Strengthening concrete structures with prestressed CFRP sheets Laboratory and numerical investigations to field application

Library and Archives CanadaBibliotheque et Archives Canada Published Heritage Branch 395 W ellington Street Ottawa ON K1A 0N4 Canada Your file Votre reference ISBN: 978-0-494-18522-3 Our

with Prestressed CFRP Sheets:

Laboratory and Numerical Investigations

to Field Application

by

Y ail (Jim m y) K im

A thesis subm itted to the D epartm ent o f C ivil E ngineering

in co nform ity w ith th e requirem ents for the degree o f

Library and Archives Canada

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It a in ’t o ver till it ’s o ver

i Yail J K im , P E ng., P h.D T hesis

G eneral

Abstract

M any o f the structures in C anada w ere constructed during the 1950’s and 19 6 0 ’s and they

are in need o f reh ab ilitatio n due to deterioration T he application o f carbon fibre

reinforced p o ly m er (C F R P ) sheets fo r strengthening dam aged structures is a v iable and

prom ising solution C FR P is an em erging advanced com posite m aterial w ith v ery high

tensile strength (i.e., 10 tim es stro n g er th an that o f steel) The strengthening effec t w hen

using C FR P sheets can b e significantly im p ro v ed b y applying p restress to the sheets T his

thesis p resents the ap p licatio n o f p re stressed C FR P sheets for concrete structures and

consists o f four m ain categories as follow s:

• C om putational sim ulation:

A n o n lin ear 3-D finite elem ent analysis (F E A ) is conducted to in v estig ate the b eh av io u r

o f p re stressed concrete beam s stren g th en ed w ith p restressed C F R P sheets, including

experim ental validation T he flexural beh av io u r o f the b eam s, befo re and after

strengthening, is pred icted and com p ared against experim ental results in cluding the

increase o f lo ad-carrying capacity, failure m ode, ductility, and cracking behaviour The

m od ellin g tech n iq u e is extended to a tw o -w ay flat slab strengthened w ith p re stressed

C FR P sheets, including investigations on the load-carrying capacity, n u m erical crack

grow th, and slab-colum n conn ectio n behaviour

• E xperim ental investigation:

T en reinforced concrete beam s stren g th en ed w ith prestressed C FR P sheets are tested as

part o f the d evelopm ent o f a n o n -m etallic anchor system N o n -m etallic anchors are

ii Y ail J K im , P E ng., P h.D T hesis

n ecessary to avoid corrosion dam age T he load-carrying capacity o f the stren g th en ed

beam s u sin g the innovative m eth o d is up to 3 tim es greater than the u n stren g th en e d beam

V arious failure m odes are o b served d epending on the type o f the applied an c h o r system

The develo p ed n o n -m etallic an ch o r system overcom es brittle and abru p t failures that are

com m only o b serv ed in C F R P -stren g th en ed structures

• T heoretical investigation:

C losed-form solutions fo r the b eh a v io u r o f strengthened concrete beam s are derived, and

they exhibited g o o d agreem ent w ith the experim ental results P ractical n o n lin ear fracture

m echanics m odels, rep resen tin g the b eh a v io u r o f the anchor system that is req u ired to

prestress C FR P sheets, are also developed

• S ite application:

The technology studied in the labo rato ry is applied to a site application T he M ain Street

B ridge-overpass No 4, W innipeg, M B , has been significantly dam aged by frequent

collisions o f h ea v y trucks T he innovative strengthening m ethod u sin g prestressed C FR P

sheets is su ccessfully applied T he lo ad-carrying capacity o f the dam aged brid g e is

recovered w ith resp ect to the un d am ag ed state N o tice that this rep air p ro ject is the first

N orth A m erican site ap p licatio n u sin g prestressed C FR P sheets

iii Y ail J K im , P E ng., P h.D T hesis

G eneral

Co-authorship

T his thesis is p art o f the P h.D w o rk co nducted b y the au th o r w ho p erfo rm ed the

experim ental and analytical investigations, exam ined the research results, and w ro te the

entire m anuscripts u n d er the supervision o f Dr M ark F G reen an d Dr R G ord o n W ight

T he follow ing m an u scrip ts h ave b een p rep ared w ith contribution o f the co-authors

C oncrete B eam s S trengthened

w ith P restressed C FR P Sheets

A S C E ,

J Eng

M ech.

S ubm itted(M E /2006/024384)

5

F lexure o f T w o-w ay Slabs

S trengthened w ith P restressed

or N o n -p restressed C FR P Sheets

K im , Y.J.;

L ongw orth, J.M ; W ight,

6

T w o -w ay S lab-C olum n

C onnections: R etro fit w ith

P restressed or N on-p restressed

C FR P Sheets

K im , Y.J.;

L ongw orth, J.M ; W ight,

7

F lexural B eh av io u r o f

R ein fo rced or P restressed

C oncrete B eam s S trengthened

iv Y ail J K im , P E ng., P h.D T hesis

w ith P restressed C FR P Sheets:

A c cep ted(B E /2006/023236)

9

F lexural B eh av io u r o f an

Im p ac t-d am ag e d P restressed

C oncrete G ird er B ridge

S trengthened w ith P restressed

C FR P Sheets

K im , Y.J.;

G reen, M F ;

and W ight, R.G

N R C ,

Can J

Civ Eng.

