seismic design of diaphragms - c.ymcdn.com€¦ · 1 s. k. ghosh associates inc. - 1 - seismic...
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S. K. Ghosh Associates Inc.
www.skghoshassociates.com
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Seismic Design of Diaphragms
S. K. Ghosh
S. K. Ghosh Associates Inc.
Palatine, IL and Aliso Viejo, CA
www.skghoshassociates.com
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2009 NEHRP Provisions
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2009 NEHRP ProvisionsPart 3 Resource Paper 10
Replace withMulti-partResource Paper
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BSSC PUC IT-6 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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Multi-Part Resource Paper
Global (ASCE 7) Issues
Cast-in-Place Concrete Diaphragms
Precast Concrete Diaphragms (topped and untopped)
Steel Deck Diaphragms (topped and untopped)
Wood Diaphragms
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Global (ASCE 7) Issues
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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
Fpx = the diaphragm design force
Fi = the design force applied to Level i
wi = the weight tributary to Level i
wpx = the weight tributary to the
diaphragm at Level x
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Diaphragms, Chords, and Collectors
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Diaphragm Design Forces
0
1
2
3
4
5
6
7
0 50 100 150 200
Fpx
Fx
Force (kips)
Flo
or
Lev
el
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Diaphragm Design Force
Recommendations in PCI’s Seismic Design Manual, based on results of research:
For structures assigned to SDC B or C, if every floor diaphragm is designed for the force at the uppermost level derived from the IBC, additional load factors are not required for elastic diaphragm response under the design earthquake.
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Diaphragm Design Force
Recommendations in PCI’s Seismic Design Manual, based on results of research:
For structures assigned to SDC D, E, or F, if lateral forces are resisted entirely by special moment frames, additional load factors are not required if every floor diaphragm is designed for the force at the uppermost level derived from ASCE 7.
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Diaphragm Design Force
Recommendations in PCI’s Seismic Design Manual, based on results of research:
For structures assigned to SDC D, E, or F, if shear walls are part of the lateral force-resisting system, it is sufficient to apply a diaphragm load factor of 2 to the force at the uppermost level derived from ASCE 7 and to design each floor for that force.
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Diaphragm IT Contributors
Ned Cleland Mario Rodriguez
Kelly Cobeen Richard Sause
Robert Fleischman
S. K. Ghosh William Gould
Neil Hawkins Dichuan Zhang
Dominic Kelly
Tom R. Meyer
Jose Restrepo
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Diaphragm IT Products
Design Force Level Proposal for Part 1 of the 2015 NEHRP Provisions – modifies ASCE 7-10 Section 12.10 Approved for inclusion in ASCE 7-16
Design Force Level Proposal for Part 3 of the 2015 NEHRP Provisions – modifies ASCE 7-10 Section 12.10
Precast Diaphragm Design Proposal for Part 1 of the 2015 NEHRP Provisions – modifies ASCE 7-10 Section 14.2 Approved for inclusion in ASCE 7-16
Resource Paper for Part 3 of the 2015 NEHRP Provisions
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2015 NEHRP Provisions
p. 16 of Set 8
Each mode’s contribution is reduced by R( )
2
1
,n
ij j j
i
F f w φ=
=
∑( )a iS T
g R
Fj
j
j
jj
ASCE 7 Method
Fjw j
jFpj
Floor Accelerations for Diaphragm Design
and
0 2 0 4 0 4
0 5
0 5 Acceleration "Magnification" 1 0
DS e px px DS e DS
e px px e
e e
PGA. S I F / w . S I but . S
g
PGA PGA. I F / w I
g g
or . I . I
≤ ≤ ≈
→ ≤ ≤
≤ ≤
SRSS
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0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
Peak ground acceleration (g)
Flo
or m
agni
ficat
ion
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
Northridge Earthquake Data
Repaired PCI building
p. 17 of Set 8
?Floor Accelerations for Diaphragm Design
ASCE 7 Method
ASCE 7 Range, I e =1
0 5 Acceleration "Magnification" 1 0e e
. I . I≤ ≤
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
Northridge earthquake and shaketable test data
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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.
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Diaphragm Design
Fpx = Cpxwpx/Rs
≥ 0.2SDS Ie wpx
Cpx comes from Cp0, Cpi, and Cpn
Note: Cpi is not used in the 2015 NEHRP Provisions
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Diaphragm Design
2015 NEHRPProvisions
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Diaphragm Design
ASCE 7-16
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Diaphragm Design
Cp0 = 0.4 SDS Ie
Cpn= Γm1Ω0CS2
+ Γm2CS2
2 Cpi
Note: The lower-bound limit on Cpn is in ASCE 7-16 only, not in the 2015 NEHRP Provisions.
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Diaphragm Design
Γm1 = 1 + 0.5zS (1 – 1/n)
Γm2 = 0.9zS (1 – 1/n) 2
where zS = modal contribution coefficient modifier dependent on seismic force-resisting system.
