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

Strengthening Concrete Structures with Prestressed CFRP Sheets: Laboratory and Numerical Investigations to Field Application by Y ail (Jim m y) Kim A thesis subm itted to the D epartm ent o f C ivil E ngineering in conform ity with the requirem ents for the degree o f D octor o f Philosophy Q ueen's U niversity K ingston, O ntario, C anada S eptem ber 2006 C o p y rig h t0 Y ail J K im , 2006 R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission Library and Archives Canada Bibliotheque et Archives Canada Published Heritage Branch Direction du Patrimoine de I'edition 395 W ellington Street Ottawa ON K1A 0N4 Canada 395, rue W ellington Ottawa ON K1A 0N4 Canada Your file Votre reference ISBN: 978-0-494-18522-3 Our file Notre reference ISBN: 978-0-494-18522-3 NOTICE: The author has granted a non­ exclusive license allowing Library and Archives Canada to reproduce, publish, archive, preserve, conserve, communicate to the public by telecommunication or on the Internet, loan, distribute and sell theses worldwide, for commercial or non­ commercial purposes, in microform, paper, electronic and/or any other formats AVIS: L'auteur a accorde une licence non exclusive permettant a la Bibliotheque et Archives Canada de reproduire, publier, archiver, sauvegarder, conserver, transmettre au public par telecommunication ou par I'lnternet, preter, distribuer et vendre des theses partout dans le monde, a des fins commerciales ou autres, sur support microforme, papier, electronique et/ou autres formats The author retains copyright ownership and moral rights in this thesis Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission L'auteur conserve la propriete du droit d'auteur et des droits moraux qui protege cette these Ni la these ni des extraits substantiels de celle-ci ne doivent etre imprimes ou autrement reproduits sans son autorisation In compliance with the Canadian Privacy Act some supporting forms may have been removed from this thesis Conformement a la loi canadienne sur la protection de la vie privee, quelques formulaires secondaires ont ete enleves de cette these While these forms may be included in the document page count, their removal does not represent any loss of content from the thesis Bien que ces formulaires aient inclus dans la pagination, il n'y aura aucun contenu manquant i*i Canada R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral It a in ’t over till it’s over i Yail J K im , P.Eng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral Abstract M any o f the structures in C anada w ere constructed during the 1950’s and 1960’s and they are in need o f rehabilitation due to deterioration T he application o f carbon fibre reinforced polym er (C FR P) sheets for strengthening dam aged structures is a viable and prom ising solution C FR P is an em erging advanced com posite m aterial w ith very high tensile strength (i.e., 10 tim es stronger than that o f steel) The strengthening effect w hen using C FR P sheets can be significantly im proved by applying prestress to the sheets This thesis presents the application o f prestressed C FR P sheets for concrete structures and consists o f four m ain categories as follow s: • C om putational sim ulation: A nonlinear 3-D finite elem ent analysis (FE A ) is conducted to investigate the behaviour o f prestressed concrete beam s strengthened w ith prestressed C FR P sheets, including experim ental validation T he flexural behaviour o f the beam s, before and after strengthening, is predicted and com pared against experim ental results including the increase o f load-carrying capacity, failure m ode, ductility, and cracking behaviour The m odelling technique is extended to a tw o-w ay flat slab strengthened w ith prestressed C FR P sheets, including investigations on the load-carrying capacity, num erical crack grow th, and slab-colum n connection behaviour • E xperim ental investigation: T en reinforced concrete beam s strengthened w ith prestressed C FR P sheets are tested as part o f the developm ent o f a non-m etallic anchor system N on-m etallic anchors are ii Y ail J K im , P.Eng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral n ecessary to avoid corrosion dam age T he load-carrying capacity o f the strengthened beam s using the innovative m ethod is up to tim es greater than the unstrengthened beam V arious failure m odes are observed depending on the type o f the applied anchor system The developed non-m etallic anchor system overcom es brittle and abrupt failures that are com m only observed in C FR P -strengthened structures • T heoretical investigation: C losed-form solutions for the behaviour o f strengthened concrete beam s are derived, and they exhibited good agreem ent w ith the experim ental results Practical nonlinear fracture m echanics m odels, representing the b ehaviour o f the anchor system that is required to prestress C FR P sheets, are also developed • Site application: The technology studied in the laboratory 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 heavy trucks T he innovative strengthening m ethod using prestressed C FR P sheets is successfully applied T he load-carrying capacity o f the dam aged bridge is recovered w ith respect to the undam aged state N otice that this repair project is the first N orth A m erican site application using prestressed C FR P sheets iii Y ail J K im , P E ng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral Co-authorship This thesis is part o f the Ph.D w ork conducted by the author w ho perform ed the experim ental and analytical investigations, exam ined the research results, and w rote the entire m anuscripts under the supervision o f Dr M ark F G reen and Dr R G ordon W ight The follow ing m anuscripts have been prepared w ith contribution o f the co-authors • Journal contribution Thesis Ch 4 Title D uctility and C racking B ehaviour o f Prestressed C oncrete B eam s S trengthened w ith P restressed C FR P Sheets M echanical A nchorages for A pplication o f P restressed C arbon F iber R einforced P olym er Sheets Flexural S trengthening o f RC B eam s w ith P restressed CFR P Sheets: D evelopm ent o f N onm etallic A nchor System s Flexural Strengthening o f RC B eam s w ith P restressed C FR P Sheets: U sing N on-m etallic A nchor System s Flexure o f T w o-w ay Slabs S trengthened w ith P restressed or N on-prestressed CFR P Sheets T w o-w ay Slab-C olum n C onnections: R etrofit w ith P restressed or N on-prestressed C FR P Sheets F lexural B ehaviour o f R einforced or Prestressed C oncrete B eam s S trengthened Authors Kim, Y.J.; Shi, C.; and G reen, M F Kim, Y.J.; G reen, M F.; and W ight, R.G Kim , Y.J.; W ight, R.G ; and G reen M F Kim , Y.J.; W ight, R.G.; and G reen M F Kim, Y.J.; L ongw orth, J.M ; W ight, R G ; and G reen M F Kim, Y.J.; L ongw orth, J.M ; W ight, R G ; and G reen M F Kim , Y.J.; G reen, M F.; and W ight, iv Journal Remarks A SC E , J Compos Constr Subm itted (C C /2006/0227 45) A SC E , J Eng M ech Subm itted (M E /2006/0243 84) A SC E, J Compos Constr Subm itted (C C /2006/0227 60) A SC