S ubm itted(06-184)

3 ld Int C onf on C onstruction

M aterials (C onM at05),

V ancouver, B C , A ug 2005

4

C lo sed -fo rm S olutions for the

T ra n sfer o f P restressed C FR P Sheets

Kim , Y.J.;

W ight, R G , and G reen,

3ld Int C onf on C onstruction

M aterials (C onM at05),

v Y ail J K im , P E ng., P h.D T hesis

P restressed C oncrete G irder

B ridge: C lause 5.7 L ive L oad

K im , Y.J.;

G reen, M F ;

and W ight, R.G

34th C anadian Society for

C ivil E n g in eerin g ( C SCE)

A nnual C onf., C algary, A B ,

M ay 2006

vi Y ail J K im , P E ng., P h.D T hesis

Acknowledgem ents Thank-you to

Issac N ew ton, C hristian O tto M ohr, D u P erro n R ene D escartes, L eo n h ard E uler, T hom as

Y oung, S im on-D enis Poisson, R o b ert H ooke, G alileo G alilei, L eonardo da V inci,

M ich aelan g elo B uonarroti

Dr M u rty K S M adugula, Dr S ungchul L ee, D r C hangsik M in, D r T Iv an C am pbell,

Dr C olin M acD ougall, Dr A m ir F am , Dr L uke B isby, Dr L au ren t B izindavyi, Dr

M arie-A n n e E rki, Dr D ave T urcke, Dr K e v in H all, Dr K eith P ilkey, M r G arth J Fallis,

M s M ax in e W ilson, M s F io n a F roats, M s C athy W agar, M r Jam ie E scoba, M r D ave

T ryon, M r Paul T hrasher, M s D arlene G affney, M s D anielle G rondin, M r L eo M anes,

M r O scar R ielo, M r D e x te r G askin

Intelligent Sensing for Innovative Structures N etw o rk s (ISIS C anada)

N atural Sciences and E ngineering R esearch C ouncil o f C anada (N S E R C )

Q ueen's U niversity

T he R oyal M ilitary C ollege o f C anada

V ector C onstruction G roup, W innipeg, M an ito b a

G raduate students at Q ueen's U niv ersity

F am ilies in S eoul, K orea

vii Y ail J K im , P E ng., P h.D T hesis

G eneral

Table o f Contents

1.2.1 T h e B e h a v io u r o f S tre n g th e n e d B eam s w ith P re s tre s se d C F R P

1.2.5 R ep air o f a D am ag ed B ridge S uperstructure 7

P art A Effectiveness o f Strengthened Structures with Prestressed Carbon F ibre

R einforced P olym er (CFRP) Sheets: Laboratory-scale Investigations

2.7.5 C ontribution o f T en sio n in C oncrete 31

viii Y ail J K im , P E ng., P h.D T hesis

Chapter 3 M ech an ical A n ch o rag e fo r A p p licatio n o f P restressed C F R P Sheets 48

3.4.2 M odel P ro p o sed b y K im et al (2004) 52

3.4.3.1 L in ear E lastic F racture M echanics (L E F M ) A pproach 533.4.3.2 N o n linea r F racture M echanics (N L FM ) A pp ro ach 553.4.3.3 V alid atio n o f the P roposed M odels 57

P restressed C FR P Sheets: N o n -m etallic A n c h o r S ystem 88

G eneral

4.6.1.2 C orrelatio n w ith the L aboratory 106

4.7.1.1 B eam s w ith N on-anchored U -w raps 1084.7.1.2 B eam s w ith M echanically A nchored U -w rap s 1094.7.1.3 B eam s w ith C F R P -anchored U -w raps 1114.7.2 P e e lin g -o ff C rack P ro p ag atio n 111

4.7.3.1 B eam s w ith N on -an ch o red U -w raps 1124.7.3.2 B eam s w ith A n ch o red U -w raps 1134.7.3.3 B eh av io u r o f Side Sheets D epending on A n ch o r-ty p e 1144.7.4 Stress R ed istrib u tio n in the R einfo rcem en t 114

4.7.4.1 T he C oncept (K im et al 2005b) 114

4.7.5 T ransverse D e fo rm atio n in the A nchored R eg io n 1174.7.6 S train P rofiles and F ailure o f U -w raps 117

5.6.1 F lexural B eh av io u r and the E ffect o f S trengthening 144

5.6.4 C rack M outh O p ening D isp lacem en t 151

6.4.4 P restressin g O peration 172

6.7.4 C o rrelatio n o f the P redictio n s w ith the E x p erim en t 184

7.3.2 P ractical A pplicatio n s o f H illerborg M odel 202

7.3.2.1 R ein fo rced C oncrete B eam (K im et al 2006) 203

7.3.2.3 P restressed C oncrete B eam S trengthened w ith P restressed

7.6 N o n lin ear Iterative M odel: S trength-based T heory 212

7.7.1 E ffect o f the S ize-d ep en d en t P aram eter 2137.7.2 S tress-strain R elatio n o f C oncrete in B ending 214

P art B Innovative Strengthening Application to Site

8.3 D esign and R ep air o f the D am ag ed B ridge 231

8.3.1 D e scrip tio n o f the D am ag ed B ridge 231

xi Y ail J K im , P E ng., P h.D T hesis

G eneral

8.4 F easib ility o f the R ep air D esig n (K im et al 2004) 235

8.7 A ssessm en t on E ffectiveness o f the R ep air 249

9.3 R eview o f E xisting F E A for F u ll-scale B ridge M odelling 2729.4 B ackground o f R esearch (K im et al 2006a) 2749.5 C alibration o f the F E A m odel (K im et al 2006b) 275

9.6 F ull-scale M odelling o f the M ain S treet B ridge (K im et al 2006b) 2779.7 T he C oncept o f the L ive L oad D istrib u tio n F acto r 277

9.7.1 T he B en d in g M o m e n t-b a se d A pproach 277

9.8 M eth o d o lo g y to C alculate the Live L oad D istribution 278

9.11.1 C om parison o f Live L oad D istribution F actors 285

9.11.1.1 C om parison to A A S H T O L R FD 2869.11.1.2 C om parison o f the U ndam aged, D am aged, and R epaired

xii Y ail J K im , P E ng., Ph.D T hesis

9.11.2 D istrib u tio n o f L ive L oad M om ent 287

9.11.2.1 C o m p ariso n to A A S H T O L R FD and C H B D C 287

9 1 1 2 2 C o m p a ris o n a m o n g th e U n d a m a g e d , D a m a g e d , an d

A ppendix B In n o v ativ e F lexural S treng th en in g for R C B eam s 324

A ppendix C R ep air o f B ridge G ird er D am aged by Im pact L oads 337

xiii Y ail J K im , P E ng., Ph.D T hesis

G eneral

List o f Tables

T able 1.1 S um m ary o f specim ens investigated in the thesis 13

T able 2.2 D escrip tio n o f the investig ated beam s 38

T able 2.3 S um m ary o f significant values in flexure 39

T able 3.2 S um m ary o f laboratory results (im m ediate loss) 78

T able 3.3 M easu red short-term loss (up to 56 days) o f applied p restress 79

T able 5.2 S um m ary o f flexural b eh a v io u r o f the slabs 158

T able 5.3 S um m ary o f energy absorption and ductility index {jig) 159

T able 6.4 S um m ary o f p unching shear b eh a v io u r o f each slab 191

T able 8.1 D esig n p roperties o f the M ain S treet B ridge ex terio r g ird er 256

T able 8.2 S um m ary o f the m om ents ap p lied to the external g ird er u n d er the extrem e

xiv Y ail J K im , P E ng., P h.D T hesis

loading based on A A S H T O L R F D at critical section 256

T able 8.3 S u m m a ry o f a p p lie d m o m en ts o b tain ed from th e F E A u n d e r th e ex trem e

T able 8.4 F ailure loads and m odes o f the specim ens (K im et al 2004) 257

T able 8.5 C om parison o f net deflectio n o f the ex terio r girder at critical section u n d er the

Table 8.6 T he operating rating factors at critical section o f the external gird er u n d er the

T able 9.1 D esig n p ro perties for calculating live load d istribution (K im et al 2006a) 295

T able 9.2 S um m ary o f live load effects based on C H B D C (K im et al 2006a) 295

T able 9.3 C om parison o f live load distribution factors (undam aged state only) 295

T able 9.4 C o m parison o f live load distribution factors in the M ain S treet B ridge 296

T able 9.5 T he load com binations at critical section in the u n dam aged state 296

T able 9.6 S um m ary o f the load com b in atio n s at critical section in the dam aged state 297

Table 9.7 S um m ary o f the load com binations at critical section in the repaired state 298

Table A l M aterial p ro perties o f Wabo® M B race C F 160 322

T able A 2 M aterial pro p erties o f Wabo® M B race C F 130 322

T able A 3 M aterial p ro perties o f Wabo® M B race S aturant 323

T able C l T he m ultiple presen ce factor (A A S H T O L R F D Cl 3.6.1.1.2) 353

Table C.2 S um m ary o f L ive load D istrib u tio n F actors fo r the ex terio r gird er 353

Table C 3 T he m ultiple p resen ce factor (C H B D C T able 3.8.4.2) 353

Table C 4 S um m ary o f L ive load effects b ase d on C H B D C 353

T able C.5 S um m ary o f the F E A in the u n d am ag ed state 354

x v Y ail J K im , P E ng., P h.D T hesis

G eneral

T able C.6 S um m ary o f the F E A in the dam aged state 355

T able C l S um m ary o f the F E A in the repaired state 356

T able C.8 T he load com binations at critical section in the u n d am aged state 357

T able C.9 S um m ary o f the load com binations at critical section in the d am aged state 358

T able C 10 S um m ary o f the load com binations at critical section in the rep aired state 359

T able D 3 SO L ID 45 item and sequence n u m bers for the E T A B L E and E S O L 374

T able D 8 SOL1D65 item and sequence n u m bers fo r the E T A B L E and E S O L 384

T able D l 1 S H ELL63 item and sequence n um bers for the E T A B L E and E S O L 395

T able D 13 L IN K 8 item and sequence n u m bers fo r the E T A B L E and E S O L 401

xvi Y ail J K im , P E ng., P h.D T hesis

List o f Figures

Fig 2.6 C om parison o f typical crack patterns b etw e en the laboratory an d the F E A 45

Fig 2.9 C ontribution o f tension in concrete after cracking 47

Fig 3.2 L oad-d isp lacem en t resp o n se o f the ten sio n an ch o r 80

Fig 3.4 T ypical com parison b etw een the laboratory and the theory (Eqs 1 and 2) 81

Fig 3.5 P aram etric study on the p late an c h o r system 82

Fig 3.7 S h ort-term prestress losses in the C FR P sheet 83

Fig 3.8 S train d istributions on the an ch o r plates (J-3) 84

Fig 3.10 T ypical com parison o f the p restress in the C FR P sheet 86

Fig 3.11 C om parison o f the theo retical m odel vs laboratory 86

Fig 3.13 C om parison b etw een the experim ental and F E A strains 87

xvii Y ail J K im , P E ng., Ph.D T hesis

G en eral

Fig 4.4 S hear stress co ncentration n ea r the c u t-o ff p o in t o f C FR P sheets 127

Fig 4.5 S train v ariations along the b eam d uring p restressing C FR P sheets (J-3) 127

Fig 4.6 T ypical prestress loss in the C FR P sheets afte r anchor-set (J-5) 128

Fig 4.8 R em oval o f steel an ch o r (K im et al 2005a) 129

Fig 4.9 T ypical variations o f prestress before and after the cut (J-3) 129

Fig 4.11 T ypical com p ariso n b etw e en the th eo re tic al m odel and the lab o rato ry afte r

rem oval o f the steel anchors (K im et al 2005a) 130

Fig 4.16 L o ad -strain resp o n se in re b ar (stren g th en ed vs u n stren g th en e d ) (K im et al

Fig 4.17 L oad-strain response o f tested beam s at m id -sp an 135

Fig 4.19 S train pro file w ith po ssib le failure m ode o f U -w raps 136

xviii Y ail J K im , P E ng., P h.D T hesis

Fig 5.2 C onstructed F E A slab m odel (cut-aw ay v iew to show the rein fo rcem en t) 160

Fig 5.3 L o ad -d eflectio n resp o n se o f each slab 161

Fig 5.5 T ypical cracking pattern s and failure m odes o f the tested slabs 163

Fig 5.7 T ypical n um erical crack p ro p a g atio n o f a slab w ith prestressed C FR P s 164

Fig 6.1 T ypical experim ental set-up and instru m en tatio n 192

Fig 6.3 T im e vs prestress v aria tio n in C F R P 193

Fig 6.6 S train p ro fd es in re b ar along the loading span 195

Fig 6.8 F orm ation and inclination o f p u n ch in g shear cracks 196

Fig 6.9 C om parison o f co m putational crack p attern s 197

Fig 6.10 S hear stress pro file along the loading span 198

Fig 6.11 C om parison o f the pred ictio n s w ith the laboratory 198

Fig 7.1 T he concept o f p ro p o sed fracture m echanics m odel by H illerborg (1990) and

xix Y ail J K im , P E ng., P h.D T hesis

G eneral

Fig 7.4 B rie f flow -chart o f the n o n lin ear iterative m odel 223

Fig 7.5 E ffect o f the size-dependent p aram eter on load-strain re sp o n se 224

Fig 7.6 S tress-strain response com p ariso n o f concrete in bending to u n iax ial loading 225

Fig 7.7 C om prehensive com parison o f load-strain response 226

Fig 7.8 C om prehensive com parison o f m o m ent-curvature response 227

Fig 8.1 S chem atic o f the M ain S treet B ridge (N o.4 overpass) 258

Fig 8.2 C ross-sectional v iew o f the dam aged gird er (F allis et al 2004) 258

Fig 8.4 D etailed anchor system fo r p restressin g C F R P sheets 259

Fig 8.5 T ypical ten sio n test specim en (K im et al 2004) 260

Fig 8.6 T ypical failure o f the specim ens (K im et al 2004) 261

Fig 8.7 T ypical strain v ariations on the C FR P sheet ( A - l) (K im et al 2004) 262

Fig 8.8 T ypical load-strain curves at m id-span ( A - l) (K im et al 2004) 262

Fig 8.9 D ev elo p m en t o f T heoretical M o d els (K im et al 2004) 263

Fig 8.10 C onstructed finite elem ent analysis m odel for the anchor test 263

Fig 8.11 C o m parison o f the ten sio n test results (K im et al 2004) 264

Fig 8.14 N et increase o f deflection u n d e r the extrem e loading 268

Fig 8.15 N et increase o f strain in steel strands u n d er the extrem e loading 269

Fig 9.1 V arious F E A m od ellin g techniques (K im et al 2006b) 299

Fig 9.2 S chem atic o f the M ain S treet B ridge (K im et al 2006b) 299

xx Y ail J K im , P E ng., P h.D T hesis

Fig 9.3 S chem atic o f the internal reinfo rcem en t 300

Fig 9.5 S im ulated double T -b eam bridge for calibration o f the F E A technique 302

Fig 9.6 C alibration o f the F E A w ith the experim ental data (K im et al 2006b) 303

Fig 9.7 C onstructed full-scale F E A m odel o f the M ain Street B ridge 303

Fig 9.8 T he effect o f loading span on live load distributions on the exterio r and interio r

Fig 9.9 T he effect o f daily traffic v olum e o n live load distributions on the exterio r and

Fig 9.10 L o ngitudinal d eflection along the exterio r girder 305

Fig 9.11 T ransverse deflection across the critical section 306

Fig 9.12 N et deflectio n increase o f each loading case across the critical section 307

Fig 9.13 D eflectio n co n to u r on the brid g e u n d er various loadings (K im et al 2006a) 308

Fig 9.14 C om prehensive com p ariso n o f the dam aged exterior gird er u n d e r the extrem e

Fig 9.15 C om parison o f strains in the p restressin g strands located at 153 m m from the

Fig 9.16 N et strain increase along the exterio r gird er 310

Fig 9.17 L ive load distribution across the bridge at critical section 311

Fig 9.18 C om parison o f the live load d istrib u tio n am ong the undam aged, dam aged, and

Fig 9.19 C om parison o f the live load distribution am ong the undam aged, dam aged, and

xxi Y ail J K im , P E ng., P h.D T hesis

G eneral

Fig B 4 S train v ariations on the C FR P sheets during prestressin g 328

Fig B 5 S train v ariations on the C FR P sheets during beam testing 329

Fig B 6 S train variations before and after cutting the prestressed C F R P sheets 331

Fig B 9 T he finite elem ent analysis for the end-cap an ch o r 336

Fig C 4 L ive loads p er lane to induce the m axim um m om ents in the g ird er 362

Fig C 5 L oading com binations for live load d istrib u tio n factor 363

Fig C.6 T he m axim um m om ent based on C H B D C (2000) 364

Fig D L C onstitutive beh av io u r o f m aterial m o d ellin g 365

xxii Y ail J K im , P E ng., P h.D T hesis

Fig D 9 L IN K 8 3-D sp ar output 399

Fig D 10 3-D F ailure surface in prin cip al stress space 406

Fig D 12 F ailu re surface in prin cip al stress space 411

xxiii Y ail J K im , P E ng., P h.D T hesis

A s = cross-sectio n al areas o f steel p late (m m ); area o f tension rein fo rcin g steel (m m )

As = area o f com p ressio n rein fo rcin g steel (m m 2)

A rocj = cross-sectio n al area o f ro d (m m 2)

a = infinitesim al initial flaw (m m ); partial lengths o f the p late (m m ); ind icato r for critical

p erim eter

b = w id th o f reinforced or p restressed concrete beam (m m ); total bon d ed w id th o f C FR P

(m m ); the p artia l lengths o f the p late (m m ); indicator for critical p erim eter

bbond ~ w idth o f C F R P -bonded area (m m )

bo = length o f colum n w idth plus effective depth o f slab (m m )

