strengthening of concrete beams using fiber-reinforced plastics

8/13/2019 Strengthening of Concrete Beams Using Fiber-reinforced Plastics

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M a t e r i a ls a n d S t r u c t u r e s / M a t 6 ri a u x e t C o n s t r u c t io n s V o l . 3 0 A p r il 1 9 9 7 p p 1 6 0 - 1 6 6

S t re n g t h e n i n g o f c o n c r e t e b e a m s u s in g f ib e r r e in f o r c e dplasticsH Va r a st eh p ou r a n d P H ame l i n 2( I ) M .S Eng ineeb Researcherof M echanics and Ma terials Laboratorieso f the U niversi t y o f Lyon I .(2) ProfesssorD. ing, Directorof Mechanics and M aterials Laboratories of the Universi ty of Lyo n I .

A B S T R A C TO n e a p p l i c a t i o n o f c o m p o s i t e m a t e r ia l s i n c iv i l e n g i -n e e r i n g is e x a m i n e d : t h e s t r e n g t h e n i n g o f a r e i n f o r c e d

c o n c r e te b e a m in s i tu b y e x t e r n a l l y - b o n d e d f i b e r r e i n f o rc e dplast ic ( FRP ) . S tud ies of the m echan ica l p r ope r t ie s o f thei n t e rf a c e a n d t h e r h e o l o g ic a l b e h a v i o u r o f c o m p o s i t e m a t e -r i a l s a r e v e r y i m p o r t a n t t o d e s i g n . F o r t h e e x p e r i m e n t a ld e t e r m i n a t i o n o f t h e m e c h a n i c a l p r o p e r t i e s o f t h e c o n -c r e te /g lue /p la te in te r f ace , a new tes t is suggested . A n i t e r a -t i v e an a ly t ic a l m o d e l c a p a b le o f s i m u l a t i n g t h e b o n d - s l i pa n d t h e m a t e r ia l n o n - l i n e a r it y , b as ed o n t h e c o m p a t i b i li t yo f d e f o r m a t i o n s a n d t h e e q u i l i b r i u m o f fo rc e s, i s d e v e l o p e di n o r d e r t o p r e d i c t t h e u l t i m a t e fo r ce s a n d d e f l e c t io n s . An e w e q u a t i o n i s p r o p o s e d t o a n t i c ip a t e t h e m a x i m a l s h e a rand nor mal s t r e s ses a t the in te r f ace goa l to an t ic ipa te thef ai lu re m o d e d u e t o t h e & b o n d i n g o f th e p l a te . F i n al ly , as e ri es o f l a rg e - s ca l e b e a m s s t r e n g t h e n e d w i t h f i b e r r e i n -f or ced p last ic i s t e s ted up to f a i lu r e ; load- d ef lec t io n cur vesa re m e a s u r e d a n d c o m p a r e d w i t h t h e p r e d i c t e d v al u e s t os t u d y t h e e f f i c i en c y o f t h e e x t e r n a l l y - b o n d e d p l a te a n d t ov e r i fy t h e t h e o r e t ic a l m e t h o d .

R I ~ S U M EN o u s e x a m i n o n s u n c as d ' a p p l ic a t io n d es m a t & i a u x

c o m p o s i t e s p o u r l e g ~ n i e c i v i l l e r e n f o r c e m e n t p a r p l a c a g ed e t i ss u s c o m p o s i t e s d e p o u t r e s e n b ~ t o n a rm ~ . L ac o n n a is s a n c e d e s p r o p r i ~ t& d ' a d h & e n c e b & o n - c o m p o s i t e se t d u c o m p o r t e m e n t r h ~ o lo g i q ue d e c es m a t & i a u x e s ti n d i s p e n s a b l e . P o u r c e la , u n n o u v e l e s s a i a ~ t~ p r o p o s ~p o u r d ~ t e r m i n e r l es p r o p r i ~ t & m ~ c a n i q u e s d e t ' in t e r fa c eb & o n / c o l le / p l a q u e . P o u r d i m e n s i o n n e r l es o uv ra y , e s, n o u sp r o p o s o n s u n e m & h o d e d ' a u a l y s e i t & a t i v e c a p a b l e d es i m u l e r l a n o n - l i n ~ a r i t ~ d e s m a t & i a u x e t l e g t i s s e m e n t d e sp l a q u e s a f i n d ' ~ v a l u e r l e s n i v e a u x d e p o r t a n c e d e c e s s t r u c -t ur e s. U n e n o u v e l l e e q u a t i o n a ~ t8 d & e l o p p & p o u r p r ~ v o i rla c o n t ra i n te m a x i m u m d e l 'i n te r fa c e e t f i n a l e m e n t u n es & i e d e p o u t r e s r e n fo r c ~ es p a r p la c a q e d e t i s s u s c o m p o s i t e sa ~ t ~ t e s t & j u s q u ' a r u p t u r e p o u r ~ t u d i e r l 'e f fi c a ci t~ d e t am & h o d e d e p la c a g e e t v & ~ ' e r l a m & h o d e d e ca lc u l.

