預力預鑄節塊橋柱之遲滯模型與地震作用下之反應

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Hysteretic Model and Seismic Response of Post-tensioned

Segmental Bridge Columns

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Hysteretic Model and Seismic Response of Post-tensioned

Segmental Bridge Columns

: Student : C. P. Hsu : Advisor: Dr. C. C. Chou

A Thesis

Submitted Institude of Civil Engineering National Chiao Tung University In Partial Fulfillment of the Requirements

For the Degree of Master of Scienec in

Civil Engineering September 2006

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1 2 2 :(1) (2) (3)

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Hysteretic Model and Seismic Response of

Post-tensioned Segmental Bridge Columns

Student: C. P. Hsu Advisor: Dr. C. C. Chou

Institute of Civil Engineering National Chiao Tung University

Abstract

The purpose of this research is to develop a hysteretic model of the Post-tensioned Segmental Bridge Columns. Because the Flag-Shaped Model is unable to reflect degradation of column stiffness .The force-deformation relationship cannot be predicted. The research is to develop a Stiffness Degrading Flag-Shaped Model based on stiffness degrading of the post-tensioned column observed in tests. The model is also implemented into a computer program NONSPEC to study seismic responses of the post-tensioned column subjected to earthquakes. A post-tensioned segmental column is tested twice with the same loading protocol to compare cyclic responses. The result of study shows: (1) Stiffness Degrading Flag-Shaped Model can model the force-deformation relationship of the post-tensioned column acurtely. (2) The Stiffness Degrading Flag-Shaped Model can predict the reserved strength and stiffness for the post-tensioned column subjected to first ground motiom. (3)Doubling energy dissipation reduces slightly the ductility of the cilumn.

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DSI

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... ... ... ……….. ……….. ……….. ……….. ...1 1.1 ...1 1.2 ...1 1.3 ...3 1.4 ...3 ...5 2.1 ……….5 2.2 - ……….5 2.3 1 ……….6 2.3.1 ………..7 2.3.2 ………..8 2.3.4 ………..8 2.4 ……….9 2.4.1 1 1 ………..10 2.4.2 2 1 ……….12 2.5 ………...15 2.5.1 ………18

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2.5.1.1 1 1 ………..19 2.5.1.2 2 1 ………..20 2.6 ………...…22 2.6.1 ………....22 2.6.2 ………....24 2 ………...26 3.1 ……….26 3.2 ...………26 3.2.1 ………26 3.2.2 ………26 3.2.3 ………27 3.2.4 ………27 3.3 1 2 ………28 3.3.1 ………28 3.3.2 ………31 3.3.2.1 - ………31 3.3.2.2 ……….32 3.3.2.3 ……….……….33 3.3.2.4 ……….33 3.4 2 2 ………34 3.4.1 ………34 3.4.2 ………35 3.4.3 ……….35 3.4.4 ………38 3.4.4.1 - ……….………38

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3.4.4.2 ……….38 3.4.4.3 ……….39 3.4.4.4 ……….40 3.5 1 2 2 2 ………40 3.5.1 - ………40 3.5.2 ………..40 3.5.3 ………41 3.5.4 ………42 3.6 2 ………43 3.7 2 ………45 ………48 4.1 ……….48 4.2 NONSPEC ………48 4.3 ….………...…50

4.3.1 (Elastic Responses Spectra)………50

4.3.2 ………50 4.3.3 ………51 4.3.4 ………55 4.4 ………...58 ………62 5.1 ………...62 5.2 ………...63 ………..64 ………..169

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2.1 Kel,pus ………...66 2.2 Kpl,pus ………..66 2.3 Kpu,pus ……….66 2.4 Keu,pus ……….66 2.5 Kel,pul ……….……….67 2.6 Kpl,pul ……….……….67 2.7 Kpu,pul ……….……….67 2.8 Keu,pul ……….……….67 2.9 ………68 2.10 ………..68 2.11 ……….68 2.12 ………69 2.13 ……….69 3.1 (Nafufill KM 250) ………..70 3.2 2 2 ………70 3.3 ………...71 3.4 2 ………..71 4.1 8 ……….72 4.2 8 ………...73 4.3 8 ………...74 4.4 8 ………75 4.5 2 ………76 4.6 ………77

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2.1 - ………78 2.2 ……….78 2.3 1 1 - ……….79 2.4 2 1 - ……….79 2.5 ……….80 2.6 1 ……….81 2.7 2 ……….82 2.8 ……….83 2.9 ……….83 2.10 ………...84 2.11 ………84 2.12 ………...85 2.13 ……….86 2.14 ………...87 2.15 1 1 ………87 2.16 1 1 ………88 2.17 1 1 ………89 2.18 1 1 ……89 2.19 1 1 ………90 2.20 1 1 ………90 2.21 1 1 …………91 2.22 2 1 ………91 2.23 2 1 ……….92 2.24 2 1 ………93

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2.25 2 1 ……93 2.26 2 1 ………94 2.27 2 1 ………94 2.28 2 1 ………..95 2.29 ……….95 2.30 ……….96 2.31 ……….97 2.32 ……….97 2.33 …….98 2.34 1 ………..99 2.35 1 ………99 2.36 1 ………..100 2.37 2 ………..100 2.38 1 1 ..101 2.39 2 1 ..102 2.40 ………103 3.1 ………..104 3.2 ………...104 3.3 1 2 ………..105 3.4 2 2 ………..106 3.5 1 2 - ………...107 3.6 1 1 2 - .107 3.7 - ………...108 3.8 ………...108 3.9 1 ………109

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3.10 2 ………..109 3.11 2 - ………110 3.12 2 2 ……….….110 3.13 1 2 2 - …….111 3.14 1 2 ………112 3.15 1 2 …….113 3.16 1 2 ….113 3.17 1 2 …….114 3.18 1 2 …….114 3.19 1 2 ……….115 3.20 2 2 ………116 3.21 2 2 …….117 3.22 2 2 ….117 3.23 2 2 …….118 3.24 2 2 …….118 3.25 2 2 ……….119 3.26 SDFS 1 2 ( )…120 3.27 SDFS 1 2 ( )…121 3.28 2 2 ..122 4.1 ……….123 4.2 ……….123 4.3 8 ………..124 4.4 8 ………..125 4.5 1 ………126 4.6 ……….127

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4.7 …….128 4.8 ….129 4.9 ….130 4.10 ……132 4.11 …...133 4.12 ...134 4.13 ………...135 4.14 ………..135 4.15 ………..136 4.16 FS SDFS Model 2 ………..137 4.17 SDFS Model 1 2 ….138 4.18 SDFS Model 1 2 ….139 4.19 T=0.5 (sec) (Landers: Joshus Tree)………….140

4.20 T=1.0 (sec) (Landers: Joshus Tree)………….141

4.21 T=0.5 (sec) (Loma Prieta:Saratoga)……….142

4.22 T=1.0 (sec) (Loma Prieta:Saratoga)………..143

4.23 T=0.5 (sec) (Northridge: Beverly Hills)……..144

4.24 T=1.0 (sec) (Northridge: Beverly Hills)……..145

4.25 T=0.5 (sec) (Chi-Chi: Tcu039)………146

4.26 T=1.0 (sec) (Chi-Chi: Tcu039)………147

4.27 ………...148

4.28 …...….………...149

4.29 …….………..150

4.30 ……….………..151

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3.1 1 ………153 3.2 1 2 ……….153 3.3 45 ( = -0.009 )…154 3.4 45 ( = +0.015 )……….154 3.5 ( = -0.02 )…155 3.6 ( = -0.03 )………155 3.7 ( = -0.05 )………156 3.8 ( = +0.06 )………...156 3.9 ( = +0.06 )………..157 3.10 ( = -0.06 )………...157 3.11 ( = -0.06 )…………..158 3.12 ………...158 3.13 ………...………159 3.14 2 2 ………159 3.15 ( = +0.004 )………...160 3.16 ( = -0.006 )………160 3.17 ( = +0.009 )………...……161 3.18 ( = +0.009 )………161 3.19 ( = +0.015 )………162 3.20 ( = -0.015 )…………162 3.21 ( = +0.02 )………163 3.22 ( = -0.02 )………..163 3.23 ( = -0.02 )…………..164 3.24 ( = -0.03 )………..164

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3.25 ( = +0.03 )….165 3.26 (( = +0.03 )………….165 3.27 ( = -0.04 )………..166 3.28 ( = +0.04 )…………..166 3.29 ( = -0.05 )………..…167 3.30 ( = -0.05 )…………...167 3.31 ( = -0.05 )…………..168

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1.1

1.2

(Hews and Priestley 2002,2003 1999

2003 , 2004 2004 Kwan and Billington 2003)

1.Hews and Priestley (2002,2003)

Mander(1988)

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(2004) : 1. 2. 30-50% 3. 5mm 4. 5. 6. 7. 8. 9.