C = co m pliance o f a system (m 2/N ); resu ltan t com p ressio n force (kN )

C f= correctio n factor

C; = constant o f general solution

c = clear concrete cov er (m m ); d istance from the extrem e com pression fibre to the neutral

axis (m m ); n eutral axis o f rein fo rced or p re stressed concrete beam (m m ); in d icato r for

critical p erim eter

C 2 = colum n w id th (m m )

D = un facto red dead load effect

d = effective depth o f the tension rein fo rcem en t (m m )

db = re b ar d iam eter (m m )

xxiv Y ail J K im , P E ng., P h.D T hesis

E f= elastic m odulus o f C FR P (G Pa) (El)transformed- transform ed flexural rig id ity (N m 2)

E p = elastic m odulus o f p restressing strands (G Pa)

E p ‘ = secant m odulus o f p restressin g strands (G P a) Epiate = elastic m odulus o f ja c k in g p late (G Pa) Erod = elastic m odulus o f rod (G Pa)

E s = elastic m odulus o f steel (G Pa)

e = eccentricity o f p restress (m m ); eccen tricity o f d esig n truck or a d esign lane load from

centre o f g ravity o f p attern o f g ird er (m m )

F = w o rk done by the applied load (kN m ); w id th d im ension factor

F m = am plification factor

f = prestress levels o f C FR P sheet w ith resp ect to the ultim ate capacity

f c = specified concrete strength (M Pa)

f Pi = initially ap p lied prestress in strands (M Pa)

f pe = effective prestress in strands (M P a)

f , = m odulus o f ru pture (M Pa)

f , = ultim ate strength o f rein fo rcem en t (M P a)

f y = yield strength o f reinforcem ent (M P a)

G = energy release rate

G f = fracture energy (kN m ); critical strain energy release rate Gepoxy = sh ea r m odulus and thickness o f adhesiv e (G Pa)

h = h eig h t o f rein fo rced or p re stressed con crete beam (m m ); thickness o f slab (m m )

I = dynam ic load allow ance

xxv Y ail J K im , P E ng., Ph.D T hesis

G eneral

I conc = m om en t o f inertia o f concrete section (m m 4) brack = m om en t o f inertia o f cracked section (m m 4) Ix.x = m om en t o f in ertia o f gross section (m m 4)

ki = co efficient for b o n d p ro perties o f rebar

k 2 = co efficient to account for strain gradient

L = span length o f specim en (m m ); live load effect Lbond = length o f C F R P -bonded area (m m )

L F j = load fractio n factor for zth girder/ = total b o n d ed length o f C FR P (m m ); adjusted d epth (m m ); gripping length o f anchor

p late (m m )

/ ’ = effective length o f C FR P sheet (m m )

Ipiate = length o f jac k in g p late (m m )

I rod = length o f rod (m m )

A f o.ooi = m om ent w hen the m axim um concrete com pressive strain reaches 0.001 (kN m ) Mappijed(x) = m om ent applied to m odel (kN m )

Mbeam-ijne = m ax im u m bending m om ent ob tain ed from a sim ple b eam analysis w ith a

single lane o f traffic (kN m )

M cr = cracking m om ent (kN m )

M o = m o m en t due to dead load (kN m )

^distributed = largest bending m om ent that a g ird er m ay experience (kN m )

M j„, - m om ent due to prestress (kN m )

M f= factored m om ent (kN m )

M g_avg = average bending m om en t p e r gird er (kN m )

xxvi Y ail J K im , P E ng., P h.D T hesis

M i = m o m en t due to live load (kN m )

M n = n om inal m o m en t (kN m )

M r = resisting m om en t (kN m )

M steei(x) = internal m om ent in steel p late (kN m )

M r = m axim um bend in g m om en t p e r d esig n lane (kN m )

M uit = ultim ate m om ent capacity o f the sectio n (kN m )

M with u = m o m en t w ith live loads (kN m )

M Wi(iout l l = m om ent w ithout live loads (kN m )

m c = rad ial m o m en t resistan ce co lu m n strip (kN m )

m u = ultim ate m om en t capacity o f slab (kN m )

mo = radial m om ent resistances in o u ter strip (kN m )

N = n u m b er o f girders

N l = n u m b er o f loaded lanes u n d er consideration; n u m b er o f girder

n = n u m b er o f bon d ed surfaces; n u m b er o f design lanes

P - total applied tensile force in an an ch o r system (kN ); applied load (kN )

P f r p - resu ltan t force o f C FR P (kN )

Psteel= resu ltan t force o f steel (kN)

P ( l ) = applied force at x = I (kN )

xx v ii Y ail J K im , P E ng., P h.D T hesis

G eneral

P ui, = ultim ate load o f reinforced or p re stressed concrete beam (kN )

p = p restress levels o f p restressin g strands w ith respect to the ultim ate cap acity (% )

R = fracture resistance; reaction on an exterio r beam in term s o f lanes (kN )

R 2 = co efficient o f d eterm ination

R F = rating factor

R l = m odificatio n factor for m ultiple loading

S = prestress effect; spacing o f beam s (m m ); cen tre-to-centre gird er spacing (m m )

s = spacing b etw een the rein fo rcem en t (m m )

s m = average crack spacing (m m )

U = strain energy stored in structure (kN m ) Uvieid = energy ab sorbed until yield load (kN m ) Unit= energy absorbed until u ltim ate load (kN m ) u(x,y) = horizontal d isplacem ent o f m odel (m m ) uo(x) = initial length o f the beam (m m )

Uconc(x) = defo rm ed length o f concrete (m m ) ufrp(x) = deform ed length o f the C FR P sheet (m m )

xxviii Y ail J K im , P E ng., P h.D T hesis

list (x) = defo rm ed length o f an ch o r p late (m m ) us,.o(x) = initial length o f an ch o r p late (m m ) Vfjex = flexural load capacity (kN )

