預力鋼梁與鋼筋混凝土柱自行復位接頭之耐震行為研究 · i...

I

Seismic Behavior of Self-centering Connections with a Reinforced Concrete Column and Post-tensioned Steel Beams

StudentJ. H.Chen

AdvisorDr. 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 Science

in

Civil Engineering

September 2005

Hsinchu, Taiwan, Republic of China

I

(1)

(2)

0.04 (3) 0.05

(ABAQUS)

II

Seismic Behavior of Self-centering Connections with a Reinforced

Concrete Column and Post-tensioned Steel Beams StudentJ. H. Chen AdvisorDr. C. C. Chou

Institude of Civil Engineering

National Chiao Tung University

Abstract

The seismic performance of post-tensioned steel connections for moment-resisting

frames was ewamined experimentally and analytically. Cyclic tests were conducted on three

full-scale subassemblies, which had two steel beams post-tensioned to a reinforced concrete

column (RCS) with high-strength strands to provide recentering response. Reduced flange

plates (RFPs) welded to the column and bolted to the beam flange were used to incrase the

dissipation of energy. Test results indicated that (1) the proposed buckling-restrained RFP was

effective in dissipating energy in axial tension and compression, (2) the subassemblies could

reach an interstory drift of 4% without strength degradation, and (3) buckling of the beam

occurred at an interstory drift of 5%, causing a loss of the strand force, the recentering

response, and the moment capacity. A general-purpose nonlinear finite element analysis

program (ABAQUS) was used to perform a correlation study. The behavior of the steel beam

under both post-tensioning and flexural loadings was described based on the experimental

investigation and finite element analysis.

III

DSI

IV

.

.

.

.

..1

1.1 .1

1.2 .2

1.3 .3

1.4 .3

1.5 .4

..5

2.1 .5

2.2 .5

2.2.1 ..5

2.2.2 10

2.2.3 13

2.2.4 15

2.2.5 15

2.3 ...16

2.3.1 117

2.3.2 2 ...18

V

2.3.3 318

2.3.4 419

2.3.5 519

2.4 ...20

2.5 ...21

23

3.1 .23

3.2 .23

3.3 1 24

3.3.1 24

3.3.2 25

3.3.3 28

3.4 2 29

3.4.1 29

3.4.2 30

3.4.3 32

3.5 3 32

3.5.1 32

3.5.2 33

3.5.3 35

3.6 4 36

3.6.1 36

3.6.2 37

3.6.3 38

3.7 5 39

VI

3.7.1 39

3.7.2 40

3.7.3 41

42

4.1 ... 42

4.2 .. .42

4.3 ...44

4.4 45

47

5.1 ...47

5.2 ...49

..50

VII

2.1 .53

2.2 .53

2.3 .54

2.4 .54

2.5 .55

2.6 .55

2.7 .55

3.1 .56

3.2 .56

3.3 .57

4.1 .58

4.2 .59

VIII

1.1 (Chou & Uang 2002) ..60

1.2 RCS(CourtesyDeierlein 1997) ..60

1.3 ....61

2.1 .62

2.2 ..63

2.3 -64

2.4 .65

2.5 .65

2.6 .66

2.7 .66

2.8 .67

2.9 1 .68

2.10 2 .69

2.11 3 70

2.12 4 .71

2.13 5 .72

2.14 .73

2.15 74

2.16 -.75

2.17 -75

2.18 76

2.19 .76

2.20 1 .78

2.21 2 .80

IX

2.22 3 .82

2.23 4 .84

2.24 5 .86

2.25 .87

3.1 1 88

3.2 89

3.3 1 89

3.4 90

3.5 1 90

3.6 1 91

3.7 92

3.8 1 93

3.9 1 93

3.10 194

3.11 94

3.12 95

3.13 195

3.14 196

3.15 97

3.16 198

3.17 199

3.18 1(g = 0.01 rad) 100

3.19 1 100

3.20 2 101

3.21 2 102

X

3.22 2 102

3.23 2 103

3.24 2 104

3.25 2 104

3.26 2 105

3.27 2 106

3.28 2 107

3.29 2 108

3.30 2(g = 0.01 rad) 109

3.31 2 109

3.32 3 110

3.33 3 111

3.34 3 111

3.35 3 112

3.36 3 112

3.37 3 113

3.38 3 114

3.39 3 115

3.40 3 116

3.41 3 117

3.42 3 117

3.43 4 118

3.44 4 119

3.45 4 119

3.46 4 120

XI

3.47 4 120

3.48 4 121

3.49 4 121

3.50 4 122

3.51 4 123

3.52 4 124

3.53 4 125

3.54 4 125

3.55 5 126

3.56 5 127

3.57 5 127

3.58 5 128

3.59 128

3.60 5 129

3.61 5 129

3.62 5 130

3.63 5 131

3.64 5 132

3.65 5 133

4.1 4134

4.2 4134

4.3 135

4.4 4 136

4.5 4Mises136

4.6 4 Mises137

XII

4.7 4138

4.8 4139

4.9 140

4.10 141

4.11 -142

4.12 1 143

4.13 2 143

4.14 3 144

4.15 4 144

4.16 5 145

4.17 145

4.18 4 146

4.19 147

4.20 148

4.21 149

4.22 150

4.23 151

4.24 151

XIII

3.1 1152

3.2 1 3152

3.3 4 5153

3.4 2 153

3.5 1154

3.6 1154

3.7 1155

3.8 1155

3.9 1 ( = 0.005 rad) 156

3.10 1 ( = 0.03 rad) 156

3.11 1 ( = 0.03 rad) 157

3.12 1 157

3.13 1( = 0.04 rad) 158

3.14 1 ( = 0.04 rad)158

3.15 2 159

3.16 2 ( = 0.005 rad) 159

3.17 2( = 0.01 rad)160

3.18 2( = 0.05 rad) 160

3.19 2 0.05161

3.20 3 162

3.21 3 162

3.22 3( = 0.03 rad)163

3.23 3 ( = 0.04 rad) 163

3.24 3(2nd = 0.04 rad)164

XIV

3.25 4 164

3.26 4( = 0.03 rad) 165

3.27 4( = 0.04 rad) 165

3.28 4( = 0.04 rad) 166

3.29 4 ( = 0.05 rad) 166

3.30 4( = 0.05 rad) 167

3.31 5 167

3.32 5( = 0.03 rad) 168

3.33 5( = 0.04 rad) 168

3.34 5 ( = 0.04 rad, 1st Test) 169

3.35 5( = 0.04 rad, 2nd Test) 169

1

1.1

(Chou and Chen 2005, Hewes and Priestley 2002)

(Englekirk 1996, Cheok and Stone 1994, Cheok and Lew 1993,

Priestley and Tao 1993)

-

1988 PRESSS (PREcast Seismic

Structural System) 1990 NSF (National Science

Foundation)

60 m (Watanabe et al. 2000)

()

(Priestley and MacRae 1996, Pampanin et al. 1999)

()

1999

2

(Priestley 1996, Nakaki et al. 1999, Pampanin et al. 1999)

2002

39 (Englekirk 2002)

(Chou and Uang 2002)( 1.1)

(

)

1.2

(Ricles et al. 2001, 2002,

Christopoulos et al. 2002, Chou et al. 2004, 2005, Garlock et al. 2005,)

Ricles et al. (2001, 2002)

0.03

(1)()

(2)

Christopoulos et al. (2002)

H

(1)

(2)

0.04

3

(Chou et al. 2004)

0.05

(Chou et al. 2005)

1.3

(Deierlein and Noguch 2004)

( 1.2 )

1.4

1.3

[ 1.3 (a)][ 1.3

(b)][ 1.3 (c)]

4

ABAQUS(2003)

1.5

5

2.1

1 2

0.01 3

0.02 4 5

0.03

2.22.3

2.4 2.5

2.2

2.2.1

M g 2.1

7 [ 2.1(a)][

2.1(b)] Md[ 2.1(c)]

( 1) 2

My 3

4 5 6 2.2(a)

6

LR in

( ) =RL

s

inSTin dxxAE

TN0

(2.1)

NST( 2.2 NST = 4)

Es(= 200 GPa)A(x)

Tu,in

Tl,in Tin f

es

inSTf AE

TN= (2.2)

Ae

2.2(b) C

inSTd

xt

fs TNdAdxEC t

c

=

= 2 (2.3)

Md()

( )[ ]RtRtind

xt

fs

RR

RtR

d

x linluinut

fs

RdSTdd

tdTdT2dAdxE

tTtdCdTdTxdAdxE

MMM

t

c

t

c

++

=

+

++

=

+=

2

,,

,,

2

22222

(2.4)

tRdtdu

dl

TRCR(2.1)in2.32.3(a)

