NEES/EERI Webinar April 23 2012 PCI/NSF/ CPF PART 2: 1 of 30 Outline 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: 1 of 30 NEES/EERI Webinar April 23 2012 Outline Introduce PCI/NSF/CPF DSDM Research Effort Review Key Behaviors of Precast Diaphragms.
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NEES/EERI Webinar
April 23 2012PCI/NSF/CPFPART 2:1 of 30
OutlineOutline
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
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 (Eeff ) and shear modulus (Geff)
Step 12: Check the diaphragm-induced gravity column drift
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Design ProcedureStep 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 7-11.6
(3) Calculate the controlling seismic response coefficient Cs as determined in accordance with ASCE 7-12.8.1. Use structure fundamental period T as determined in accordance with ASCE 7-12.8.2
(4) Calculate the vertical distribution factor Cvc, at each floor level in accordance with ASCE 7-12.8.3
(5) Calculate the lateral seismic design force Fx at each floor level as per ASCE 7 Section 12.8.3
(6) Calculate maximum diaphragm design acceleration, Cdia, max
Cdia,max= max (Fx / wx) (Eqn.1)
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Design ProcedureStep 1: Baseline design force (con’t)
Calculate Baseline Diaphragm Force at each level x, FDx
FDx = x Cdia,max wx (Eqn. 2)
where wx = 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
(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
Le Le Lm
d1
d2
d1
a
Span = max (Lm, 2Le, 2d1, d2) AR = max (Lm/a, 2Le/a)
Chord reinforcement
Design for VQ/I (see 3.1.C of PART3)
Lm
d1
d2
d1
Span = max (Lm, 2d1, d2)
AR = Lm/d1
Chord reinforcement
Design for combined M, N and V (see 3.1.C of PART3)
(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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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 ProcedureStep 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 DBEuses 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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Design Option
Diaphragm Seismic Demand Level
Low Moderate High
Elastic Recommended With Penalty* Not Allowed
Basic Alternative Recommended With Penalty*
Reduced Alternative Alternative 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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Design ProcedureCommentary Step 3: Design Option
0
0.1
0.2
0.3
0 100 200 300
Length (ft)
d(i
n)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 100 200 300
Length (ft)
d (i
n)
n=6n=4n=2
0
0.1
0.2
0.3
0 100 200 300
increase designstrength by 15%
0
0.1
0.2
0.3
0 100 200 300
HighModerateLow
Design Force Penalty determined through analytical results (MCE response):• BDO Designs for High Diaphragm Seismic
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:
Design ProcedureStep 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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0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6
d (in)
T (k)
0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6
0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6
Local
E – Diaphragm force amplification factor used in the EDO. Calibrated to produce elastic diaphragm response in the MCE.
Design Procedure
GlobalLDE 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”
0
500
1000
1500
2000
2500
3000
3500
0 2 4 6 8 10
D (in)
Fpx (k)
EDO-2.66
MCEDBEd = 0.6"Yield0
500
1000
1500
2000
2500
3000
3500
0 2 4 6 8 10
BDO-1.93
0
500
1000
1500
2000
2500
3000
3500
0 2 4 6 8 10
RDO-1.39
HDE
Test
Req.
MDE
Test
Req.
Mean response from suite of spectrum compatible earthquakes
SDC E n=6 SWL= 240’
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Design ProcedureCommentary 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).
where AR is diaphragm aspect ratio: 0.25 ≤ AR ≤ 4.0
(1) For elastic design option, v = vE: 0.1vE (Eqn. 6)
(2) For basic design option, v = vB:
7.142.1 13.0 ARvB (Eqn. 7)
(3) For reduced design option, v = vR:
46.292.1 18.0 ARvR (Eqn. 8)
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0 1 2 3 4 5
AR
B
N=2N=4N=6
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
0 1 2 3 4 5
AR
R
N=2
N=4
N=6Commentary Step 6: The overstrength factors equations are similarly based on the statistical data from the analytical earthquake simulations.
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Design ProcedureStep 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
FDia,x= FDx (Eqn. 9)
The precast diaphragm design procedure presented here can be aligned to work with these factors.
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Design ProcedureStep 8: 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.
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, 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.
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Diaphragm Design Example
Nlite
Nbeam
w=(Fpx/3)/L
Vbeam
VSW VSW
LLbeam
L'Lbeam
Nbeam
Vbeam
d
x
Parking flat under transverse loading
Joint Axial Force
0
50
100
150
200
250
0 100 200 300x (ft)
N (
kips
)
Top floor
Other floors
Joint Shear Force
-200
-150
-100
-50
0
50
100
150
200
0 100 200 300
x (ft)
V (
kips
)
Top floor
Other floors
Joint Moment
-2000
-1000
0
1000
2000
3000
4000
5000
6000
7000
0 100 200 300
x (ft)M
omen
t (k-
ft)
Top floor
Other floors
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.
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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Design ProcedureStep 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: kt, kv
(b) Yield strength in tension and shear: tn , vn
1) Select diaphragm reinforcement type based on required Diaphragm Reinforcement Classification.
• Use the cyclic testing protocols and qualification backbones in the Precast Diaphragm Reinforcement Qualification Procedure to classify and determine properties of new diaphragm reinforcement.
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.
d
d0
b
s’ s
s
s
s
s
s
s0
s0
s
s
s
s
s
s
s0
s0
s
s
s
s
s
s
s0
s0
N.A.
C
Tchord
Tconn
1
c/3
cb
Cconc
Ttopping
2/3(
d-c)
2/3(
d-s 0-
c)
cc0
V
M
d0
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Design ProcedureStep 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.
DLFRS,i
ddia,i
Ddia,i
LFRSDiaphragm
col,iLFRS, i
LFRS
Gravity column
Diaphragm
h
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Design ProcedureStep 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 CDC1 = 0.05
for BDO: Cd,dia = 1.5 CDC1 = 0.08
for RDO: Cd,dia = 2.9 CDC1 = 0.10
and CD is the diaphragm drift P-D multiplier,
where C1 is a the design option factor shown above
)4/)(240/(1 1 ARLCC D
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Design ProcedureStep 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)
dia = d diaCr,dia h (Eqn. 12)
where h is the floor-to-floor height and Cr,dia is calculated from:
(4) Check the diaphragm induced gravity column drift with design limit:
- If dia ≤ 0.01 OK
- If dia > 0.01 then check dia + LFRS
where LFRS is the LFRS story drift determined per ASCE 7, 12.8.6: