Long-Term Deflections of Beams Strengthened by Prestressed and non-prestressed FRP Sheets Hesham Diab, Zhishen Wu, Ehsan Ahmed

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1 ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT Volum 3, Iu, Augu 03 Long-Trm Dflion of Bam Srnghnd b Prrd and non-prrd FRP Sh Hham Diab, Zhihn Wu, Ehan Ahmd Abra Exrnal bonding of fibr rinford olmr (FRP h ha bn rovn o b an ffiv mhod o rnghn and rrofi driorad or damag RC or PC ruur. Howvr, h long-rm rviabili of uh FRP-rnghnd bam i ill a onrn du o lak of long-rm rforman daa iall for rrd FRP h. Thi ud rn a manual mhod for rdiing h hor-rm and im-dndn dflion for RC bam rnghnd b rrd or non-rrd FRP h. Th ag-adjud ffiv modulu mhod i ud o modl h r bhavior in onr and h rlaxaion in FRP rring h. A nion-iffning modl i rnd o valua h iffn of h rakd ion. Th analial valu ar omard o h rul obaind from a fini lmn od, and o h xrimnal rul from om xiing ar. I i found ha h analial mhod i in a good agrmn wih fini lmn mhod. Indx Trm Cr, onr, Fibr rinford olmr, rrd FRP h, im dndn dflion. I. INTRDUCTIN Srviabili of onr an b dfind a aifaor rforman undr rvi load ondiion whih in urn an b dribd in rm of wo aramr-raking and dflion. Dflion oniu on of h imoran rviabili riria in h dign of onr ruur. To k h dflion of rinford onr (RC mmbr wihin allowabl limi, om onrol mhanim, uh a aroria dign and onruion rodur and h u of aroria marial lik hor fibr rinformn o rovid highr bam iffn and br rak onrol, hav bn rommndd b ACI Commi 435[]. Diab and Wu [,3] and Wu and Diab [4] rood a violai modl and rvald ha i i oibl o ima h im-dndn bhavior wih rgard o h adhiv lar bonding of h inrfa bwn onr and h FRP h. Tan and Saha [5] ondud a ud on h hararii of h im-dndan dflion of RC bam xrnall bondd wih FRP. Howvr, h formr ud onrnd onl on h im-dndan bhavior hararii of h inrfa modl wih rgard o h FRP h, whil h lar ud onnrad onl on h im-dndan dflion of RC bam wih xrnall bondd FRP. In ordr o rdi a ignifianl mor raonabl im-dndan bhavior, a r rain rlaionhi wihin h FRP-rnghnd bam hould fir b larifid. Th u of rrd fibr rinford olmr (FRP h in rinformn onr ha bn ud for vral ruur and bridg a a oluion of h orroion roblm (Wu al. [6] and Diab al. [7]. Thi marial rrn a rlaivl nw hnolog; hrfor muh rarh i ndd o inrodu a imlifid mhod o alula h hor and long-rm dflion of h ruur. Thi ar rn a gnral imlifid mhod for alulaing dilamn in rrd and non-rrd rinford onr wih FRP h. Th mhod i bad on h anali of rain diribuion a individual ion o drmin axial rain and urvaur undr rribd loading ondiion. Saring wih h alulaion of axial rain and urvaur a individual ion, h variaion of h aramr ovr h lngh of mmbr i drmind and ud o alula h ranlaion or roaion a an ion. Th omrhniv anali rquir mor alulaion han h imlifid mhod and alo rquir mor inu daa. Th omrhniv anali i rommndd whn h dflion i riial and aura i nar. Th gnral mhod in hi ar drmin h dilamn in rrd and nonrrd rinford onr lan fram. Thi mhod i bad on an anali of rain diribuion a a ion onidring h ff of a normal for and a momn aud b alid load, rring, r and hrinkag of onr, and rlaxaion of rring FRP h. Th alulad axial rain and h urvaur a variou ion of h