stiffness in tension and shear: kt, kv
(b) Yield strength in tension and shear: tn , vn
See Prequalified Precast Diaphragm Reinforcement in PART 2 to determine the classification and look up the properties of commonly-used existing diaphragm reinforcement.
Prequalified to a Classification Level
Needed properties in tension and shear for design
NEES/EERI Webinar
April

59. 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.
NEES/EERI Webinar
April

60. Design Procedure Step 10: Diaphragm Strength Design
Step 10: Design the diaphragm reinforcement to resist the diaphragm internal forces.
Diaphragm reinforcement must possess sufficient strength (Nn, Vn, Mn) at joints between precast elements to resist the diaphragm internal forces.
The following interaction formula is used for diaphragm reinforcement design:
where ff = 0.9 and fv = 0.85
Comments:
The interpretation of nominal flexural strength (Mn) depends on the design option selected.
NEES/EERI Webinar
April

61. 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.
NEES/EERI Webinar
April

62. Design Procedure Step 11: Diaphragm Stiffness
Step 11: Determine the diaphragm effective elastic modulus (Eeff ) and shear modulus (Geff)
Comments:
The rational method used to estimate diaphragm strength also produces effective stiffness parameters Eeff and Geff (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 Eeff and Geff shall be checked with respect to the values estimated in Step 8, and the analysis repeated if necessary.
NEES/EERI Webinar
April

63. Design Procedure Step 12: Drift Check
Step 12: Check the diaphragm induced gravity column drift
(1) Determine the diaphragm elastic deformation (d dia, el) under design force (FDia):
Semi-rigid diaphragm model: Extract the maximum diaphragm deformation from the static analysis performed in Step 8 using the calculated Eeff and Geff
Free-body Method: Obtain the maximum diaphragm deformation based on classical methods using the M, V diagrams obtained in Step 8 using the calculated Eeff and Geff
(2) Determine the diaphragm inelastic deformation by applying the deformation amplifier (Cd,dia) to elastic diaphragm deformation (d dia, el):
d dia = Cd,dia d dia, el (Eqn. 11)
where for EDO: Cd,dia = 1.0 CD C1 = 0.05
for BDO: Cd,dia = 1.5 CD C1 = 0.08
for RDO: Cd,dia = 2.9 CD C1 = 0.10
and CD is the diaphragm drift P-D multiplier,
where C1 is a the design option factor shown above
NEES/EERI Webinar
April

64. Design Procedure Step 12: Drift Check (con’t)
(3) Determine the diaphragm induced gravity column drift by introducing a diaphragm drift reduction factor (Cr,dia) to the diaphragm inelastic deformation (d dia)
q dia = d diaCr,dia /h (Eqn. 12)
where h is the floor-to-floor height and Cr,dia is calculated from:
For EDO: ≤ Cr,dia = 1.1 1– 0.13AR ≤ (Eqn. 13)
For BDO: ≤ Cr,dia = 1.08 – 0.11AR ≤ (Eqn. 14)
For RDO: ≤ Cr,dia = 1.00 – 0.11AR ≤ (Eqn. 15)
and AR is diaphragm aspect ratio as limited by Step 6.
(4) Check the diaphragm induced gravity column drift with design limit:
- If q dia ≤ 0.01 OK
- If q dia > 0.01 then check q dia + q LFRS
where q LFRS is the LFRS story drift determined per ASCE 7, :
If q dia + q LFRS ≤ 0.04 OK
If q dia + q LFRS > 0.04, then redesign the diaphragm to increase diaphragm stiffness (via diaphragm reinforcement or span)
NEES/EERI Webinar
April

65. 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
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
NEES/EERI Webinar
April 65

66. Design Methodology Documents
NEES/EERI Webinar
April

67. Design Methodology PART 4
The procedure will be demonstrated for the Elastic Design Option, but will be compared to the design forces and details of the other options
NEES/EERI Webinar
April