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1 I N T R O D U C T I O NT h e m a i n t e n a n c e o f s t ru c t u r e s h a s b e c o m e a n i n c r e a s -ing ly se r ious pr oblem , s ince the cos t o f new s t r uc tur es has

b e c o m e v e r y e x p e n s i v e , a n d r e p ai rs m a y b e v e r y d i f f i cu l t .Br idges , tunne ls , w a te r r e se r voi r s and the r mal or nuc lea rp o w e r p l a n ts m u s t b e m a i n t a i n e d i n a n a c c ep ta b le s e rv i c es ta te . T h e p a t h o l o g i c a l s t u d y o f c o n c r e t e s t ru c t u r e s s h o w sd a m a g e t o t h e s e s t ru c t u r e s b e ca u s e o f t h e d e t e r i o r a ti o n o fmater ials , d es ign er rors or accidents .I n t h e c a se o f d e t e r i o r a t i o n o f t h e m a t e r i al s , c o n c r e t em a y b e s u b j e c t e d t o e r o s i o n , a b r a s i o n a n d t h e e f f e c t o ff ro s t, a n d m a y b e d e s t ro y e d b y p h y s i c o - c h e m i c a l m e c h a -n i s m s s uc h a s ca r b o n a t io n a n d t h e p h e n o m e n o n o f al k a li -a g g r e g a t e re a c t i o n s . A l l o f th e s e d i f f e r e n t m o d e s o f d e t e -

r i o r a t i o n c a n b e s e e n a s c a u s i n g d e b o n d i n g b e t w e e nc e m e n t a n d g r a v e l b y t h e p r o p a g a t i o n s o f c r a ck s ( lo s s o fm a t e r i a l p r o p e r t i e s ) . I n g e n e r a l , t h i s p h e n o m e n o n i s t h eo r i g i n o f t h e c o r r o s i o n o f st ee l a n d t h e d e c r e a se i n r e i n -f o r c e m e n t p e r f o r m a n c e . D e s i g n e r r o r s c o u l d b e d u e t oi m p e r f e c t i o n s i n c a l cu l a t i o n s d e p e n d e n t u p o n a nu n k n o w n f o rc e ( i n fe r io r d e si g n ) o r an i n c o r r e c t m o d e l -l i n g o f s t r u c t u r a l b e h a v i o u r . F i n a ll y , d a m a g e u n d e r a c c i -d e n t a l l o a d i n g m a y o c c u r f o r s t r u c t u r e s i n m a r i n e o rp o l a r e n v i r o n m e n t s o r d u r i n g t h e i m p a c t o f a s h o c k o r a ne a r t h q u a k e . T h e m a i n t e n a n c e o f t h e s e st r u c t u r e s r e q u i r e sthe i n v e n t i o n o f n e w r e h a b il i ta t io n t e c h n iq u e s ; i n o t h e rw o r d s , t h e m a i n t e n a n c e o f t h e s e s t ru c t u re s m u s t c o n s i s ti n p r o t e c t i n g t h e m t o i n s u r e g o o d t ig h t n e ss a n d l i m i t c o r -r os ion , in r ep a i r ing th em to of f se t the los s of s t if fnes s and

Editorial notP r o f P a t r ic e H a m e l i n i s a R I L E M S e n io r M e m b e r

0025-5432/97 9 RILE M 1 6


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Varastehpour Hamelin

Fig.1 - Different methods for strengthening a concrete beamusing an FRP plate.strength, and in strengthening them to improve the per-forman ce and the durability of the structures.

2 INTEREST IN THE SO LU TIO N O FUSING COMPOSITE MATERIALS

compatibility of composites with concrete and steel. Inthe case of repair and maintenance of structures, cost isno t nece ssarily the l imit ing factor.The principle of repair consists of external bondingby woven textiles or previously-cast stratified plates, asdescribed in Fig. 1, to strengthen the RC beam. Therepair and the retrofitting o f concrete structures can beachieved in situ by the REPLAI-ZK met hod, using carbonfiber prepreg sheets without autoclave [2]. The externalbond ing plate technique, by moldi ng in situ is preferableinsofar as it allows one to retrofit pieces of complexgeometry. In this investigation, we developed equ ipme ntfor site use whi ch allows us to achieve the cycles o f pres-sure and temperature described in Fig. 2 [3]. The differ-en t s t eps o f in s ta l l ing and r epa i r ing m em be rs a redescribed as follows: - evaluation o f the level of deterio-rat ion o f the R.C beam - preparat io n of the surfacesandblast .... ) - selec tion of the pla te nu mb er o f layers,character of f iber, textile structure, . . . ) - placem ent ofthe woven tex t i l e and the po lym er iza t ion in situ byapplying a comb ination of temperature heating cover)and pressure vacuum bag).

