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Distributed Yielding Concept for Improved Seismic Collapse Performance of Rigid Wall- Flexible Roof
Diaphragm Buildings
Maria Koliou, Ph.D. Candidate
Advisor: Andre Filiatrault, Ph.D., Eng.
Department of Civil, Structural and Environmental Engineering
University at Buffalo – The State University of New York
Rigid Wall – Flexible Roof Diaphragm (RWFD) structures are buildings framed with:
Exterior concrete (cast-in-place or precast) or masonry walls
Interior columns
Horizontal roof diaphragms (wood, steel or “hybrid”)
Rigid Wall – Flexible Diaphragm (RWFD) structures Structures
with large footprint !!!
Applications:
Light industrial and low-rise commercial construction (i.e. warehouses, storage units & shopping complexes)
Introduction
Performance in past earthquakes Poor seismic response during past earthquake events:
1. Structural damage at wall panel – to – roof connections & wall panel –to – wall panel connections (1964 Alaska, 1971 San Fernando & 2010/2011 Christchurch)
2. Seismic response dominated by flexible roof diaphragms
partial building collapses (1987 Whittier Narrows, 1989 Loma Prieta & 1994 Northridge)
Photo courtesy of Doc Nghiem
1994 Northridge
Photo courtesy of Doc Nghiem
1994 Northridge
Problem statement & Research objectives
Problem Statement:
Current design provisions do not account for this type of structure:
• Unrealistic design & prediction of seismic response
• Diaphragm flexibility is not accounted into the design
• Response modification factors (R-values) based on vertical elements of SFRS
• Fundamental design period: significantly underestimated by the code formula
Research Objectives:
Develop simplified numerical models of RWFD buildings with relative good accuracy and efficient computational overhead
Evaluate the seismic collapse capacity of RWFD buildings
Develop, propose & validate a stand-alone simplified seismic design of RWFD buildings
2D numerical framework based on a three step sub-structuring approach:
Step 1: hysteretic response database for roof diaphragm connectors
Step 2: 2D inelastic diaphragm model incorporating local hysteretic connector responses
Step 3: 2D simplified building model incorporating global hysteretic diaphragm model responses
Steps 2 and 3 of numerical framework were validated with experimental and analytical studies available in the literature
Sensitivity study conducted on the modeling assumptions of simplified building model (step 3)
Concept of distributed roof diaphragm yielding Current design of large diaphragms intentionally reduces the shear capacity towards the center of the diaphragm
Inelastic roof diaphragm behavior remains concentrated towards the diaphragm boundaries
Localized inelastic response limited ability to dissipate large amounts of energy that can lead to premature building failure
Concept of distributed yielding intentionally weakening certain intermediate diaphragm zones below current code-based force demands
Roof segment/spring 1
Center of roof diaphragm
Roof diaphragm boundary
Roof segment/spring 2
Roof segment/spring 3
Roof segment/spring 4
Roof segment/spring 5
Roof segment/spring 6
Roof segment/spring 7
Roof segment/spring 8
Roof segment/spring 9
Conventional (ASCE7-10)
diaphragm design
(a) (b)
Center of roof diaphragm
Roof diaphragm boundary
Fo
rce
Displacement
Fo
rce
Displacement
Diaphragm distributed
yielding design
(c)
Roof diaphragm boundary
Center of roof diaphragm
0 5 10 15 20 25 30-0.2
-0.1
0
0.1
0.2
0.3
Time[sec]
Acce
lerati
on [g
]
Direction of shaking
Potential advantages:
Protection of perimeter diaphragm boundary areas from excessive inelastic demand
Reduction/control of premature diaphragm permanent deformations & consequent building collapse
Cost-effective enhancement of seismic collapse resistance of RWFD buildings
Possible increase of natural period of vibration reduced seismic
demand in terms of spectral acceleration
Potential disadvantage:
Possible increase in spectral displacement due to increase in natural period of vibration
But: spectral displacement maybe reduced within acceptable limits due to an increase of effective damping of the building system
CASE STUDY: RWFD building with steel roof diaphragm
Single story concrete tilt – up building Plan dimensions: 400ft X 200ft
Use: Warehouse or distribution center
Walls: Precast concrete walls 30ft tall, 3ft tall parapet & 9.25in thick
Roof: panelized 1.5’’ deep wide-rib steel roof deck
Vertical SFRS: Intermediate precast shear walls (R=4)
Designed with current US design provisions
Fastener pattern:
12 23 3
50ft 60ft 90ft 90ft 60ft 50ft
Zone Conventional (ASCE 7-10)