fram an hn b ud o alula dilamn b virual work or ohr laial hniqu. Th ional anali an aommoda h ff of r and hrinkag of onr and rlaxaion of rring FRP h. Th ional anali i inndd for rvi ondiion. A linar r-rain rlaionhi an b aumd for h onr undr rvi ondiion, rovidd ha h onr r do no xd abou h half h omriv rngh [8]. Th rodur rnd in hi ar i inndd o omu dformaion in rvi; i do no rak h bhavior a h load aroah ulima. ACI 440[9] ummarizd h udi arrid ou o far on h dflion of FRP-rinford onr rinford wih FRP bar and rovid a guid o alula h ffiv momn of inria for rakd ion. B aking ino aoun h ff of onr nion iffning, h guid alo diud h long-rm dflion. Alo, ACI 440.R-0 [0] ummarizd h udi for ruur rinford wih nonrrd FRP-h. Thi ar rovid a imlifid rodur o alula h long-rm dflion of ruur rnghning b rrd or nonrrd FRP-h inluding r and hrinkag of onr bid h rlaxaion of rring FRP h. Thi mhod ha bn validad again h rul from a Two-dimnional FE anali 08

2 ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT rnd b h 990 Euroan CEB-FIP od [] and xrimnal rul from om xiing ar. II. TIME-DEPENDENT PRPERTIES F MATERIALS Th marial im-dndn aramr rquird o alula h dformaion of h onr ruur ar a follow: A. Cr of Conr Th r offiin of onr dnd on h onr omriv rngh, rlaiv humidi of h nvironmn a wll a h ag of onr a h im of loading. Thr hav bn man modl rood o drmin h dvlomn r and hrinkag ovr im. Th guidan o alula h r valu o b ud in dign for xa oluion i givn in ACI 09R, CEB-FIP990 and Duh NEN 670 od. Howvr, o imlif h alulaion, quaion an b ud o obain h r valu of onr. Thi quaion do no giv h xa valu a rviou modl bu how a good agrmn wih CEB-FIP 990 modl. 0.6 C.75 ( 0. 6 ( RH x f Volum 3, Iu, Augu 03 III. INSTANTANEUS ANALYSIS ( Whr; i h im (in da afr alid load, i h orrion faor for ambin rlaiv humidi RH, and for f h 8 da omriv rngh of onr. B. Shrinkag of Conr If h onr mmbr wr fr o hrink, wihou rrain, hrinkag of onr would no b a major onrn o ruural nginr. Howvr, hi i no h a. Th onraion of a onr mmbr i ofn rraind b i uor or b h adjan ruur. Bondd rinformn and FRP h alo rrain hrinkag. Th rain ruld (, from rrain hrinkag SH 0 dnd on man faor and an b alulad b h am od ud for r. C. Cr of FRP Sh Th r offiin of FRP i dfind a h raio of r rain o lai rain undr a onan uaind r. Th r offiin of variou FRP ndon ha bn udid rnl []. I wa onludd ha h rlaxaion of CFRP ndon an b onidrd o b zro a obaind from ohr alo. In h a of an AFRP ndon h r rah o 5% and hi rul agr wih man rarhr. Th following mirial quaion wa ud o modl h r offiin of AFRP ndon[3] ln(4.053 (3 A. Unrakd Sion A h rvi load lvl, h hor-rm anali of a ro ion an b arrid b ranforming h bondd rinformn and FRP h ino quivaln ara of onr and rforming a iml lai anali on h quivaln onr ion. In h ranformaion, n i alld h modulu raio for FRP h and n E / E, whr E and E ar h lai modulu of FRP h and onr, rivl. Th orronding modulu raio for h onvnional nonrrd rinformn i dignad n and n E / E. Th ara A, h fir and ond momn B and I of h ranformd ion ar akn abou h o fibr of h ion a oin a hown a Fig.. Chooing a a fixd oin (for xaml, h o fibr rahr han h nroid ha h advanag ha h loaion of h nroid do no hav o b drmind for h rakd and unrakd ag. Th