1888 williams
TRANSCRIPT
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Application of Pushover Analysis to
the Design of Structures ContainingDissipative Elements
Martin S. Williams1 and Denis E. Clment2
1 University of Oxford, UK2 Thomas Jundt Civil Engineers, Geneva, Switzerland
13th World Conference on Earthquake Engineering
Vancouver, August 2004
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Outline
Introduction to knee braced frames
Modelling using Drain-2DX
Five and ten-storey frame designs
Pushover and time-history analyses
Results
Conclusions and future work
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Introduction to knee braced frames (KBFs)
Knee elements can be designed to:
Yield early, maximizing protection to main frame
Yield in web shear rather than flexure
Remain stable under large non-linear excursions
Cross brace
Knee element
Seismic energydissipated through
hysteresis of
short, replaceable
knee elements:
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Modelling a knee element using Drain-2DX
An assemblage of standard truss and beam elements was used torepresent observed shear, flexural and axial behaviour:
Kneeelement
Brace
Connecting
bracket
Brace
Rigid offset
Connection
stiffness
Beam element -
flexural stiffness
Truss element -
axial stiffness
Short cantilever -
shear stiffness
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Hysteresis response of model
Element properties chosen semi-empirically
Comparison with full-scale cyclic test data:
-600
-300
0
300
600
-20 -10 0 10 20
Deflection (mm)
Force
(kN)
Physical testDrain-2DX
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Frame designs
6m6m 6m
6m
6m
6m
4m
4m
4m
4m
4m
4m
4m
4m
4m
4m
Five-storey frame
designed as KBF:Ten-storey frame designed as
ductile MRF, then retrofitted:
5.2m5.2m 5.2m
5.2m
5.2m
Knee braced bay
3m
3m
3m
3m
3m
PLAN:
ELEVATION:
PLAN: ELEVATION:
Designed to EC8, PGA = 0.35g
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Pushover analysis
EC 8:
modal and uniform load patterns
simplify pushover curve to elastic-perfectlyplastic
FEMA 356: other load patterns (e.g. adaptive) permitted,
but not used here
simplify to bi-linear with post-yield stiffnessequal to initial stiffness
ATC 40: capacity spectrum method
Modal pushover(Chopra and Goel, 2002):combine results of pushovers using first few modalload patterns
F
d
F
d
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Time history analyses
30 time-histories generated using SIMQKE
Compatible with EC8 Type 1 spectrum, soil type C
Analysed using DRAIN-2DX (Newmark implicit integration
scheme)
Typical EC8 spectrum-compatible time history
-1
-0.5
0
0.5
1
0 5 10 15 20
Time (s)
Acc
n
(g)
Comparison with EC8 spectrum, TH1-5
0
1
2
3
0 1 2 3
Period (s)
Acceleration
(g)
EC8
TH1
TH2
TH3
TH4
TH5
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Pushover curves
Results shown for 5-storey frame
Post-yield stiffness ~16% of elastic stiffness
As a result, EC8 under-estimates initial stiffness
Modal load pattern
0
500
1000
1500
0 50 100 150Displacement [mm]
Force[kN]
Pushover
EC8
FEMA356
Uniform load
pattern
0
500
1000
1500
0 50 100 150Displacement [mm]
Force[kN]
Pushover
EC8
FEMA356
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Estimated roof displacements
5-storey KBF
10-storey MRF
10-storey KBF
0.8 1 1.2 1.4 1.6 1.8
EC8 Modal
EC8 Uniform
FEMA ModalFEMA Uniform
ATC Modal
ATC Uniform
Multi-modal
Roof disp from pushover
Mean roof disp from TH analyses
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Element yielding
In 5-storey frame, all knee elements yielded and all main elementsremained elastic under design earthquake
In 10-storey retrofitted frame, limited plasticity occurred in main
frame under design earthquake
e.g. 5-storey frame - EC8 pushover analysis undermodal loading:
0.15g
Yielded knee element Plastic hinge
0.35g 0.5g
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Element yielding
5-storey frame
EC8 pushover analysis underuniform loading:
Time history analyses:
first knee element yield at around 0.08g
no hinges in main frame elements below 0.56g
0.15g
Yielded knee element Plastic hinge
0.35g 0.5g
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Inter-storey drifts under design earthquake
5-storey KBF
EC 8
0
1
2
3
4
5
0 0.5 1
Storey drift (%)
Storey
FEMA 356
0
1
2
3
4
5
0 0.5 1
Storey drift (%)
Storey
ATC 40
0
1
2
3
4
5
0 0.5 1
Storey drift (%)
Storey
Mean Mean +/- st. dev.
Uniform Modal
Time history analysis:
Pushover analysis:
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Inter-storey drifts under design earthquake
10-storey MRF (i.e. before retrofit):
EC8
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
FEMA 356
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
ATC 40
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
Modal Pushover
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
Mean Mean +/- st. dev.
Uniform Modal
Time history analysis:
Pushover analysis:
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Inter-storey drifts under design earthquake
10-storey KBF (i.e. after retrofit with knee elements):
Mean Mean +/- st. dev.
Uniform Modal
Time history analysis:
Pushover analysis:
EC8
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
FEMA 356
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
ATC 40
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
Modal Pushover
0
1
2
3
4
5
6
7
8
9
10
0 1 2
Drift (%)
Storey
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Conclusions
A Drain-2DX knee element model capable of representing shear,
flexural and axial behaviour has been developed and validated.
Pushover analyses of 5 and10-storey knee braced frames
showed that they possess high ductility (~6) and post-yield
stiffness (~16%). In time-history analyses, knee elements began to yield at just
0.08g but remained stable up to 0.56g.
Use of pushover analysis does not necessarily lead to optimal
design. Multi-modal pushover offers some advantages in this
respect.
In comparison with time-history analyses, FEMA 356 pushover
approach gave most consistent results, EC8 approach appears
highly conservative for this type of structure.