A36 2.3(a)

y u

Am Py Pu

mRymyy btAP == (2.5)

mRumuu btAP == (2.6)

7

bm

2.3(b)

x b(x)

( ) ( )( ) cbaxcbBxb

bcxccxbxbcxcxRbRxb

R

R

m

+++=++=

+=60tan2

2)2()( 22

(2.7a)

mm98bb

RRc

mmbBb

mma

mR

RR

=

=

=

=

=

22

2

17460cot2

80

(2.7b)

R x ab c

P R

( ) ( ) RR txbPx

= (2.8)

(2.8) 2.3(a)

R(x)

P

( ) ( ) ( )

( ) ( )

+

++

+=

===

++

+

+

++++

++

c

c

cba

bcR

bc

cRmsR

cba

c-sR

cba

cRcba

c R

dxB

dxcxb

dxxRbREt

P

dxEtxb

PdxE

xdxx

160tan2

122

122

(2.9)

E Es Ep 2.3(c)

(2.9)(2.1) in

CRTR

2.2(c)

g

Pampania et al. (2000) Christopoulos et al. (2002)

8

1. c

2.2(c)

( )

STSTSTSTb

STST

ST

gtSTinSTSTinSTST AEANA

ANL

cdNNTNTNTNT

+

+=+= 12

(2.10)

N( N = 1 N =

2)g LSTAST

AbEST(= 195 GPa)c

max

+=

+= d

dt

gd

t

gxma M

Md

cd

c

(2.11)

d Md

t

fd d

2= (2.12)

(= M/Md) C

dAMM

dxEdA

dxEdA

cxEdAC d

dt

gsd

t

gsxmasx

+=

+===

c

0

c

0

c

0

c

0

(2.13)

xx g

gRtint ctd

++=

2 (2.14)

gRinc ct

++=

2 (2.15)

tc 2.3(c)

- TR

CR

2. c

= 1 TST C TR CR

(2.10)(2.13)(2.14)(2.15)

9

RSTR TTCC +=+ (2.16)

c c

3.

RST

RR

RtR

tST

MM

ctCctdTcCcd

TM

+=

++

++

+

=

2232

2 (2.17)

MMd (2.11)

(1)(3) g

2.1 23 4

2.1 MR

MST

MR g 2.1(b)

KR,2KR,3 KR,4

2,

1,2,

1,2,

1,2,R,2

g

RR

gg

RR MMMMK

=

= (2.18)

2,3,

2,3,3

gg

RRR,

MMK

= (2.19)

3,4,

3,4,4

gg

RRR,

MMK

= (2.20)

MR,1MR,2MR,3MR,4g,1g,2g,3g,4 2.1(b)

1 2 3 4 4

5 MR,5 g,5

R,2

2,4,5, 2 K

M Rgg = (2.21)

10

2,4,5, 2 RRR MMM = (2.22)

6 g,6 MR,6

)( 2,3,5,6, gggg = (2.23)

)( 2356 RRRR MMMM = (2.24)

7 g,7 0

Mc,R KR,7 3

4

47 R,R, KK = (2.25)

7,6,,,, Rg6R7RRc KMMM == (2.26)

[ 2.1(c)](2.26)Md,ST

0,, + STdRc MM (2.27)

Mc,R MR,4

Md,ST

STdR MM ,4, (2.28)

2.2.2

2.4

Kc

KPZ Kb KER 2.5

2

6

=

HH

LL

HEI

K cc

bcracc (2.29)

11

HHc

Lb Lc EIcrac

ACI 318M/318RM (2002) 10.11.1

gccrac IEEI 7.0= (2.30)

IgEc

PZ

=

==

cb

c

bcvc

b

cbcvc

c

cvPZ

c

PZPZ

HLL

dAGM

Vd

MAG

GAV

G

295.02

95.021

(2.31)

VcGcAcv

PZ

=

= c

c

b

c

b

cc

b

bcvc

bc

c

b

c

bPZPZ LH

dLL

HLL

d2

AGM

LHd

LL 22 2

95.0 (2.32)

KPZ

( )

=

==

c

b

c

b

cc

b

b

cvc

cPZ

b

PZ

bPZ

Hd

LL

HLL

d2

AGL

MMK

2

2295.0

(2.33)

Ricles et al. (2002)

Kb

2

3

b

cbsb L

LIEK = (2.34)

Ib KER

STd

RdbER M

MKK

,

,= (2.35)

Md,R Md,ST(2.4)

12

2.4 K1

ERbPZc KKKK

K

+++

=111

11 (2.36)

M

( )gtT

t

STSTb

STST

ST

gtSTSTST

tST

Kcd

ANAAN

LNcd

AEN

cd

TNM

,S21

2

2

=

+

=

=

(2.37)

0.015 (

2.6)(2.37)

gtSTsSTSTb

STST

ST

gsSTSTSTsST KdANA

ANL

NdAENTdNM

,1 =

+

== (2.38)

ds

KST

tSTb

ST

KK

K

,

111

+= (2.39)

1 2 K2

ERSTPZc KKKK

K

+++

=111

12 (2.40)

2 3

KPR1

2.2(c)

12,1, PRgcRtR KdFdFM =+= (2.41)

FR,t FR,c

d1 d2

13

2.3(c)

apgapttR KdKF 1, == (2.42)

aegaeccR KdKF 2, == (2.43)

tcKap

Kae(2.42)(2.43)

(2.41)

( )1

22

212,1,

PRg

aeapgcRtR

K

dKdKdFdFM

=

+=+= (2.44)

2.4 K3

1

3 1111

PRSTPZc KKKK

K

+++

= (2.45)

(2.41)

apgapccR KdKF 2, == (2.46)

( ) 222212,1, PRgapgcRtR KddKdFdFM =+=+= (2.47) 2.4 K4

2

4 1111

PRSTPZc KKKK

K

+++

= (2.48)

2.4 4

5 6 K5 K6 K2

K3 K7 K4

2.2.3

14

ASTM A 572 Gr. 50

TST

Mc

( ) ( )( )

f

STeyc y

xIxA

TxM )( = (2.49)

( ) ( ) bfrfr AxbtxA += 2 (2.50)

( ) ( ) ( )[ ] bbfrbfr IdtdxbxI ++= 332121 (2.51)

A(x)I(x)yf

ye(= 1.1y)tfrbfr(x)

2.7 Mc Mdm

Mdm Mc

tfr bfr

(2.50)(2.51)

Mc Mdm(2.49)

( ) ( )xItyM

xAT frfdmST

ye

)( ++ (2.52)

fffrfr

STSTye tbtb

TAT

+=

min

(2.53)

2.7 A

M1 B M2

M1M2

( )

=

11

11AAy

xIMbf

(2.54)

RMM = 2 (2.55)

A1

15

2.2.4

TSTMdi

1. c c=c/c

2. i i y

y Es i

3. Ti

Ti TST

4. 1 3 c

5. 4Mi

6. 5Mi

Md

7. 1 6 6

2.2.5

(RFP)[ 2.2(c)g]

1. RFPg =0.03 0.1

Mnp RFP MR

MnpLR RFP(450 mm) tR =

8 mm

16

2. bR

RRRt

npR Fttd

Mb

)( +

(2.56)

FR A36 0.1[ 2.3(a)]

bR 120 mm

3. LR[2.3 (b)]RFP-[2.3 (c)]

4. g =0.03RFP(2.14)(2.15) 2.3(c)

5. RFP MR

Md,ST

2.3

650650 mm28

350 kg/cm2 12#11 Grade 60

2.8(a) Response (2000)

[ 2.8(b)] Mc =1526 kN-m A572 Gr. 50 H

(5002001016) Mnp = 723 kN-m

npc MM = 2.11(=bf /2tf) 6.25

(=h /tw) 50 AISC (2002)

48.012.1

33.2 =ys

w

yb

u

FEth

PP

(2.57)

Pu 1650 kN

2.9 2.13 1

2

17

3

4

5

AISC(2002)

2.1

2.3.1 1

Md,ST 0.42

Mnp Md,R 0.12 Mnp 2.2.1

1300 kN 1 4 13 mm ASTM A416 Grade 270

0.44 Fpu Fpu

(= 1860 MPa) A36 12 mm

2.9(d)

2.14(a)

0.01

2.2.3

0.01 Mc Mdm[ 2.15(a)]

750 mm (= 1.5 db) 0.03

(2.10)(2.17)( 2.2)(2.52)(2.53)

tfr = 8.1 mm 9 mm

2.2.2 2.3g

t 2.4cbePZ

18

2.3.2 2

Md,ST 0.3

Mnp Md,R 0.07 Mnp 2.2.1

975 kN 2 7 13 mm ASTM A416 Grade

270 14 0.38 Fpu

A36 8 mm

2.10(d)

