Flexural analysis and design of reinforced concrete beams with externally bonded FRP reinforcement

Transcription

1 Avalable ole at Materal a Struture 8 (Marh 005) lexural aal a eg o reore orete beam wth exterall boe RP reoremet N. Peš a K. Plakouta Uvert o Sheel, Dept. o Cvl & Strutural Egeerg, Mapp Street, Sr reerk Mapp Bulg, Sheel, S1 JD, UK Reeve: 1 Otober 00; aepte: Jul 004 ABSTRACT Th work aree the lexural aal o reore orete beam wth exterall boe RP (bre Reore Polmer) reoremet. A umeral metho ha bee evelope or the omputato o the beg momet apat o RP-plate reore orete beam a preto o the lexural alure moe. The expreo or the upper a lower value o the haratert plate reoremet rato are erve or retagular a T-eto ug the Eurooe moel or orete. A low-hart o the umeral proeure, utable or omputer mplemetato, lue a t aura valate wth avalable expermetal reult. Some o the ovel eature o the umeral aal are emotrate through a bre vetgato o the eet o loa atg at the tage o tregtheg o the ultmate lexural apat a eormato behavour o RP-plate R.C. beam RILEM. All rght reerve. RÉSUMÉ Ce traval aale le omportemet e lexo e poutre e béto armé ave reoremet extéreur par PR (polmère reoré e bre). Ue méthoe umérque a été éveloppée pour le alul e la apaté u momet e lexo e poutre e béto reoré e plaque e PR, et pour la prévo e moe e éallae e lexo. De expreo pour le valeur upéreure et éreure e rapport aratértque e e reoremet ot été érvée pour ue eto retagulare et e eto e T e utlat le moèle Eurooe pour le béto. U orgagramme u proéé umérque, appropré à l exéuto umérque, et lu et o exattue et valée par le réultat expérmetaux poble. Certae e aratértque orgale e l aale umérque ot été émotrée par la brève reherhe ur le eet u hargemet prééemmet applqué ur la apaté e lexo ale et le éormato e poutre e béto armé reoré e plaque e PR. 1. INTRODUCTION The lexural tregtheg o reore orete beam wth exterall boe tele RP reoremet ha bee prove to gatl reae the ultmate loag apat o reore orete beam. Prevou vetgato [1-] have how that, oe the exteral RP reoremet apple, the reore orete beam a exhbt a umber o eret alure moe. Bae o expermetal obervato, the haratert alure moe or RP-plate orete beam ubjete to lexural loag a be lae to the two ategore: The brttle ebog alure: a) peelg-o or the plate-e ebog wth or wthout the ormato o aoate hear rak; b) orete over elamato wth the ormato o horzotal rak, propagatg rom the plate e, a laer betwee the boe plate a tele teel reoremet; ) lexural plate ebog the rego o the maxmum beg momet. ull ompote lexural alure: a) orete ruhg ompreo; b) orete ruhg ompreo preee b the elg o tele teel reoremet; ) the rature o boe RP plate teo whh preee b the elg o tele teel reoremet. Whe RP plate are apple ol o the bottom tele urae, the brttle alure a prevet the ull utlato o the lexural apat o reore orete beam. Some reet tue gave the aaltal ormulato or the earl plate elamato alure ue to the tre oetrato at the plate e [4] or at the loato o the lexural rak RILEM. All rght reerve. o:.1617/19

2 184 N. Peš, K. Plakouta / Materal a Struture 8 (005) orete at the m-pa o the beam [5]. O the other ha, b mplemetg atoal plate ahorg heme uh a U-hape RP wrappg or rlle teel bolt, the premature alure oul be avoe a the ou eg hte towar the more erable lexural alure moe. Hee, th tu aree ol the ull ompote lexural alure wth the am to preet a veratle aaltal metho a orm utable or pratal applato.. CONSTITUTIVE MATERIAL LAWS.1 Corete eg moel I a mple maer, the beg momet apat o the RP-plate orete eto a be approxmatel evaluate b ug the equvalet retagular tre-blok agram or orete ompreo [6]. or the etoal eg preete th paper, a le wth the Eurooe [7] (or CEB-IP Moel Coe 90 [8]) reommeato, a more realt parabol-retagular ompreo tre-tra ( - ) agram or orete how g. 1 aopte. g. - No-lear orete ompreo moel. g. 1 - Deg moel or orete ompreo. or the haratert tregth o orete k a the ultmate ompreve tra u = (the egatve value or ompreo), the tre-tra agram ee b: ), or k (4 k, or (1). Corete olear moel A whle Eurooe a CEB-IP 90 moel oe allow the orete tele tregth to be eglete eg o orete eto reore wth teel bar, t expete that the tregtheg b mea o RP reoremet oul have a gat eet o teo teg a o the urther evelopmet o eleto. Thereore, t ma be more approprate to umerall evaluate eleto o the RP-plate RC beam ug the o-lear ottutve moel or orete. or o-lear aal, the tre-tra ( - ) relato or orete ompreo rom g. reommee b CEB- IP MC 90. The moel ee b the ollowg relato: ( ) k () k 1 ( k ) g. - Nolear orete ottutve law or teo. where = / 1, 1 =-0.00 the tra orrepog to the haratert orete tregth ( k ), k=1.1e 1 / k a E the elat moulu o orete. The orete teo teg eet hematall preete g.. A eal lear elat behavour tpall aume or orete utl the tele tre reahe the value o t mea tele tregth eote a tm. The potrakg tre-tra behavour a be mpltall repreete wth a blear brah o the ottutve moel (the hage te ee wth the tre a tra value o t,r 0. tm a t,r t ) or whh the ultmate tele tra o orete a be take a tu 5 t.. Steel reoremet Steel ommol oere eg a peretl elatoplat materal ee b t elg tregth,, a elat moulu, E, but other uaxal ottutve moel or teel teo, uh a the more aurate Meegotto-Pto moel [9], oul be aopte or a umeral etoal aal whe upple a the tre-tra ( - ) par o ata. However, a the etale expermetal tre-tra urve or teel reoremet ote ot avalable, a trlear hareg moel or teel rom g. 4 a be apple. It ee b:

3 N. Peš, K. Plakouta / Materal a Struture 8 (005) CROSS-SECTIONAL RELATIONS The lexural aal o orete eto wth exterall boe tele RP reoremet bae o the ollowg aumpto: Plae eto (beore eormato) rema plae at all tme. There o lp betwee the teel or RP reoremet a orete. The otrbuto o the aheve laer to the lexural apat eglete. g. 4 - Trlear tele tre-tra agram or teel..1 Stra trbuto The relato betwee the eutral ax epth, x, the tra teel a RP reoremet a the maxmum ompreve tra orete are govere b the tra ompatblt equato: ( x ) / x (5) 1 ( a ) / x (6) ( h' x ) /( x ) (7) t 1 Here, ompreve tra orete a teel, a, are take a egatve, t = 1 (h-x )/(-x ) the tele tra orete uer the extg loag pror to the applato o the RP plate a h =h+t a +0.5t the tae rom the etro o boe plate to the top ege o a eto a how later g. 6 a 7. g. 5 - Lear elat tele tre-tra agram or RP. E, 0 (-a) ( k ), (-b) k k k k ( u k ), k u (-) u.4 RP reoremet k or RP materal, a eal elat behavour aume utl the alure (g. 5) a the uaxal tele tre-tra ( - ) relato mpl gve b: E, k 0 (4) where E the elat moulu a the haratert tra at rupture o the RP materal. g. 6 - The tre-tra agram or retagular eto.