E, J Compos Constr Subm itted (C C /2006/0227 62) A SC E, J Compos Constr Subm itted (C C /2006/0227 53) ACI, Struct J Subm itted (S -2006-280) NRC, Can J Civ Eng A ccepted (06-168) Y ail J K im , P E ng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral Thesis Ch Title w ith P restressed C FR P Sheets: A pplication o f Fracture M echanics A pproach R epair o f B ridge G irder D am aged by Im pact L oads w ith P restressed C FR P Sheets S trengthening D am aged B ridge G irder (S tate-of-thePractice) F lexural B ehaviour o f an Im pact-dam aged Prestressed C oncrete G irder B ridge S trengthened w ith P restressed C FR P Sheets Journal Authors Rem arks R.G Kim, Y.J.; G reen, M F.; and F allis, G.J Kim, Y.J.; G reen, M F.; Fallis, G.J.; W ight, R.G ; and Eden, R Kim, Y.J.; G reen, M F.; and W ight, R.G A SC E, J B ridge Eng ACI, Cone Int A ccepted (B E /2006/0232 36) A ccepted (M S 0 153) NRC, Can J Civ Eng Subm itted (06-184) • C onference contribution Thesis Ch 4 Title A nchoring T echniques for S trengthening R einforced C oncrete B eam s w ith Prestressed C FR P Sheets Authors Conference Kim, Y.J.; B izindavyi, L.; W ight, R.G.; and G reen, M F C losed-form Solutions for the T ransfer o f P restressed CFR P Sheets Kim, Y.J.; S m eared C rack M odels o f T w o-w ay Slabs S trengthened w ith P restressed C FR P Sheets Kim , Y.J.; Predictions on Flexural B ehaviour o f R C B eam s: A pplication o f Fracture M echanics A pproach A p plicability o f Steel A nchor Plates for P restressing M ultilayered C FR P sheets Kim, Y.J.; 33rd C anadian Society for C ivil E ngineering (C SC E) A nnual C onf., T oronto, ON, June 2005 3ld Int Conf on C onstruction M aterials (C onM at05), V ancouver, BC A ug 2005 W ight, R.G , and G reen, M F W ight, R G ; and G reen, M F 7th Int Conf on Short and M edium Span B ridges, M ontreal, Q C , Aug 2006 W ight, R G ; and G reen, M F Kim, Y.J.; B izindavyi, L.; and G reen, M F v ld Int Conf on C onstruction M aterials (C onM at05), V ancouver, B C., A ug 2005 4th Int Conf on A dvanced C om posite M aterials in B ridges and Structures (A C M B S-IV ), C algary, AB, July 2004 Y ail J K im , P.Eng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral Thesis Ch 9 Title D am aged B ridge G irder R epaired U sing P ost-tensioned C FR P Sheets Authors Conference F allis, G.J.; Eden, R.; Kim, Y.J.; B izindavyi, L.; and G reen, M F L ive L oad D istributions on Im pact D am aged P restressed C oncrete G irder B ridge Kim, Y.J.; A ssessm ent o f C anadian H ighw ay B ridge D esign C ode (C H B D C ) for C -shaped P restressed C oncrete G irder B ridge: C lause 5.7 L ive L oad Kim, Y.J.; G reen, M F.; and W ight, R.G G reen, M F.; and W ight, R.G vi 4th Int Conf on A dvanced C om posite M aterials in B ridges and Structures (A C M B S -IV ), C algary, A B , July 2004 7th Int Conf on Short and M edium Span B ridges, M ontreal, Q C , A ug 2006 34th C anadian Society for C ivil E ngineering ( CSCE) A nnual C onf., C algary, A B , M ay 2006 Y ail J K im , P.Eng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral Acknowledgem ents Thank-you to Issac N ew ton, C hristian O tto M ohr, D u P erron R ene D escartes, L eonhard Euler, T hom as Y oung, S im on-D enis Poisson, R obert H ooke, G alileo G alilei, Leonardo da V inci, M ichaelangelo B uonarroti Dr M urty K.S M adugula, Dr Sungchul L ee, D r C hangsik M in, D r T Ivan C am pbell, Dr C olin M acD ougall, Dr A m ir Fam , Dr L uke B isby, Dr L aurent B izindavyi, Dr M arie-A nne Erki, Dr D ave Turcke, Dr K evin H all, Dr K eith Pilkey, M r G