2.14(b) 0.01

2.2.3 Mc Mdm

2.15(b) 630 mm (= 1.25

db) 0.03(2.10)(2.17)

( 2.2) 2.2.2 2.3

0.01 0.0168

2.3.3 3

Md,ST 0.42

Mnp Md,R 0.12 Mnp 2.2.1


270 16 0.44 Fpu

A36 12 mm

2.11(d) 2.14(c)

0.02

2.2.3 Mc Mdm

2.15(c) 1000 mm (= 2 db) 0.03

19

(2.10)(2.17)( 2.2)

2.3 2.4

2.3.4 4

Md,ST

0.3 Mnp Md,R 0.09 Mnp 2.2.1


270 14 0.38 Fpu

A36 8 mm 6 mm

2.12

2.14(d) 0.03

2.2.3

McMdm 2.15(d)

750 mm (= 1.5 db) 0.03(2.10)(2.17)

( 2.2) 2.2.2

2.3 0.03 0.0357

( 2.4)

2.3.5 5

Md,ST 0.3

Mnp Md,R 0.1 Mnp

2.2.1 975 kN 5 4 13

mm ASTM A416 Grade 270 16

0.33 Fpu A36 8 mm

6 mm 2.13

20

2.14(c)

0.03 AISC(2002)

2.2.3 Mc Md

2.15(e) 1000 mm (= 2 db)

0.03(2.10)(2.17)(

2.2) 2.2.2 2.3

0.036( 2.4)

2.4

A572 Gr. 50

A36

( 2.5)

2.16

2.6 28

fc = 34.5 MPa 3

3

2.7

7ASTM

A416 Grad 270 13 mm Fpu = 1860 MPa 2.17

7 -(CSDCV

1999)

sss f 1965000086.0 = (2.58)

007.0276.018600086.0

=

sss f

(2.59)

21

2.5

2.18 1

2.19

1 5 2.20 2.24

2

g

total PZ

c b

g

1. PZ

Uang Bonded (1996)

( 2.25)

( )4322

2 +=

abba (2.60)

34 a b

+=

2c

bb

bPZd

LHd

L

(2.61)

Lb(2675 mm)H

22

(3480 mm)dc(650 mm)

2. c

( )

=

Hd

db

bc 121

(2.62)

1 2 2.25

+=

2c

bccd

L (2.63)

3. b

=

LL

EIFL b

b 3

3

(2.64)

F

4. g

g

bgg L = (2.65)

(1)( S)

(2)( R )

23

3.1

3.2

3.3 3.7

3.2

1 2

3 4 5

1 2

3.1

135 90

( 3.2)( 3.3) 28

( 3.4) 4

( 3.5) T(3.1)

jA

TP = (3.1)

24

Aj(= 40.1cm2) T

(3.1)

3.3 1

3.3.1

1

( 3.6) 3.7

= 0.00375

= 0.005

1 2 ( 3.8)

( 3.9)

= 0.0075 25 cm

0.1 mm

= 0.01

150 mm 42 cm

0.3 mm

= 0.02

2

0.7 mm = 0.03 1 2

( 3.10) 3.11

0.04 1 2

0.8 mm ( 3.12) =

25

0.04 1( 3.13)

1

0.05 1 ( 3.14) 1

1( 3.1)

3.3.2

3.1 1 2 M

Mnp

0.04

0.05

( 3.13 3.14) 3.2

KTE(= 81,000 kN-m) 0.005

0.04

839 kN-m( = 1.12 Mnp)

3.3

3.4

95% 3.3

0.04 1200 kN

1150 kN 3.5

2.2(2.10)

2.2

26

()

0.04

(P4%/bPy) 3.1

3.6(a) 1

2.20(a) L1 L2(2.60) 400

kN-m

3.6(b) c(2.62)

2.5

3.7(a)

1

3.7(b) 0.01

L3 L4[ 2.20(b)]

( 3.8)

0.02

( 2.2)

g L3 L4[ 2.20(b)]

27

3.9 3.2

( 3.10)

TEg K

M= (3.2)

1 1300 kN

1205 kN

3.11 1 = 0.05

0.8

3.12

1

L9 L10 [ 2.20(b)]

3.13

0.03

15.2 mm()

drc 29 mm drt 497 mm(3.3)

t c:

grcc

grtt

d

d

=

=

- (3.3)

3.13

28

0.01

3.14

0.075 (

1 )( 2 )

3.3

3.3.3

3.15 2

3.16 (S11S13

S14)(S15) 0.03

3.17 1.5

(450 mm)

2.2

3.18

0.01

3.19 0.02

0.03 (

0.038) 1.5( 2.2)

29

0.034 = 0.029 (= 1.5y)

( 3.13)

3.4 2

3.4.1

2 1

( 3.15

) = 0.00375

= 0.005 1 2

( 3.16)

= 0.0075

25 cm 0.1 mm

0.1 mm

= 0.01

( 3.17) 0.1 mm

= 0.02

= 0.03 1 2

0.04 1 2

0.05 2 1

( 3.18) 1 2

( 3.19)

30

3.4.2

3.20 1 2

0.02

3.2 KTE 71,700

kN-m 0.04 696 kN-m( = 0.93

Mnp) 3.21 1

3.21( 3.4) 2

(956 kN)(8 mm) 1

1

8% 0.03

( 3.21) 957 kN 835 kN 3.22

2.2

(2.10) 2.2

3.23(a) 2

3.23 (b) c 2

3.7(a)

1

[ 3.7(b)]

1

(

31

3.24) 1

0.015

(3.2) g

( 3.25)

2 975 kN

957 kN

3.11 2 = 0.005

= 0.05

10% 3.12 2

1

3.26

0.03 16.7 mm

() drc = 4 mm

drt = 514 mm(3.3)

3.26

32

3.4.3

3.27

2 3.28

(S17) 0.03

3.29

2.2

3.30

0.02

3.31

0.005

2

0.02 2

( 3.2) Garlock et al. (2005)

0.05 = 0.12 (= 6y)

3.5 3

3.5.1

3 10 mm

12 mm

33

( 3.20)

3.21 =

0.005

= 0.0075

21 cm 0.1 mm

= 0.01

0.1 mm

= 0.02 1

= 0.03

( 3.22) 0.04( 3.23)

2

0.04

AISC(2002)

0.04 2( 3.24)

3.5.2

3.32 1 2

0.04

3.2 KTE 87,807 kN-m

0.04 916 kN-m( = 1.2 Mnp)

3.33

34

3(1286 kN)

1 1

0.03

( 3.33) 1286 kN 1198

kN 3.34 2.2

(2.10)

() 2.2

()

3.7(a) 1

3.7(b)

3.35

0.015

L3L4(3.2)

3.36

3 1300 kN

1286 kN

3.11 3 = 0.03

3

0.04 7% 3

3.12

3.32

35

3.37 0.03 15.3

mm

drc = 31 mm drt = 499 mm(3.3)

() 3.37

3.5.3

3.38

[

3.38 (h)]

2 3.39

2

S15 0.03

3.40 0.03

3.41

0.03

3.42 0.03

36

3.6 4

3.6.1

4 6 mm 8 mm

( 3.25) = 0.005

28 mm 0.1 mm

= 0.0075 = 0.01

0.2 mm

= 0.02

4 mm

= 0.03

8 mm

( 3.26) 0.04 2

0.04 ( 3.27) 2

1

( 3.28)

0.05 2 1

2( 3.29)

( 3.30)

37

3.6.2

3.43 1 2

3.2 KTE 74,700

kN-m 0.04 644 kN-m( = 0.85

Mnp) 3.44

( 3.4) 230 kN-m 0.04

186 kN-m 977 kN 871 kN 11% 3.45

3.46 c 2

3.7(a)

3.7(b) 0.01

0.04

73%

3.47

0.015

(3.2) g

( 3.48)

4 975 kN 971 kN

3.11 0.05

10% 4

38

3.12

4 8 mm 1

3

( 2.14)

0.04

3.49

0.03 15.6 mm

drc = 29 mm drt =

497 mm(3.3)

3.6.3

3.50

L1 L2

3.50(b)

2 3.51 1.5

3.52 750 mm

450 mm

3.53

39

0.03

3.54 0.04

3.7 5

3.7.1

5 6 mm 8 mm

( 3.31) = 0.00375

= 0.005

42 cm 0.1 mm = 0.0075

= 0.01

0.2 mm

= 0.02

= 0.03

( 3.32) 0.04

4 2 (

3.33) 0.04(

3.34)