4 186 N. Peš, K. Plakouta / Materal a Struture 8 (005) ompreo ore orete a t tae rom the top ege o the eto are: x 0 ( x) b( x) x (1) g. 7 - The haratert ompreve tre-tra agram or T-eto.. Iteral ore reoremet Whe the ro-eto o a hape ubjete to the potve beg momet M, the mot geeral orm o equato erbg the equlbrum o the teral etoal ore : 0 (8) 1 t x x 0 ( x) b( x) xx (1) I the ollowg oerato, the oluto to the above equato are gve or a ommo retagular eto a or a T-eto, repetvel. The otato wll reer to the haratert tregth o materal whh are ormall ue verato wth expermetal reult whe the ultmate lexural apat o tregthee beam o oer. The evaluato o eg value o beg momet apate woul ol requre the trouto o partal aet ator or orete,, teel,, a RP,, a replaemet o repetve haratert tregth wth ther eg value.e. = k /, = / a = k /. 1 h' a t t M (9) The tele ore the boe RP plate wth the etoal area A rp =b p t p : A E () rp a the reultg tele a ompreve ore the teel reorg bar are: (11-a) 1 A 1 1 (11-b) A where the tele tre the teel bar eterme rom Equato (4) a (-a, -b or -) a the ompreve tre eterme whe Equato (6) ubttute Equato (-a, -b or -) otg that eret aaltal tre-tra moel or teel teo a ompreo a be ue the aal. t the reultg tele ore orete a t t tae rom the upper ege o the ro-eto. I the orete teo teg eet take to aout, the overall tele ore obtae ug the tre-tra ottutve law rom g. a the area uer the ( t - t ) urve multple b the wth o orete eto. 4. COMPRESSIVE ORCE IN CONCRETE or a gve epth o the eutral ax x a the kow wth o a eto b(x), the geeral expreo or the 4.1 Retagular eto or value o a maxmum orete ompreve tra 0.00, the tre agram ha ol a parabol part (g. 6-a) a that ae a are eterme rom [9]: (6 ) kbx (14) 1 8 x (15) 4(6 ) I the maxmum ompreve tra or orete the rage , the tre agram wll take the parabol-retagular hape how g. 6-b. I th ae, the reultg ore a t tae rom the top ompreo ege are [9]: kbx (16) ( 4) 0.5x ( ) (17) 4. T-eto I the eutral ax wth the lage o the T-eto (x < ), the equato erve or the retagular eto appl, but wth the lage wth b ue tea o the wth o the retagular eto b.

5 N. Peš, K. Plakouta / Materal a Struture 8 (005) Whe the eutral ax the web o the T-eto (x > ), three eret ae mut be aale eparatel whe tegratg Equato (1) a (1). g. 7 how that the ompreo ore a t poto ow epe, apart rom the maxmum orete ompreo tra, alo o the value o the ompreve tra at the bottom o the lage w a, whe >0.000, alo o the tae x r betwee the upper ege o a eto a the bre where the ompreve tra reahe the value o : x w (18) x x r x (19) Ater tegratg Equato (1) a (1), a, wth the trouto o the ollowg auxlar parameter: b x (0-a) 1 k (6 ) (6 w ) w (1 b / b )(1 / x 4 w 5 ( b x ) / k (8 ) 6 (8 w ) w 7 ) (0-b) (0-) (0-) (0-e) (0-) (0-g) the loe-orm oluto or the ompreve ore,, orete T-eto a t poto,, are eterme rom the ollowg expreo: (g. 7-a) 1( 4 ) (1) (1 ) () 48 x a (g. 7-b) w xr 1( ) () x 1 xr xr x 5 (1 )( x x x r 7 5 (1 ) (4) 1 x 4 x a (g. 7-) w k b bw ( xr ) bw ( x xr ) (5) k b bw ( xr r ) + k 7 bw ( x xr ) xr ( x xr ) 4 (6) 5. LIMIT RP PLATE REINORCEMENT RATIOS The plate reoremet rato or retagular a T- eto, repetvel, are ee b the area o the boe RP plate, A rp, a the eetve area o the orete eto: A rp (7) b b A b rp (8) w ( 5.1 The lower haratert or balae reoremet rato ) The lower lmt value o orrepo to the multaeou tele rature o the RP plate a orete ruhg ompreo. or th moe o alure, the eutral ax epth eterme rom: x, u u (9) k Itroug Equato (9) a (16) to the equlbrum oto gve b Equato (8), the lower lmt value o the RP plate reoremet rato or retagular eto obtae a:, l. A 1A1 8 k (0-a) k u 8 (0-b) u where a are the rato a the elg tregth o teel reoremet wth ubrpt 1 a eotg the tele a ompreve reoremet, repetvel. I a more geeral orm, or T-eto, the above equato a be wrtte a: t