3.Kwan and Billington (2003)

8 0 8 20 7 ;1. 2. 3. 10% 4.

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4. (2004) 1 2

1.3

(Christopoulos 2002) 2

1.4

5 ( 2004) (Christopoulos 2002)

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2 1

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2.1

(Chou and Chen 2006) 2.2 - 2.3 1 2.4 1 2.5 2.6

2.2

2.1 -[ 2.2 (a) 2.2(b)] F [ 2.2(b)

]

(Decompression Point) 2.1 1 (Decompression Moment) [ 2.2(c)] 2.1 2 ” ”(First Yield) F2 -[

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2.2(d)] -” ”(Ideal Yield) ” ” 004 . 0 = c ε ” ” p K K_e ” ” ”

2.3

1

1 2.3 (2.1) (2.3) ” ” ” ” ” ” 2.5 ” ” 2.1 2.10 : w g l l ) (∆₂ −∆₁ = φ (2.1) φ ε x l_g c − ∆ = 2 (2.2) φ ε_c c= (2.3) φ εC c 1 ∆ ∆₂ l_g 200 mm lw 640 mm x 70 mm

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2.6 1 2 -2.7 2

2.3.1

2.8 2.9 1 1 1 1 1 = +0.006 9.3 kN /mm = +0.06 2.7 kN /mm 70% = +0.009 3.5 kN /mm = +0.06 1 kN /mm 65% 2 1 = +0.006 10.6 kN /mm = +0.06 2.8 kN /mm 73% = +0.009 3.9 kN /mm = +0.06 1 kN /mm 74%

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2.3.2

2.10 1 1 2 1 2 1 (2.4) -2.11 1 1 6.5% 2 1 8.3% eq(Priestley et al. 1996) (2.4) : eq m m h V A ∆ = π 2 (2.4) m V -m ∆ -h A

-2.3.4

2.1 ” ” 2.9 1 2 1 ” ”( 2.1 ∆y) 2.10 1

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2.4

1980

NONSPEC(Mahin and Lin 1983)

-T ( K) ( Ry)

(Stiffness

Degrading Model) (Bilinear Elastoplastic Model)

(Flag-Shaped Model) [ 2.12(a)]

[ 2.12(b)] [ 2.13(a)] 1 2 1 (Constantin et al. 2002) 2004 ( 2004)

(Flag-Shaped Model) 2.11 1 2 2.14 2.1

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NONSPEC e K y ∆ Kp -e K K_p

2.4.1

1

e K K_p ∆_y α e K K_p ∆_y - 2.14 2.1 -e K K_p 1 1 K_e =9.3 kN /mm K_p =0.4 kN /mm ” ” ∆y =17.9 mm α α ( 2.12) 1 1 0.33 2 1 0.45

2.15 1 1 2.16 1 1 - 2.16

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-” ” ” ” -1 1 2.8 2.9 Ke Kp 2.17 1 Ke = ±0.06 Ke 2.34 2.35 1

2.18 1 1 p K p K - = ±0.035 2.8 2.9 Kp Ke p K 2.1 -p K 1 1 e K K_p 1 1 2.1 -e K e K

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e K = ±0.06 2.1 - Kp = ±0.06 Kp

2.19 -α α(=0.33) Fy y F = ±0.06

2.20 2.1 - ” ” 2.21

2.4.2

2

1

2.22 2 1 e K K_p 1 1 2 1 2.1 - Ke =10.5 kN /mm(

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2.11) Kp =0.6 kN /mm( 2.11) ∆y ” ” ∆y =16 mm( 2.11) α eq 1 ( 2.12) 2 1 1 1 1 1 0.45

2.23 2 1 - -1 1 ” ” ” ” -e K Kp 2 Ke Kp 2.1 p K θ=0.035 θ=0.04

2.24 2 1 e K 2.1 -1 = ±0.006 Ke

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2.25 2 1 p K p K - = ±0.035 2.8 2.9 p K 2.1 -2 1

2.26 -y F y F 2 = ±0.004 = ±0.004

2.27 1 1 ” ” 2.28 1 1 2 1 1

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2.5

2.13(b) : 0 1 e K 1 y ∆ 1 2 p β ( 2.29) p piK β 1 2 2 2 2 3 e K 0 1 3 2 αFy α

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2 3 3 4 3 4 1 2 4 y ∆ 4 0 4 4 0 Keo 0 0 5 y ∆ − 0 5 e K 5 pi β 5 6 5 6 5 6 β piKp 6 6 7 Ke 0 5 7 6 y F α 7 7 8 7 8 5 6 8 7 8 8 0

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8 0 0 8 2 2 e + β Ke β e2Ke 0 9 1 2 1 0 9 0 1 ( 2.9) 9 11 9 11 10 2 9 10 2 10 9 10 10 10 11 11 11 12 0 9 β e2Ke 12 11 β e2Fy 11 12 12 13 12 13 9 11 13 ∆y 13 0 13 Keo 0 0 14 6 βe6

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e K 0 14 β e6Ke 0 5 14 y ∆ − 14 16 14 16 15 6 14 16 15 6 β e6 14 15 15 15 16 16 0 14 β e6Ke 17 16 αF_yβ e6 16 17 17 18 17 18 14 16 18 y ∆ − 18 0 18 eo K

2.5.1

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2.5.1.1

1

2.30 e β βp 2.34 ( 2.13) 3 . 9 = e K kN /mm( 2.11) Kp =3.5 kN /mm( 2.11) 12.2 mm( 2.11) α =0.46( 2.12)

2.36 2.38 1 1 ( 2.16) 2.17 2.18

2.19 2.31

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2.20 ( 2.9) 2.30 2.21

2.5.1.2

2

1

2.30 6 . 10 = e K kN /mm Kp =3.9 kN /mm 12.2 mm ( 2.11) eq ( 2.12) 2 1 0.52 βe βp 2 1 2.35 ( 2.13)

2.37 2.39 2 1 = ±0.03 = ±0.04 2 1 = ±0.04 = ±0.03

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2.24 2.25

2.26 2 = ±0.04

2.27 2.30 2.28

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2.6

2.6.1

2.13(b) (Stiffness Degrading Flag Shaped

Model) 1 1 2 1 e K 2.8 e K K_e ( ) 2.29 (∆ /∆y) (Stiffness Degrading Ratio) 2.29 A 1 ∆y β Ke 1 β1 1 B C 2.29 C BC 0.1

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2.29 2.29 1 1 2 1 2.1 β K_e p K 2.1 - 2.30 - 2 ( ) 2.1 ” ” ( 0.004) p K 2 2.30 2 2.31

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α 2.32 2.33 1 1 2 (α =0.92)

2.6.2

χ χ 1

γ γ 1

2.40 (_α+ − α )

(40)

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2

3.1

2 2 2 2 3160 kN

3.2

2

3.2.1

3.1 4 36 mm 1 MTS 500 kN ±200mm 0.5 mm/sec

3.2.2

2 InstruNet 100 InstruNet World

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InstruNet World 0.016 48 0.016 48 0.8 (Sample Rate) 1

3.2.3

2 1 2 1 3.2 - 2.1 F1= 62 kN d= 0.0013 ” ” F2= 138 kN d= 0.004 d= 0.0013 d= 0.003 d= 0.004 d= 0.06

3.2.4

1 3.3 2 3.4

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: (1) ( S ) (2) ( C ) (3) ( R ) 3.3 3.4

3.3

1

2

1 2 1

(Gap Opening) 1 d= 0.06 3.1 2 1 2 50 mm×50 mm×50 mm 7 49 MPa 56 MPa

3.3.1

3.2 ( )