diaphragm design
Diaphragm distributed
yielding design
1 Button punches @ 12’’ o.c. Button punches @ 12’’ o.c.
2 Top seam welds @ 12’’ o.c. Button punches @ 24’’ o.c.
3 Top seam welds @ 6’’ o.c. Top seam welds @ 6’’ o.c.
Numerical framework
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
400
Displacement (inches)
Fo
rce(l
bs)
Test
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
SAWS model-estimated
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
Wyane-Stewart model-estimatedConnector Database (1/3) Roof Diaphragm Model (2/3) Simplified Building Model (3/3)
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
400
Displacement (inches)
Fo
rce(l
bs)
Test
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
SAWS model-estimated
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
Wyane-Stewart model-estimated
Connector DatabaseDiaphragm model
V
4rx 3rx2rx 1rx
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
400
Displacement (inches)
Fo
rce(l
bs)
Test
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
SAWS model-estimated
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
Wyane-Stewart model-estimatedV
xr4 –xr3-1 -0.5 0 0.5 1
-300
-200
-100
0
100
200
300
400
Displacement (inches)
Fo
rce(l
bs)
Test
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
SAWS model-estimated
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
Wyane-Stewart model-estimatedV
xr3 –xr2-1 -0.5 0 0.5 1
-300
-200
-100
0
100
200
300
400
Displacement (inches)
Fo
rce(l
bs)
Test
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
SAWS model-estimated
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
Wyane-Stewart model-estimatedV
xr2 –xr1-1 -0.5 0 0.5 1
-300
-200
-100
0
100
200
300
400
Displacement (inches)
Fo
rce(l
bs)
Test
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
SAWS model-estimated
-1 -0.5 0 0.5 1-300
-200
-100
0
100
200
300
Displacement (inches)
Fo
rce(l
bs)
Wyane-Stewart model-estimatedV
xr1
Simplified Building Model
md2
md3
xiw
xd1xd2
xd3xd4
md1 miw
xd5
md5
0
5
10
15
20
25
30
-0.2
-0.1
0
0.1
0.2
0.3
Time[s
ec]
Acc
eler
atio
n [g
]
kd5kd4
kd3kd2
kd1
kiw
md4
0
100
200
0
100
200
0
10
20
30
X (ft)Y (ft)
Heig
ht
Z (
ft)
0
100
200
0
100
200
0
10
20
30
X (ft)Y (ft)
Heig
ht
Z (
ft)
T1=0.57 s
Conventional diaphragm design
Center of
roof diaphragm
T1=0.52 s
Diaphragm distributed yielding design
Center of
roof diaphragm
Short direction excitation
Minor influence on the RWFD building’s mode shapes and fundamental periods associated
Measured periods considerably longer than predicted by the design
empirical formula of ASCE 7-10
0.75 0.750.02 0.02 30 0.26secT h
Modal analysis:
Dynamic time history analysis:
IDA conducted using the FEMA P695 Far Field Ground Motion Ensemble
Damage measure (DM): Building Drift Ratio (BDR)
Intensity Measure (IM): Median spectral acceleration at the 1st mode of vibration
,% 100
2
in planewallsmid roof
wallroof
xxBDR
hL
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
IM = Sa (T1) [g]
P[C
oll
ap
se]
Diaphragm distributed yielding design
Conventional diaphragm design
Median()
Conventional diaphragm
design=1.49
Diaphragm distributed
yielding design=2.66
0 2 4 6 80
0.2
0.4
0.6
0.8
1
IM = Sa (T1) [g]
P[C
oll
ap
se]
Diaphragm distributed yielding design
Conventional diaphragm design
Median()
Conventional diaphragm
design=2.68
Diaphragm distributed
yielding design=3.45
Displacement ductility ratio:
Δu is the ultimate/maximum displacement of the diaphragm segment & Δy is the yield displacement of the same diaphragm segment
Median MCE ductility evenly distributed along the span of
diaphragm for the building by applying the distributed yielding concept
Diaphragm hysteretic response for one earthquake motion (Friuli, Italy) scaled at the MCE intensity level
u y
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
Fo
rce (
kN
)
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
-15 -10 -5 0 5 10 15-1000
0
1000
x=0 ft
Center of roof diaphragm
x=12.5 ft
x=37.5 ft
x=62.5 ft
x=87.5 ft
x=112.5 ft
x=137.5 ft
x=162.5 ft
x=187.5 ft
x=200 ft
μ=3.5
μ=3.2
μ=1.1
μ=1.0
μ=1.0
μ=1.0
μ=1.0
μ=1.0
μ=1.0
μ=2.6
μ=2.0
μ=1.2
μ=1.2
μ=1.2
μ=1.0
μ=1.0
μ=1.0
μ=1.0
Displacement [in]
Fo
rce [
kip
s]
Fo
rce [
kip
s]
Displacement [in]
Conventional design Distributed diaphragm yielding design
Collapse fragility results
Significant increase of median collapse intensity
TOWARDS A DESIGN PERSPECTIVE
Response modification (R) factor for diaphragm design
Overstrength factor for the edges of roof diaphragm roof perimeter stronger &
ensure distributed yielding in the roof diaphragm
Conclusions
Simple & cost effective solution to improve the seismic collapse performance of RWFD buildings & reduce damage during extreme ground shaking
Better ductility distribution along the diaphragm span less damage at roof
boundaries
Simple design methodology adopting this concept is currently being developed & verified
Acknowledgements Mr. D. J. Kelly, Simpson Gumpertz & Heger (SGH)
Prof. J. Lawson, Cal Poly San Luis Obispo
Federal Emergency Management Agency (FEMA) & National Institute of Building Sciences (NIBS)
Project Management Committee: Mr. B. Holmes (Rutherford & Chekene), Mr. J. Harris (J.R. Harris & Co.), Mr. J. Hooper (Magnusson Klemencic Associates) & Mr. B. H. Welliver (BHW Engineers, L.L.C. )
Prof. R. Tremblay, Ecole Polytechnique, Montreal
Prof. C. Rogers, McGill University