6 188 N. Peš, K. Plakouta / Materal a Struture 8 (005) , l. ( A 1A1 9 ) k (1-a) 9 (1-b) b b ( ) w Reallg that the ompreve ore epe o the value o x r, houl be alulate rom Eq. () x r <, whle Equato (5) houl be ue or x r >. Approxmatel, the beg momet apat or the lower lmt value o the plate reoremet rato M u,l. a a be evaluate rom: M u, l. rp k ( 1 1 A h' ) A ( ) () 5. The upper lmt value o the RP plate reoremet rato The upper haratert or the maxmum reommee value o the RP-plate reoremet rato orrepo to the lexural alure where orete ruhe ompreo jut beore the elg o tele teel reoremet our. The eutral ax epth or th tpe o alure gve b: x, u () u B troug Equato (), (0-b), (16) a (7) to Equato (8), the maxmum reommee RP reoremet rato or retagular eto eterme rom:, u. A A (4-b) h' E 1 t (4-b) (1 ) a or T-eto, the upper haratert RP plate reoremet rato ee b: 1, u. ( A 1 A 1 9 ) (5) The beg momet apat oormg to the upper lmt value o the RP plate reoremet rato a be approxmatel evaluate rom: M u, u. rp ( 1 1 A h' ) A ( ) (6) or pratal tregtheg or upgrag oerato, Equato (6) gve the maxmum lexural apat whh a be aheve or the gve ro-eto, materal properte a the extg loag at the tme o tregtheg. 5. lexural alure moe The gae o the haratert value o the RP k plate reoremet rato or the gve etoal geometr a materal properte etermg the goverg moe o lexural alure. or the aopte ro-eto area o boe RP plate a the aoate reoremet rato, oe o the three poble ae a our:, u. The plate reoremet rato greater the the upper lmt value a the R.C. beam over-reore. The ultmate lexural alure woul be o-utle through the orete ruhg ompreo wthout the elg o tele teel reoremet., l., u. The plate reoremet rato betwee the lower a the upper lmt value. The alure woul be utle wth the elg o tele teel reoremet ollowe b orete ruhg ompreo.,l. The RP plate reoremet rato maller tha the lower lmt value. The R.C. beam uerreore a the evetual lexural alure woul our ue to tele rature o the RP plate, preee b the elg o tele teel reoremet. 6. NUMERICAL PROCEDURE OR CROSS-SECTIONAL ANALYSIS A large umber o parameter ou to luee the aal a the mot oveet wa to have them lue the lexural aal o RP-plate RC beam through the applato o umeral metho. The ottutve moel rom eto -5 are mplemete to a robut teratve proeure whh wll, to the maxmum extet poble, avo ueear eg a aaltal mplato. Bult o the remetal tra tehque whh ha alrea bee ue or the o-lear lexural aal o RPplate RC beam [11], a omplete aal algorthm how g. 8 together wth the ommetare explag the vual alulato tep. or the apple beg momet at both tage, the terato wll top whe: the retg momet o teral ore beome equal (wth the ere aura) to the apple beg momet or; the maxmum ompreve tra orete or/a tele tra teel or RP reoremet exee the materal lmtg tra at the pot o lexural alure. The preete umeral proeure mprove b logal vo to Stage I (beore...) a Stage II (... ater the RP plate ae, repetvel). I th wa, the atual tra trbuto whh ext the RC eto pror to plate bog properl herte Stage II o the aal. The eet o pre-loag take to aout through the omputato o the orete tele tra at the bottom o a eto, t, (appear Equato (9), (4), (5) a (6)) obtae a oe o the reult at the e o Stage I.