68. Diaphragm Design Example
Example 1: 4-story Parking Garage - Knoxville (SDC C)
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April

69. Diaphragm Design Example
Step 1: Baseline design force
Step 1: Determine the diaphragm seismic baseline design forces as per ASCE 7-05
Seismic design parameters
Design site: Knoxville, TN
SDC C Ss S
Soil site class C Fa Fv
Sms= Fa Ss
Sm1= Fv S
SDS= 2/3 Sms
SD1= 2/3 Sm
N-S: Intermediate Precast Shear Walls R=5, W0=2.5, Cd=4.5
E-W: Intermediate precast bearing wall R=4, W0=2.5, Cd=4
NEES/EERI Webinar
April

70. Diaphragm Design Example
Step 1: Baseline design force (con’t)
Diaphragm maximum design acceleration: Cdia, max=max (Fx/wx) [Eqn.1]
Diaphragm baseline design force FDx = ax Cdia, max wx [Eqn.2]
See Tables next page
NEES/EERI Webinar
April

71. Diaphragm Design Example
Step 1: Baseline design force (con’t)
Baseline (unamplified) forces
N-S direction
hx (ft) Wx (k) Wx hxk Cvx Fx (k) Cdia, max (1) ax FDx (k) (2)
Roof *
4th
3rd
2nd
Sum
Parking structure: ax =1.0 at top floor and ax =0.68 at lower floors.
E-W direction
hx (ft) Wx (k) Wx hxk Cvx Fx (k) Cdia, max (1) ax FDx (k) (2)
Roof *
4th
3rd
2nd
Sum
NEES/EERI Webinar
April
* The top floor has less seismic mass due to ramp.