The repair of concrete beams by the external bondingof a composite plate is an effective method to protectconcrete and restore a part of the stiffi~ess of the structure[1]. Co mpo site materials, because of their high strength,high stiffness, resistance to corrosion and low weight, canbe o f great benefit in structures in order to min imize theweigh t and increase the structural performanc e. Also sig-nificant are their ease of forming, speed of installation,resistance to corrosion, mechanical properties, possibilityof optimiza tion choice of reinforce ment, direction), andmultifunctionality strength, watertightness, anti-corro-sion). These are the principal parameters for choosing acomp osi te mater ia l in the repair of s t ructures . Tw oobstacles limit their d evelopm ent: the cost of these mate-rials in comparison with traditional materials in civilengineering, and the limited knowledge concerning the

Thermocoul~e( I ZS'C) Vacuum=6OOmmHg

Mastic Concrete

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lh 30 ' i 125 C Unpunched film(A50O0) ~ . . . . . .600 rnm H~ Nylon material T89) e = ~ = = = = = ~

Heating plaque r~ '~ ~r ~r lTime Drainage carpet

Vacuum bag

3 METH OD OF CHARACTERIZATIONAND CONTROL OF COMPOSITE

In additio n to the usual data ultimate strength, stiff-ness of the plate), an im porta nt piece o f data for the evalu-ation o f the level of perform ance o f the retrofitting is theadhesion of the FR P plate to the concrete support. Forthe determination of the mechanical interface propertiesstrength, stiffness) and the interaction between the plateand the concrete interface perfect bon d, partial bon d ands l ip) , the s ingle- lap tes t specimen was used. F ig . 3describes the experimental set-up; this test allows us tochoose the best surface treatment and the most efficientglue. It is necessary to emphasize the impor tance of test-ing large specimen sizes in order to take into a ccount thescale effect and the natural heterogeneity of the supportdimens ions of aggregates, character and da m-age level of matrix). Th e fields of stress and

displacement generated by the experimentalset-up were studied by numerical modellingusing specific finite elem ents [4 ]. Fig. 4 showsthe significantly-different behaviours obta inedfrom various combinatio ns of materials glue,plate, surface treatment). It shows the bi-lin-ear behaviour .a t the in ter face, and we cannot ice that the r ig idi ty of the in ter face isQ) dep end en t on the adhesive characteristics, theshear strength on the mechanical properties of| the concrete and the failure mo de on the sur-| face treatme nt [5]. Th e existence of a non -

g) ncgligible slip indicates eithc r thc necessity ofD taking into accoun t the analysis of the beam,| or the necessity of anticipating the mechanical@ connectors and modifying the technologicalrepair procedure.Fig. 2 - Plate bonding by polymerization in-situmethod nd extern l set-up.

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F i g . 3 S i n g l e la p s p e c i m e n t es t d e t a il s a n d e x p e r i m e n t a l s e t u p .

Fig. 4 Interface shear stress versu s shear s t r a i n f o r d i f f e r e n t surface treatments

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4 ANALYSIS OF RC BEAMSTRENGTHENING WITH FRPa ClassicalmethodThis calculation technique can be used toanalyse the bending behaviour of an FIkPreinforced concrete beam by employing theclassical theo ry of RC beams. In addition tothe conventional hypotheses used for rein-fo rced concre te beams, two add i t iona lhypotheses are admitted: the ad herence of theFR P plate is perfect this means there is norelative slip betw een plate an d concrete), andthe tensile strength of con crete is negligible.The behaviour of the FP,.P plate is lin-early elastic up to failure; the behaviour ofsteel i s per fect ly elasto-plast ic , and thebehaviour of concrete in compression isshow n in Fig. 5 c) ACI code). Acc ordin g tothe classical hypotheses of an RC beam, asection subjected to a bending moment Mdistorts as indic ated in Fig. 5 a). On thebasis of this diagram and the stress diagramFig. 5 b)), it is possible to calculate thethree forces in the section at each step byapplying the equations of equilibrium; theposition of the neutral axis is determ inedand this allows us to calculate the bendingmoment and the curvature. Then, the con-juga te beam method and the numer ica l

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0.002 0 . 0 0 3 ec)F i g . 5 M e c h a n i c a l b e h a v i o u r o f the section and o e c u r v e f o r c o n c r e t e i n c o m p r e s s i o n .