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θ ( ) ( 3.2 ) : (1) = ±0.001 (Pmax=14.5 kN Pmin=4.5 kN) = ±0.004 (Pmax=42 kN Pmin=28 kN) (2) = ±0.006 (Pmax=57 kN Pmin=44 kN) = ±0.006 (3) = ±0.009 (Pmax=74.5 kN Pmin=65.8 kN) = ±0.009 45 ( 3.3 ) (4) = ±0.015 (Pmax=99 kN Pmin=-95 kN) = ±0.015 45 ( 3.4 ) 1.5 mm (5) = ±0.02 (Pmax=116 kN Pmin=-113 kN) = ±0.02 ( 3.5 )

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(6) = ±0.03 (Pmax=141 kN Pmin=-138 kN) = ±0.03 5 mm ( 3.6 ) 1 mm (5) = ±0.04 (Pmax=162 kN Pmin=-156 kN) = +0.04 8 mm 30 mm 2 mm =-0.04 8mm (6) = ±0.05 (Pmax=174 kN Pmin=-167 kN) = +0.05 12 mm 45 40 mm 2.5 mm = -0.05 12 mm ( 3.7 ) 3 mm (7) = ±0.06 (Pmax=186 kN Pmin=-183 kN) = +0.06 15 mm ( 3.8 ) 4 mm( 3.9 ) = -0.06 15 mm

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50 mm( 3.10 ) 4 mm( 3.11 )

3.3.2

2 -:

3.3.2.1

1 2 3.5 183 kN 182 kN (2.1) (2.3) ” ” 2.1 2.10 2.6 SP1 1

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-2.6 -3.6 1 1 = ±0.06 - 1 2 -1 1 = ±0.06 1 2 = ±0.06 1 2 1 = ±0.06

3.3.2.2

2.8 2.9 = ±0.006 = e K 3.8 kN /mm 1 = e K 9.3 kN /mm = ±0.009 2 = p K 2.7 kN /mm ∆y=12.1 mm y F =45 kN = ±0.009 1 = p K 3.5 kN /mm ∆y=12.2mm y F =91.5 kN 2 1 2.8 = ±0.06 = e K 2.4 kN /mm = ±0.006 36 % 1 70%

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= ±0.06 = p K 1 kN /mm = ±0.009 62 % 1 71% 2 1 70% 36% 2.8 2 1 1 2 2.9

3.3.2.3

eq (2.4) -2.11 1 eq 6% 2 4% 1 2 1 2 1

3.3.2.4

3.7 s k 19

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230000 = s k MPa Strain 3.8 1 1 2 ( 3.3) 3.9 1 2 1 1 (2.1) (2.3)

3.4

2

2 2 2

3.4.1

2 (Nafufill KM 250) ( 3.12 ) 1 mm 2 (Nafufill KM 250) 100 KM 250 15 17

(50)

3.1

3.4.2

2

( 3.13 )

7

ASTM A416 Grad 270 16mm fpu=1860 Mpa

SP2 0.25f ′cAc 0.35 f ′cAc A_c c f ′ 28 3.2 (1bar=0.953T) 16 1 5 40 T 392 kN 5 16 20 T 196 kN 16 3653 kN 3850 mm 3 mm 494 kN 3160 kN

3.4.3

3.14 : (1) = ±0.001 (Pmax=19.6 kN Pmin=7.5 kN) = ±0.003 (Pmax=41 kN Pmin=33 kN)

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(2) = ±0.004 (Pmax=68 kN Pmin=51 kN) = +0.004 ( 3.15) (3) = ±0.006 (Pmax=89 kN Pmin=70 kN) = ±0.006 ( 3.16) (4) = ±0.009 (Pmax=107 kN Pmin=84 kN) = ±0.009 = ±0.006 ( 3.17) (Gap Opening)( 3.18) (5) = ±0.015 (Pmax=143 kN Pmin=-118 kN) = ±0.015 5 mm ( 3.19) 100 mm 1 mm ( 3.20) (5) = ±0.02 (Pmax=160 kN Pmin=-139 kN)

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= ±0.02 ( 3.21) 7 mm 270 mm( 3.22) 60 mm 1.5 mm( 3.23 ) (5) = ±0.03 (Pmax=185 kN Pmin=-173 kN) = ±0.03 12 mm 280 mm( 3.24) ( 3.25) 2.5 mm 200 mm ( 3.26) (5) = ±0.04 (Pmax=200 kN Pmin=-189 kN) = ±0.04 17 mm ( 3.27) 305 mm 3 mm( 3.28) (5) = ±0.05 (Pmax=194 kN Pmin=-192 kN) = ±0.05 30 mm 300 mm 18 mm( 3.29)

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3 mm( 3.30 ) 20 mm( 3.31) 3 mm 1 = ±0.05 580 kN 3740 kN ( 3.3)

3.4.4

2

-3.4.4.1

2 2 3.11 192 kN 200 kN ( 2.1 2.10)

3.4.4.2

2.8 2.9 = ±0.006 7 . 4 = e K kN /mm( 2.1) 2 1 6 . 10 = e K kN /mm( 2.1) = ±0.009 4 . 3 = p K kN /mm ∆y=12 mm y F =54 kN 2 1

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9 . 3 = p K kN /mm ∆y=12.2 mm Fy=103.7 kN 2 1 1 2.8 1 2 = ±0.05 Ke =3.1 kN /mm = ±0.009 34 % 1 73% 2 = ±0.05 Kp =1 kN /mm = ±0.009 70 % 1 70% 1 2 1

3.4.4.3

- 2.10 2.11 2.10 2 2 1 2 1 -1 2 2.11 2 2 1 1 8.3% 2 4.7%

(55)

3.4.4.4

19 s k ( 3.7 ) 3.8 2 2 1 3.3 2 1 2 3.10 2 1 1 1 = ±0.03 = ±0.03 3.12 2 2 = ±0.05

3.5

1

2

2 2 1 2 2 2 2

3.5.1

3.13 1 2 2 -2

(56)

= ±0.006 2 67 kN 1 57 kN 2 17% = +0.05 2 207 kN 1 174 kN 2 18% 2 2 1 18%

3.5.2

2.8 = +0.006 2 4.7 kN /mm 1 3.8 kN /mm 24% = +0.006 2 3.4 kN /mm 1 2.7 kN /mm 26% = -0.006 2 4.8 kN /mm 1 3.8 kN /mm 26% = -0.006 2 3.5 kN /mm 1 2.8 kN /mm 25% 2360 3160 25% 25.5%

3.5.3

2.10 2 1 = ±0.03 2 1 =

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±0.04 = ±0.05 = ±0.03 = ±0.04 62% = ±0.05 92% 2 2 2 2 1 2 2 2 2 = -0.04 (2.4) 2.11 2 = ±0.04 = ±0.05 1 2 3.8% 2 2 4.7%

3.5.4

3.8 2 2 2360 3160 2 2 1 2 1 2 = +0.05 340 kN( 3.3) 2

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2 = +0.05 300 kN( 3.3) = -0.05 260 kN 1 = -0.05 200 kN 3.12 2 2 = +0.05

3.6

2

1 2 1 2 1 2 1 1 2.1 -” ” 1 3.8 kN /mm 1.2 kN /mm 17.8 mm eq = 0.45( 3.4) 2 4.7 kN /mm 1.5 kN /mm 16 mm = 0.46( 3.4) 3.14 1 2 - 1 2 - 1 1 2.8 2.9 1 2 1 1 = ±0.06

(59)

1 1 = ±0.06 1 2 1 2 1 1 3.20 2 3.15 3.21 2 2.1 -1 2 = ±0.06 1 2 2 1

3.16 3.22 2 = ±0.04 2.1 -= ±0.035 = ±0.035 = ±0.035 1 2 2.1 -2 1 2

(60)

3.17 3.23 -y F y F eq 1 2 3.18 3.24 1 2.1 ” ” 3.19 3.25

3.7

2

2 2 1 2.30 1 3.8 kN /mm 12.1 mm eq = 0.5( 3.4) 2 4.7 kN /mm 12 mm eq = 0.6( 3.4) 2 1

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2.29 1 2.30 p K 2.1 2.2 1 2 36% 2 2 35% 1 2 63% 2 2 71% 2.30 2.30 ” ” = ±0.035 1 35 . 1 = p K kN /mm 2 Kp =1.95 kN /mm