0.04 1( 3.35)

40

3.7.2 5

3.55 1 2

KTE

80,400 kN-m 0.04 723

kN-m( = 1 Mnp) 3.56

1 957 kN 926 kN 2

954 kN

2 3.56

3.4 3.57

3.58

c 2

3.7

3.59

1 3 0.02

2

(3.2) g

( 3.60)

5 975 kN

957 kN

3.11 5 = 0.04

2.2 fp/y = 0.85

41

( 2.2)

3.1

0.04 MR

Md,ST

3.61 0.03 15.1

mm

drc = 29 mm drt = 497 mm(3.3)

3.7.3

3.62

3.62(b)

[ 3.62(h)]

1 3.63

3.64

3.65

0.03

42

4.1

Hibbit,

Karlsson and Sorensen ABAQUS(2003)

4.2

4.3

4.4 4.5

4.2

4(

4.1)

4.2 4

4(S4R) 5

5

203,000 MPa 0.3

A36 ( 4.3)

(Isotropic Hardening)

43

si

sb

binST

STST

STinsi EA

LTNEALT

+= (4.1)

TinLSTLbAST

AbESTEs

NST

(Contact)

(Rough)

2.2 A36

( 4.3) 4

4.4

330 kN

305 kN 8 %(Mises Stress)

( 4.5)

(

4.6) 11S 4.7(a)

340 MPa Fy = 318 MPa

( 4.8)

11S

8%

44

bm tR R 4.1 4.9

810 mm 80 mm

220 mm 180 mm

R

R 60 mm127 mm 180

mm 4.9

(Pyt,R)(bmtR)(Py)

(=Pyt,R/Py) (Pu,R) (Pu)

(=Pu,R/Pu) 4.10 bm

1 bm

=

4.3

4.11 127 mm 120 mm

1.08 2.2

4.12 4.16

45

(Isotropic Hardening)

4.2

4.17

LFRP ( 4.2)

4.4

8

(C3D8R) 3

3

(Beam) 3

Ec 29,370 MPa ( = 'cf57000 ) 'cf 34.5 MPa

0.2

DSI

195,000MPa 0.3

46

(Hard)

(Rough)

(Frictionless)

4.18 4

4.19(a)

4.19(b) 4%

4.22

410 MPa

4.20

4.21

ABAQUS

4.23

4.24

47

5.1

650650 H5002001016

1 2

1.25db 2db( db)

1 0.04

2 4 0.020.03 0.04

5 0.04

0.04

1. 2 4 5-

2

4 5 0.04

( 3.12) 1.5% 1

3

( 3.1) 0.04

2.3%

2. 5

16 4 14

48

( 3.1) 4 5 971 kN 957 kN

318 kN-m 311 kN-m

3. 2 4 5

1.25db1.5db 2db

2.2 1 1.5db 2

1.25db 1300 kN 2 975 kN 1

0.02

2.2 0.03

1.5y 1 2

0.01 0.03

1.5y 2

0.04 6

4.

( 3.3)

5.

R bm( 4.10)

6. ABAQUS

49

( 4.21)

5.2

1.

2.

50

1. AISC. (2002). Seismic provisions for structural steel buildings. AISC, Chicago. IL.

2. ACI. (2002). Building Code and Commentary. ACI 318M-02/318RM-02.

3. Cheok, G. and Lew, H. (1993). Model precast cncrete beam-to-column connections

subject to cyclic loading. PCI J., 38 (4), 80-92.

4. Cheok, G. and Stone, W. (1994). Performance of 1/3 scale model precast concrete

beam-column connections subjected to cyclic inelastic loadsReport No. 4, Rep. No.

NISTIR 5436, National Institute of Standards and Technology, NIST, Gaithersburg, Md.

5. Chou, C. C. and Uang, C. M. (2002). Cyclic performance of a type of steel beam to

steel-encased reinforced concrete column moment connection. J. Constructional Steel

Research, 58, 637-663.

6. Christopoulos, C., Filiatrault, A., Uang, C. M., and Folz, B. (2002). Posttensioned energy

dissipating connections for moment-resisting steel frames. J. Struct. Eng., ASCE, 128(9),

11111120.

7. Christopoulos, C., Filiatrault, A., and Folz, B. (2002). Seismic response of self-centring

hysteretic SDOF systems. Earthquake Eng. Struct. Dyn., 31, 11311150.

8. Chou, C. C., Chen, J. H., Chen, Y. C., (2004) Performance evaluation of posttensioned

steel connections for moment-resisting frames 6th Korea-Japan-Taiwan Joint Seminar on

Earthquake Engineering for Building Structures, Taiwan.

9. Chou, C. C. and Chen, Y. H. (2005). Cyclic tests of post-tensioned precast CFT segmental

bridge columns with unbonded strands. Earthguake Eng. Struct. Dyn. (Accepted)

10. Chou, C. C., Chen, J. H., Chen, Y. C., and Tsai, K. C. (2005). Experimental and

Analytical Studies of Self-Centering Steel Connections. US-Taiwan Workshop on

Self-Centering Structural Systems, NCREE Report No:05-004, Taipei, Taiwan.

11.Chou, C. C., Tsai, K. C., Chen, J. H., Chen, Y. C., and Chuang, S. C. (2005) Cyclic

Behavior of Post-tensioned Steel Connections with Reduced Flange Plate and Slab. 1st

International Conference on Advances in Experimental Structural Engineering, Nagoya,

Japan.

12.Deierlein, G. G. and Noguchi, H. (2004). Overview of U.S.-Tapan Research on the

Seismic Design of Composite Reinforced Concrete and Steel moment frame Structures. J.

51

Struct. Eng. ASCE, 130(2), 361-367.

13.Englekirk, R. E. (1996). An innovative design solution for precast prestressed concrete

buildings in high seismic zones. PCI J., 41(4), 4453.

14.Englekirk, R. E. (2002). Design-construction of the paramount a 39-story precast

prestressed concrete apartment building. PCI J., 47(4), 5671.

15.Garlock, M., Ricles, J. M., Sause, R. (2005). Experimental studies of full-scale

posttensioned steel connections. J. Struct. Eng., 131(3), 448448.

16.Hews J. T. and Priestley, M. T. N. (2002). Seismic design and performance of precast

concrete segmental bridge columns. Rep. NO. SSRP 2001/25, University of California,

San Diego, La Jella. CA.

17.Nakaki, S. D., Stanton, J. F., and Sritharan, S. (1999). An overview of the PRESSS

five-story precast test building. PCI J., 44(2), 2639.

18.Nishiyama, M., Watanabe, F., and Muaguruma, H. (1991). Seismic performance of

prestressed concrete beam-column joint assemblages. Pacific Conference on Earthquake

Engineering, New Zealand, 217228.

19.Park, R., and Thompson, K. J. (1977). Cyclic load tests on prestressed and partially

prestressed beam-column joints. PCI J., 22(5), 84100.

20.Pampanin, S., Priestley, M. J. N., and Sritharan, S. (1999). Frame direction modeling of

the five-story PRESSS precast test building. Rep. No. SSRP 99/20, University of

California, San Diego, La Jolla, CA.

21.Priestley, M. J. N., and Tao, J. R. (1993). Seismic response of precast prestressed

concrete frames with partially debonded tendons. PCI J., 38(1), 5866.

22.Priestley, M. J. N., and MacRae, G. A. (1996). Seismic tests of precast beam-to-column

joint subassemblages with unbonded tendons. PCI J., 41(1), 6481.

23.Priestley, M. J. N. (1996). The PRESSS program-current status and proposed plans for

phase III. PCI J., 41(2), 2240.

24.Ricles, J. M., Sause, R., Garlock, M. M., and Zhao, C. (2001). Posttensioned

seismic-resistant connections for steel frames. J. Struct. Eng., ASCE, 127(2), 113121.

25.Ricles, J. M., Sause, R., Peng, S. W., and Lu, L. W. (2002). Experimental evaluation of

earthquake resistant posttensioned steel connections. J. Struct. Eng., ASCE, 128(7),

52

850859.

26.Rojas, P., Ricles, J. M., Sause, R. (2005). Seismic performance of post-tensioned steel

moment resisting frames with friction devices. J. Struct. Eng., ASCE, 131(4), 529540.

27.Uang, C. M. and Bonded, D. (1996). Static Cyclic Testing of Pre-Northridge and haunch

repaired Steel moment Connections. SSRP 96/102, University of California, Sau Diego,

CA.

28.Watanabe, F., Okamoto, S., Hiraishi, H. (2000). Development of the Structual design and

construction guideline for high-rise PC buildings Japanese PC project. 12WCEE.