Mater ia ls and St ruc tures /Mat6r iaux et Const ruc t ions Vol. 30 , April 1997

Fig. 6 Mechanica l behav iour o f m a t e r i a l s .

in tegrat ion enable us to calculate the relat ionshipbetween the curvature and the displacement.b terat ive calcu la t ion m ethodThe method developed in this study to predict thestrength and stiffness of P,C beams strengthened by F RPplates is an iterative analysis technique, using a computer.Several assumptions com mo nly made in re inforced con-crete th eor y are used: a) plane sections rem ain plane; b) noslip occurs between any longitudinal reinforcement andconcrete; and c) stress-strain relationships of materials canbe determined by standard tests. This iterative analysis is

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Fig. 7 - General f lowchart of the calculat ion model.

entered into the computer program, the load and thedeflection are d eter min ed using strain com patibility.Initially, a top-fiber concrete strain and a neutral axisdepth are assigned. The depth of the beam is dividedinto 200 slices, using the average strain for each shce;the compressive and tensile stresses can then be foun dfrom th e concrete stress-strain curve.Mu lt iplying this value by the area of the sl icegives the compressive and tensile forces. A similarmethod is used to determine the two tensi le forceson the reinforced steel and the external plate. Thetensile force on the external plate must be correctedbecause of the bond-slips in each iteration by deter-mining the shear stress at the interface. The shearstress is dete rm ined in each step o f loading for twosections at a distance ~x in Fig. 8. T he neutr al axis isthen adjusted until the sum of the compressive forcesequals the sum of the tensi le forces (equil ibrium).When this has been at tained, the moment and thecurvature are determined . This calculation continuesup to the m axim um strength of the beam, which isde termine d wh en e i ther the concre te crushes, theFRP fails or plate separation occurs. Th e deflectionof the beam is found using a finite difference model(half of the b eam cut into five sections).

Fig. 8 Calcu latio n of interfacia l shear stress.

c@able of simulating t he material no n-linea rity includingconcrete cracking in tension and the associated tensionstiffening, the plasticity o f conc rete in com pression , theplasticity of the r einforcing steel, and the non-line arity dueto bond-slip betw een plate and concrete.This model is able to predict the ultimate strength inbending, the load-deflection characteristics and failuremo de due to the tensile fracture o f the FBd2, the crushingof conc retc in compression, or platc separat ion. Themechanical behaviour of the material in tension, in co m-pression and at the interface is described by Fig. 6. Thegeneral algo rithm of calculation is described in Fig. 7. First,all the dimensions of the beam (height, width, depth ofsteal, external plate dimensions) mus t be kno wn. Also, thespan and the external load points are required to determ inethe load-deflection relationships. The entire stress-strainrelationships o f the steel, the FP,2 plate, the concrete ( ten-sile, compression) and the interface material law must alsobe known with precision. Once all the data have been

5 SHEAR AND NO RM AL STRESSES ATTHE INTERFACEa General

I t i s obvious tha t in order to an t ic ipa te thebon din g o f the plate, it is necessary to de term inethe d istribution of the shear and nor ma l stresses atthe level of the interface du ring th e loading. In thispart, we suggest a new equation to derive the maxi-mal shear stress at the plate/concrete interface on thebasis of a parametric study. Based on the e quilibriumof the system of internal forces and the compatibilityof the strain in the transverse section, assuming a lin-ear elast ic behaviour of the materials, the averageshear stress at the in terfac e is obtain ed [6]:z in t = )~. V (1)

wh ere V is the shear force and ~. the rigidity of the section.)~ = y p . T p . r l ) / I t and r I - E p / E c (2)

where Tp is the thickness of the plate, 11 the modularratio and It the transformed second m om ent of area interms o f concrete. Th e shear stress calculat ion at theinterface, according to the software, could be describedat each step o f the loading for tw o sections at a distanceax by Fig. 8.Fig. 9 indicates the evolution of shear stress at theinterface as a function of XV for the two methods; theresults show that there is a similar correlation betweenthe two methods up to the point of steel plastification.Beyond th is po in t , the gap be tween the two curvesincreases significantly. The reason for this differentbehaviour is clear: wh en steel reaches the point ofplasti-

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a t e r ia l s a n d Structures/Mat6riaux e t Constructions Vol 30 Apr i l 1997

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Fig . 9 - C om par i son o f d i s t r ibu t ion o f t h e s h e a r s t r e s s a t t h e i n t e r face .

f i c a t i o n , t h e F P , ,P p l a t e m u s t c a r r y t h e w h o l e t e n s i le l o a di n t h e s e c t i o n . C o n s e q u e n t l y , t h e s h e a r s t r e s s a t t h ei n t e r f a c e i n c r e a s e s , a n d t h u s t h e s l o p e o f th e c u r v ec h a n g e s a b r u p t ly . H o w e v e r , e q u a t i o n 1 ), w h i c h d i s r e-ga r ds the p las t ic beh av iou r of stee l, a lw ays g ives a con -s t a n t s l o p e o f t h e c u r v e .b P r o po s i t i o n o f n e w equa t i o n