72. Diaphragm Design Example
Steps 2-4: Design Option and Classifications
Step 2: Determine the Diaphragm Seismic Demand Level
For SDC C: Low
Step 3: Select Diaphragm Design Option
For low seismic demand: Elastic design option (EDO)
Step 4: Determine Required Diaphragm Reinforcement Classification
For elastic design option: Low deformability element (LDE)
Note: The Basic design option (BDO) and the Reduced design option (RDO) are also available to the designer, requiring improved details (MDE and HDE), but permitting lower design forces.
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73. Diaphragm Design Example
Step 5: Force Amplification Factor
Step 5: Determine Diaphragm Force Amplification Factor
The entire diaphragm is treated as three individual sub-diaphragms for the diaphragm design (North, South and Ramp):
L = 300 ft
AR = 300/60 = 5
Limit: 0.25 ≤ AR ≤ Use AR = 4 in Eqns. 3-8
n = 4
L/60-AR = 1
YE=1.7  [1 – 0.04(3-4)2]  1.05(300/60-4) =2.9
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74. Diaphragm Design Example
Step 6: Force Overstrength Factor
Step 6: Determine Diaphragm Shear Overstrength Factor
For elastic design (EDO), no further overstrength required.
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75. Diaphragm Design Example
Design Force Comparison
Diaphragm Design Forces Required for Different Available Options in Design Procedure
Design example 1A: (EDO)
Eqn. 3: YE = 1.740.38[1-0.04(3-4)2]1.05(300/60-4) = 2.9
Eqn. 6: WE = 1.0
Design example 1B: (BDO)
Eqn. 4: YD = 1.6540.21[1-0.03(3-4)2]1.05(300/60-4) = 2.25
Eqn. 7: WB = 1.42 AR-0.13 = 1.42  = 1.19
Design example 1C: (RDO)
Eqn. 5: YR = 1.0540.3 [1-0.03(2.5-4)2]1.05(300/60-4) = 1.56
Eqn. 8: WR = 1.92 AR-0.18 = 1.92  = 1.5
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76. Diaphragm Design Example
Step 7: Diaphragm Design Force
Step 7: Determine Diaphragm Design Force
Continuing with EDO Design: Insert baseline diaphragm forces (Step 1) and diaphragm amplification factor (Step 5) into Equation 9
N-S direction:
Top Floor: Fdia = YEFDx = 2.9482 =1398 kips > 0.2SDSIwx= 498 kips
Other Floors Fdia = YEFDx = 2.9370 = 1073 kips > 0.2SDSIwx= 562 kips
E-W direction:
Top Floor Fdia = YEFDx = 2.9602 = 1747 kips > 0.2SDSIwx= 498 kips
Other Floors Fdia = YEFDx = 2.9462 = 1342 kips > 0.2SDSIwx= 562 kips
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77. Diaphragm Design Example
Step 8: Diaphragm Internal Force
Step 8: Determine Diaphragm Internal Forces
The structure has a commonly-used configuration.
Select free-body diagram method.
Step 8 makes use of PART 3: Analysis Techniques and Design Aids for Diaphragm Design
Part 3 is used here for:
existing free body diagrams created for common precast diaphragm layouts
a design spreadsheet program embedded with associated free body calculations
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78. Diaphragm Design Analysis Techniques
Step 8: Internal Force (con’t) x w
Vsw
Nbeam
Vbeam
Nlw
Distributed Load:
Top floor: w = YEFDx (3L − L’/2)
Other floors: w = YEFDx /3L
Top part animate expression. Three equation
Diaphragm Joint along Ramp, Lbeam< x ≤ Lbeam/2:
Nu = Vbeam
Vu = Vsw− wx − Nbeam + Nlw( x − Lbeam)
Mu = xVsw− wx2/2 − Nbeam( x − 2Lbeam/3) + Nlw( x − Lbeam)2/2
Diaphragm Joint at End Flat, 0≤ x ≤ Lbeam:
Nu = xVbeam/Lbeam
Vu = Vsw− wx − xNbeam/Lbeam
Mu = xVsw− wx2/2 − x2Nbeam/3Lbeam
Reactions at Boundary:
Nlw = w
Nbea = 0.5(wL − Nlw L’ )/2
VSW = 0.5(wL − Nlw L’ )/2
Vbeam= VQ Lbeam / I
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79. Diaphragm Design Analysis Techniques
Step 8: Internal Force (con’t)
DIAPHRAGM DESIGN: SPREADSHEET PROGRAM
Enter Site Information
Enter Bldg Geometry
Enter LFRS Factors
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80. Diaphragm Design Spreadsheet Program
Step 8: Internal Force (con’t)
Calculates FBD Forces
Generates diaphragm joint locations (Col D) based on span and panel width and calcs all internal forces Nu , Vu , Mu
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81. Diaphragm Design Example
Step 8: Internal Force (con’t)
The maximum internal forces Nu , Vu , Mu represent the required strength at each diaphragm joint. These values calculated considering the effect of two orthogonal directions (transverse and longitudinal) independently.
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82. Diaphragm Design Example
Step 9: Diaphragm Reinforcement
Step 9: Select Diaphragm Reinforcement
Diaphragm reinforcement types selected must meet the Required Diaphragm Reinforcement Classification from Step 4.
Prequalified connectors will be used in this example. Select appropriate diaphragm reinforcement types from PART 2: Table 2A-1.
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April