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Diaphragm Design
Values of mode shape factor zs
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 force-resisting systems
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Diaphragm Design
1.0
1.1
1.2
1.3
1.4
1.5
1.6
0 5 10 15 20 25
Γm1
Eq. 3.1 zs = 1
Eq. 3.1 zs = 0.7
Wall buildings
Frame buildings
Number of levels, n
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Diaphragm Design
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25
Γm2
Eq. 3.1 zs = 1
Eq. 3.1 zs = 0.7
Wall buildings
Frame buildings
Number of levels, n
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Diaphragm Design
Cpi is the greater of values given by:
Cpi = Cp0
Cpi = 0.9Γm1Ω0CS
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Diaphragm Design
CS = V/W or Vt/W
CS2 = minimum of:
(0.15n + 0.25) Ie SDS
Ie SDS
Ie SD1/[0.03(n-1)] for n ≥ 2 or 0 for n = 1
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Consistent Look into the Design Spectra CsR
For the “Second mode”, R = 1
CS(T2) = min(0.15n+0.25, 1)IeSDS
≤ IeSD1/ [0.03(n-1)]
n: number of levels above ground, n ≥ 2
Comparison of Results (RR for ASCE7 and Measured)
7-story bearing wall building
p. 30
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.5 1.0 1.5
Re
lati
ve h
eig
ht
Cpx / Cpo
Measured EQ4
Proposed
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Comparison of Results (RR for ASCE7 and Measured)
5-story special MRF building
p. 31
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.5 1.0 1.5
Re
lati
ve
he
igh
t
Cpx / Cpo
Measured DEN67
Proposed
Comparison of Results(RR for ASCE7 and Measured)
3-story PCI building
p. 32
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Comparison of Results(RR for ASCE7 and Measured)
NEES Wood Capstone Building (data Processed by R Hanson)
p. 33
Comparison of Results (RR for ASCE7 and Computed)
Steel BRB and special MRF buildings
p. 34
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.5 1 1.5 2
Re
lati
ve h
eig
ht
Cpx / Cpo
6 story
BRB Analysis
SMRF Analysis
BRB Proposed
SMRF Proposed
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.5 1 1.5 2
Re
lati
ve h
eig
ht
Cpx / Cpo
12 story
BRB Analysis
SMRF Analysis
BRB Proposed
SMRF Proposed
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Comparison using Updated DSDM Equations
Berk
ele
y (
SD
C E
)
Seatt
le (
SD
C D
)
Charlest
on (
SD
C D
)
Knoxvill
e (
SD
C C
)
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12
Acc
eler
atio
n (g
)
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12Number of Stories
RR
ΨE
ΨD
ΨR
ASCE7DSDM
Acc
eler
atio
n (g
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10 11 12
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10 11 12
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10 11 12
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10 11 12
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10 11 12Number of Stories
RR
ΨE
ΨD
ΨR
ASCE7DSDM
00.20.40.60.8
11.21.41.61.8
2
1 2 3 4 5 6 7 8 9 10 11 12
00.20.40.60.8
11.21.41.61.8
2
1 2 3 4 5 6 7 8 9 10 11 12
00.20.40.60.8
11.21.41.61.8
2
1 2 3 4 5 6 7 8 9 10 11 12
00.20.40.60.8
11.21.41.61.8
2
1 2 3 4 5 6 7 8 9 10 11 12
UCSD
00.20.40.60.8
11.21.41.61.8
2
1 2 3 4 5 6 7 8 9 10 11 12
00.20.40.60.8
11.21.41.61.8
2
1 2 3 4 5 6 7 8 9 10 11 12Number of Stories
Acc
eler
atio
n (g
)
RR
ΨE
ΨD
ΨR
ASCE7DSDM
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12Number of Stories
ASCE7
Acc
eler
atio
n (g
)
RR
ΨE
ΨD
ΨR
DSDM
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Diaphragm Capacity
Why are we not seeing inadequate performance of diaphragms in seismic events?
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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,
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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.
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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.
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Diaphragm Design
Shear-controlled diaphragm: Diaphragm that does not meet the requirements of a flexure-controlled diaphragm.
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Diaphragm Design (NEHRP Provisions)
Diaphragm System Shear Control Flexure ControlCIP Concrete 1.5 2
Precast concreteEDO 1.0 0.7BDO 1.0 1.0RDO 1.0 1.3
Untopped Steel Deck
Ductile 3.0 NA
Low ductility 2.0 NA
Topped Steel Deck
Reinforced topped Steel Deck with shear stud connection to framing
2.0 2.5
Other topped Steel Deck with structural concrete fill
1.5 2.0
Wood Typical 3.0 NA
When Rs 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.
pxpx px
s
CF = w
R
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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
Precast concrete designed in accordance with Section 14.2.4 and ACI 318
EDO 1 0.7 0.7
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.
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Diaphragm Design Force Level Comparisons
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4-Story Perimeter Wall Precast Concrete Parking Structure (SDC C, Knoxville)
16'
10'-6"
10'-6"
10'-6"
47'-6"
204'
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4-Story Perimeter Wall Precast Concrete Parking Structure (SDC C, Knoxville)
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4-Story Interior Wall Precast Concrete Parking Structure (SDC D, Seattle)
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4-Story Interior Wall Precast Concrete Parking Structure (SDC D, Seattle)
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8-Story Precast Concrete Moment Frame Office Building
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8-Story Precast Concrete Moment Frame Office Building
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8-Story Precast Concrete Shear Wall Office Building
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8-Story Precast Concrete Shear Wall Office Building
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Steel-Framed Assembly Structure in Southern California
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Steel-Framed Office Structure in Seattle, WA
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Cast-in-Place Concrete Framed Parking Structure in Southern California
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Cast-in-Place Concrete Framed Residential Structure in Northern California
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Cast-in-Place Concrete Framed Residential Structure in Seattle, WA
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Cast-in-Place Concrete Framed Residential Structure in Hawaii
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Steel Framed Office Structure in Southern California
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