7 N. Peš, K. Plakouta / Materal a Struture 8 (005) g. 8 - Algorthm o the umeral proeure or etoal aal o RP-tregthee RC beam.

8 190 N. Peš, K. Plakouta / Materal a Struture 8 (005) Wth the orporate ottutve moel or orete omputato o the orete tele tra at the bottom o a eto, t, (appear Equato (9), (4), (5) a (6)) obtae a oe o the reult at the e o Stage I. Wth the orporate ottutve moel or orete ompreo a teo rom g. a, the aura o the umeral proeure pretg lexural alure moe a ultmate beg momet apate ha bee valate wth the avalable expermetal ata reporte the lterature a how Table CALCULATION O DELECTIONS Whe extg R.C. beam are tregthee lexure to arr a hgher loag tha the were tall ege or, aother mportat ue whh requre oerato the verato o the m-pa eleto whh wa the prpal objetve or troug umeral proeure the prevou eto. Negletg the hear eormato, the maxmum tataeou eleto o a R.C. beam, v max, : L vmax ( x) M '( x) x (7) 0 Table 1 - Expermetal a aaltall prete ultmate lexural apate o R.C. beam tregthee wth CRP (arbo RP) a gla RP (GRP) plate Beam RP Seto Geometr a Materal Properte Beg Momet Error alure Re. Plate b/h k 1 1 E k M u,exp. M u,al. M Tpe 1 No. Mat. [mm] [MPa] [MPa] [%] [GPa] [MPa] [%] [knm] [knm] [%] (Materal) Rthe et al. [1] E GRP 15/ SY, L CRP 15/ SY, Saaatmaeh a Eha [] A GRP 05/ CC, SY Tratallou a Plevr [1] B CRP 76/ SY, B CRP 76/ SY, Ro et al. [1] 4B CRP 00/ CC, SY 4C CRP 00/ CC, SY 4D CRP 00/ CC, SY 5B CRP 00/ CC, SY 5C CRP 00/ CC, SY 5D CRP 00/ CC, SY 6C CRP 00/ CC, SY 6D CRP 00/ CC, SY Ahme a Va Gemert [14] D.1 CRP 15/ SY, Ngue et al. [15] A1500 CRP / CC, SY Rahm a Hutho [16] C4 CRP 00/ CC, SY C5 CRP 00/ CC, SY C6 CRP 00/ CC, SY Almuallam a Al-Salloum [17] G1 GRP 150/ CC, SY G GRP 150/ CC, SY G4 GRP 150/ CC, SY C1 CRP 150/ CC, SY C CRP 150/ CC, SY Laboère et al. [18] T-eto: b w /h b =900 mm, =66 mm (the wth a thke o the lage) T CRP 150/ SY, 1 Abbrevato or alure tpe: CC = orete ruhg ompreo, SY = teel elg teo a = RP plate rature teo. Plate beam eature RP abr ole to orm the U-hape wrappg boe to the vertal e alog the whole pa.