arth J Fallis, M s M axine W ilson, M s F iona Froats, M s C athy W agar, M r Jam ie Escoba, M r D ave Tryon, M r Paul T hrasher, M s D arlene G affney, M s D anielle G rondin, M r Leo M anes, M r O scar R ielo, M r D exter G askin Intelligent Sensing for Innovative Structures N etw orks (ISIS C anada) N atural Sciences and E ngineering R esearch C ouncil o f C anada (N SER C ) Q ueen's U niversity The R oyal M ilitary C ollege o f C anada V ector C onstruction G roup, W innipeg, M anitoba G raduate students at Q ueen's U niversity Fam ilies in Seoul, K orea Special thank-you to Dr M ark F G reen and Dr R G ordon W ight Very special thank-you to H abin, Jisu, and Seohoung K im vii Y ail J K im , P.Eng., Ph.D T hesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission G eneral Table o f Contents A bstract C o-authorship A cknow ledgem ents Table o f C ontents List o f Tables List o f Figures N otation ii iv vii viii xiv xvii xxiv Chapter G eneral Introduction 1.1 Introduction 1.2 T he D efinition o f Problem s 1.2.1 T he 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 stre sse d C F R P Sheets 1.2.2 A nchorage for P restressing 1.2.3 A pplication to T w o-w ay Slabs 1.2.4 C onventional A nalysis and D esign 1.2.5 R epair o f a D am aged B ridge Superstructure 1.3 O bjective o f the Thesis 1.4 O utline o f the T hesis 1.5 R eferences 10 Part A Effectiveness o f Strengthened Structures with Prestressed Carbon F ibre R einforced Polym er (CFRP) Sheets: Laboratory-scale Investigations C h a p ter D u c tility a n d C c k in g B e h a v io u r o f P re s tre s s e d C o n c re te B e a m s Strengthened w ith P restressed C FR P Sheets 2.1 Synopsis 2.2 Introduction 2.3 R esearch Significance 2.4 Structural D uctility 2.5 E xperim ental P rogram 2.6 A nalytical M odelling 2.6.1 C om putational M odel 2.6.2 N onlinear Iterative A nalytical M odel 2.7 A nalysis o f R esults 2.7.1 Flexural B ehaviour 2.7.2 Structural D uctility 2.7.3 C rack Patterns 2.7.4 L oad-crack R esponse 2.7.5 C ontribution o f T ension in C oncrete 2.8 Sum m ary and C onclusions 2.9 R eferences viii 15 15 15 17 18 19 20 20 21 23 23 26 28 29 31 32 34 Y ail J K im , P E ng., Ph.D Thesis R eproduced with perm ission of the copyright owner Further reproduction prohibited without permission A ppendix D: M odelling P roperties for FE A E s e q u e n c e n u m b e r fo r s in g le - v a lu e d o r c o n s ta n t e le m e n t d a ta I,J s e q u e n c e n u m b e r fo r d a ta a t n o d e s I a n d J T a b le D L I N K ite m a n d s e q u e n c e n u m b e r s f o r th e E T A B L E a n d E S O L c o m m a n d s Name Item E 1J SAXL l.S |l - - EPELAXL LEPEL |l - - EPTHAXL [l e p t h jl - - tPSW A X L LEP'l'H I2 L PIN 4X1 I EPTH |3 - - EPPLAXL - LhPPl *i - - PPCR \ XI EEPCR ii - SIPI INLIN SKAT N UN Ih p r e s NUN Ml - - Ie p e q NLIN 14 - - Im f o r x SMISC (l - - fluen >NMISC TEMP [LBFI i so - M2 1- [1 A s s u m p tio n s a n d R e s tr ic tio n s T h e s p a r e le m e n t a s s u m e s a s tr a ig h t b a r , a x ia lly lo a d e d at its e n d s , a n d o f u n if o r m p r o p e r tie s f ro m e n d to e n d T h e le n g th o f th e s p a r m u s t b e g r e a te r th a n z e r o so n o d e s I a n d J m u s t n o t b e c o in c id e n t T h e a r e a m u s t b e g r e a te r th a n z e ro T h e te m p e r a tu r e is a s s u m e d to v a r y lin e a r ly a lo n g th e le n g th o f th e s p a r T h is d is p la c e m e n t f u n c tio n im p lie s a u n if o r m s tre s s in th e sp a r T h e in itia l s tr a in is a ls o u s e d in c a lc u