T o s i m u l a te t h e n o n - l i n e a r b e h a v i o u r o f m a t e r ia l i nt h e d i s t r i b u t i o n o f th e m a x i m u m s tr es s at t h e in t e r f a c e ,i t is n e c e ss a r y to d e v e l o p a n e w e q u a t i o n b a s e d o n t h er e s u lt s o f n o n - l i n e a r c a l c u l a ti o n s . S o , w e e x a m i n e d t h ee f f e c t o f t h e d i f f e r e n t v a r i a b l e s, s u c h a s r i g i d i t y a n dt h i c k n e ss o f t h e p l a t e, g e o m e t r y o f t h e s e c ti o n , l o a d i n gm o d e , e t c. A s a c o n s e q u e n c e o f t h is p a r a m e t r i c s t ud y , w eh a v e i n t r o d u c e d a f a c t o r ~, c o m p o s e d o f th e d i f f e r e n tv a ri a bl e s w h i c h h a v e a n i m p o r t a n t i n f l u e n c e o n t h e d i s -t r i b u t i o n o f s h e a r st re ss a t t h e i n t e r f a c e . F i g . 1 0 s h o w st h e d i s p e rs i o n o f t h e m a x i m u m n o r m a l i z e d v a l u e m u l t i -p l ied by [3) o f the shea r s t re s s f or va r ious e xam ples de te r -m i n e d b y n o n - l i n e a r s o ft w a re as a f u n c t i o n o f ~ k V o n al o g a r i t h m i c s c a le . B y u s i n g r e g r e s s i o n a n al y si s, t h e b e s tf i t l i n e w a s t r a c e d i n o r d e r t o d e t e r m i n e t h e r e l a t i o n s h i pbe tw ee n shea r f or ce and sh ea r st re s s.

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( h ) .7 X Tp x E pP y p x T p r lT p b p K= I ' ~

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/ n a2 0 2 5 3 0L N I ] . X . V )

Fig. 10 - Regression to evaluate the s h e a r s t r e s s l o a d relationships.

1 ~ 0 . 5" li n t = ~ 9 . ( ~ . . V ) 1 "5 ( 3 )W h e n f ai lu r e o c c u r s b y d e b o n d i n g , t h i s is c h a r-a c t e ri s e d b y d i a g o n a l a n d h o r i z o n t a l c r a c k i n g i nt h e c o n c r e t e i m m e d i a t e l y a b o v e t h e g l u e l i n e . T h i s

t y p e o f c ra c k i n g c o u l d a l so b e d u e t o n o r m a ls t res ses a t the e nd of the p la te . F or the s impl i f iedcase in w hic h in te r f ace shea r s t re s ses a r e con s tan t int h e a n c h o r a g e z o n e , t h e f o r c e s y s te m i n F i g . 7 m a yb e r e p l a c e d w i t h a n e q u i v a l e n t s i n g l e f o rc e a n dc o u p l e a c t i n g t h r o u g h t h e c e n t r o i d o f th e p la te :M x y - b p . r a + r p / 2 ) , z i n t 4)

w h e r e M x y i s t h e t w i s t i n g m o m e n t p e r u n i tl e n g t h , T a t h e a v e ra g e g l u e l in e t h i c k n e s s a n d T pt h e p l a t e t h i c k n e s s . T h e n o r m a l s t r e s s a t t h e e n do f t h e p l a t e i s th e r e s u lt o f t h is t w i s t in g m o m e n t ,w h i c h i s d e p e n d e n t o n t h e i n t e r f a c e s h e a r st re s s:

o n = K . z i n t 5)I n t h i s e q u a t i o n , K i s a p a r a m e t e r r e l a t i n g t h e s h e a rs tr es s a n d t h e n o r m a l s t re s s a t t h e e n d o f t h e p l a t e ; i t

d e p e n d s o n t h e p h y s i ca l a n d m e c h a n i c a l p r o p e r t ie s o f th eg l u e a n d p l a t e [ 7 ].1 3 1 ( T p E a ] /4K = . t T a m ~ ) 6)

w h e r e E a a n d E p a re t h e e la st ic m o d u l u s o f t h e g l u e a n do f t h e F R P p l a t e , re s p e c ti v e ly .