53

2.1

Specimen No. 1 2 3 4 5

Jacket No NO Yes Yes Yes

RFP-to-Column Detail Embedemet Bolt Weld Weld Weld

FRP Length 1.5 db 1.25 db 2 db 1.5 db 2 db

NO. of Strands 16 14 16 14 16

Target Drift (%) 2 2 3 4 4

tR (mm) 12 8 12 8 8

Notedb = 500 mm

2.2

Specimen

No. STdRd

MM

,

, np

d

MM

uST

in

TT

,

np

y

MM

np

R

MM 03.0,

np

ST

MM 03.0,

npMM 03.0

uST

ST

TT

,

03.0, R y

fp

1 0.29 0.54 0.44 0.85 0.5 0.60 1.01 0.63 0.107 1.25

2 0.22 0.37 0.38 0.67 0.32 0.47 0.76 0.56 0.098 0.95

3 0.29 0.54 0.44 0.85 0.5 0.60 1.01 0.63 0.107 1.05

4 0.3 0.39 0.38 0.67 0.32 0.47 0.76 0.56 0.104 0.9

5 0.33 0.40 0.33 0.67 0.32 0.49 0.8 0.52 0.111 0.85

Note R g

fp g = 0.03

54

2.3

Specimen No. 1 2 3 4 5

Kc (kN-m) 748725 748725 748725 748725 748725 KPZ (kN-m) 385711 385711 800749 634737 634737 Kb (kN-m) 115805 115805 115805 115805 115805

KST,t (kN-m) 4253 4158 4253 4158 4253 KST (kN-m) 4102 4014 4102 4014 4102 KER (kN-m) 39374 32425 40532 34742 37058 KPR1 (kN-m) 2225 1736 2225 2051 2051 KPR2 (kN-m) 1487 1678 1487 1561 1561 K1 (kN-m) 96410 93681 111348 104673 105788

K2= K5 (kN-m) 37134 31876 40018 34826 36756 K3= K6 (kN-m) 6174 5623 6225 5959 6045 K4= K7 (kN-m) 5469 5567 5510 5486 5572

2.4

Specimen c (rad) be (rad) PZ (rad) g (rad) t (rad) 1 0.0007 0.0047 0.0014 0.01 0.0168 2 0.0005 0.0033 0.0010 0.01 0.0148 3 0.0008 0.0052 0.0007 0.02 0.0267 4 0.0007 0.0042 0.0008 0.03 0.0357 5 0.0007 0.0045 0.0008 0.03 0.0360

55

2.5

Beam Item Web Flange FRP

Jacket RFP

Grade A572 A572 A572 A36 A36 Thickness (mm) 10 16 9 6 10 8 12

Fy (MPa) 400 393 418 310 290 324 290 Fu (MPa) 517 496 545 431 428 441 434 y (%) 0.202 0.197 0.209 0.155 0.144 0.163 0.146u (%) 18.9 18.1 19.2 21.8 20.7 22.3 21.5

2.6

No. Fy (MPa) Fu (MPa) y (%) u (%) 4 372 448 0.186 20.2 11 398 487 0.199 19.2

2.7

Cylinder NO. 1 2 3 Average 28 Day (MPa) 39 39 38 39

Specimen 1 D.O.T (MPa) 34 35 38 36 Specimen 2 D.O.T (MPa) 38 29 33 32 Specimen 3 D.O.T (MPa) 34 35 39 36 Specimen 4 D.O.T (MPa) 34 34 40 36 Specimen 5 D.O.T (MPa) 37 38 32 36

56

3.1

Specimen

NO. inT

(kN) uin

TT

TEK

(kN-m)

TPK

(kN-m)

dM

(kN-m) npSTd

MM ,

np

d

MM

np

y

MM

yPP

%4 npM

M %4 %4

np

ST

MM

%4

np

R

MM

1 1203 0.41 81000 6270 412 0.45 0.57 0.76 0.43 1.02 0.54 0.48

2 957 0.37 71748 6960 340 0.38 0.47 0.59 0.33 0.96 0.45 0.51

3 1286 0.44 87807 7320 427 0.47 0.59 0.80 0.46 1.27 0.63 0.64

4 971 0.38 74700 4620 318 0.36 0.44 0.63 0.37 0.89 0.47 0.42

5 957 0.33 80400 7800 311 0.35 0.43 0.62 0.39 0.96 0.54 0.42

3.2

2% 3%

Beam 1

g,exp

(0.01 rad)

Beam 2

g,exp

(0.01 rad)

Beam 1

g,exp

(0.01 rad)

Beam 2

g,exp

(0.01 rad)

Specimen g,th (0.01 rad)

+ - + -

g,th

(0.01 rad)

+ - + -

1 1.36 1.07 1.12 1.06 1.12 2.29 1.98 2.03 1.97 2.02

2 1.48 1.24 1.29 1.25 1.30 2.44 2.16 2.20 2.14 2.22

3 1.31 1.18 1.22 1.16 1.26 2.24 2.11 2.14 2.08 2.19

4 1.44 1.31 1.31 1.32 1.32 2.40 2.24 2.24 2.26 2.26

5 1.44 1.29 1.33 1.28 1.33 2.39 2.21 2.25 2.22 2.27

4% 5%

Beam 1

g,exp

(0.01 rad)

Beam 2

g,exp

(0.01 rad)

Beam 1

g,exp

(0.01 rad)

Beam 2

g,exp

(0.01 rad)

Specimen g,th

(0.01 rad)

+ - + -

g,th

(0.01 rad)

+ - + -

1 3.22 2.92 3.09 2.98 2.99 4.16 4.22 4.17 4.43 4.46

2 3.40 3.10 3.14 3.10 3.17 4.36 4.06 4.12 4.06 4.11

3 3.17 3.06 3.06 3.03 3.12 - - - - -

4 3.36 3.19 3.19 3.20 3.21 4.32 4.43 4.39 4.42 4.17

5 3.34 3.15 3.19 3.16 3.21 - - - - -

57

3.3

0.75 % 1 % 2 % 3 % 4 % Specimen

No.

sST,

iST,

MM

sR,

iR,

MM

sST,

iST,

MM

sR,

iR,

MM

sST,

iST,

MM

sR,

iR,

MM

sST,

iST,

MM

sR,

iR,

MM

sST,

iST,

MM

sR,

iR,

MM

1 0.99 0.52 0.96 1.03 0.97 1.16 0.96 1.18 0.95 1.15 2 0.95 0.70 0.87 1.03 0.92 1.16 0.90 1.17 0.87 1.31 3 0.96 0.56 0.91 0.98 0.97 1.13 0.97 1.12 0.97 1.08 4 0.98 0.80 0.93 0.94 1.01 1.10 1.00 1.14 0.99 1.16 5 0.98 0.98 0.89 1.08 0.98 1.17 0.98 1.22 0.97 1.24 Note iST,M =

iR,M =

sST,M =

sR,M =

58

4.1

Specimen bR(mm) R(mm) tR(mm)Elastic Stiffness

(kN/mm) yRyt

PP ,

u

Ru

PP ,

y

Ryc

PP ,

BR50R60T5 50 60 5 468 1.12 1.14 1.13

BR50R127T5 50 120 5 379 1.08 1.06 1.09

BR50R180T5 50 180 5 342 1.07 1.03 1.08

BR120R60T5 120 60 5 690 1.13 1.14 1.14

BR120R127T5 120 120 5 618 1.09 1.06 1.10

BR120R180T5 120 180 5 573 1.07 1.02 1.08

BR150R60tT 150 60 5 794 1.11 1.16 1.12

BR150R127T5 150 120 5 729 1.07 1.10 1.08

BR150R180T5 150 180 5 717 1.05 1.07 1.06

BR50R60T8 50 60 8 590 1.11 1.16 1.12

BR50R127T8 50 120 8 569 1.07 1.09 1.08

BR50R180T8 50 180 8 513 1.05 1.07 1.06

BR120R60T8 120 60 8 1062 1.13 1.13 1.14

BR120R127T8 120 120 8 927 1.09 1.05 1.10

BR120R180T8 120 180 8 860 1.07 1.02 1.08

BR150R60T8 150 60 8 1191 1.12 1.14 1.13

BR150R127T8 150 120 8 1093 1.08 1.06 1.09

BR150R180T8 150 180 8 1075 1.07 1.03 1.08

59

4.2

Name bR

(mm)

R

(mm)

tR (mm)

Tin (kN)

Md,R (kN-m)