3.26 3.28 2 -= ±0.04 = ±0.04 2.1 - = ±0.035 3.15 3.21 2 1 3.16 3.22 2 = ±0.04 ” ” = ±0.035 =

(62)

±0.035 = ±0.035 -= ±0.04 = ±0.04 3.17 3.23 2 3.16 1 2 = ±0.035 2 1 3.18 3.24 2.1 ” ” 3.19 3.25 1 1 = ±0.06 1 2 3.27 1 2

(63)

4.1

(Flag-Shaped Model)

(Stiffness Degrading Flag-Shaped Model)

( )

4.2 NONSPEC

) (t

NONSPEC (Single Degree Of

Freedom) (t) 4.1 Mu(t)+Cu(t)+R(t)=P(t) (4.1) ) (t 4.2 Mu(t)+Cu(t)+R(t)=−Mu_g(t) (4.2)

M (system mass) C (system damping) R(t)

(resistance function of the system) u(t)

(system displacement) P(t) (the load action on the

system) ug(t) (ground acceleration)

(4.1) (4.2) M : M t P M t R t u M C t u()+ ()+ () = () (4.3) () () () u (t) M t R t u M C t u + + =− _g (4.4)

(64)

ω ξ M C 2 = M K = ω ) ( ) (t K u t R = × (4.3) (4.4) : M t P t u t u t u()₊2_ωξ ()₊_ω2 ()₌ ()_(4.5) ) ( ) ( ) ( 2 ) (_t _u _t 2_u _t _u _t u + ωξ +ω =− _g (4.6) y u t u t) () ( = µ (4.7) y F t R t) () ( = ρ (4.8) y

u (yield displacement of the system) F_y

(yield force of the system) µ(t) (displacement

ductility of the system)

(4.6) uy : y g y y y u t u Mu t R u t u u t u () () ( ) 2 ) ( ₊ _ωξ ₊ ₌₋ _(4.9) : ) ( ) ( ) ( ) ( 2 2 _t F t R Ku t R M K Mu t R y y y ρ ω ω = = = (4.10) ) ( ) ( ) ( ₂ t u F M u t u K K u t u g y y g y g ₌ ₌_ω _(4.11) (4.9) : ) ( ) ( ) ( 2 ) ( 2 2 _u _t F M t t u t g y − = + + ωξ ω ρ ω µ (4.12) (4.12) : max g y u M F = η (4.13) y C :

(65)

g M C W C F_y = _y× = _y× × (4.14) (strength ratio) (4.13) (4.14) η : g u C g y max = η (4.15)

4.3 (FS Model)

(SDFS Model)

4.3.1 (Elastic Responses Spectra)

( 4.3 ) ATC 32(1996) C ATC 32(1996) C 25 . 0 25 . 7 ± = M PGA=0.7g 8 4.1 4.4

4.3.2

1. 1 1:6 ( 36 ) ( 6 ) 4.5 ” ” Fy(=6012 kN) ∆y(=108 mm) e K (=56 kN /mm) T₀(=1.26 sec)

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W(=21920 kN) Cy(=0.27) (4.15) η 4.1 Kp(=0.04Ke) 0.04 ξ=0.05 α(=0.33) 1 1 1 1 2. ” ” ( 36 ) ( 6 ) y F (= 4215 kN) ∆y(=75 mm) Ke(=56 kN /mm) T0(=1.26 sec) W(=21920 kN) C_y(=0.19) (4.15) η 4.1 Kp(=0.37Ke) 0.37 ξ=0.05 α(=0.46) 1 1 1 1

4.3.3

4.6 4.8 8 (FS Model)

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4.6 4.7 4.8 1. 4.10 4.12 4.13 1 2 3 6 7 4.13 1 2.09 ( 4.2) 4.13 4 5 8 4 0.48 ( 4.2) 18% 4.11 4.12 4.13 2 3 5 8

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2 0.49 ( 4.2) 1 4 6 7 6 1.64 ( 4.2) 2% 4.13 2 3 4 5 8 8 0.61 ( 4.2) 1 6 7 1 1.35 ( 4.2) 3% 4.9 4.9 4.6 5% 2 2 2 2 2. 4.14 1 3

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6 8 1 1.89 ( 4.3) 2 4 5 7 4 0.32 ( 4.3) 5% 4.14 3 2.76 ( 4.3) 67% 1 2.75 ( 4.3) 81% 3. 4.15 1 3 6 7 1 1.86 ( 4.4) 2 4 5 8 4 0.49 ( 4.4) 13%

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10% 4.15 2 7 8 2 0.85 ( 4.4) 1 3 4 5 6 3 2.64 ( 4.4) 43% 4.15 2 7 7 0.97 ( 4.4) 1 2.2 ( 4.4) 43%

4.3.4

1

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2 (T) y C 1 Fy 1 Fy 2 ) (T C_y 1 1 Fy ) (T y C 4.5 2 1 2 α(=0.45) α(=0.5) 1 2 1 4.5

4.16 2 1

(72)

1 2 2 1 2 4.17 1 2 2 1 2 1 2 1 4.17 (c) (f) (h) 2 1. 4.18 4.13 1 3 6 7 8 2 1 8 2 1 1.81 ( 4.2) 2 4 5 2 1 4 2 1 0.78 ( 4.2) 2 1 13% 2. 4.14 1 7 2 1 2 1 1 2

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1 1.30 ( 4.3) 7 2 1 1.89 ( 4.3) 2 1 5 2 1 0.45 ( 4.3) 2 1 7% 2 1 1

4.4

4.3.1 8 8 8 T(= 0.1 0.25 0.5 1 1.5 2 2.5 3) 5 Cy(=0.1 0.2 0.4 0.5 0.8) 8 y C (4.15) η 4.5 1 1 4.3.2 :

8 4 (Landers: Joshua Tree

Loma Prieta: Saratoga Northridge: Beverly Hills Chi-Chi: Tcu039)

T(=0.5 1.0) C_y(=0.2 0.4 0.8)

α(=0.46 0.92) 4.19 4.26

Landers: Joshua Tree 4.19

T=0.5 Cy

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y

C

2

Northridge: Beverly Hills 4.23 4.24

y

C T=1.0

Landers: Joshua Tree

Northridge: Beverly Hills 2 Chi-Chi: Tcu039 4.25 4.26 4.25 T=0.5 Cy 4.19 4.26 y C y C 8 1. 4.27(a)

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y C (=0.2 0.4 0.5 0.8) y C (=0.1) 2 y C =0.1 4.27(b) y C 1 2 y C =0.1 1 1 1 2 1 4.28 1 = 0.035 c ε 12εcu 4.28 = 0.035 6.8 4.27(b) y C y C 4.28 y C 2. 4.29(a) 4.29(b) Vh T (=0.5) T (=1.0) 0.5

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1 T=3.0 0 4.26 (c) 4.30(a) Va 4.30(b) 0.5 0.5 1.0 3. 4.31 8 y C 2 2 y C (=0.1) y C (=0.8) Cy(=0.1) y C (=0.8) C_y(=0.4 0.5 0.8) 0.5 0.5 y C (=0.1 0.2)

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5.1

1 2 : 1. 2. -3. 4. 2 1 = ±0.06 2

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1 = ±0.06 2 2 ” ” 5.

5.2

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1. (2004) ” ” : 2. (2002) ( ) 3. (2004) ( ) 4. (1999) ( )

5.Wing-Pin Kwan, and Sarah L. Billington,(2003)”Unbonded Posttensioned Concrete Bridge Pier. :Monotonic and Cyclic Analyses”, Journal of Bridge Engineering, Vol.8,No3,pp.92-101

6. Wing-Pin Kwan, and Sarah L. Billington,(2003)”Unbonded Posttensioned Concrete

Bridge Pier. :Seismic Analyses”, Journal of Bridge Engineering,

Vol.8,No3,pp.102-111

7.AISC,”Load and Resistance Factor Design Specification for Structural Buildings” Steel,American Institute of Steel Construction, Chicago, Illinois, 2002.

8.Constantin Christpoulos (2002)”Seismic Response of Self-Centering Hysteretic Systems”,Earthquake Engineering and Structure Dynamic,Vol.31,pp.1131-1150. 9.Improved Seismic Design Criteria for California Bridges: Provisional

Report.ATC-32.Applied TechnologyCouncil.Redwood City,California,1996. 10.Joshua T. Hews ,M.J.N. Priestley “Seismic Response of Unbound

Post-Tensioned Precast Concrete Segmental Bridge Column”. M.S. Thesis,

University of California San Diego,2000.