la tin g th e s tr e s s s tiff n e s s m a tr ix , i f a n y , f o r th e f irs t c u m u la tiv e ite r a tio n 401 Yail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FEA T h e f o llo w in g is r e g a r d in g th e b e h a v io u r o f c o n c r e te (A N S Y S 0 ) • Concrete T h e c o n c r e te m a te r ia l m o d e l p r e d ic ts th e fa ilu re o f b r ittle m a te r ia ls B o th c r a c k in g a n d c r u s h in g f a ilu re m o d e s a re a c c o u n te d fo r T B , C O N C R a c c e s s e s th is m a te r ia l m o d e l, w h ic h is a v a ila b le w ith th e r e in f o r c e d c o n c r e te e le m e n t S O L ID T h e c r ite r io n f o r fa ilu re o f c o n c r e te d u e to a m u ltia x ia l s tre s s s ta te c a n b e e x p r e s s e d in th e fo rm [ D l] — - S > (E q in A N S Y S m a n u a l) ■f: w h e re : F = a function (to be discussed) o f the principal stress state (oxp, oyp, a zp) S = failure surface (to be discussed) expressed in terms o f principal stresses and five input parameters f,, fc, fcb, h and f2 defined in Concrete Material Table fc = uniaxial crushing strength a xp, oyp, crzp = principal stresses in principal directions I f E q u a tio n is n o t s a tis f ie d , th e r e is n o a tte n d a n t c r a c k in g o r c ru s h in g O th e r w is e , th e m a te r ia l w ill c r a c k i f a n y p r in c ip a l s tr e s s is te n s ile w h ile c r u s h in g w ill o c c u r i f a ll p r in c ip a l s tr e s s e s a r e c o m p re s s iv e A to ta l o f fiv e in p u t s tr e n g th p a r a m e te r s ( e a c h o f w h ic h c a n b e te m p e r a tu r e d e p e n d e n t) a re n e e d e d to d e f in e th e f a ilu re s u r fa c e as w e ll as an a m b ie n t h y d r o s ta tic s tre s s sta te T h e s e a re p r e s e n te d in C o n c re te M a te r ia l T a b le T a b le D C o n c re te n n t c r i a l ta b le (Input on TBDATA Commands with TB,CONCK) Description Label Constant If* If (Ultimate uniaxial tensile strength (Ultimate uniaxial compressive strength |fc (Ultimate biaxial compressive strength 402 Y ail J Kim , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FEA (Input on TBDATA Commands with TB,CONCR) L abel i 3 ) [D ] + ( — C q )“ (E q in A N S Y S m a n u a l) a n d S is d e f in e d as 404 Yail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FEA 212(0 - rf1) c o s ri + r2 (2r-! - r ) (r2 - r f ) c s rs + rf - r2 b = b, [D ] ’^ l,r2 h ) COb q+pv D ]! ^ q in A N S Y S m a n u a l) T e r m s u s e d to d e f in e S are : COS p = 2(J1 - C o - (J q -! - q ) T h is c lo s u re o f th e f a ilu r e s u r fa c e h a s n o t b e e n v e r if ie d e x p e r im e n ta lly a n d it h a s b e e n s u g g e s te d th a t a v o n M is e s ty p e c y lin d e r is a m o r e v a lid fa ilu re s u r fa c e fo r la rg e c o m p re s s iv e s h v a lu e s (W illa m ( ) )- C o n s e q u e n tly , it is r e c o m m e n d e d th a t v a lu e s o f f| a n d f? a re s e le c te d a t a h y d r o s ta tic s tr e s s le v e l I ) h in th e v ic in ity o f o r a b o v e th e e x p e c te d m a x im u m h y d r o s ta tic s tre s s e n c o u n te r e d in th e s tru c tu re E q u a tio n e x p r e s s e s th e c o n d itio n th a t th e f a ilu re s u r fa c e h a s a n a p e x a t ^ = ^o- A p r o f ile o f ri a n d iy as a fu n c tio n o f c is s h o w n in A P r o f ile o f th e F a ilu r e S u rfa c e F ig D l A p r o f ile o f th e fa ilu re s u r fa c e A s a F u n c tio n o f ^a T h e lo w e r c u r v e r e p r e s e n ts a ll s tr e s s s ta te s s u c h th a t q = ° w h ile th e u