6. FAILURE CRITERIA AN D EXPERIMENTAL STUDY TO DETERMINE C AN D 0

T he in te r f ace could a l so c r ack in a d i r ec t ion pa r a lle l tot h e g l u e l i n e u n d e r c o m b i n e d s h e a r a n d n o r m a l s t r e s s e s ,w h i c h h a s b e e n e x p l a i n e d i n t h e p r e c e d i n g s e c t i o n .H o w e v e r , w h e n d e b o n d i n g , f ai lu r e is g o v e r n e d b y t h eM o h r - C o u l o m b la w , w h i c h m a y b e e x p r e ss e d i n t h e f o r m :

zma x o . . - C 7 )w h e r e x m a x i s th e u l t i m a t e s h e a r st r e n g t h o f t h ei n t e r f a c e , C t h e c o h e s i o n , o n t h e s t r e s s n o r m a lt o t h e g l u e l i n e a n d ~ t h e a n g l e o f i n t e r n a l f r i c -t i o n . T h e r a n g e s o f C a n d ~ ar e a t t r i b u t e d t ov a r i a t io n s i n s u r f a c e p r e p a r a t i o n a n d t h e p r o p e r -t ie s o f t h e a d h e s i v e a n d c o n c r e t e . I n t h i s s e c t i o n ,t o d e t e r m i n e t h e c o h e s i o n p a r a m e t e r C , w e h a v eu s e d t h e e x p e r i m e n t a l s e t - u p d e s c r i b e d i n F i g .3 . T h i s p r o p o s e d s i n g l e - l a p s p e c i m e n , w h i c ho n l y h a s a s h e a r s tr es s fi e l d , is u s e d i n t h e d e t e r -m i n a t i o n o f C . T h e s p e c i m e n c o n s i st s e ss e n ti a ll yo f t w o L - s h a p e d c o n c r e t e b l o c k s w h i c h a r eb o n d e d b y a n F P , .P p l at e 2 m m t h i c k a n d 1 40m m w i d e . T h e d i s ta n c e a lo n g t h e g l u e d l in e w a sk e p t c o n s t a n t a t 1 8 0 m m , a n d t h e g l u e t h i ck n e s sw a s m a i n t a i n e d a t 2 m m . T h e w h o l e a s s e m b l yw a s s u b j e c t e d t o a c o m p r e s s i v e l o a d i n g t e st . T h e

6 4


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1098

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2

R e s u l t o f s h e a r s i n g l e- l ap t e st

D

[] Tin=5.4 M P a

9 i . ! . i . ! . I . i . ! . i . i i

C_./H V/H O/H C/S V/S O/S C/C V/C O/CS p e c i m e n

1C98

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R e s u l t o f b e n d i n g t e s t ( 7 x 7 x 2 8 )

9 T-m=4.2 MP a[ ] 9 it

[]D

i I 9 i 9 i i ! , t 9 i I I i i i i I

S1 S2 S3 e l C 2 C 3 H 1 H 2 H 3S p e c i m e n

Fig . 11 -Experimentalstudy for theevaluated cohe-sion (C) andthe frictionangle (@).

test variables were the adhesive and the FRP types. Fig.11 shows the variat ion o f the shear s t rength for di fferentspecimens. T he average value of C is suggested to equal5.4 MPa.In the second part , in order to determine the fr ict ionang le ~) , d i f fe ren t smal l beams s t reng thened wi th FRPwer e used [8 ] . Each smal l beam had a c ross -sec t ion o f7 0 m m x 7 0 m m a n d a to t al le n g t h o f 28 0 r a m . T h eexperim ental set -up consisted o f a s imply-supported beamsub jec ted to two concen t ra t ed loads , symm et r i ca l abou tthe mid-span. T he specimens were equipped with elect r i -cal strain gauges positioned o n the plate. All o f the speci-mens were loaded to failure at the same loading rate (0.2mm/ mi n ) . D u r i n g t h e t e s t , s t r a i n s o n t h e p l a t e w e r erecorded by an au tomat i c da ta acqu i s i t i on sys t em. Thevar i ab le parameters fo r the smal l beams were the FRPtypes and the type of adhesive. Using the average results ofdifferent specimens w hich failed by debond ing, the shearstress at the interface was equal to 4.2 MPa (Fig. 11); byusing equation (5) (relationship between shear and normalstresses), the average norm al stress in failure was equal to1 .6 MPa. To ca lcu la t e the f r i c t ion ang le , we used theM ohr -C oul om b equation wi th C = 5.4 MPa, ~ = 4 .2 MP aand on = 1.6 MPa. In this case, a friction angle o f 33 ~ wasob ta ined . Beg inn ing wi th the Mohr-Coulomb equat ionthat takes into accou nt the failure cri ter ion o f the interfacewith the r and C values found in this investigation, them ax im um shear stress could be calculated as:

5.4" [ m a x - - ( 8 )1 + k. tg33 ~

T o p r e d i c t t h e u l t i m a t e c a p a c i ty o f an R C b e a ms t reng thened wi th an ex te rna l ly -bonded FRP p la te tha tfails by plate separation, we can use equation (4). In thecase o f four -po in t bend ing (V - P/2 ), t he separat ion loadis obtain ed as:2s e p - 3 2x3ax (9 )

~ . [ ~ 3

P 2 ~ P 2

2 0 0 0 mat2 3 0 0 mm

150mm

Fig. 12 - Geom etryo f the beam and test set-up.

