A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND YIELD MECHANISM AS PERFORMANCE OBJECTIVES
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Transcript of A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND YIELD MECHANISM AS PERFORMANCE OBJECTIVES
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A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND YIELD MECHANISM AS PERFORMANCE OBJECTIVESYIELD MECHANISM AS PERFORMANCE OBJECTIVES
(PERFORMANCE-BASED PLASTIC DESIGN)(PERFORMANCE-BASED PLASTIC DESIGN)
DESIGN BASE SHEAR & VERTICAL DISTRIBUTIONDESIGN BASE SHEAR & VERTICAL DISTRIBUTION
Subhash C. GoelSubhash C. GoelSutat LeelataviwatSutat Leelataviwat
Bozidar StojadinovicBozidar StojadinovicSoon-Sik LeeSoon-Sik Lee
Prabuddha DasguptaPrabuddha DasguptaShih-Ho ChaoShih-Ho Chao
Department of Civil and Environmental Engineering Department of Civil and Environmental Engineering The University of MichiganThe University of Michigan
Ann Arbor, MIAnn Arbor, MI
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CURRENT DESIGN PRACTICE
• Design Base Shear
V = Ce W/R• Elastic Design/Analysis• Drift Check
Cd Δ < Δlimit
• Prescribed Ductility Detailing
(Works most of the time – But not always!)
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CONCEPTCONCEPT
Ve
Vu = ΩoV
V = Ve /R
Δ CdΔ ≤ Δu
Base Shear
Displacement (Story Drift)
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Selected Mechanism at Target DriftSelected Mechanism at Target Drift
i pbrMb
pcMpq pq
1( )i i i nF Fb b
u
ih
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DESIGN BASE SHEARWork needed to “ push” the system monotonically up to the target drift = Energy needed for an equivalent SDOF to be monotonically “ pushed” up to the target ductility level ( )
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For the given system,
Using Newmark-Hall Inelastic Spectra (Rµ-µs-T) for E-P SDOF,
Ref: Housner (1956, 1960)
Solution of Work-Energy Equation gives Design Base Shear
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Ductility Reduction Factors Ductility Reduction Factors Proposed by Newmark and Proposed by Newmark and Hall [1973]Hall [1973]
0
1
2
3
4
5
6
7
0 0.5 1 1.5 2 2.5 3
Period (sec)
s=2
s=6
s=5
s=4
s=3
R
Modification Factor for Modification Factor for Energy Equation versus Energy Equation versus PeriodPeriod
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3
Period (sec)
s=2
s=6
s=5
s=4
s=3
Acceleration Region
Velocity, Displacement Region
Acceleration Region
Velocity, Displacement Region
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Effect of Target Inelastic DriftEffect of Target Inelastic Drift
0.2
0.4
0.6
0.8
1.2
0 0.5 1 1.5 2 2.5
Period (T)
V/W
0 0.5 1 1.5 2 2.5
Period (T)
V/W
=0.000pq
0.005
0.0100.0150.020
1.0
0.0
Elastic
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Comparison of the Design Base Shear Comparison of the Design Base Shear Coefficients at Ultimate Strength LevelCoefficients at Ultimate Strength Level
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5
Period (T)
V/W
Modified Energy
2.8(1.4UBC-94)
2.8UBC-97
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Comparison of Base shear-Roof drift curves of two frames Comparison of Base shear-Roof drift curves of two frames
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00
500
1000
1500
2000
2500
3000
Roof Drift (%)
Bas
e S
hear
(K
ips)
10-Story PPD FrameOverstrength = 1.81
Design Base Shear according to IBC 2000 Approach V=1600 kips
Design Base Shear according to Proposed Approach V=1358 kips
10-Story IBC FrameOverstrength = 1.74
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Design Lateral Force Distribution Based on Inelastic Response
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Lateral Force Distributions in Current Building Codes :
First-Mode Dynamic Solution of Lumped MDOF System
Elastic Response
(Clough and Penzien 1993; Chopra 2000; NEHRP 2001)
Close to a straight line (k =1) when the T is 0.5 second or less;
Close to a parabola (k = 2) when T period is 2.5 seconds or more
IBC 2003
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A New Lateral Force Distribution Based on Inelastic Response of Structures (Lee and Goel, 2001; Chao and Goel, 2005):
was originally proposed as 0.5, which was revised to 0.75 based on more extensive nonlinear dynamic analyses on EBFs, CBFs, and STMFs.