p p e r c u r v e r e p r e s e n ts s tre s s s ta te s s u c h th a t q = ° I f th e f a ilu re c r ite r io n is s a tis f ie d , th e m a te r ia l is a s s u m e d to c ru s h T h e D o m a in ( te n s io n - c o m p r e s s io n - c o m p r e s s io n ) 408 Y a il J K im , P E n g , P h D T h e s is R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FEA o, > ^ o2 ^ a In th e r e g im e , F ta k e s th e fo rm 1 r + a i + a i [D 2 ] (E q in A N S Y S m a n u a l) a n d S is d e f in e d as f b=b- ^ \ 2P2(P2-P?)cos r)+p2 (2p1-p2 ) 4( P2 ■P?)c o s2 T|+ 5p^ -4 p jp2 -^ *L [D ] tt ( P - P l " ) C0 / tq + (p2 - p^|}" (E q in A N S Y S m a n u a l) w h e r e c o s q is d e f in e d b y E q u a tio n a n d [D ] P '1 [D ] ° + + a 2X Do = bn + biY + boY Z u ( E q _ in A N S Y S m a n u a l) (E q in A N S Y S m a n u a l) T h e c o e f f ic ie n ts ao, a\, a 2, bo, b i, b a r e d e f in e d b y E q u a tio n a n d E q u a tio n w h ile / \ X = x ( o +Ct3) [D ] (E q 7 in A N S Y S m a n u a l) I f th e fa ilu re c r ite r io n is s a tis f ie d , c r a c k in g o c c u r s in th e p la n e p e r p e n d ic u la r to p r in c ip a l s tre s s c i 409 Y ail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FE A T h e D o m a in ( te n s io n - te n s io n - c o m p r e s s io n ) Oi ^ - ^ In th e te n s io n - te n s io n - c o m p r e s s io n r e g im e , F ta k e s th e fo rm [D ] ^ ~ - O i >i - ( E q _ g in A N S Y S m a n u a l) a n d S is d e f in e d as f S = So = i f [D ] j _ Oo, + ^ I ' f C \ r ' I f th e fa ilu re c r ite r io n f o r b o th i = ,2 (E q m A N S Y S m a n u a l) 1, is s a tis f ie d , c r a c k in g o c c u r s in th e p la n e s p e r p e n d ic u la r to p r in c ip a l s tr e s s e s a i a n d I f th e fa ilu re c r ite r io n is s a tis f ie d o n ly f o r i = , c r a c k in g o c c u r s o n ly in th e p la n e p e r p e n d ic u la r to p r in c ip a l s tre s s C | T h e D o m a in ( te n s io n - te n s io n - te n s io n ) Gi —02 —03 —0 In th e te n s io n - te n s io n - te n s io n r e g im e s , F ta k e s th e f o rm [D ] F = F = O j , i = , , (E q in A N S Y S m a n u a l) a n d S is d e f in e d as s = s4 = i [D ] c (E q in A N S Y S m a n u a l) 410 Yail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FEA I f th e fa ilu re c r ite r io n is s a tis f ie d in d ir e c tio n s , , a n d , c r a c k in g o c c u r s in th e p la n e s p e r p e n d ic u la r to p r in c ip a l s tr e s s e s a i , a 2, a n d I f th e fa ilu re c r ite r io n is s a tis f ie d in d ir e c tio n s a n d , c r a c k in g o c c u r s in th e p la n e p e r p e n d ic u la r to p r in c ip a l s tr e s s e s 01 a n d o I f th e fa ilu re c r ite r io n is s a tis f ie d o n ly in d ir e c tio n 1, c r a c k in g o c c u r s in th e p la n e p e r p e n d ic u la r to p r in c ip a l s tr e s s C c k in g C c k in g /// j j p = (C c k in g ) a ZD < (C c k in g ) w F ig D F a ilu r e s u r fa c e in p r in c ip a l s tre s s s p a c e F a ilu r e S u rf a c e in P rin c ip a l S tre s s S p a c e r e p r e s e n ts th e -D f a ilu re s u r fa c e f o r s ta te s o f stre s s th a t a re b ia x ia l o r n e a r ly b ia x ia l I f th e m o s t s ig n ific a n t n o n z e r o p r in c ip a l s tr e s s e s a re in th e a xp a n d c yp d ir e c tio n s , th e th r e e s u r fa c e s p r e s e n te d a r e f o r o zp s lig h tly g r e a te r th a n z e ro , o zp e q u a l to z e r o , a n d a zp s lig h tly le s s th a n z e ro A lth o u g h th e th r e e s u r fa c e s , s h o w n a s p r o je c tio