11.Joshua T. Hews ,M.J.N. Priestley “Seismic Response of Unbound Post-Tensioned Precast Concrete Segmental Bridge Column”. P.H.D. Thesis,

University of California San Diego,2000.

12.K.A.S.Susanttha,Hanbin Ge and TsutomuUsami,(2002)”CyclicAnalysis and Capacity Prediction Concrete Steel Box Columns. ”Earthquake Engineering and

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Structure Dynamic,Vol.31,pp.195-216.

13.Mervyn J. Kowalsky and M.J.N. Priestley,(2000)”Improved Analytical Model for Shear Strength of Circular Reinforced Concrete Column in Seismic Regions”,ACI

Structure Jornal,Vol.97,No.3,pp.388-396

14.M.J.N. Priestley, F. Seible and G.M. Calvi, ”Seismic Design and Retrofit of

Brdges”,1996.

15.Mohsen Issa,Robert L. Yuan(1989) “Prestressed Concrete Column Behavior”,

PCI Journal, November-December,pp.51-67.

16.Y. H. Chai, M.J.N. Priestley,and F.Seible,(1994)”Analytical Model For Steel-Jacketed RC Circular Columns”, Journal of Structure Engineering, Vol.120, No.8,pp.2358-2375.

17.Yi Zheng, Tsutomu Usami, Hanbin Ge,(2001)”Ductility of Thin-walled Steel Box Stub-Columns”, Journal of Structure Engineering, Vol.126, No.11,pp.1304-1311.

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2.1 Kel,pus

Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 9.3 7.5 6.7 5.7 4.9 4.0 3.2 2.7 1 2nd 3.8 3.7 3.6 3.4 3.2 2.9 2.5 2.4 1st 10.6 8.5 7.3 6.1 5.4 4.4 3.3 2.8 2 2nd 4.7 4.5 4.2 4.0 3.6 3.2 3.1 Unit: kN /mm 2.2 Kpl,pus Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 3.5 2.5 2.1 1.6 1.3 1.1 1.0 1 2nd 2.7 2.1 1.8 1.4 1.2 1.1 1.0 1st 3.9 3.1 2.6 1.9 1.4 1.2 1.0 2 2nd 3.4 2.8 2.4 1.9 1.5 1.0 Unit: kN /mm 2.3 Kpu,pus Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 6.2 3.6 2.8 2.4 1.8 1.4 1.2 1 2nd 3.4 2.4 2.1 1.6 1.3 1.2 1.0 1st 8.2 5.0 3.8 2.6 1.8 1.4 1.3 2 2nd 6.3 3.7 3.1 2.3 2.0 1.5 Unit: kN /mm 2.4 Keu,pus Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 9.3 7.9 6.8 5.9 5.0 4.0 3.4 2.7 1 2nd 4.0 3.8 3.5 3.4 3.2 3.0 2.7 2.4 1st 10.6 8.7 6.7 5.7 4.7 3.8 3.0 2.3 2 2nd 5.6 4.7 4.3 3.4 3.6 2..22 1.5 Unit: kN /mm

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2.5 Kel,pul

Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 9.0 7.1 6.2 5.2 4.4 4.1 3.4 2.7 1 2nd 3.8 3.7 3.6 3.4 3.4 3.0 2.8 2.5 1st 9.8 8.2 7.0 6.0 4.8 4.1 3.3 2.6 2 2nd 4.8 4.6 4.3 4.3 3.6 3.5 3.0 Unit: kN /mm 2.6 Kpl,pul Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 3.4 2.6 2.3 1.5 1.2 1.1 1.0 1 2nd 2.8 2.3 2.0 1.6 1.3 1.1 1.0 1st 3.8 3.1 2.7 1.8 1.3 1.1 1.0 2 2nd 3.5 3.2 3.0 2.6 2.0 1.2 Unit: kN /mm 2.7 Kpu,pul Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 5.9 3.4 2.7 2.2 1.6 1.3 1.1 1 2nd 3.7 2.9 2.3 1.8 1.4 1.2 1.1 1st 8.7 5.0 3.8 2.6 1.8 1.5 1.2 2 2nd 7.0 4.9 3.4 2.6 2.0 1.6 Unit: kN /mm 2.8 Keu,pul Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 5.9 3.4 2.7 2.2 1.6 1.3 1.1 1 2nd 3.7 2.9 2.3 1.8 1.4 1.2 1.1 1st 8.7 5.0 3.8 2.6 1.8 1.5 1.2 2 2nd 7.0 4.9 3.4 2.6 2.0 1.6 Unit: kN /mm

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2.9

Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 12.2 11.9 12.2 11.9 12.0 12.6 12.5 1 2nd 12.1 9.1 10.2 9.4 10.0 10.3 11.9 1st 12.2 12.0 11.6 11.7 12.5 12.0 10.1 2 2nd 12.0 12.1 11.9 12.2 12.7 11.6 Unit: mm 2.10 Drift(%)

Specimen No. Test

0.6 0.9 1.5 2.0 3.0 4.0 5.0 6.0 1st 91.5 79.7 69.5 58.3 48.0 40.3 33.8 1 2nd 33.7 32.8 34.7 30.1 29.0 25.8 28.6 1st 103.7 87.6 70.8 63.2 55.0 39.6 28.3 2 2nd 54.0 50.8 47.6 43.9 40.6 36.0 Unit: kN 2.11 Model Specimen No. (kN /mm) (kN /mm) ∆ ( mm ) y Fy( kN ) 1 10.3 0.5 16 165 Analysis 2 11.2 0.5 16 180 1 9.3 0.4 17.9 167 FS Test 2 10.5 0.6 16 171 1 10.3 4.0 11 130 Analysis 2 11.2 3.3 10 130 1 9.3 3.5 12.2 125 SDFS Test 2 10.6 3.9 12.2 138

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2.12

Drift(%) Model. Specimen No.

0.9 1.5 2.0 3.0 4.0 5.0 6.0 average 1 0.42 0.42 0.35 0.3 0.3 0.3 0.3 0.33 FS 2 0.57 0.57 0.47 0.42 0.41 0.42 0.43 0.45 1 0.46 0.47 0.47 0.46 0.47 0.47 0.46 0.46 SDFS 2 0.52 0.52 0.5 0.48 0.46 0.46 0.5 0.52 2.13 Specimen No A B C A′ B′ C′ y ∆ ∆ / 1 4 8 1 4 8 1 Ratio 1 0.64 0.48 1 0.58 0.36 y ∆ ∆ / 1 4 8 1 4 8 2 Ratio 1 0.57 0.4 1 0.66 0.35

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3.1 (Nafufill KM 250)

Cylinder NO. Specimen 1 2nd

Test((MPa) Specimen 1 2nd Test(MPa) 1 73 65 2 69 63 Average 71 64 3.2 2 2

Step (bar) TStrand(kN)

1 20 188 2 58 543 3 97 908 4 136 1272 5 176 1645 6 195 1823 7 215 2010 8 234 2187 9 254 2374 10 273 2551 11 293 2738 12 313 2925 13 332 3102 14 352 3289 15 371 3467 16 391 3653 Power Seating 322 3160 : 1Bar=0.953T

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3.3

Specimen 1 Specimen 2

1st 2nd 1st 2nd

Drift% PT Force ∆Force PT Force ∆Force PT Force ∆Force PT Force ∆Force

0.9 2370 10 2369 9 2470 8 3169 9 1.5 2400 40 2393 33 2490 28 3194 34 2.0 2440 80 2427 67 2510 48 3225 65 3.0 2500 140 2505 145 2620 158 3308 148 4.0 2550 190 2597 237 2700 238 3382 222 5.0 2640 280 2700 340 2740 278 3459 299 -0.9 2370 10 2371 11 2510 48 3214 54 -1.5 2400 40 2395 35 2600 138 3220 60 -2.0 2440 80 2427 67 2660 198 3300 140 -3.0 2530 170 2498 138 2800 338 3450 290 -4.0 2650 290 2580 220 2940 478 3600 440 -5.0 2720 360 2660 300 3030 568 3720 560 Unit:kN 3.4 2 Drift(%) Model. Specimen No.