9 N. Peš, K. Plakouta / Materal a Struture 8 (005) M ( x) ( x) (8) E I( x) where (x) the uto o the beam urvature, L the beam pa, M (x) the beg momet ue to the ut ore apple at the pot or whh the eleto beg alulate wth the kow beg momet ue to a apple loag M(x). The exat loe-orm oluto to Equato (7) a ot be obtae ue to the rregular varato o the eo momet o area o rake beam, I(x). or a RP-plate reore orete beam ve alog t pa, L, to a uetl large umber o N egmet o legth l, Equato (7) a (8) traorm to: v N max M ' ( x) 1 M or E I l (9), (40) x, where, or the -th egmet, M the apple beg momet whle, a x, are the maxmum orete ompreve tra a the orrepog eutral ax epth whh houl be obtae umerall. To ompletel evaluate the loa-eleto htor, P-v, the urvature remet + =(, +, )/(x, +x, ) ee to be teratvel alulate or all egmet (ug the ame proeure rom eto 6) a umme at ever loag tep, P+P, a requre b Equato (9). Note that the value are evaluate b takg to aout the otrbuto o orete teo erbe eto.. 8. THE LOADING HISTORY The metho ow emploe a bre vetgato o the eet o pre-loag o the ultmate lexural apat a eormato behavour o tregthee beam. Two beam tregthee wth gla RP plate a tete ourpot beg b Saaatmaeh a Eha [] are hoe or the aal. or both beam, A a C, the umeral o-lear aal ha orrelate ver well to the expermetal loa-eleto urve a how g. 9. The graph alo lue the aaltall obtae urve or the reeree (o-tregthee) beam a beam pre-loae beore the GRP plate are boe, a thee are how wth otte le. The properte o beam A are alrea prove Table 1. The beam wa over-reore a ale through orete ruhg ompreo. The ultmate loag apat wa reae b.% rom 40 kn (aaltall ou or the reeree o-plate beam) to 0 kn whe o loag wa apple pror to the bog o GRP plate. However, or the beam pre-loae wth kn (50% o t omal apat) beore the GRP-plate wa ae, the apat at lexural alure wa ou umerall to be 90 kn a that wa a reae b 0.8% over the reeree beam. The lower apat or th partular ae learl emotrate that the extg loag ha a mpat o the ultmate lexural apat o the RP-plate beam wth hgher reoremet rato ( >,l. ). Coequetl, the pre-loag alo aete the value o the beg momet apat orrepog to elg o teral tele teel reoremet whh wa reue rom 65 knm (o pre-loag) to 46 knm (wth pre-loag). Apart rom the muh lower tele reoremet rato o 1 =0.1%, beam C ha the ame geometr a materal properte a beam A. The beam wa uer-reore a g. 9 - Loa-eleto urve or GRP-tregthee RC beam A a C [].

10 19 N. Peš, K. Plakouta / Materal a Struture 8 (005) ale at the loa o approxmatel 180 kn ue to plate ebog, but t prete lexural alure loa wa ou to be kn. The alure o the reeree o-tregthee beam ue to the exeve elg o the tele teel reoremet at the loa level o arou 50 kn. The applato o the GRP plate th ae otrbute to the reae lexural te a ultmate apat b more tha 00% llutratg hgher eetvee o RP tregtheg or beam wth lower tele teel reoremet rato. all, the aal o the orgall o-tregthee reeree beam ubjete to 70% o t omal loa apat at elg beore the GRP plate wa ae how o hage the ultmate lexural loag. Thu, the eo exere reveale that, or uer-reore RP-plate beam, the eet o the hgher level o pre-loag reult larger eleto rather tha reuto o the ultmate lexural apat. 9. CONCLUSIONS I th tu, the metho or lexural aal o RP-plate R.C. beam bae o the Eurooe (or CEB-IP MC 90) parabol-retagular tre-tra moel or orete ompreo wa preete. The erve equato a be ue or the evelopmet o a ere o eg hart or the lexural aal o