Story Shear Distribution Factor
Lateral Force at level i
Lateral Force at Top level n
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Justification of the New Lateral Force Distribution
1. Relative Story Shear Distributions
Relative Distribution of Story Shear Vi / Vn
0 1 2 3 4 50.5 1.5 2.5 3.5 4.51
2
3
4
5
6
7
8
9
Sto
ry L
eve
l
El Centro
Newhall
Sylmar
Synthetic
IBC 2003
Eq. 4
9-Story SMF
UBC 97
0.5
Eq. 4 0.75
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0 1 2 3 4 50.5 1.5 2.5 3.5 4.5
1
2
3
4
5
6
7
8
9LA02 (El Centro)LA04 (Array #05)
LA07 (Barstow)
LA09 (Yermo)
LA12 (Loma Prieta)LA13 (Newhall)LA17 (Sylmar)
LA18 (Sylmar-2)LA19 (North Palm)
LA21(Kobe_2%in50yr)
LA23 (Loma Prieta_2%in50yr)LA26 (Rinaldi_2%in50yr)
LA27 (Sylmar_2%in50yr)
LA30 (Tabas_2%in50yr)
Sto
ry L
evel
Relative Distribution of Story Shear Vi / Vn
NEHRP 2000 (IBC 2003)
Eq. 4 0.75
9-Story STMF
Eq. 4 0.5
0 1 2 3 4 50.5 1.5 2.5 3.5 4.51
2
3
4
5
6
7
8
9
10
IBC 2003
la01la02la09la12la13la16la17la19
Sto
ry L
evel
Relative Distribution of Story Shear Vi / Vn
10-Story EBF
Eq. 4 0.5
Eq. 4 0.75
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0 1 2 3 40.5 1.5 2.5 3.51
2
3
4
5
6
Sto
ry L
evel
La02
La04
La09
La16
La17
La20
NEHRP 2003
Relative Distribution of Story Shear Vi / Vn
Eq. 4 0.75
6-Story CBF
0 1 2 3 4 50.5 1.5 2.5 3.5 4.51
2
3
4
5
6
7
8
9
10
Sto
ry L
eve
l
Relative Distribution of Story Shear Vi / Vn
Taft Event (1952)
Elastic AnalysisInelastic Analysis
10-Story SMF (Goel, 1967)
IBC 2003
Eq. 4 0.5
Eq. 4 0.75
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0 1 2 3 4 50.5 1.5 2.5 3.5 4.51
2
3
4
5
6
7
8
9
10
IBC 2003
LA01 Earthquake
Sto
ry L
evel
Relative Distribution of Story Shear Vi / Vn
Elastic AnalysisInelastic Analysis
10-Story EBF
Eq. 4 0.75
Relative Story Shear Distributions (comparison between elastic and inelastic responses):
0 1 2 3 4 50.5 1.5 2.5 3.5 4.51
2
3
4
5
6
7
8
9
10
IBC 2003
LA09 Earthquake
Sto
ry L
evel
Relative Distribution of Story Shear Vi / Vn
Elastic AnalysisInelastic Analysis
10-Story EBF
Eq. 4 0.75
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4. Higher Mode Effect Accentuated by Inelastic Behavior
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Beams impose no restraint on joint rotations
(Chopra, 2005)
Beams impose complete restraint on joint rotations
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2. Maximum Interstory Drift Distributions
Sto
ry L
evel
Maximum Interstory Drift (%)
Interstory DriftIBCPPD
-2.0 -1.0 0.0 1.0 2.0-1.5 -0.5 0.5 1.50
2
4
6
8
10
1
3
5
7
9
10-Story EBF
LA16 Earthquake
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pcM
i pbiMiuF
pcM
cM h
ih
3. Column Design Moments
Free body diagram of an exterior “column tree”
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0
1
2
3
4
5
6
7
8
9
Moment (kip-ft)
Sto
ry
0
1
2
3
4
5
6
7
8
9
Moment (kip-ft)
Sto
ryDesign Moment
Design Moment(UBC Distribution)El Centro
New hall
Sylmar
Synthetic
(Lee and Goel, 2001)
Exterior column Interior column
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0123456789
1011121314151617181920
Moment (kip-ft)
Sto
ry
0123456789
1011121314151617181920
Moment (kip-ft)
Sto
ry
Design Moment
Design Moment(UBC Distribution)El Centro
New hall
Synthetic
Sylmar
(a) Exterior (b) Interior
(Lee and Goel, 2001)
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SOME RESULTS
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Plastic Hinge Plastic Hinge Distribution in 3-Story Distribution in 3-Story
SMRF and 9-Story SMRF and 9-Story SMRFSMRF
(b) 9-Story
(a) 3-Story
Sylmar
El Centro
Sylmar
El Centro
Newhall
Synthetic
Synthetic
Newhall
Rotational Ductility Demands: 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0
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Sylmar
El Centro
Synthetic
Newhall
Rotational Ductility Demands : 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0
Plastic Hinge Plastic Hinge Distribution in 20-Story Distribution in 20-Story
SMRFSMRF
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0
5
10
15
20
0 1 2 3 4
Story Drift (%)
Stor
y
4
20- Story
0123456789
10
Stor
y
0
1
2
3
Stor
y
0 1 2 3 4
0 1 2 3 4
Story Drift (%)
3- Story
9- Story
El Centro NewhallSylmar Synthetic
Maximum Story Drift due to Selected Earthquake Records
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0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4
Story Drift (%)
Sto
ry
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4
Story Drift (%)
Sto
ry
El Centro Newhall Synthetic Sylmar
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4
Story Drift (%)
Sto
ry
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4
Story Drift (%)
Sto
ry
Ta
rge
t D
rift
(a) 1.5% Target Drift (b) 2.0% Target Drift
(c) 2.5% Target Drift (d) 3.0% Target Drift
Maximum Story Drifts of Four 20-Story Frames Designed with (a) 1.5% Target Drift, (b) 2.0% Target Drift, (c) 2.5% Target Drift, and (d) 3.0% Target Drift under Four Earthquakes