iniial rain and r diribuion on unrakd ion ar aumd o b linar ovr h dh of h ion. Whn xrnal loading N and M ar known, h orronding rain and r aramr ar givn b ACI 435R-95[8]. IN BM ( 0 E ( AI B BN AM k 0 E ( AI B (4 ( (5 ( 0 E (6 ( 0 Ek (7 whr;, ar h rain and r a, and k i h urvaur of bam, and d. d Th onr rain and r a blow h o fibr a an im ar k (8 E ( k (9 Th orronding r in h rinformn a FRP h an b drmind uing h linar marial rori. d=d d d Poin A A d k d A b Srain Sr Fig.. Dimnion of ro ion and rain r diribuion in a ro ion d d 09

3 B. Crakd Sion ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT Fig.. Momn urvaur rlaion In a rakd ion, h nil r of onr xd h flxural nil r f, du o h aliaion of xrnal load M and N o h rrd bam. In hi a, h alulaion an b arrid ou uing bilinar omuaion mhod b ariioning M and N ino wo ar, uh a M=M +M and N=N +N. Th air N and M rrn h r rulan ha will bring o zro h onr r xiing bfor h inroduion of M and N; h air N and M rrn h rmaindr. Wih N and M, h ion rmain unrakd whra, raking i rodu onl whn N i ombind wih M. For h anali uro, wo loading ag i ndd o b onidrd. Firl, N and M ar alid on an unrakd ion and finall N and M ar alid on a rakd ion, in whih h onr ouid h omrion zon i ignord h rain in h wo ag-dflion- ar addd o giv h oal inananou hang a hown a Fig.. Th valu of N and M ar givn b N M A B (0 B I ( whr; and h iniial r bfor aling h load M and N wih rvrd ign, and A, B, and I rori of unrakd ranformd ion. Afr N and M hav bn drmind, N and M ar alulad b N =N-N and M =M-M. Th load ar hn alid on a rinford onr rak ion, h rori of rak ion A r,b r, and I r an b drmind afr alulaing h, h dh of omrion onr zon. For h ro ion ubjd o N and M, h dh of omrion zon an ail b alulad (Ghali and Favr 00. b M +M d 3 n A d d d n A d d d b M I g n A d n A d n A d 0 M I r I k r k Curvaur (k Th dimnion of h ro ion ar hown in Fig.. Volum 3, Iu, Augu 03 C. Tnion iffning ( Sin onr ha h abili o arr nil r bwn rak in h nion zon du o h bond bwn h rinformn-bar and FRP h, a nion iffning modl i ud in h rakd ro-ional anali of bam or fram. Th nion iffning modl ha bn rood for rrd or nonrrd rinford onr ion b CEB FIP modl od []. Th man rain aramr m and k m an b drmind b inrolaion bwn unrakd and rakd a (3 k m m k k (4 whr; and k ar rain aramr alulad uing unrakd ranformd ion, and and k ar rain aramr alulad uing h rakd ranformd ion. i an mirial inrolaion offiin and i givn b f (5 max whr; f i h nil rngh of onr, i h alulad nil r a xrm fibr whn raking i ignord and i mu b grar han max f. i a offiin o aoun for h ff of bond quali of rinformn, li, and uaind loading on nion iffning. In mo a, =0.5 an b ud whn dformd bar ar mlod and.0 whn li or uaind load ar alid. I hould b oind ou ha h offiin wa drivd for rr or nonrrd bar, no for rrd FRP h. So, furhr udi ar ndd o inviga h valu of for FRP h. II. TIME-DEPENDENT ANALYSIS F CRSS SECTIN Tim anali of h ro ion onidrd in hi ar u h ag-adjud ffiv modulu mhod (AEMM oghr wih rlaxaion aroah. Afr alulaing h inananou rain aramr, and ( 0 k( 0 (from quaion 4 and 5 for undr rakd ion or quaion 3 and 4 for rakd ion and h inananou hang in h r aramr ; h and ( 0 aramr for h hohial rain hang ha would our in h riod 0 o, if r and hrinkag wr unrraind ar obaind a follow:, (, C (, (6 fr ( 0 SH 0 0 k C, k( (7 fr ( 0 0 Howvr, if i i aumd ha h r and h hrinkag ar rraind, hn h wo aramr dfining h ( 0 0