0.9 1.5 2.0 3.0 4.0 5.0 6.0 average 1 0.4 0.41 0.45 0.43 0.45 0.48 0.49 0.45 FS 2 0.4 0.44 0.42 0.45 0.5 0.56 0.46 1 0.41 0.47 0.5 0.5 0.5 0.52 0.56 0.5 SDFS 2 0.52 0.55 0.52 0.6 0.65 0.7 0.6

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72

4.1 8

Type Earthquake

Event Year Station

PGA (g) Scaling Factor Scaled PGA Soil Type Distance (km) Number of Data T (sec) FS Model (C_y =0.27) SDFS Model (C_y =0.19)

a Loma Prieta 1989 1652 Anderson Dam (Downsteam) 0.24 3.6 0.86 C 21 7925 0.005 0.32 0.22

b Loma Prieta 1989 58065 Saratoga-Aloha Ave 0.32 3 0.96 C 13 7995 0.005 0.29 0.20

c Landers 1992 22170 Joshua Tree 0.283 2.6 0.73 C 11 4000 0.02 0.37 0.26

d Landers 1992 Coolwater 0.42 2.2 0.92 C 21 11190 0.0025 0.30 0.21

e Northridge 1994 90013 Beverly Hills-14145 Mulhol 0.52 1.8 0.93 C 20 3000 0.01 0.29 0.21

f Northridge 1994 24278 Castsic- Old Ridge Route 0.51 1.3 0.66 C 21 3000 0.02 0.41 0.29

g Chi-Chi 1999 TCU034 0.25 2.3 0.57 C 33 18000 0.005 0.48 0.33

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73

4.2 8

NO. Record

SDFS

Model FS Model BE Model SD Model

SDFS Model

(2nd Motion) Ratio 1 Ratio 2 Ratio 3 Ratio 4

1 Anderson Dam 131 274 171 177 177 2.09 1.31 1.35 1.06

2 Saratoga 443 587 218 294 294 1.33 0.49 0.66 0.96

3 Joshua Tree 439 525 344 397 397 1.20 0.78 0.90 1.03

4 Coolwater 360 172 437 302 302 0.48 1.21 0.84 0.78

5 Beverly Hills 476 418 435 464 464 0.88 0.91 0.97 0.98

6 Castsic Old Ridge 245 300 402 265 265 1.22 1.64 1.08 1.23

7 TCU034 92 120 120 120 120 1.30 1.30 1.30 1.20

8 TCU039 968 936 511 588 588 0.97 0.53 0.61 1.81

Note:Ratio 1: FS Model / SDFS Model Ratio 2: Bilinear Model / SDFS Model Ratio 3: Degrading Model / SDFS Model

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74

4.3 8

NO. Record

SDFS

SDFS Model

1 Anderson Dam 0.86 1.63 1.84 2.37 1.12 1.89 2.14 2.75 1.30

2 Saratoga 3.15 2.14 3.36 4.28 1.85 0.68 1.07 1.36 0.59

3 Joshua Tree 4.73 5.07 13.04 10.35 3.80 1.07 2.76 2.19 0.80

4 Coolwater 2.29 0.73 3.31 3.43 1.28 0.32 1.45 1.50 0.56

5 Beverly Hills 3.13 2.01 5.06 4.83 1.42 0.64 1.62 1.54 0.46 6 Castsic Old Ridge 1.61 2.14 3.08 3.22 1.42 1.33 1.91 2.00 0.88

7 TCU034 0.24 0.08 0.26 0.25 0.45 0.35 1.08 1.05 1.89

8 TCU039 9.94 12.97 13.36 21.25 9.25 1.31 1.34 2.14 0.93

Note: Ratio 1: FS Model / SDFS Model Ratio 2: Bilinear Model / SDFS Model Ratio 3: Degrading Model / SDFS Model

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75

4.4 8

NO. Record

SDFS

SDFS Model

1 Anderson Dam 1.08 2.01 2.18 2.37 1.32 1.86 2.02 2.20 1.22

2 Saratoga 4.37 3.29 3.70 4.28 2.78 0.75 0.85 0.98 0.63

3 Joshua Tree 5.07 6.81 13.39 10.35 4.14 1.34 2.64 2.04 0.81

4 Coolwater 3.04 1.48 3.66 3.43 1.50 0.49 1.20 1.13 0.49

5 Beverly Hills 4.44 4.18 5.38 4.83 2.48 0.94 1.21 1.09 0.55 6 Castsic Old Ridge 2.10 3.29 3.36 3.22 1.75 1.57 1.60 1.54 0.83

7 TCU034 0.43 0.47 0.42 0.42 0.67 1.10 0.96 0.97 1.55

8 TCU039 13.96 13.48 13.71 21.25 15.39 0.97 0.98 1.52 1.10

Note: Ratio 1: FS Model / SDFS Model Ratio 2: Bilinear Model / SDFS Model Ratio 3: Degrading Model / SDFS Model

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76

4.5 2

Max. Disp. SD Ratio Yield Force η(Spectra)

NO. Record Pos. Neg. Pos. Neg. Pos. Neg.

0 T (sec) (2nd Motion) y C (2nd Motion) η (2nd Motion) Cy=0.1 Cy=0.2 Cy=0.4 Cy=0.5 Cy=0.8 1 Anderson Dam 109 131 0.98 0.94 4.17 3.97 1.29 0.18 0.21 0.10 0.23 0.46 0.58 0.93 2 Saratoga 443 398 0.53 0.57 2.27 2.44 1.70 0.10 0.11 0.09 0.21 0.42 0.52 0.83 3 Joshua Tree 300 439 0.60 0.55 2.54 2.33 1.68 0.11 0.14 0.12 0.27 0.54 0.68 1.09 4 Coolwater 360 268 0.56 0.70 2.40 2.97 1.65 0.11 0.12 0.10 0.22 0.43 0.54 0.87 5 Beverly Hills 476 404 0.49 0.56 2.10 2.37 1.77 0.10 0.10 0.10 0.21 0.43 0.53 0.85

6 Castsic Old Ridge 245 232 0.73 0.75 3.10 3.20 1.46 0.14 0.21 0.14 0.30 0.60 0.75 1.21

7 TCU034 88 92 1 1 4.21 4.21 1.26 0.19 0.33 0.16 0.35 0.70 0.87 1.39

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77 4.6 46 . 0 = α α =0.92 NO. Record

Max Disp.(mm) Eh(kN-m) Ea(kN-m) Max Disp.(mm) Eh(kN-m) Ea((kN-m)

1 Anderson Dam 131 861 1079 135 1914 2169

2 Saratoga 443 3154 4373 385 3712 4038

3 Joshua Tree 439 4731 5067 443 7070 7122

4 Coolwater 360 2289 3033 333 3255 3398

5 Beverly Hills 476 3126 4438 458 3789 4149

6 Castsic Old Ridge 245 1612 2096 246 2737 2827

7 TCU034 92 238 431 98 361 529

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Lateral Displacement La te ra l F or ce 3 (Ultimate) 2 (First Yield) 1 F_y F₁ 1 y 0 (Ideal Yield) K_e K_p F3 3 n Fn n 2.1

-(a) Initial Step c=D Segment Strands p p L c D/2 c=D c=D/2 c<D/2 (d) Step 3 (c) Step 2 (b) Step 1 P+F_S P+FS P+FS P+FS+ FS θp 2.2

(94)

-160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L at er al F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%)

Pull Direction Push Direction

2.3 1 1 --160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L at er al F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%)

(95)

--160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 La te ra l F or ce (k N )

Kel,pus Kpl,pus Kpu,pus Keu,pus Kel,pul Kpl,pul Kpu,pul Keu,pul 2.5

(96)

Drift 0.9% Drift 1.5% -50 -25 0 25 50 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.9 % - 1.5% Drift 1.5% Drift 2% -60 -30 0 30 60 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5 % - 2% Drift 2% Drift 3% -80 -40 0 40 80 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 2 % - 3% Drift 3% Drift 4% -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 3 % - 4% Drift 4% Drift 5% -150 -75 0 75 150 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 4 % - 5% Drift 5% Drift 6% -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 5 % - 6% 2.6 1

(97)