83. Diaphragm Design Example
Reinforcement Detail Comparison
Chord Details Meeting Requirements for Different Design Options
Design example 1A: (EDO)
Dry chord connector ( LDE )
Increasing Deformation Capacity
Design example 1B: (BDO)
Flat plate connector ( MDE )
Design example 1C: (RDO)
Continuous Bars in Pour strip ( HDE )
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84. Diaphragm Design Analysis Techniques
Reinforcement Detail Comparison
Web Details Meeting Requirements for Different Design Options
Wire Mesh
JVI Vector
Topped Hairpin w/ Ductile Mesh
LDE
HDE
HDE
Top part animate expression. Three equation
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85. Diaphragm Design Analysis Techniques
Reinforcement Detail Comparison
LFRS-to-Diaphragm Connections
Straight Bar Connector
Angled Plate Bar Connector
MDE
MDE
Top part animate expression. Three equation
Threaded Inserts, Dowel Bars in pour strip
HDE
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86. Diaphragm Design Example
Step 9: Diaphragm Reinforcement (con’t)
Determine Diaphragm Reinforcement Properties:
The diaphragm reinforcement selected is prequalified. Thus, diaphragm reinforcement properties can be looked up in PART 2: Table 2A-1.
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87. Diaphragm Design Example
Step 10: Diaphragm Strength Design
Step 10: Design the Diaphragm Reinforcement at Joints
Use the interaction equation (Eqn. 10) to determine the required diaphragm reinforcement at each joint:
The diaphragm joint required strength values (Mu, Nu and Vu) are from Step 8.
The diaphragm joint nominal design strength values (Mn, Nn and Vn) are based on vn and tn from Step 9.
Nn = S tn
Vn = S vn
Mn = S tn yi
Selection of a trial design is greatly facilitated through the use of spreadsheet methods.
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88. Diaphragm Design Example
Step 10: Strength Design (con’t)
OUPUT FROM SPREADSHEET DESIGN PROGRAM
Enter trial chord and shear reinforcement at each joint
Automatically imports diaphragm internal forces calculated in Step 8
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89. Diaphragm Design Example
Step 10: Strength Design (con’t)
Final Design Summary Table: Top Floor
Joint
North/South flat
Ramp
Chord
JVI
M-N-V
Size #
s (ft)
Transverse
Longitudinal 1 #6 4 12
4.8
0.52
0.32 8 18
3.1
0.94
0.18 2
0.79
0.65
0.77
0.36 3 6
0.82
0.70
0.58
0.55 16
3.5
0.97
0.92 7
0.42
0.83 5
0.43
0.86
0.96
0.75
0.46
0.89 13
4.4
0.88
0.54
0.53
0.95
0.50
0.57 9
1.02
0.47
0.59
1.00 10
8.8
0.99
0.56 11
0.48
1.03
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90. Diaphragm Design Example
Step 10: Strength Design (con’t)
Comparison of Simple Beam Method Design to FBD Method
Simple Beam method produces higher internal force demand. Thus the FBD Method will produce a more economical design
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91. Diaphragm Design Example
Step 10: Strength Design (con’t)
LFRS-to-Diaphragm Connection
Check YE  WvE= 2.9  1.0=2.9> Wo= OK
Wall length V u N M v n * t
Req'd #
Provide
Anchorage design
[ft]
kips
[kips] [k -
ft]
Per wall
#4 angled bar
Top 25
349
31.1
18.6
13.2 14
NS shear
wall
Others
268
10.2 11 8 31
6.2
1.2 2
EW lite wall
S/N Flat 1
4.3
0.8
Ramp
All floors
Provide flexible connector: 4"x3"x1/2"
5" angle plate with C
shape weld per wall
Diaphragm collector reinforcement:
Collectors designed to the shear tributary to the shear wall
As=WVu/ffy= 1.0  117/0.9/60 = 2.16 in2
Select 5 # 6 at each end of structure
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92. Diaphragm Design Example
Step 11: Diaphragm Stiffness
Step 11: Determine the diaphragm effective elastic modulus and shear modulus
The diaphragm joint effective elastic Young’s modulus (Eeff ) and effective shear modulus (Geff ) are calculated using an analytical procedure based on the stiffness (kv , kt) of the selected diaphragm reinforcement.
Eeff and Geff were calculated at each joint in the spreadsheet during Step 10.
An average value across the joints is recommended for use in the design.
Joint
Top Floor
Other Floors
North/South flat
Ramp
Eeff
Geff
[ksi]
Min
715
213
1025
222
566
142
841
191
Max
1174
281
1122
327
914
238
933
267
Ave
1002.9
255.5
1068.8
277.8
768.3
199.9
882.3
244.5
Des
944.5
247
1073.5
274.5
740
190
887
229
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93. Diaphragm Design Example
Step 12: Drift Check
Step 12: Check the diaphragm amplified gravity column drift
The table shows the diaphragm amplified gravity column drift at the midspan column from the spreadsheet design program in PART 3.
Sub
Floor CD
Cd,dia
Cr,dia
ddia,el
ddia
qdia
Diaphragm
[in]
[rad]
N/S Flat
Top
1.09
0.59
0.708
0.775
0.0036
Others
0.637
0.697
0.0033
Ramp
0.934
1.021
0.0048
0.746
0.816
0.0038
Amplified deflection
Converted to drift
Reduction factor for combining diaphragm and LFRS drifts (not needed in this example)
The maximum diaphragm amplified gravity column drift < 0.01, OK
9% increase from P-D due to Flexible Diaphragm
No further increase for inelastic diaphragm action (EDO)
Elastic diaphragm midspan deflection based here on FBD (or computer structural analysis model)
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94. Diaphragm Design Example
Final Diaphragm Design
Top floor
SDC C EDO
Secondary reinforcement
Other floors
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95. 4-story parking garage structure
Cost Comparison
Steel Comparison: Current vs. New
4-story parking garage structure
SDC C, Knoxville
Chord reinforcement
Shear reinforcement
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96. Diaphragm Design Example
Other Examples are Provided
Example 3: 8-story Moment Frame Office – Seattle (SDC D)
RDO Design
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97. Diaphragm Design Example
Office Building Force Diagrams
transverse loading
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98. Diaphragm Design Example
Office Building Final Design
SDC D RDO
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99. 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
There were some problems that can be addressed
There are successful systems that are different from US practice that are notable
There are innovative systems for seismic design in use that are not common in the US
PCI/NSF/CPF
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April 99 99