Equat ion (9 ) descr ibes the debond ing load and canp r e d i c t t h e u l t i ma t e c a p a c i t y w h i l e t h e a v e r ag e s h e a rs tress at the interface reaches ' tmax.

7 EXPERIMENTAL STUDY OF THERC BEAM REINFOR CED BY FRP

A t o ta l o f t h r e e r e c t a n g u l a r r e i n f o r c e d c o n c r e t eb e a m s w e r e c a s t . T w o w e r e s t r e n g t h e n e d w i t h F R . Pplates by the polymerizat ion in situ me t h o d ( P l , P2 ) ; o n ebeam was used as a con t ro l spec imen (P0) . The beamswere tes ted to fai lure in order to invest igate the effec-t iveness o f the repa i r and ca lcu la t ion metho d . On e typeof FP, .P plate was used durin g the tests: a u nidirect iona lFILP with the f ibers oriented solely in the longi tudinald i r e c t io n . I t is c o m p o s e d o f H R c a r b o n f i b e r , s u b -me rged in an epox y resin. T he mechan ica l p roper t ies o fthe mater i a l s , t he t cs t s c t -up and the p la t e d imens ionsare shown in Fig. 12.Tab le 1 compares the u l t imate load , t he cu rva tu reand the fa i lu re m ode ob ta ined exper im en ta l ly wi th thetheore t i ca l resu lt s ca l cu la ted us ing the non - l inear so f t -w a r e ( w i t h o u t p r e ma t u r e f a il u re e f f e ct ) a n d u s i n g t h emeasured m echan ica l p roper ti es . T he fa ilu re was due tothe debo nd ing o f the p la te a t t he in t e r face . Th i s & bo nd -i n g w a s c a u s e d b y t h e c o u p l i n g o f t h e d i a g o n a l a n dbend ing c racks. At the m om en t o f debond ing , t he aver -age shear s tress was equal to 1 .65 MP a. O ne ma y note in

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M a t e r i a l s a n d S t r u c t u r e s / M a t 6 r i a u x e t C o n s t r u c t io n s Vol . 30 Apr il 1997

O0

80

60

40

20

T a b l e 1 - R e s u lt o f e x p e r i m e n t a l t e s tExperimental Theoretical

PO P1 P2 PO P1 P2U l ti mate l o ad kN ) 125 193 195 114 . 6 236 236Ul t imate mom ent 4 3 . 7 6 7 . 5 6 8 . 2 4 0 . 1 8 2 . 5 8 2 . 5{kN.m)Ultimate curvature 0 . 0 9 0 . 0 2 3 0 . 0 2 5 0 . 0 8 1 0 . 0 3 7 0 . 0 3 4( l / m)F ailu re m o d e C o n c r e t e Debonding Debonding Con crete Con crete Concrete

crushed crushed cru sh ed crushed

1 ~ P0 (The.)P0 (Exp.)Pn (The.)P1 (Exp.)P2 (Exp.)

I I I

0.02 0.04 0.06C o u r v a t u r e (1/m)

I I i

0 0 0 0,08 O,10

Fig. 13 - Com parison of mom ent-curvature relationships for different beams.

t h e t a b le a s i g n i f i c a n t in c r e a s e i n s t r e n g t h r e la t i v e t o t h eu n p l a t e d s p e c i m e n s ; t h i s i n c r e as e , w h i c h i s 5 5 , a c c o m -p a n i e d a r e d u c t i o n i n t h e d u c t i l i t y . F i g . 1 3 s h o w s t h ec u r v a t u r e s i n t h e c e n t r a l s e c t i o n a s a f u n c t i o n o f t h ea p p li ed m o m e n t ; t h e m e a s u r e d m o m e n t - c u r v a t u r e r e la -t i o n sh i p s o f t h e b e a m a p p r o a c h e d t h e t h e o r e ti c a l c u rv eo b t a i n e d b y t h e n o n - l i n e a r s o f t w a r e w i t h s a t i s f a c t o r yaccuracy.