retagular a T-eto wth boe RP plate. I the eo part, the aura o the umeral proeure omprg orete teo teg eet or the omputato o the lexural apat a eleto or RPplate RC beam wa vere wth avalable expermetal ata. The etale lowhart o the preete umeral proeure a erve a guae or the omputer mplemetato o the preete metho whh ha the ablt to apture the eet o pre-loag (apple beore the tregtheg wth boe RP plate) o the pottregtheg te a loa apat o RC beam. It wa emotrate how the pre-loag a reue the ultmate a elg lexural apat o over-reore RC beam or arou 5-% a alo reae the overall eleto o uer-reore beam. Thee g emphae the ee or upatg the urret orete eg guele areg lexural tregtheg b mea o RP plate bog wth provo agat the eet o utae loa o the ultmate lexural apat o tregthee beam. ACKNOWLEDGEMENTS The author wh to akowlege the aal upport prove b the Brth Uverte ORS awarg bo a the E.U. Commo (or ug the Europea CobreCrete TMR etwork). Our thak are extee to the reeree whoe ommet a uggeto have oerabl mprove the qualt o the paper. REERENCES [1] Rthe, P.A., Thoma, D.A., Lu, L.W. a Coell, G.M., Exteral reoremet o orete beam ug ber reore plat, ACI Strutural Joural 88 (4) (1991) [] Saaatmaeh, H. a Eha, M.R., RC beam tregthee wth GRP plate I: Expermetal tu, ASCE Joural o Strutural Egeerg 117 (11) (1991) [] Sebata, W.M., Sgae o mpa ebog alure RP-plate RC beam, ASCE Joural o Strutural Egeerg 17 (7) (001) [4] Smth, S.T. a Teg, J.G., Iteraal tree plate beam, ELSEVIER S. Egeerg Struture (7) (001) [5] Leug, C.K.Y., Delamato alure orete beam retrotte wth a boe plate, ASCE Joural o Materal Cvl Egeerg 1 () (001) [6] El-Mhlm, M.T. a Teeo, J.W., Aal o reore orete beam tregthee wth RP lamate, ASCE Joural o Strutural Egeerg 16 (6) (000) [7] Eurooe [ENV ], Deg o Corete Struture: Part Geeral Rule a Rule or Bulg, (Commo o the E.U., Bruel, 199). [8] CEB-IP Moel Coe 90, éérato teratoale u béto, CEB Bullet 1/14, (Lauae, Swtzerla, 1990). [9] Kato, B., Aok, H. a Yamaouh, H., Staarze mathematal expreo or tre-tra relato o trutural teel uer mooto a uaxal teo loag, RILEM Mater. Strut. (1) (1991) [] Ebl, J. [E.], Corete Struture: Euro-Deg Habook 1994/96 (Ert & Soh, Berl, 1995). [11] Kamka, M.E. a Kota, R., Stregtheg o reore orete beam wth exterall boe ompote lamate (uo to Re. [1]), ACI Strutural Joural 97 (1) (000) [1] Tratallou, T.C. a Plevr, N., Stregtheg o R.C. beam wth epox-boe bre-ompote materal, RILEM Mater. Strut. 5 (148) (199) [1] Ro, A.C., Jerome, D.M, Teeo, J.W. a Hughe, M.L., Stregtheg o reore orete beam wth exterall boe ompote lamate, ACI Strutural Joural 96 () (1999) 1-0. [14] Ahme, O. a Va Gemert, D., Eet o logtual arbo ber reore plat lamate o hear apat o reore orete beam, Pro. RPRCS-4 (ber Reore Polmer Reoremet or Reore Corete Struture), (E. Dola, Rzkalla a Na), (Baltmore 1999) [15] Ngue, D.M., Cha, T.K. a Cheog, H.K., Brttle alure a bo evelopmet legth o CRP-orete beam, ASCE Joural o Compote or Cotruto 5 (1) (001) [16] Rahm, H. a Hutho, A., Corete beam tregthee wth exterall boe RP plate, ASCE Joural o Compote or Cotruto 5 (1) (001) [17] Almuallam, T.H. a Al-Salloum, Y.A., Ultmate tregth preto o RC beam exterall tregthee b ompote materal, ELSEVIER S. Compote Part B: Egeerg (7) (001) [18] Laboère, P., Neale, K.W., Rohette, P., Demer, M., Lamothe, P., Lappere, P. a Degagé, G., bre reore polmer tregtheg o the Sate-Éméle-e-l Éerge brge: eg, trumetato a tetg, CSCE Caaa Joural o Cvl Egeerg 7 (5) (000)