MR,0.03 (kN-m) b

FRP

dL

BR50R60T5P975 50 60 5 975 37 542 0.43

BR50R127T5P975 50 127 5 975 30 536 0.38

BR150R127T5P975 150 127 5 975 27 559 0.58

BR150R127T8P975 150 127 8 975 54 597 0.89

BR150R180T8P975 150 180 8 975 49 588 0.82

BR150R127T8P1300 150 127 8 1300 95 673 1.8

BR150R127T12P1300 150 127 12 1300 142 813 2.4

60

1.1 (CourtesyChou & Uang 2002)

1.2 RCS (Courtesy: Deierlein and Noguchi 2004)

61

(a) Welded RFP

(b) Embeded RFP

(c) Bolted RFP

1.3

RFP Beam

FRP

Strands

Jacket

RFP Beam

FRP

Strands

Column

RFP Beam

FRP

Strands

Column

Column

62

M

g

1 2 356

4

7

o

Md,ST

(a) Strands

g1

23 4

567

Md,R

Mc,Ro

KR,2KR,3 KR,4

KR,5

KR,6KR,7

(b) Reduced Flange Plates (RFPs)

1

M

23

4

56

7

MyMd

og

(c) Strands + RFPs

2.1

63

l,in

u,in

dldu

dt

Tu,in

T l,in

LR

fAx

(a) Post-tensioning State

x Tu,in

T l,inV br

CR

TR

xc

2fc

C

VblTl,in

Tu,in

V clM cl

V cuM cu

(b) Before Decompression

g

TR

CR

C

V clM cl

bl

V cuM cu

Tu

Tlx c

Tu

TlV br

(c) Decompression

2.2

64

Strain, St

ress

,

(y, y)(u, u)

Bi-linearApproximation

Es1

Ep1

(a) Stress-Strain Relationship

o

b(x)

60R=127 mm

x

B R(8

10 m

m)

x

a b c -c

b R(2

20 m

m)

b m

LR (b) RFP

Deformation,

Forc

e, P

(y, Py)(u, Pu)

Bi-linearApproximation

Kae1

Kap1

(c) Force Deformation Relationship

2.3-

65

7

K1

K2K3

K4

K5K6

M

K712

3

4

56

o 2.4

LcLc

Hc db

Vc

Vc

Vb

VbV PZ

Lb

2.5

66

0 0.01 0.02 0.03 0.04Gap Opening Angle, g (rad)

0

200

400

Neu

tral A

xis P

ositi

on (m

m)

0.015

2.6

Distance from Column Face, L/db

Mom

ent

Mc (Moment Capacity)

Mdm (Moment Demand)

B A

M1M2

2.7

67

#4 #11

650

650

(a) Column Details and Input Data

0 40 80 120 160Curvature (rad/km)

0

400

800

1200

1600

Mom

ent (

kN-m

)

(b) Moment-curature Relationship

2.8

68

Beam 5002001016

CL

Shear Tab28 mm Bolt

16 mm BoltStrands

B

BRFP 12 mm

Column 650650

A A

Flange Reinforcing Plate

(a) Elevation

RFP 12 mm

Beam 5002001016

Flange Reinforcing Plate 9 mm

28 mm Bolt

16 mm Bolt

Strands 750 650 750

#4 @ 100 mm

Cover Plate

150 mm Hole

CL

205

205

400

(b) Section A-A

Strands

RFPFRP

270

190

Shear Tab

Bolt

A36 RFP 12 mm

650630 630

295

220

120

32 mm Hole

295

LC

(c) Section B-B (d) RFP Detail

2.9 1

69

Column 650650

LC

Shear Tab

A

Symm about

B

A

B

Flange Reinforcing PlateStrands

Shear Tab

Beam 5002001016

LC

16 mm BoltRFP 8 mm

A

25 mm BoltColumn 650650

Vertical Stiffener

(a) Elevation

120

CL

#4 @ 100 mm 16 mm BoltReinforcing Plate 9 mm

RFP 8 mm

205

400

205

630Strands 650

Cover Plate

Beam 5002001016

25 mm Bolt

630

(b) Section A-A

Strands

RFPFRP

190

Shear Tab

Bolt

220

630

30 mmHole

A36 RFP 8 mm

120

(c) Section B-B (d) RFP Details

2.10 2

70

Jacket 10 mm

CL

16 mm BoltRFP 12 mm

A


Shear TabBeam 5002001016

B

B

Flange Reinforcing Plate

A

Strands

(a) Elevation

LC

#4 @ 100 mm 16 mm BoltFlange Reinforcing Plate 9 mm

RFP 12 mm

205

400

205

1000Strands 650300 mm Hole

Cover Plate

Beam 5002001016

28 mm Bolt

1000

(b) Section A-A

Strands

RFPFRP

270

190

Shear Tab

Bolt

A36 RFP 12 mm

120

32 mmHole

630630 650

220

295

295

16 mmSlot HoleJacket 10 mm


2.11 3

71

CL

StrandsFlange Reinforcing Plate

Jacket 6 mm

Column 65065025 mm Bolt

A

RFP 8 mm16 mm Bolt

Beam 5002001016Shear Tab

A

B

B

(a) Elevation

LC

#4 @ 100 mm16 mm Bolt

Flange Reinforcing Plate 9 mmRFP 8 mm

205

400

205

750Strands 650

Cover Plate

Beam 5002001016

25 mm Bolt

750

(b) Section A-A

Strands

RFPFRP

190

Shear Tab

Bolt

A36 RFP 8 mm

120

30 mmHole

630630 650

220

295

295

16 mmSlot HoleJacket 6 mm


2.12 4

72

LC

BShear TabBeam 5002001016

B

A

Flange Reinforcing PlateJacket 6 mm

Strands16 mm Bolt

RFP 8 mm


A

(a) Elevation

LC

#4 @ 100 mm 16 mm BoltFlange Reinforcing Plate 9 mm

RFP 8 mm

205

400

205

1000Strands 650

Cover Plate

Beam 5002001016

25 mm Bolt

1000

(b) Section A-A

Strands

RFPFRP

270

190

Shear Tab

Bolt

A36 RFP 8 mm

120

30 mm Hole

630630 650

220

295

295

Jacket 6 mm16 mmSlot Hole


2.13 5

73

-0.04 -0.02 0 0.02 0.04Gap Opening Angle, g(rad)

-800

-400

0

400

800M

omen

t (kN

-m)

-1

-0.5

0

0.5

1

M/M

np

MST


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MRFP


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST+RFP

(a) Specimen 1


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1M

/Mnp

MST


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MRFP


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST+RFP

(b) Specimen 2


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MRFP


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST+RFP

(c) Specimen 3


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MRFP


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST+RFP

(d) Specimen 4


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MRFP


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

MST+RFP

(e) Specimen 5

2.14

74

0 1000 2000 3000Distance from Column Face (mm)

0

400

800

1200

1600

Mom

ent (

kN-m

)

0 2 4 6L/Lb

MdmMc

0 1000 2000 3000

Distance from Column Face (mm)

0

400

800

1200

1600

Mom

ent (

kN-m

)

0 2 4 6L/Lb

MdmMc

(a) Specimen 1 (g = 0.01 rad) (b) Specimen 2 (g = 0.01 rad)


0

400

800

1200

1600

Mom

ent (

kN-m

)

0 2 4 6L/Lb

MdmMc

0 1000 2000 3000


0

400

800

1200

1600

Mom

ent (

kN-m

)0 2 4 6

L/Lb

MdmMc

(c) Specimen 1 (g = 0.02 rad) (d) Specimen 2 (g = 0.03 rad)

0 1000 2000 3000


0

400

800

1200

1600

Mom

ent (

kN-m

)

0 2 4 6L/Lb

MdmMc

(e) Specimen 5 (g = 0.03 rad)

2.15

75

0 0.05 0.1 0.15 0.2 0.25Strain

0

200

400

600St

ress

(M

Pa)

0 0.05 0.1 0.15 0.2 0.25

Strain

0

200

400

600

Stre

ss (

MPa

)

(a) Flange (b)Web

0 0.1 0.2 0.3Strain

0

200

400

600

Stre

ss (

MPa

)

0 0.1 0.2 0.3

Strain

0

200

400

600

Str

ess

(MP

a)

(c) 8 mm RFP (d) 12 mm RFP

2.16 -

0 0.005 0.01 0.015 0.02 0.025 0.03Strain

0

400

800

1200

1600

2000

Stre

ss (M

Pa)

fpu=1860 MPaEST=1965,00 MPa

EST

flpfpu

lp=0.0086

2.17 -

76

Beam 1

1520

Strands

3000

250

1740

34003400

3000

1740

RC Column650 650

Beam 2

500200 10 16H

2.18

0 10 20 30 40 50-6-5-4-3-2-10123456

Inte

rsto

ry D

rift (

%)