n s o n th e o xp - o yp p la n e , a re n e a r ly e q u iv a le n t a n d th e -D fa ilu re s u r fa c e is c o n tin u o u s , th e m o d e o f m a te r ia l fa ilu re is a f u n c tio n o f th e s ig n o f c a zp F o r 411 Y ail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix D: M odelling P roperties for FE A e x a m p le , i f o xp a n d o yp a re b o th n e g a tiv e a n d o zp is s lig h tly p o s itiv e , c r a c k in g w o u ld b e p r e d ic te d in a d ir e c tio n p e r p e n d ic u la r to th e o zp d ir e c tio n H o w e v e r , if a zp is z e ro o r s lig h tly n e g a tiv e , th e m a te r ia l is a s s u m e d to c ru s h • R e fe r e n c e s A N S Y S , 0 , “ A N S Y S O n lin e M a n u a l,” A N S Y S In c C P C I, 9 , “ D e s ig n M a n u a l: P r e c a s t a n d P r e s tr e s s e d C o n c r e te ,” C a n a d ia n P r e s tr e s s e d C o n c re te I n s titu te , O tta w a , O N M a c G re g o r , J G , 9 , “ R e in f o r c e d C o n c r e te M e c h a n ic s a n d D e s ig n ,” P r e n tic e h a ll, N e w J e rs y , U S A 412 Yail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix E: P erm ission to P ublish Form s Appendix E: Permission to Publish Forms A p p e n d ix E in c lu d e s th e p e r m is s io n to u s e th e c o n te n ts th a t h a v e b e e n p u b lis h e d d u r in g th e a u t h o r ’s P h D w o rk T h e c o p y r ig h t o f th e c o n te n ts h a v e b e e n tr a n s f e r r e d to th e p u b lis h e r T h e c o m m u n ic a tio n th a t h a s b e e n m a d e w ith th e p r im a r y p u b lis h e r r e g a r d in g th is m a tte r is a s f o llo w s 413 Y ail J K im , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix E: P erm ission to P ublish Form s Yail (Jimmy) Kim, P.Eng., Ph.D Cand D e p a r tm e n t o f C iv il E n g in e e r in g , Q u e e n 's U n iv e r s ity , K in g s to n , O N , K L N , T e l: - 3 - 0 e x t 5 ; F a x : -5 3 -2 E -m a il: iim m v @ c iv il.q u e e n s u c a ; H o m e p a g e : h ttp ://m v h o m e n a v e r c o m /a n a lv s is 9 Ju n e , 2006 T h e C a n a d ia n S o c ie ty f o r C iv il E n g in e e r in g d e M a is o n n e u v e B lv d W S u ite M o n tr e a l, Q C , H Z I N I D ear C SC E, h a v e p u b lis h e d s e v e r a l te c h n ic a l p a p e r s in th e c o n f e r e n c e s o r g a n iz e d b y C S C E N o w , I w o u ld lik e to c o m p ile th e m f o r m y P h D th e s is I m a y n e e d p e r m is s io n f ro m C S C E b e c a u s e I h a v e s u b m itte d th e c o p y r ig h t tr a n s f e r fo rm It w o u ld b e a p p r e c ia te d i f y o u p r o v id e m e w ith a n o f fic ia l le tte r o f P e r m is s io n to P u b lis h F o rm s T h e lis t o f p a p e r s is a s fo llo w s : (1) Non-linear Analysis of Reinforced Concrete Beams with Externally Bonded and Un-bonded Strengthening Methods - by Kim, Y.J.; Wight, R.G.; and Green M.F (CSCE Annual Conference 2004, Saskatoon, SK), pp (2) Applicability o f Steel Anchor Plates for Prestressing Multilayered CFRP Sheets - by Kim, Y.J.; Bizindavyi, L.; and Green, M.F (4th International Conference on Advanced Composite Materials in Bridges and Structures, ACMBS, Calgary, AB, 2004), pp (3) Damaged Bridge Girder Repaired Using Post-Tensioned CFRP Sheets - by Fallis, G.J.; Eden, R.; Kim, Y.J.; Bizindavyi, L.; and Green, M.F (4th International Conference on Advanced Composite Materials in Bridges and Structures, ACMBS, Calgary, AB, 2004), pp (4) Closed-form Solutions for the Transfer of Prestressed CFRP Sheets - by Kim, Y.J.; Wight, R.G.; and Green M.F (CSCE Annual Conference 2005, Toronto, ON), pp (5) Anchoring Techniques for Strengthening Reinforced Cocncrete Beams with Prestressed CFRP Sheets by Kim, Y.J.; Bizindavyi, L.; Wight, R.G.; and Green, M.F (3rd International Conference on Construction Materials, ConMat 05, Vancouver, BC, 2005), 10 pp (6) Smeared Crack Models o f Two-way Slabs Strengthened with Prestressed CFRP Sheets - by Kim, Y.J.; Wight, R.G.; and Green M.F.