100. ASCE 7-10 Including Supplement No.1
Entry into the IBC
2012 IBC
ASCE Including Supplement No.1
ACI
2009 NEHRP Provisions
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101. 2009 NEHRP Provisions
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102. 2009 NEHRP Provisions
2009 NEHRP RECOMMENDED SEISMIC PROVISIONS FOR NEW BUILDINGS AND OTHER STRUCTURES
Part 1: Provisions
Part 2: Commentary to ASCE/SEI 7-05
Part 3: Resource Papers (RP) on Special Topics in Seismic Design
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103. 2009 NEHRP Provisions Part 3 Resource Paper 10 NEES/EERI Webinar
April

104. Entry into the IBC 2018 IBC ASCE 7-16 ACI 318-17 ?
2014 NEHRP Provisions
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105. BSSC PUC Issue Team (IT) 6 on Diaphragm Issues
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106. Scope
Reexamine and refine seismic design provisions for cast-in-place concrete, precast concrete (with or without topping), metal, and wood diaphragms, focusing on objectives with regards to performance in the design earthquake.
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107. Global (ASCE 7) Issues
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108. Metal Diaphragms including Composite and Noncomposite Concrete-Filled Metal Decks – Current Practice, Performance in Past Earthquakes, Areas of Potential Improvement
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April

109. NIST Technical Brief No. 5
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April

110. Wood Diaphragms – Current Practice, Performance in Past Earthquakes, Areas of Potential Improvement
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April

111. NIST TechBrief Series 2012: Seismic Design of Steel Special Braced Frame Systems and Structural Wood Diaphragm Systems
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April

112. Cast-in-Place Concrete Diaphragms – Current Practice, Performance in Past Earthquakes, Areas of Potential Improvement
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April

113. NIST Technical Brief No. 3
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April

114. Precast Concrete Diaphragms (Topped and Untopped) – Current Practice, Performance in Past Earthquakes, Areas of Needed Improvement
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115. Schedule
The IT was authorized in March A Resource Paper by the IT will be completed in 24 months from then, by the end of February 2013.
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116. Questions? Ned Cleland: drned@brd-inc.com Robert Fleischman
S.K. Ghosh
Contact information
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