Vu = ultim ate load capacity including flexure/punching in teraction (kN ) v(x,y) = v ertical d isplacem ent o f m odel (m m )

W = energy req u ired fo r crack p ro p a g atio n (kN m ); energy stored b y app lied force (kN m );

edge-to-edge w id th o f a brid g e (m m )

We = w idth o f a d esig n lane (m m )

w m = average crack w idth (m m ) Opiate= w id th o f ja c k in g p late (m m )

x = distance from the c u t-o ff p o in t o f the C FR P sheet to an arbitrary location (m m );

h orizontal d istance from the centre o f grav ity o f the pattern o f girders to each girder

(m m )

Xgxt = horizontal distance from the centre o f gravity o f the pattern o f girders to the exterio r

gird er (m m )

y = distance from centroid to the extrem e fibre o f concrete beam (m m )

Z = crack control p aram eter (N /m m )

z = shear span (m m )

a = coefficients for the equivalent concrete stress block; p unching shear angle o f slab (°);

nu m b er o f w heels

/? = coefficients for the equivalent concrete stress block; prop o rtio n ality factor depending

on the size-p aram eter

A sfrp = strain variatio n in C FR P (m m /m m )

xxix Y ail J K im , P E ng., Ph.D T hesis

G eneral

A max = m ax im u m d isplacem ent (m m )

AP = loss o f prestress (kN )

Ax = d istan ce b etw e en tw o arbitrary po in ts (m m )

S = displacem ent o f a system (m m ) Sf= disp lacem en t o f C FR P (m m )

dj = deflection o f ith gird er (m m )

Sj = deflection o f / h gird er (m m )

Ss — displacem ent o f steel p late (m m )

e = strain ob tain ed before the p eak stress (m m /m m )

e ’ = com b in ed strain (m m /m m )

sc = concrete strain at an arbitrary load level (m m /m m )

£ce = concrete strain at the level o f steel (m m /m m )

£C f = bottom concrete strain (m m /m m )

£cfe = concrete strain at the level o f C FR P (m m /m m )

£co = concrete strain at the specified concrete strength (m m /m m )

£Cu ~ ultim ate concrete strain (m m /m m )

£f= C F R P strain at an arbitrary load level (m m /m m )

£fe = C FR P strain induced by p restressin g (m m /m m )

£f-i„i = initial strain o f p restressed C FR P sheets (m m /m m )

£f, = ultim ate strain in C FR P (m m /m m )

ep = strain in p restressin g strand at arbitrary load level (m m /m m )

£pe = steel strain induced by p restressing (m m /m m )

£py = yield strain o f prestressing strand (m m /m m )

xxx Y ail J K im , P E ng., Ph.D T hesis

£totai(x) - strain variatio n in C FR P sheets (m m /m m )

eu = ultim ate strain o f rein fo rcem en t (m m /m m )

sy = yield strain o f rein fo rcem en t (m m /m m )

£0 - axial strain o f steel plate bey o n d bon d in g area (m m /m m )

Ei = size-p aram eter

£ j i = axial strain (m m /m m )

ij = m ultip lier to concrete strain to determ ine the m axim um concrete stress

He = ductility index based on the energy concept

£ = m u ltip lier indicating neutral axis o f section

p = rein fo rcem en t ratio

p ef = ratio b etw een reinfo rcem en t and its effective em bedm ent zone

G»»c= stress in concrete (M P a)

<jy = y ield strength o f steel (M Pa)

ai = concrete stress at top fibre o f b eam section (M Pa)

?ave(x) = average shear stress (M Pa) Tave-design - average ultim ate shear stress in tw o-w ay slab (M Pa)

<t> = diam eter o f strip (m m )

<I>f = resistance facto r o f C FR P

0 R n = n om inal strength o f section (kN m )

&s = resistan ce factor o f steel 9°o.ooi = curvature at M'o.ooi (1/m m ) (pui, = curvature at M „/,(l/m m )

xxxi Y ail J K im , P E ng., P h.D T hesis

C hapter 1: G eneral In tro d u ctio n

Chapter 1 G eneral Introduction

1.1 Introduction

M uch o f the civil in frastructure constructed d uring the 19 5 0 ’s and 1960’s is in need o f

reh ab ilitatio n due to deterioration, including increased service loads, corrosion, and

p hysical or environm ental dam age (K im et al 2006) V arious m ethods h ave been

p roposed and applied to inadequate structural m em bers to im prove th e ir p erform ance

R ecent technical surveys co nducted support the requirem ent for re h ab ilitatio n (R izkalla

and L abossiere 1999, A S C E 2003) T he introduction o f A dvanced C o m p o site M aterials

such as F ibre R einforced P olym ers (F R P ) has significantly im pacted the rehabilitation

industry (B alds et al 2002) E xternal strengthening m ethods u sin g F R P s have attained

popu larity b ecause o f th eir ease o f application; for instance, F R P sheets/plates are bon d ed

onto the ten sile side o f a target structure to com pensate for the deficient tensile

reinforcem ent In addition, the follow ing technical benefits are expected: high tensile

strength, in significant increase o f perm an en t dead loads, corrosion resistant

characteristics, and good fatigue resistan ce (M eier 1995, N eale 2000, T eng et al 2003)

C arbon F R P (C F R P ) generally displays su perior structural p erfo rm an ce to o th er types o f

FR Ps in external strengthening ap plications (M eier 1995) F urtherm ore, C F R P m ay be

p restressed to im prove its effectiveness P restressin g creates an active load-carrying

m echanism , in cluding im proved serviceability and durability, and requ ires an chorage that

can p o ten tially prev en t (or delay) prem atu re p e e lin g -o ff failure o f the C FR P sheets w hen

subjected to loads T o date, tensioning against the strengthened b eam its e lf is the m ost

w idely u sed m ethod to p restress C F R P sheets (Izum o et al 1997, W ight et al 2001, El-