(3rd International Conference on Construction Materials, ConMat 05, Vancouver, BC, 2005), 10 pp (7) Assessment o f Canadian Flihghway Bridge Design Code (CHBDC) for C-shaped Prcstressed Concrete Girder Bridge: Clause 5.7 Live Load - by Kim, Y.J.; Green M.F.; and Wight, R.G (CSCE Annual Conference 2006, Calgary, AB), 10 pp (8) Prediction on Flexural Behaviour o f Reinforced Concrete Beams: Application o f a Fracture Mechanics Approach - by Kim, Y.J.; Wight, R.G.; and Green M.F (7lh International Conference on Short and Medium Span Bridges, Montreal, QC, 2006), 10 pp 414 Y ail J Kim , P.Eng., Ph.D Thesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission A ppendix E: P erm ission to P ublish Form s (9) Live Load Distributions on an Impact-damaged Prestressed Concrete Girder Bridge - by Kim, Y.J.; Green M.F.; and Wight, R.G (7lh International Conference on Short and Medium Span Bridges, Montreal, QC, 2006), 10 pp Y o u rs v e r y tru ly , Y a il (J im m y ) K im Response from the publisher: June 9, 2006 H e llo J im m y , Y o u w ill n e e d to r e v ie w th e c o p y r ig h t tr a n s f e r f o rm s w h ic h s h o u ld in c lu d e a c la u s e o n r e ta in e d r ig h ts , a s fo llo w s : R e ta in e d R ig h ts / T e r m s a n d C o n d itio n s A u th o r s /e m p lo y e r s r e ta in a ll p r o p r ie ta r y r ig h ts in a n y p r o c e s s , p r o c e d u r e o r a r tic le o f m a n u f a c tu r e d e s c r ib e d in th e w o rk A u th o r s /e m p lo y e r s m a y r e p r o d u c e o r a u th o r iz e o th e rs to r e p r o d u c e th e W o r k , m a te r ia l e x tr a c te d v e r b a tim f ro m th e W o r k , o r d e r iv a tiv e w o rk s f o r th e a u th o r's p e r s o n a l u s e o r f o r c o m p a n y u s e , p r o v id e d th a t th e s o u rc e is in d ic a te d M o s t c o p y r ig h t tr a n s f e r a g r e e m e n ts a llo w f o r th is p r a c tic e T h e o n ly r e q u ir e m e n t b e in g th a t th e s o u r c e is in d ic a te d H o p e th is h e lp s L o u is e L ouis e Newm an C o m m u n ication s M a n a g e r / Directrice d e s c o m m u n ic a tio n s Editor, Canadian Civil E ngineer / Redactrice, L'Ingenieur civil ca n a d ie n Canadian Society for Civil Engineering / S o ciete c a n a d ie n n e d e genie civil 49 20 d e M aisonneuve Blvd, W Suite 201, Montreal, Q uebec, H3Z I N I T: ( ) 3 -2 # 23 / F: ( ) 3 -3 www.csce.ca 415 Y ail J K im , P.Eng., Ph.D T hesis R ep ro d u ced with p erm ission o f th e copyright ow ner Further reproduction prohibited w ithout perm ission ... The strengthening effect w hen using C FR P sheets can be significantly im proved by applying prestress to the sheets This thesis presents the application o f prestressed C FR P sheets for concrete. .. eferences 10 Part A Effectiveness o f Strengthened Structures with Prestressed Carbon F ibre R einforced Polym er (CFRP) Sheets: Laboratory- scale Investigations C h a p ter D u c tility a n d C... prestressed concrete beam s strengthened w ith prestressed C FR P sheets, including experim ental validation T he flexural behaviour o f the beam s, before and after strengthening, is predicted and com