4 ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT diribuion of hohial r graduall inrodud bwn im 0 and o rvn h rain hang ar alulad b ACI 435R-95 [8] uing; E rrain fr (8 E k (9 rrain fr whr; E i h ag-adjud modulu of laii of onr and, E, E / XC (, (0 E ( 0 0 (, 0 E( / (, 0 ( whr X i h aging offiin and i qual o 0.8[9]. E i h ag-adjud modulu of laii of FRP h Thi rodur i alo uiabl for FRP h [] hn, h rulan of r rquird o rvn r and hrinkag dformaion ar: N A B A B ( r, hrinkag rrain rrain rrain rrain M B I B I (3 r, hrinkag rrain rrain rrain rrain Volum 3, Iu, Augu 03 IV. DEFLECTIN CALCULATIN Whn h load indud and r and hrinkag indud urvaur ar alulad a ld ion along a bam or fram, h dflion a midan an b obaind b doubl ingraion of h urvaur. For a rinford or rrd onr oninuou an wih h dgr of raking varing along h mmbr, h urvaur a h lf and righ uor, k l and k r and h urvaur a midan k m ma b alulad a an im afr loading and h dflion a midan midan ma b aroximad b auming a araboli urvaur diagram along h an, l l midan kl 0km kr 96 (3 Th abov quaion will giv a raonabl ima of dflion vn whn h urvaur diagram i no araboli and i a uful xrion for u in dflion alulaion [5]. whr; A, B, and I ar h rori of onr alon wihou rinformn, A, B, and I ar h rori of FRP h a oin. Elimina h fiiiou rrain b aling N and M on h ag-adjud ranformd ion and h alulad hang in rain and r aramr from quaion 4 and 5 ar: I ( N B ( M (4 E ( A I B B ( N A ( M k E ( A I B (5 Whr; A, B, and I ar h rori of h ag-adjud ranformd ion uing h modular raio of h ag-adjud ranformd ion ar givn b and ar ud o n E / E and n E / E drmin h ranformd ara of FRP h and rinformn rivl. Th im-dndn hang of r aramr of onr a h nd of im ar in E (6 rra in E k( (7 rra Afr h im-dndn hang of rain, urvaur and r ar drmind, h final rain urvaur, and r a h ro ion ar radil found b ( 0 (8 k k ( 0 k (9 ( ( 0 (30 ( ( 0 (3 V. METHD VERIFICATIN To arain h validi of h rood mhod, a omarion bwn fini lmn mhod uing a ommriall availabl FEA od DIANA and xrimnal rul wih h rood mhod ha bn ud. A. Fini lmn vrifiaion Dail driion of FEA modl. A wo dimnional FE anali i arrid ou for h iml uord bam. Fig. 3 how h dimnion and dail of h bam. Th FRP rnghnd bam i modld uing lain r lmn for h onr (4 noddd Q8MEM, Th rrd FRP h wr rrnd b ru lmn (LTRU. Morovr, mbddd bar lmn i ud o rrn h rinformn bar. I i aumd rf bonding bwn FRP h and onr o ngl h ff of adhiv r. Th bam i rnghnd b wo lar of FRP h, 00 mm wid and hikn of 0.8 mm, h rring lvl i 33% of FRP nil rngh ( 3400 ulima MPa. Th bam i loadd a 63 da afr rlaing h rring load a midan b on onnrad load P=5.0 kn(<p r. Th marial rori ar f =36.8 MPa, f = 4.7 MPa, E = 30.4 GPa, E =0.0GPa, and E =40.0GPa. Fig. 4 how h long-rm midan dilamn for h wo modl, rood modl and FE modl. From hi figur i an b noid ha hr i an xlln agrmn bwn wo modl, whih india ha h rood modl i vr uful o alula h long rm dflion of bam rnghnd b FRP h. I hould b oind ou ha h r and hrinkag, CEB-FIP Modl Cod 990, ar ud for boh anal wih h am daa. Th iniial ambr i mm from rood modl ( mm FE modl and