H acha et al 2003, K im et al 2005)

1 Y ail J K im , P E ng., P h.D T hesis

T rian tafillo u et al (1992) conducted a p io n eerin g study on the application o f prestressed

C FR P sheets M eier (1995) reported a sim ple com parison o f a reinforced concrete beam

strengthened w ith p re stressed C FR P sheets to a beam w ith non -p restressed C F R P sheets,

as w ell as an u n stren g th en ed beam T he b eam strengthened w ith p re stressed C FR P sheets

exhibited h ig h er stiffness than o th er beam s, bu t show ed no increase o f the ultim ate load

com pared to the beam w ith n o n -p restressed C FR P sheets Izum o et al (1997) evaluated

the significance o f prestressed C F R P sheet applications and found that a rein fo rced

concrete b eam strengthened w ith p re stressed C FR P sheets show ed a 6.8 % in crease o f the

ultim ate load com p ared to a beam w ith n o n -p restressed C FR P sheets (12 % increase

com pared to the u n stren g th en e d beam ) W ight et al (2001) d escribed the effectiveness o f

prestressed C FR P applications including n u m erical m odels T he beam strengthened w ith

prestressed C FR P sheets show ed an increase o f up to 7 % in the ultim ate load com pared

to the beam w ith n o n -p restressed C F R P sheets E l-H ach a et al (2004) investigated the

beh av io u r o f p re stressed concrete beam s strengthened w ith prestressed C FR P sheets

u n d er ro o m and low tem p eratu res including analytical m odelling, and found that the

decrease in tem perature did not significantly contribute to the flexural b eh a v io u r o f the

beam s strengthened w ith prestressed C FR P sheets D espite these structural advantages,

there appears to be a dearth o f info rm atio n available on the research w ork related to the

application o f p re stressed C FR P sheets fo r strengthening concrete structures

1.2 The D efinition o f Problem s 1.2.1 The behaviour o f strengthened beam s with prestressed CFRP sheets

To enhance the effectiveness o f C F R P -strengthening, p restress m ay be directly applied to

C FR P sheets T he application w ith p o st-ten sio n ed C FR P sheets exhibits better structural

2 Y ail J K im , P E ng., Ph.D T hesis

C hapter 1: G eneral In tro d u ctio n

perfo rm an ce w ith respect to non -p restressed C FR P applications, in clu d in g significan t

increase o f load-carrying capacity u n d e r both live and sustained loads, im proved

serviceability, satisfactory fatigue resistance, and good perfo rm an ce in harsh

environm ental conditions (R izkalla and L abossiere 1999, K achlakev and M cC u rry 2000,

E l-H ach a et al 2004, H e ffem a n and E rki 2004, K im et al 2005)

T he advantages o f applications usin g p re stressed C F R P sheets w ere clearly show n above

in term s o f the increase o f load-carrying capacity and im proved serviceability;

n evertheless, m ore detailed inform ation on strengthened beam s w ith p re stressed C F R P

sheets is still req u ired to con sid er d u ctility issues (particularly consid erin g the b rittle

failure ch aracteristic o f the C FR P m aterial), d etailed investigations on local b eh aviour

including anchorage, cracking m odes including crack progression, the effect o f d ifferent

prestress levels in C FR P sheets, and the dev elo p m en t o f m ore accurate p redictive m odels

1.2.2 Anchorage for prestressing

A n chorage is req u ired to hold the C FR P sheets during a p restressing operation or during

service u n d e r various loading conditions M etallic anchors are com m o n ly used for

p re stressed C F R P sheet applications T he follow ing an ch o r system s h ave b een reported: a

box-type an ch o r (Izum o et al 1997), a ro u n d -b ar-ty p e (W ight et al 2001), a screw -bolt-

type (H o llaw ay and L eem ing 1999), and a p late-ty p e (E l-H acha et al 2003, K im et al

2005) E l-H ach a et al (2003) p articu larly co nducted an experim ental param etric study

regarding the shape o f anchors, and reco m m en d ed a plate-type anchor

3 Y ail J K im , P E ng., Ph.D T hesis

A ll o f the m en tio n ed anchors w ere m ade o f steel; thus, the anchors can be a source o f

problem s in site applications because the m etallic anchors m ay corrode and the

appearance o f the m o unted steel anchors m ay be u ndesirable w hen con sid erin g aesthetics

F urtherm ore, galvanic corrosion w ould be a concern for bonding C FR P to steel T his

p ro b lem could be red u ced by using stainless steel for the anchor or elim inated by placin g

a layer o f G F R P u n d er the C FR P H ow ever, this consideration is outside the scope o f the

current study T herefore, it m ay be desirable to rem ove the m etallic anchors, i f possible,

after adequate curing o f the strengthening system O nce the m etallic anchors are rem oved,

alternative an ch o r system s m ay be n ee d ed to re strain the prestress loss in C FR P sheets

From a practical aspect, the rem o v ed steel anchors can be used repeatedly on m ultiple

girders o f a bridge, for exam ple T he level o f sustained p restress in the C FR P sheets after

the rem oval o f m etallic anchors is one o f the critical concerns D etailed investigations on

the replacem ent o f the m etallic anchors are thus required and investigated in this thesis

1.2.3 Application to two-way slabs

The application o f C FR P sheets to rein fo rce d or prestressed concrete beam s is w ell

d ocum ented (M eier 1995, R izk alla and L abossiere 1999, N eale 2000, E l-H ach a et al

2001, B akis et al 2002, T eng et al 2003, L op ez and N anni 2006) T he application o f

C FR P sheets to tw o-w ay slabs, h o w ever, has been rarely investigated despite the com m on

use o f tw o-w ay slabs as structural elem ents in buildings E rki and H e ffem a n (1995)

conducted a study on the b eh a v io u r o f tw o w ay slabs strengthened w ith C F R P sheets and

reported that the load-carrying capacity o f C F R P -strengthened slabs increased by up to