8 C O N C L U S I O NT h e u s e o f an F I ( P p l a te f o r th e r e t ro f i t ti n g o f c o n -c r e te s t r uc tur es i s pa r t i cu la r ly a t t r ac t ive , s ince an inc r ease

i n r i g i d it y a n d s t r e n g t h c a n b e o b t a i n e d q u i c k l y b y t h ep r o c es s o f p o l y m e r i z a t i o n in s i tu T h e e f f i c i e n c y o f t h er e p a i r p r o c e s s i n c l u d e s t h e c r i t e r i a o f a n t i - c o r r o s i o n ,i m p e r m e a b i l it y a n d i m p r o v e m e n t s i n m e c h a n i c a l b e h a v -i o u r. F r o m a n e c o n o m i c p o i n t o f v i e w , t h e c o s t o f r e t r o -f i t t i n g d a m a g e d s t r u c t u r e s b y a n F R P p l a t e is j u s t i f i e d , a sl o n g a s t h e c o s t o f r e p a i r r e m a i n s n e g l i g i b l e c o m p a r e d t ot h e r e p l a c e m e n t o f a n e w s t ru c t u re . T h e p e r f o r m a n c el e ve l o f t h is t e c h n i q u e i s d e p e n d e n t o n t h e p r o p e r t i e s o f

a d h e r e n c e a n d n o n - s l i p o f t h e p l a t e / c o n c r e t ei n t e r f ace .

T h e n e w s i n g l e - l a p t e s t s e t - u p i n t r o -duced i n t h i s paper has p roven t o be r e l i ab l ei n m e a s u r i n g t h e p a r a m e t e r s n e c e s s a r y f o rt h e c h a r a c t e r i z a t i o n o f th e c o n c r e t e / g l u e /p l a te i n te r f a c e . T h e q u a l i f i c a ti o n m e t h o d o l -o g y a n d s u g g e s t e d c a l c u l a t i o n m e t h o d p r o -duc e a sa t i s f ac t o ry r esu l t , and i t i s nece ssaryt o c o m b i n e a l l o f th e s e a p p r o a c h e s t o w a r d s an o r m a l i z a t i o n p h a s e f o r t h e t e s ts a n d t o c o d -i f y t h e c a l c u l a ti o n s . T h e c o m p u t e r m o d e l , i nt h e f o r m o f a n o n - l i n e a r p r o g r a m d e v e l o p e di n t h is s t u d y , a p p e a rs t o b e a g o o d m e t h o d t op r e d i c t t h e f l e x u r a l s t r e n g t h , t h e u l t i m a t ed e f l e c ti o n a n d t h e m o m e n t - c u r v a t u r e r e la -t i o n s h ip s . R . e c e n t r e s e a rc h c o n d u c t e d i n t h i sl a b o r a t o r y h a s s h o w n t h a t t h e c o m p o s i t e s y s -t e m c o u l d s i g n i fi c a n tl y m o d i f y t h e d y n a m i cb e h a v i o u r ( v i br a t io n , i m p a c t ) o f a c o n c r e t es t ru c t u re . T h e e n e r g y c o n s u m p t i o n a n d t h edam pi ng c harac t e r i s ti cs o f t hese m at er i a l s a res i g n i f i c a n t i n s h a p i n g n e w p e r s p e c t i v e s o fi n d u s t r ia l d e v e l o p m e n t .

R E F E R E N C E S[1] M eier, U. an d Ka iser, H., 'Strengtheningof struc-tures with CFILP laminates' , Proceedings of theASCE Conference - ACM materials i l l CivilEnginee ring Structures, 1991,224-232,[2] 'Ca rbon fiber reinforcedearthquake resistant retro-fitting', Mitsubishi Kasei Techn ical Doc um ent, Toky o,Japon,

1 9 9 5 .[3} Ha m elin, P., Varastehpour, H. and La garde, G., 'L e renforc em entdes ouvrages d'art par des armatures composites' , Jou rn sEurop nnes sur des M at iaux Com posites, Avril 1995, Paris,France.[4] Sahran-Bajbouj , A. , Cour tade, lL.M. and Verchery , G. ,'Modeling of coherent interfaces by mixed finite elem ent ' ,CADCOMP 92 , Newark (USA) , 13 -15 May 1992 , i n'Com puter aided design in composite material technology' ,Editors Adv ani, Blain, De W ilde, G illespie and Griffin (Elsevier,1992) 431-442.[5] V arastehpour, H. and Ham elin, P., 'Structural behaviour of re in-forced concrete beams strengthened by epoxy-bonded F1LPplates', Sec ond InternationalSyinposiumon N on-me tallic (FRP)l~,einforcementof C oncrete Structures, 23 A ugust 1995, Ghent,Belgium , 559-567.[6] Jones, lL., Swam y, R.. N., and Charif, A., 'Plate separation andanchorage of reinforced concrete beam s strengthenedby epoxy-bon ded steel plates',The Structura l ngit~eer6 6 (5) (1988) 85-9 4.[17] lLoberts, T. M ., 'Appro xim ate analysisof shear and norm al stressconcentrations in the adhesive layer of plated lLC be ams ', T h eStructural ngineer 67 (12) (1989) 229-233.[8J Varastehpour, H. and H am elin, P., 'External reinforcemen t ofconcrete beam using fiber reinforced plastics', InternationalAssociation for B ridge and Structural Engineering Symposium,23 A ugus t 1995, San Francisco, US A, 1229-1234.

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