5 Midan DEfl. (mm ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT Volum 3, Iu, Augu 03 i inra wih im o mm ( mm a im 63 da. Uon loading h dflion inrad o 0.08 mm (.094 (downward. Wih im h dflion inrad oninuoul and i rah 0.8 mm (0.77 whih i abou.7 im of h inananou dflion. Th valu hav a rong rlaion wih rlaiv ambin humidi (RH a hi ud RH=50% i onidrd. Alo, h valu dnd on man aramr uh a r of FRP h ilf, rring lvl of FRP h, r a adhiv, and nion iffning a h a of raking load. Hn, furhr udi ar nar o inviga h im dndn bhavior of ruur rnghnd b rrd FRP h onidring h ff of abov mniond faor. 050 mm Tim (Da Prood modl FE Modl Fig 4. Tim dndn midan dilamn for h wo modl, rood modl and FE modl mm -D3 -D 6 40 mm 00 mm 40 mm 00 mm Fig 3. Dimnion and dail of h bam B. Exrimnal Vrifiaion Th xrimnal rul ud in hi ud orrond o iml bam rnghnd b FRP omoi marial a boom and ar d b Saha al. [6] and Tan and Saha [5]. Fig. 5 and 6 how h -u and h dimnion of bam and ro-ional dail of on h xrimnal bam, rivl. Th marial rori for bam ar hown in Tabl. Tabl : Prori of Marial Ba m GB -5 9 GB E GPa E G Pa E G Pa FR P raio % 7.9 % f u 8 MP a f M Pa To al load kn No: f u 8 onr rngh a 8 da, f moudulu of ruur, and E, E, and E modulu of laii of onr, l and GFRP rivl. Fig. 5. Bam ubjd o uaind loading [6] Toal Load =8.8 kn San L=800 mm D 6 mm D 0 mm 995 mm 00 mm A = 80 and 40 mm Fig. 6. Dimnion and dail of bam [6 VI. RESULTS AND DISCUSSIN Th loading lvl for boh bam nur h raking of h bam. A omarion bwn h xrimnal rul and analial rul of midan dflion ar hown in Fig. 7 and 8. I an b noid from h figur ha boh of wo analial mhod giv raonabl agrmn o xrimnal rul, howvr, h rood mhod giv lor agrmn bau i ha akn ino onidraion h nion iffning ff of onr,. 0 i onidrd a hi anali. Saha al. [5] ud an analial mhod ha dnd on h ffiv momn of inria and do no

6 ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT Volum 3, Iu, Augu 03 onidr h nion iffning of onr. Morovr, ha mhod wa for ur bnding momn and i did no onidr h a of rring load. Th rood hniqu giv h inananou dflion ar 6.5 and 4.8 for GB-59 and GB3-49 rivl and wih im h dflion inra oninuoul and i rah.36 and 0.44 mm, whih ar abou.9 and.8 im of h inananou dflion for GB-59 and GB3-49 rivl. omur and rrn a uiabl ool for analzing h long-rm rforman of FRP-rnghnd onr ruur. Thi ud howd an xlln agrmn wih DIANA od for unrakd ion, and a raonabl agrmn wih xrimnal rul for h rakd ion. Mor udi for bam rnghnd wih rrd FRP h ar ndd o inviga h ff of r of adhiv and FRP h on h long-rm dflion of uh ruur. Fig. 7. A Comarion bwn Exrimnal and analial dflion a midan for bam GB-59 vru im. I hould b oind ou ha h imlifid mhod inrodud b h auhor giv xlln agrmn in rul for unrakd ion and raonabl agrmn in rul for raking load. Th divrgn of rul afr raking load ma b bau of man faor, uh a h nion iffning faor,, ha nd mor udi o find a good rlaion a h a of onr rnghnd wih rrd FRP h, and h mhod of alulaing dflion whih aum a araboli urvaur diagram along h an (hi aumion ma b no aura a rak ion. Thi india ha mor udi for long-rm bhavior of bam rnghnd wih rrd FRP h ar ndd iall for