0.375

0.5

0.75 11.5 2

34

5

Cycle Number

2.19

77

Beam 2

L8

L3 (Top), L4 (Bottom)

L5

Beam 1

(a) Top View

L4

L3

520L8

410

130

L5

130 L6

Beam 1 Beam 2L9

438

L7

L2L1

438

(b) Elevation

78

65

8565

8510

0

350 310 210

870

870

S25S24

S23

S22S21

C1

C2

C1,C2C3,C4C5,C6C7,C8

Column

RFP

R4R3

R2

R1

View C-C

100

160

8565

8565 S19

S20S21S22

EE

DD

Beam 1

CC

21031035045

190

190

A

B B

A

Beam 2

S6

S7S8

R5

R6R7 S5

S4

S3

S18S17S16

S15S14S13S12S11S10S9

View E-E

View D-D

S27

S26

View B-B

View A-A

4@16

3

View F-F

(c) Gauge Location

2.20 1

79

Beam 2Beam 1

520

L8L5


(a) Top View

Beam 1 Beam 2L9

L8520

L6

130

L5

130

120

438

L4L2L1

L7

L3

438

(b) Elevation

80

S27

S25

S24

240

S17

S14

210 Beam 1

CC

S3

S4S5

S2825

View E-E

E

E

S9S10

190

190

310

R3R2

R1

S2

S1

S8S7

S6

35045

View C-C

S18

S15S13S11 10

085

6585

65

S12

S16

S22S21S20S19

B

A

View B-B

View A-A

Beam 2

A

B

6585

6585

100

RFP

DD

View D-D

S23

S26

350 310 210 240

730

C1

C2

View F-F

F F

Column

C1 , C2

C3 , C4C5 , C6C7 , C8C9 , C10

C11 , C12

(c) Gauge Location

2.21 2

81

Beam 1

L5


L8

Beam 2

(a) Top View

Beam 1 L6

130

L5

130

120

L8520

L3

L4

438

L1 L2

L7

438

Beam 2

(b) Elevation

82

200

658565

85 100

350 510

Panal Zone

RFP

R4R3

R2

R1

View C-C

100

8565

85 65 S19

S20S21S22

EE

DD

Beam 1

CC

26051035045

190

190

A

B B

A

Beam 2

S6

S7

S8

R5

R6

R7 S5

S4

S3

S18S17S16

S15S14S13

S12S11S10S9

View E-E

View D-D

S27

S26

View B-B

View A-A

R10

R9

R8

260

1120

1120

S25S24

S23S22S21

R12

R11

4@16

3

4@150

(c) Gauge Location

2.22 3

83

Beam 2

L8


L5

Beam 1

(a) Top View

L4

L3

520L8

410

130

L5

130 L6

Beam 1 Beam 2L9

438

L7

L2L1

438

(b) Elevation

84

240520350

240870

100

8565

8565

165

165

View C-C

View D-D

S28

View B-B

View A-A

R9R8R7

S23

S27

S26

S25

S24

350 520 240

4@150

RFP

100

S31

100

S29

View F-FView E-E

Panal Zone

F

F

E

E

R10R6

Beam 1

D

CC

D

S30

24052035045

190

190

A

B B

A

Beam 2

S6

R5

S8

S1

S2

R1

R2

R3 S5

R4

S3

S18S17S16

S15S14S13

S12S11S10S9

S22S21S20S1965

8565

85 100

(c) Gauge Location

2.23 4

85

Beam 1

L5


L8

Beam 2

(a) Top View

Beam 1 L6

130

L5

130

120

L8520

L3

L4

438

L1 L2

L7

438

Beam 2

(b) Elevation

86

520350 250

1120

250520350

6585

65 S19S20S21S22

S9S10S11S12

S13 S14 S15

S16 S17 S18

S3

R4

S5R3

R2

R1

S8

R5

S6

Beam 2

A

BB

A19

019

0

45350 520 250

S30

D

C C

D

Beam 1

R6 R10

Panal Zone

4@150

R12

R11

RFP

S24S23

R7 R8 R9

View A-A

View B-B

View D-D

View C-C

100

85

S29S28

S27

S26S25

4@16

3

(c) Gauge Local

2.24 5

87

dc Lb

db

total

ba

1

2

3 4

2.25

88

-150 -100 -50 0 50 100 150Beam Deflection (mm)

-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4

Interstory Drift (%)

(a) Beam 1


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


(b) Beam 2

3.1 1

89


-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4

Interstory Drift, (%)

Specimen 1Specimen 2Specimen 3Specimen 4Specimen 5

3.2

-400 -200 0 200 400Actuator Force (kN)

800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.3

0.4

0.5

0.6

Nor

mal

ized

For

ce

Beam Yielding

3.3 1

90

0.75 1 2 3 4


0

100

200

300

400

500

Dec

ompr

essi

on M

omen

t (kN

-m)

0

0.2

0.4

0.6

M/M

np

Specimen 1 Specimen 3 Specimen 5Specimen 2 Specimen 4

3.4

-0.04 -0.02 0 0.02 0.04Gap Opening Angle, g (rad)

800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.3

0.4

0.5

0.6

Nor

mal

ized

For

ce

TestSimplified AnalysisIterative Analysis

3.5 1

91

-0.004 -0.002 0 0.002 0.004

Shear Strain, (rad)

-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

(a) Moment-Shear Strain Relationship

-0.004 -0.002 0 0.002 0.004

Column Rotation, c(rad)

-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

(b) Moment-Column Rotation Relationship

3.6 1

92

0.75 1 2 3 4


0

40

80

120

Def

lect

ion

(mm

)

Panal ZoneColumnBeamRigid Rotation

(a) Deflection Component

0.75 1 2 3 4


0

0.25

0.5

0.75

1

1.25

Def

lect

ion

Ratio

Panal Zone BeamColumn Rigid Rotation

(b) Deflection Ratio

3.7

93


0

200

400

Dis

tanc

e fro

m B

eam

Bot

tom

Fac

e (m

m)

TestIterative Analysis

3.8 1

0.75 1 2 3 4


0

0.01

0.02

0.03

0.04

Gap

Ope

ning

Ang

le ,

g(r

ad)


3.9 1

94

-0.04 -0.02 0 0.02 0.04g (rad) based on Displacement Tranducer

-0.04

-0.02

0

0.02

0.04

g (r

ad) B

ased

on

Eq. (

3.2)

Test

3.10 1

0.75 1 2 3 4 5


0

0.4

0.8

1.2

Stra

nd F

orce

Rat

io

Specimen 1 Specimen 3 Specimen 5Specimen 2 Specimen 4

3.11

95

22.5 30 60 90 120

Beam Deflection (mm)

0

20

40

60

Resi

dual

Def

orm

atio

n (m

m)

0.75 1 2 3 4



3.12


-5

0

5

10

15

20

Dis

plac

emen

t (m

m)


3.13 1

96

0.75 1 2 3 4


0

200

400

600

800

1000

Mom

ent (

kN-m

)

MSTMR

3.14 1

97

C7 C8C5 C6C3 C4C1 C2

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(a) Strain Gauge Location (b) Strain Gauge C1

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1M

omen

t (1

000

kN-m

) -2 -1 0 1 2Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(c) Strain Gauge C2 (d) Strain Gauge C3

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(e) Strain Gauge C4 (f) Strain Gauge C5

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(g) Strain Gauge C6 (h) Strain Gauge C7

3.15

98

S14 S15S13S11

S17S16 S18

(a) Strain Gauge Location (Top Flange) (b) Strain Gauge Location (Bottom Flange)

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(c) Strain Gauge S11 (d) Strain Gauge S13

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(e) Strain Gauge S14 (f) Strain Gauge S15

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(g) Strain Gauge S16 (h) Strain Gauge S17

3.16 1

99


-0.3

-0.2

-0.1

0

Stra

in (%

)

-1.5

-1

-0.5

0

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S13 S14 S15S11

(a) Top Flange


-0.3

-0.2

-0.1

0

Stra

in (%

)

-1.5

-1

-0.5

0

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S16 S17 S18

(b) Bottom Flange

3.17 1

100


0

400

800

1200

1600

Mom

ent (

kN-m

)

0

1

2

M/M

ny

0 2 4 6

L/Lb

MdmMc

3.18 1(g = 0.01 rad)

-0.4 -0.2 0 0.2 0.4Strain (%)

-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1M

/Mnp

-2 -1 0 1 2

Normalized Strain

S2 7

db/4

0-2 %3-5 %

3.19 1

101


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


(a) Beam 1


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


(b) Beam 2

3.20 2

102


1000

1250

1500

1750

Stra

nd F

orce

(kN

)