240 % com pared to the u n stren g th en ed slab Several researchers conducted further

investigations on the b eh av io u r o f tw o -w ay slabs strengthened w ith C FR P sheets (H arajli

4 Y ail J K im , P E ng., Ph.D T hesis

C hapter 1: G eneral Intro d u ctio n

and S oudki 2003, M osallam and M o salam 2003, E bead and M a rzo u k 2004)

In v estigations into tw o-w ay slabs strengthened w ith prestressed C FR P sheets h ave been,

ho w ever, extrem ely lim ited (W ight et al 2003, L ongw orth et al 2004)

A lthough co m puter aided analysis is beco m in g m ore popular, pred ictiv e m odels o f tw o-

w ay slabs have rarely b een reported w h en com pared to beam o r one-w ay slab m odels

because o f th eir com p licated b eh a v io u r and tim e-consum ing m od ellin g efforts M odels

em ploying n o n lin ear solid elem ents and d iscrete reinfo rcem en t elem ents are especially

rare M o st o f the reported m odels for tw o-w ay slabs are based on sim plified shell

elem ents including layered shells (H orm an et al 2002, M arzouk et al 2003, M osallam

and M osalam 2003), w here i) detailed cracking analyses m ay not be p erfo rm ed in the

case o f having only in-plane G aussian quadratures, and ii) exact strain variatio n s (or

stress analysis) in the rein fo rcem en t m ay no t be investigated due to the sim p lified

sm eared stiffness F urtherm ore, the sm eared re inforcing schem e m ay con trib u te to stiffer

beh av io u r o f the m odel as show n in M arzo u k et al (2003) D espite these lim itations,

structural slabs are com m only m o d elled w ith shell elem ents b ecause o f m od ellin g

convenience A s com pared to the sim plified shell m odels, 3-D solid m odels m ay pro v id e

superior advantages: a detailed cracking investigation is available and the structural

com ponents (e.g., rein fo rcin g bars) can be represented w ith m inim al sim plifications

T herefore, a reliab le 3-D solid m odel w ith d iscrete reinforcem ent is d eveloped in this

thesis to p ro v id e a b etter u n d erstan d in g o f the b eh a v io u r o f tw o-w ay slabs strengthened

w ith C FR P sheets

5 Y ail J K im , P E ng., Ph.D T hesis

1.2.4 Conventional analysis and design

The strength-based th eo ry is co n v en tio n ally em ployed for the p re d ic tio n o f flexural

b ehaviour o f rein fo rced or p re stressed concrete beam s M ost o f the existing concrete

codes (C S A A 23.3-94 1995, A C I 318-02 2002) for design are corresp o n d in g ly based on

this theory A lthough the strength-based d esig n m ethod has b een com m only used for the

d esign o f re in fo rced concrete beam s, it does not p re d ic t detailed structural b eh a v io u r such

as fracture propagation, failure m echanism , and size effects T he introduction o f fracture

m echanics to the design o f re in fo rced or p re stressed concrete beam s m ay en hance the

effectiveness o f the design by consid erin g the factors m entioned above In spite o f the

relatively long history, m ost fracture m ech an ics applications still rem ain in the

investigations on localized p h en o m en a in cluding m icro-scale observations such as ten sio n

crack p ropagations (S hah et al 1995)

H illerborg (1990) prop o sed a un iq u e fracture m echanics approach to exam ining flexural

b ehaviour o f a reinforced concrete beam , but its validation against experim ental or any

other analytical results w as no t conducted T hus, it w as hard to evaluate that the p ro p o se d

m odel m ight enhance the analysis technique o ver the conventional strength-based theory,

as H illerborg (1990) stated A n assessm ent o f the proposed m odel is required

F urtherm ore, the ap p licatio n to strengthening re in fo rced or prestressed concrete beam s

using prestressed C F R P sheets m ay enlarge the existing analysis techniques In this thesis,

analytical m odels are developed, based on H ille rb o rg ’s fracture m echanics approach, and

experim ental and com putational valid atio n s are conducted to evaluate the developed

fracture m echanics m odel

6 Y ail J K im , P.E ng., P h.D T hesis

C hapter 1: G eneral In tro d u ctio n

1.2.5 Repair o f a damaged bridge superstructure

M o d ern bridges d eteriorate due to m any reasons m entio n ed in Sec 1.1., resu ltin g in

deficient flex u ral or shear strength in the bridges; therefore, u p g ra d in g m ay be required

T he C FR P rep air m ethods have been increasingly applied to sites in recen t years

(R izkalla and L abossiere 1999, Fallis et al 2004, L opez and N an n i 2006) D eterio rated

bridges are u su ally stren g th en ed b y bonding C FR P sheets on the tensile soffit o f

deteriorated girders to increase the insufficient load-carrying capacity D esp ite their

n um erous advantages addressed earlier, the lim it o f com m only used C F R P re p air m ethods

is found in its passiv e load-carrying m ech an ism including insig n ifican t im p ro v em en t o f

serviceability A n innovative strengthening m ethod u sin g prestressed C FR P sheets is thus

required for the case that an active load-carrying m echanism is n ecessary to im prove no t

only the strength o f the brid g e but also its serviceability

M any research results have been reported to date on the reh ab ilitatio n o f deteriorated

bridges as discu ssed above, b u t m ost o f th em have b een m ainly focused on a strength

aspect T herefore, m ore detailed investigations regarding changes o f d eflection, stress in

the reinforcem ent, load d istributions u n d er various loading conditions on a bridge

superstructure are req u ired to adequately evaluate the effectiveness o f a re p a ir m ethod

using prestressed C F R P sheets F urtherm ore, the b eh av io u r o f a bridge su perstructure

before and after dam age as w ell as after rep air needs to be investigated to im prove the

u n d erstanding o f the innovative re p air m ethod

7 Y ail J K im , P E ng., P h.D T hesis