Drift 1.5% Drift 0.9% -50 -25 0 25 50 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.9 %-1.5% Drift 2% Drift 1.5% -60 -30 0 30 60 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 2 % - 1.5 % Drift 3% Drift 2% -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 2 % - 3% Drift 4% Drift 3% -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 3 % - 4% Drift 5% Drift 4% -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 4 % - 5% Drift 6% Drift 5% -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 5 % - 6% 2.7 2

(98)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 2 4 6 8 10 12 El as tic S tif fn es s ( kN /m m

) _{Specimen 2}Specimen 1 2nd Test1st Test

2.8 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 2 4 6 8 10 12 In el as tic S tif fn es s ( kN /m m

) Specimen 1_{Specimen 2} _{2nd Test}1st Test

(99)

0 1 2 3 4 5 6 Drift (%) 0 2 4 6 8 10 12 14 16 H ys te re ri c E ne rg y (k N -m ) 2nd Test1st Test Specimen 1 Specimen 2 2.10 0 1 2 3 4 5 6 Drift (%) 0 1 2 3 4 5 6 7 8 9 10 E qu iv al en t V is co us D am pi ng (% ) 1st Test 2nd Test Specimen 1 Specimen 2 2.11

(100)

(a) Stiffness Degrading Model

y Fy Ke Ke KP Displacement Force

(b) Bilinear Elastoplastic Model

y Fy Ke Ke KP Displacement Force 2.12

(101)

2 3 4 Displacement Fy α_Fy y 0 Kp Ke 1 y -Fy Force Ke 10 9 5 6 11 12 7 8

(a) Flag-Shaped Model

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 Force Displacement F_y βe2Fy βe2αFy αFy -Fy -βe6Fy βe6αFy αFy y − y 0 Ke Kp Ke βe2Ke 14

(b)Stiffness Degrading Flag-Shaped Model 2.13

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0 25 50 75 100 125 150 Lateral Displacement (mm) 0 50 100 150 200 250 L at er al F or ce (k N ) Specimen 1 Specimen 2 Test Analysis 2.14 -160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 La te ra l F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) FS Model Test 2.15 (FS Model) 1 1

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6 % FS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5 % FS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 3 % FS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 4 % FS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 5 % FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 6 % FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) FS Model 2.16 (FS Model) 1 1

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Drift (%) 0 3 6 9 12 15 E la st ic S tif fn es s (k N /m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 6 0.6 2.17 1 1 Drift (%) 0 1 2 3 4 5 In el as tic S tif fn es s ( kN /m m ) _{FS Model} SDFS Model Test 0.9 1.5 2 3 4 5 6 2.18 1 1

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Drift (%) 0 5000 10000 15000 20000 H ys te re tic E ne rg y (k N -m m ) FS Model SDFS Model Test 0.9 1.5 2 3 4 5 6 2.19 1 1 Drift (%) 0 5 10 15 20 25 Y ie ld D is pl ac em en t (m m ) _{FS Model} SDFS Model Test 0.9 1.5 2 3 4 5 6 0.6 2.20 1 1

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Drift (%) 0 40 80 120 160 200 240 Y ie ld F or ce ( kN ) FS Model SDFS Model Test 0.9 1.5 2 3 4 5 6 0.6 2.21 1 1 -160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 La te ra l F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) FS Model Test 2.22 (FS Model) 2 1

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6 % FS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5 % FS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 3 % FS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 4 % FS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 5 % FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 6 % FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) FS Model 2.23 (FS Model) 2 1

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Drift (%) 0 3 6 9 12 15 El as tic S tif fn es s ( kN /m m ) 0.9 1.5 2 3 4 5 6 0.6 FS Model SDFS Model Test 2.24 2 1 Drift (%) 0 1 2 3 4 5 In el as tic S tif fn es s (k N /m m ) FS Model SDFS Model Test 0.9 1.5 2 3 4 5 6 2.25 2 1

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Drift (%) 0 5000 10000 15000 20000 H ys te re tic E ne rg y (k N -m m ) FS Model SDFS Model Test 0.9 1.5 2 3 4 5 6 2.26 2 1 Drift (%) 0 5 10 15 20 25 Y ie ld D is pl ac em en t (m m ) _{FS Model} SDFS Model Test 0.9 1.5 2 3 4 5 6 0.6 2.27 2 1

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Drift (%) 0 40 80 120 160 200 240 Y ie ld F or ce ( kN /m m ) FS Model_{SDFS Model} Test 0.9 1.5 2 3 4 5 6 0.6 2.28 2 1 ∆/∆y St if fn es s D eg ra di ng R at io (β ) 1.0 0.1 A A' B' B C C' Elastic Inelastic 2.29

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Lateral Displacement L at er al F or ce _(Ultimate) 2 (First Yield) 1 Fy F₁ 1 y 0 K_e K_p n F_n n 2.30

(112)

6 Force Displacement Fy -Fy Fyα − y Fyα y 2.31 6 Force Displacement Fyα Fyα -Fy − y Fy y 2.32

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-150 -100 -50 0 50 100 150 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) -6 -4 -2 0 2 4 6 Drift (%) α=0.46 -150 -100 -50 0 50 100 150 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) -6 -4 -2 0 2 4 6 Drift (%) α=0.92 -160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 La te ra l F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) α=0.46 α=0.92 2.33

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0 1 2 3 4 5 6 7 8 9 10 11 12 ∆/∆_y 0 0.2 0.4 0.6 0.8 1 1.2 St if fn es s D eg ra di ng R at io Elastic

Inelastic Specimen 1Specimen 2 Analysis

2.34 1 0 1 2 3 4 5 6 7 8 9 10 11 12 ∆/∆y 0 0.2 0.4 0.6 0.8 1 1.2 St if fn es s D eg ra di ng R at io Elastic

Inelastic Specimen 1Specimen 2 Analysis

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-160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 La te ra l F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) SDFS Model Test 2.36 1 -160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 La te ra l F or ce (k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) FS Model Test 2.37 2

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6 % SDFS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5 % SDFS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 3 % SDFS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 4 % SDFS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 5 % SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 6 % SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) SDFS Model 2.38 (SDFS Model) 1 1

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6 % SDFS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5 % SDFS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 3 % SDFS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 4 % SDFS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 5 % SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 6 % SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) SDFS Model 2.39 (SDFS Model) 2 1

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1 2 3 4 9 10 11 12 13 Force Displacement F_y β+ e2Fy β+_e₂α+_F y α+_F y -χFy -χβ−e6Fy -χβ−e6α−Fy

y

− y

0 K_e K_p K_e β+e2Ke 6 18 8 5 14 15 16 17 7 -α−_χF y γKp 2.40

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50 Ton Actuator

Footing Tie-down

Laboratory Strong Floor Laboratory Strong Wall 33 00 Curvature Instrumentation S N Footing 85 0 20 30 42 0 19-15 mm Grade 270 low-relaxation prestressing strands Segment 3340 Load Stub 3.1 0 5 10 15 20 25 30 Cycle Number -8 -6 -4 -2 0 2 4 6 8 D ri ft (% ) 6.0% 5.0% 4.0% 3.0% 2.0% 1.5% 0.9% 0.6% 0.4% 0.2% 0.15% 0.3% 0.1% 3.2

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S8 S3 S2 S4 S7 S6 R2 R3 S10 S9 Rosset

Cross Strain Guages Uniaxial Strain Guages

20 0 C1 L9 B C A L8 C6 C5 C4 C2 C3 L5 L6 L7 70 C8 C7 20 0 S1 ,S 2, S3 ,S 4, S5 20 0 20 0 R1,R2,R3,S6,S7 Section A-A Section B-B S11,S12,S13 C 1, C 2, C 3, C 4, C 5 84 0 N

Tendon Strain Gauge Location

S8 ,S 9, S1 0 S W Section C-C C 6, C 7, C 8 E N S 20 30 33 00 S13S12 S11 1500 85 0 S1 R1 L4 L3 L2 L1 C A B S5 ST 2 ST 4 ST3 ST1 3.3 1 2

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S12 S4

S2 S3 S11

Cross Strain GuagesUniaxial Strain Guages

20 0 S5 L9 B C A L8 S8 S6 S7 L5 L6 L7 70 C2 C1 20 0 20 0 20 0 S1,S2,S3,S4 Section A-A Section B-BS9,S10 S5 ,S 6, S4 ,S 8 84 0 N