0.4

0.5

0.6

0.7

Nor

mal

ized

For

ce

Beam Yielding

3.21 2


800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.4

0.5

0.6

0.7

Nor

mal

ized

For

ce


3.22 2

103

-0.004 -0.002 0 0.002 0.004

Shear Strain , (rad)

-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

(a) Moment-Shear Strain Relationship

-0.004 -0.002 0 0.002 0.004

Column Rotation ,c(rad)

-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

(b) Moment-Column Rotation Relationship

3.23 2

104


0

200

400

Dis

tanc

e fro

m B

eam

Bot

tom

Fac

e (m

m)


3.24 2


-0.04

-0.02

0

0.02

0.04

g (r

ad) B

ased

on

Eq. (

3.2)

Test

3.25 2

105


-5

0

5

10

15

20D

ispl

acem

ent (

mm

)


3.26 2

106

C1,C2C3,C4C5,C6C7,C8C9,C10

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(a) Strain Gauge Location (b) Strain Gauge C4

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(c) Strain Gauge C5 (d) Strain Gauge C6

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(e) Strain Gauge C7 (f) Strain Gauge C8

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(g) Strain Gauge C9 (h) Strain Gauge C10

3.27 2

107

S14S13 S15S11

S17S16 S18


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -3 -2 -1 0 1 2 3

Normalized Strain

-1.5-1-0.500.511.5

M/M

np


3.28 2

108


-0.2

-0.1

0

0.1

Stra

in (%

)

-1

-0.5

0

0.5

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S13 S14 S15S11

(a) Top Flange

0 200 400 600 800 1000Distance from Column Face (mm)

-0.2

-0.1

0

0.1

Stra

in (%

)

-1

-0.5

0

0.5

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S16 S17 S18

(b) Bottom Flange

3.29 2

109


0

400

800

1200

1600

Mom

ent (

kN-m

)

0

1

2

M/M

ny

0 2 4 6

L/Lb

MdmMc

3.30 2(g = 0.01 rad)

-1.2 -0.8 -0.4 0 0.4 0.8 1.2Strain (%)

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

Mom

ent (

100

0 kN

-m)

-1

-0.5

0

0.5

1M

/Mnp

-6 -4 -2 0 2 4 6


S23

db/4

0 - 0.5 %0.75 - 5 %

3.31 2

110


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


1st Test2nd Test

(a) Beam 1


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1M

/Mnp

-4 -2 0 2 4


1st Test2nd Test

(b) Beam 2

3.32 3

111


800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.3

0.4

0.5

0.6

Nor

mal

ized

For

ce

Beam Yielding

1st Test2nd Test

3.33 3


800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.3

0.4

0.5

0.6

Nor

mal

ized

For

ce


3.34 3

112


0

200

400

Dis

tanc

e fro

m B

eam

Bot

tom

Fac

e (m

m)

1st Test2nd TestIterative Analysis

3.35 3


-0.04

-0.02

0

0.02

0.04

g (r

ad) B

ased

on

Eq. (

3.2)

Test

3.36 3

113


-5

0

5

10

15

20D

ispl

acem

ent (

mm

)


3.37 3

114

R9

R8

R7

R6 R10

L2 L1

-400 -200 0 200 400

Distance from Column Centerline (mm)

-0.16-0.12-0.08-0.04

0

Shea

r Stra

in (

0.01

rad)

-0.6

-0.4

-0.2

0

Nor

mal

ized

She

ar S

train

0.5 % 1 % 2 % 3 % 4 %

(a) Rosette Location (b) Shear Strain Profiles

-0.4 -0.2 0 0.2 0.4Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1

Normalized Shear Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

(c) Rosette R6 (d) Rosette R7

-0.4 -0.2 0 0.2 0.4Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4


-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

(e) Rosette R8 (f) Rosette R9

-0.4 -0.2 0 0.2 0.4Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4


-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m)

-1.5-1-0.500.511.5

M/M

np

(g) Rosette R10 (h) Overall Shear Strain

3.38 3

115

S14 S15S13S11

S16 S17 S18


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(b) Strain Gauge S11 (c) Strain Gauge S13

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(d) Strain Gauge S14 (e) Strain Gauge S15

-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

(f) Strain Gauge S16 (g) Strain Gauge S18

3.39 3

116


-0.3

-0.2

-0.1

0

Stra

in (%

)

-1.5

-1

-0.5

0

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S13 S14 S15S11

(a) Top Flange


-0.3

-0.2

-0.1

0

Stra

in (%

)

-1.5

-1

-0.5

0

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S16 S18

(b) Bottom Flange

3.40 3

117

0 1000 2000 3000Beam Deflection (mm)

0

400

800

1200

1600

Mom

ent (

kN-m

)

0

1

2

M/M

np

0 2 4 6

L/Lb

MdmMc

3.41 3(g = 0.02 rad)

-0.4 -0.2 0 0.2 0.4Strain (%)

-1200

-800

-400

0

400

800

1200

Mom

ent (

kN-m

)

-1.5

-1

-0.5

0

0.5

1

1.5M

/Mnp

-2 -1 0 1 2

Normalized Strain

0-3 %4-5 %

S18

db/4

3.42 3

118


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


(a) Beam 1


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


(b) Beam 2

3.43 4

119


800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.4

0.5

0.6

0.7

Nor

mal

ized

For

ce

Beam Yielding

3.44 4


800

1000

1200

1400

1600

1800

Stra

nd F

orce

(kN

)

0.4

0.5

0.6

0.7

Nor

mal

ized

For

ce


3.45 4

120

-0.004 -0.002 0 0.002 0.004

Column Rotation,c (rad)

-800

-400

0

400

800

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

3.46 4


0

200

400

Dis

tanc

e fro

m B

eam

Bot

tom

Fac

e (m

m)


3.47 4

121


-0.04

-0.02

0

0.02

0.04

g (r

ad) B

ased

on

Eq. (

3.2)

Test

3.48 4


-5

0

5

10

15

20

Dis

plac

emen

t (m

m)


3.49 4

122

R9

R8

R7

R6 R10

L2 L1

-400 -200 0 200 400

Distance from Column Centerline (mm)

-0.2-0.15-0.1

-0.050

Shea

r Stra

in (

0.01

rad)

-0.6

-0.4

-0.2

0

Nor

mal

ized

She

ar S

train

0.5 % 1 % 2 % 3 % 4 %

(a)Rosette Location (b) Shear Strain Profiles

-0.4 -0.2 0 0.2 0.4Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4


-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

(c)Rosette R6 (d) Rosette R7

-0.4 -0.2 0 0.2 0.4Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4


-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

(e)Rosette R8 (f) Rosette R9

-0.4 -0.2 0 0.2 0.4Shear Strain (0.01 rad)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -1 -0.5 0 0.5 1


-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4


-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m)

-1.5-1-0.500.511.5

M/M

np

(e)Rosette R10 (f) Overall Shear Strain

3.50 4

123

S14 S15S13S11

S17 S18S16


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np


-0.4 -0.2 0 0.2 0.4Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np

-0.4 -0.2 0 0.2 0.4

Strain (%)

-1-0.5

00.5

1

Mom

ent (

100

0 kN

-m) -2 -1 0 1 2

Normalized Strain

-1.5-1-0.500.511.5

M/M

np


3.51 4

124


-0.3

-0.2

-0.1

0

Stra

in (%

)

-1.5

-1

-0.5

0

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 %

S13 S14 S15S11

(a) Top Flange


-0.3

-0.2

-0.1

0

Stra

in (%

)

-1.5

-1

-0.5

0

Nor

mal

ized

Stra

in

0 0.5 1 1.5 2

Lb/db

0.5 % 1 % 2 % 3 % 4 % S16 S17 S18

(b) Bottom Flange

3.52 4

125


0

400

800

1200

1600

Mom

ent (

kN-m

)

0

1

2

M/M

ny

0 2 4 6

L/Lb

MdmMc

3.53 4(g = 0.03 rad)

-0.4 -0.2 0 0.2 0.4Strain (%)

-800

-400

0

400

800

Mom

ent (

kN-m

)

-1.5

-1

-0.5

0

0.5

1

1.5M

/Mnp

-2 -1 0 1 2

Normalized Strain

0-3 %4-5 %

S1 8

db/4

3.54 4

126


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

0.5

1

M/M

np

-4 -2 0 2 4


1st Test2nd Test

(a) Beam 1


-1000

-750

-500

-250

0

250

500

750

1000

Mom

ent (

kN-m

)

-1

-0.5

0

預力鋼梁與鋼筋混凝土柱自行復位接頭 之耐震行為研究 · i...

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預力鋼梁與鋼筋混凝土柱自行復位接頭之耐震行為研究 · i...