rakd ion. Fig. 8. A Comarion bwn Exrimnal and analial dflion a mid-an for bam GB3-49 vru im. VII. CNCLUSIN A imlifid mhod ha bn rood o analz h long-rm bhavior of onr ruur rnghnd b rrd or nonrrd FRP omoi marial. Thi rood hniqu an b ail rogrammd in a ronal REFERENCES [] ACI Commi 435R 995, Conrol of dflion in onr ruur, Amrian Conr Iniu, Rdford Saion, Droi, Mihigan, [] Diab, H.M and Wu, Z.S. (007, Nonlinar Coniuiv Modl for Tim-Dndn Bhavior of FRP-Conr Inrfa, Journal of Comoi in and Thnolog, Vol. (67, [3] Diab, H.M, and Wu, Z. (008, A Linar Violai Modl for Inrfaial Long-Trm Bhavior of FRP Conr Inrfa, Comoi Par B: Enginring, Comoi: ar B 39, [4] Wu, Z.S., and Diab, H.M. (007, Coniuiv Modl for Tim-Dndn Bhavior of FRP-Conr Inrfa, Journal of Comoi for Conruion, ASCE, Vol. (, [5] Tan, K.H, and Saha, M.K. (006, Long-Trm Dflion of Rinford Conr Bam Exrnall Bondd wih FRP Sm, Journal omoi for onruion, 0(6, [6] Wu, Z. S., Mauzaki, T. Fukuzawa, K. and Kanda, T. (000, Srnghning Eff on R Girdr wih Exrnall Prrd Carbon Fibr h, Journal of Marial, onr ruur and Pavmn, JSCE, [7] Diab, H.M, Wu, Z.S, and Iwahia, K. (009, Shor and Long-Trm Bond Prforman of Prrd FRP Sh Anhorag, Enginring Sruur, Vol. (3, [8] ACI Commi 435R , Conrol of dflion in onr ruur, Amrian Conr Iniu, Rdford Saion, Droi, Mihigan [9] ACI Commi , guid for h dign and onruion of onr rinford wih FRP bar, Amrian Conr Iniu, Rdford Saion, Droi, Mihigan [0] ACI 440.R-0 (00, Guid for h dign and onruion of xrnall bondd FRP m for rnghning onr ruur, Amrian Conr Iniu, Rdford Saion, Droi, Mihigan [] CEB-FIB, 990, modl od for onr ruur, Thoma Tlford, London [] Zou, P. X. W. (003, Long-rm rori and ranfr lngh of fibr rinford olmr, Journal of omoi for onruion, 7(, 0-9. [3] Zou, P. X.W. (003, Thorial Sud on Shor-rm and long-rm dflion Fibr Rinford olmr rrd onr bam, Journal of omoi for onruion, 7(4,

7 ISSN: IS 900:008 Crifid Inrnaional Journal of Enginring and Innovaiv Thnolog (IJEIT Volum 3, Iu, Augu 03 [4] Ghali, A., Favr, R., and Elbadr, M. 00, Conr ruur: r and dformaion, 3rd diion, on r, London and Nw York. [5] Gilbr R. I., 00, Shrinkag, raking and dflion h rviabili of onr ruur, Elri Journal of Sruural Enginring. [6] Saha, M. K. and Tan, K. H. (004, Long-rm dflion of FRP-Srnghnd bam undr uaind load, FRP Comoi in Civil nginring-cice 004-Sraino(d- London. AUTHR S PRFILE Mr. Hham Diab i an aian rofor a Civil Enginring Darmn, Aiu Univri, Eg. H ha don hi B.E. and M.S. in ivil nginring from Aiu Univri. Hi ara of inr ar rhabiliaion/rnghning of onr ruur, Tim dndn bhaviour of FRP-rnghnd ruur, Civil nginring marial and xrimnal mhod and ruural modling. Mr. Zhihn Wu i a Profor a Ibaraki univri, Jaan. H ha don hi B.E. and M.S. in ivil nginring from ouha Univri, China. Hi ar of inr ar inllign nginring, Sruural Enginring and Diar Prvnion, Comuaional, Nonlinar, Fraur Mhani and Enginring Mr. Ehan Ahmd i a rarh rofional a faul of Enginring, Univri of Shrbrook, Canada. H ha don hi B.E. and M.S. in ivil nginring from Univrii Kbangaan Malaia. Hi ara of inr ar Prforman of duil fu in rduing imi dmand on onnion of onnriall l brad fram and Non-linar bhaviour of High Prforman Conr (HPC 4