Tendon Strain Gauge Location

S1 1, S1 2 S W Section C-C C 1, C 2 E N S 20 30 33 00 S10 S9 1500 85 0 S1 L4 L3 L2 L1 C A B ST 2 ST 4 ST3 ST1 3.4 2 2

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-160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L at er al F or ce (k N ) -6 -5 -4 -3 -2 -1Drift (%)0 1 2 3 4 5 6

3.5 1 2 -0 40 80 120 160 Lateral Displacement (mm) 0 50 100 150 200 250 L at er al F or ce (k N ) 1st Test (6% Drift) 2nd Test (Envelope) 3.6 1 1 = +0.06 2

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-0 0.01 0.02 0.03 0.04 0.05 Strain Gauge on Strand (%)

0 200 400 600 800 1000 1200 1400 1600 1800 2000 A xi al S tr es s( M Pa ) ks fpu=1874 MPa 3.7 --6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 2400 2700 3000 3300 3600 3900 4200 St ra nd F or ce (k N ) 1st Test 2nd Test Specimen 1 Specimen 2 3.8

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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 5 10 15 20 G ap O pe ni ng (m m ) Segment 1 Segment 2 1st Test 2nd Test 3.9 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 5 10 15 20 G ap O pe ni ng (m m ) Segment 1 Segment 2 1st Test 2nd Test 3.10 2

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-160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L at er al F or ce (k N ) -6 -5 -4 -3 -2 -1Drift (%)0 1 2 3 4 5 6

3.11 2 2 --6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) St ra in (% ) N or m al iz ed S tra in ST 4ST 3 ST 2 W E N S _ST2 ST 4 ST3 ST1 0.76 1 2 0.5 0.6 0.7 0.8 3.12 2 2

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-160 -120 -80 -40 0 40 80 120 160 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L at er al F or ce (k N )

Specimen 1 2nd Test Specimen 2 2nd Test

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--20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6% FS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5% FS Model Test -80 -40 0 40 80 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 3.0% FS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 4.0% FS Model Test -130 -65 0 65 130 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 5.0% FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 6.0% FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (g) Test Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (a) FS Model FS Model 3.14 (FS Model) 1 2

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Drift (%) 0 3 6 9 12 15 El as tic S tif fn es s ( kN /m m ) 0.9 1.5 ₂ 3 4 5 FS Model SDFS Model Test 0.6 ₆ 3.15 1 2 Drift (%) 0 1 2 3 4 5 In el as tic S tif fn es s ( kN -m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 6 3.16 1 2

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Drift (%) 0 5000 10000 15000 20000 H ys te re tic E ne rg y (k N -m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 3.17 1 2 Drift (%) 0 5 10 15 20 25 Y ie ld D is pl ac em en t ( m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 6 3.18 1 2

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Drift (%) 0 40 80 120 160 200 240 Y ie ld F or ce (k N ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 6 3.19 1 2

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6% FS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5% FS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 3.0% FS Model Test -60 -30 0 30 60 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (c) Drift 2.0% FS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 4.0% FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 5.0% FS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (g) Test Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (a) FS Model FS Model 3.20 (FS Model) 2 2

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Drift (%) 0 3 6 9 12 15 El as tic S tif fn es s ( kN /m m ) 0.9 1.5 2 3 4 5 0.6 FS Model SDFS Model Test 3.21 2 2 Drift (%) 0 1 2 3 4 5 In el as tic S tif fn es s ( kN /m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 3.22 2 2

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Drift (%) 0 5000 10000 15000 20000 H ys te re tic E ne rg y (k N -m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 3.23 2 2 Drift (%) 0 5 10 15 20 25 Y ie ld D is pl ac em en t ( m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 3.24 2 2

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Drift (%) 0 40 80 120 160 200 240 Y ie ld D is pl ac em en t ( m m ) 0.9 1.5 2 3 4 5 FS Model SDFS Model Test 3.25 2 2

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6% SDFS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5% SDFS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 3.0% SDFS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 4.0% SDFS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 5.0% SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 6.0% SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (g) Test Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (a) FS Model FS Model 3.26 (SDFS Model) 1 2 ( )

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-20 -10 0 10 20 Lateral Displacement (mm) -160 -80 0 80 160 La te ra l F or ce (k N ) (a) Drift 0.6% SDFS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -160 -80 0 80 160 La te ra l F or ce (k N ) (b) Drift 1.5% SDFS Model Test -80 -40 0 40 80 Lateral Displacement (mm) -160 -80 0 80 160 La te ra l F or ce (k N ) (c) Drift 3.0% SDFS Model Test -120 -60 0 60 120 Lateral Displacement (mm) -160 -80 0 80 160 La te ra l F or ce (k N ) (d) Drift 4.0% SDFS Model Test -130 -65 0 65 130 Lateral Displacement (mm) -160 -800 80 160 La te ra l F or ce (k N ) (e) Drift 5.0% SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -240 -160-80 0 80 160 240 La te ra l F or ce (k N ) (f) Drift 6.0% SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -240 -160-80 0 80 160 240 La te ra l F or ce (k N ) (g) Test Test -150 -100 -50 0 50 100 150 Lateral Displacement (mm) -240 -160-80 0 80 160 240 La te ra l F or ce (k N ) (a) FS Model FS Model 3.27 (SDFS Model) 1 2 ( )

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-20 -10 0 10 20 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (a) Drift 0.6% SDFS Model Test -40 -20 0 20 40 Lateral Displacement (mm) -200 -100 0 100 200 La te ra l F or ce (k N ) (b) Drift 1.5% SDFS Model Test -90 -45 0 45 90 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (d) Drift 3.0% SDFS Model Test -60 -30 0 30 60 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (c) Drift 2.0% SDFS Model Test -140 -70 0 70 140 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (e) Drift 4.0% SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (f) Drift 5.0% SDFS Model Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (g) Test Test -160 -80 0 80 160 Lateral Displacement (mm) -250 -125 0 125 250 La te ra l F or ce (k N ) (a) FS Model SDFS Model 3.28 (SDFS Model) 2 2 ( )

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K

_T

/2

K

T

/2

P(t)

U(t)

C

4.1

U(t)

u

_g

(t)

u

_g

(t)

K

_T

/2

K

_T

/2

u

_g

(t)

C

4.2

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0 10 20 30 Time (sec) -0.3 0 0.3 A ss el er at io n (g )

(a) Loma Prieta: Anderson Dam

0 10 20 30 Time (sec) -0.6 -0.3 0 0.3 0.6 A ss el er at io n (g )

(b) Loma Prieta: Saratoga

0 10 20 30 40 Time (sec) -0.3 0 0.3 A ss el er at io n (g )

(c) Landers: Joshua Tree

0 10 20 30 Time (sec) -0.6 -0.3 0 0.3 0.6 A ss el er at io n (g ) (d) Landers: Coolwater 0 10 20 30 Time (sec) -0.6 -0.3 0 0.3 0.6 A ss el er at io n (g )

(e) Northridge: Beverly Hills

0 10 20 30 Time (sec) -0.6 -0.3 0 0.3 0.6 A ss el er at io n (g )

(f) Northridge: Castsic Old Ridge

0 10 20 30 Time (sec) -0.3 0 0.3 A ss el er at io n (g ) (g) Chi-Chi: TCU034 0 20 40 60 Time (sec) -0.3 0 0.3 A ss el er at io n (g ) (h) Chi-Chi: TCU039 4.3 8

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0 0.5 1 1.5 2 2.5 3 Period (sec) 0 1 2 3 4 5 Sp ec tr al A cc el er at io n (g )

(a) Elastic Acceleration Response Spectra

ATC 32 Soil Type C M=7.25± 0.25, PGA=0.7g Mean of 8 Scaled Records

0 0.5 1 1.5 2 2.5 3 Period (sec) 0 50 100 150 200 250 Sp ec tr al D is pl ac em en t ( cm )

(b) Elastic Displacement Response Spectra

ATC 32 Soil Type C M=7.25± 0.25, PGA=0.7g Mean of 8 Scaled Records

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0 100 200 300 400 500 600 700 800 900 Lateral Displacement (mm) 0 2 4 6 8 La te ra l F or ce (M N ) K_e= 56 kN/mm Kp(FS Model)= 2.2 kN/mm Kp(SDFS Model)= 20 kN/mm Test FS Model SDFS Model 4.5 1