Performance prediction of eccentrically loaded RC columns wrapped with FRP

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Victoria Montgomery
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1 Fourt Intrnational Conrn on FR Compoit in Civil Enginring (CICE008-4Jul 008, Zuri, Switzrlan rorman prition o ntriall loa RC olumn wrapp wit FR T. El Maaaw Unit rab Emirat Univrit, l-in, bu Dabi, Unit rab Emirat BSTRCT: Ti papr prnt an analtial mol or prorman prition o ntriall loa rinor onrt (RC olumn wrapp wit xtrnall bon ibr rinor polmr (FR. T propo mol i ba on raliti matrial law, an aount or t ang in gomtr au b t latral ormation unr ntri loaing. It alo tak into oniration t oninmnt t au b FR wrapping tm at variou loa ntriiti. n xprimntal program wa arri out to xamin t mol aura. Tt paramtr inlu t oninmnt onition (No wrapping, ull FR-wrapping, an partial FRwrapping, an t ntriit-to-tion igt (/ ratio (0.3, 0.43, 0.57, an Rar ining iniat tat t trngt gain au b FR wrapping tm wa invrl proportional to t ntriit ratio. omparion btwn t analtial an t xprimntal rult a montrat t mol aura an valiit. INTRODUCTION larg numbr o xiting RC inratrutur in vlop ountri ar uring rom itr u to ovru an/or inaquat maintnan. Strutural trngtning i an onomial olution, an n rquntl rquir to xtn t untional rvi liv o iint RC trutur. ltoug rinor onrt an grout-injt tl jakting tm ar tiv in inraing t trutural apait, t ar labor onuming an omtim iiult to implmnt on it. Hn, an innovativ, urabl, a-to-intall, an ot tiv trngtning tm, u a xtrnall bon ibr rinor polmr (FR, i ntiall rquir to rpla outat trngtning tniqu. Numrou analtial mol av bn vlop to prit t trngt o onntriall loa RC olumn wrapp wit FR (Tng t al. 00. In pratial ituation, RC olumn ar otn, owvr, xpo to ombin lxural an axial loaing. T train graint au b an ntri loaing rult in a non-uniorm onining prur wi woul ru t iin o t FR wrapping tm (Caallal & Saawa 000; arvin & Wang 00. For ntriall loa RC olumn, t onar momnt au b t - t woul rult in ruing t loa arring apait, an n aount oul b takn o t ang in gomtr au b t latral ormation. T prnt rar i tn initiat to vlop a impl, t aurat, analtial mol tat an prit t trngt o ntriall loa RC olumn wrapp wit FR. n xprimntal tu wa unrtakn to xamin t mol aura an valiit. MODEL DEVELOMENT. Matrial law Matrial ontitutiv mol u in t prnt tu ar own in Figur. T tr-train rlationip o an unonin onrt in omprion i rib b a paraboli rlationip. - -

2 = ( ( o o Wr = onrt omprion tr, = onrt omprion trngt, = onrt train, an o = onrt train orrponing to. T tr-train mol o an FR-onin onrt i ivi into two portion. T propo mol aum tat t aning bran o t urv, btwn zro tr an a tr qual to, i paraboli imilar to tat o t unonin onrt (Samaan t al. 998; Fam t al Bon, t onrt tr i aum to inra linarl until it ra t onin trngt o t onrt (Mirmiran t al. 999; Tng t al. 00. Ba on xtniv rar (Tng t al. 00, t trngt an orrponing ultimat ompriv train o an FR-onin onrt unr onntri loaing, o an u, rptivl, ar givn b: l o = ( ( l u = o(.75 0 (3 o FR-onin onrt ( = FR-onin onrt ( = 0 u E p unonin onrt E u o Conrt Figur. Matrial mol u Stl rinormnt Exprimntal tt rult ow tat t gain in t ultimat ompriv train au b FR wa invrl proportional to t ntriit ratio (El Maaaw 008. Som rarr alo rport an invr rlationip btwn t onin trngt an t ntriit ratio (Fam t al oringl t trngt an ultimat train o t onrt unr ntri loaing, an, rptivl, ar onrvativl aum to b pnnt on / a ollow: = ( o ( (4 / = u ( u u ( (5 / u l rt = k ( b (6 k ( b R ( R = [ ρ ]/( ρ (7 3 g Wr l = t tiv latral onining prur provi b FR, u = ultimat ompriv tain o an unonin onrt, k = ap ator, r = ruptur trngt o FR, t = tiv tikn o FR (t = t in a o ull wrapping an t = t w /S in a o partial wrap- - -

3 ping, t = tikn o FR, w = wit o an FR trip, S = ntr-to-ntr paing btwn FR trip, R = raiu o t olumn ornr, b = wit o tion, = igt o tion, = loa ntriit, g = gro ara o t tion, an ρ = tl ratio. T tr-train rlationip o tl i ializ to b linar lati-plati wit a pot-il train arning o %.. Compatibilit an quilibrium rquirmnt T train an tr itribution or unonin an FR-onin onrt ar own in Figur a an b, rptivl. T tional urvatur,φ, i tn givn b:, max φ = (8 Wr,max = train at t xtrm omprion ibr, an = pt o t nutral axi. t ailur,,max = u or an unonin onrt wil or a onin onrt,max =. Equilibrium onition i impo in trm o axial or, n, an bning momnt, M n : b b t = α β n (9 b b( ( t ( = ( α β M n (0 ( α β = ( β ( α β ( 3( ( Wr α an β = tr blok ator (Collin an Mitll 987, = igt o t paraboli portion o t onrt tr itribution, = igt o t trapzoial portion o t onrt tr itribution, = itan btwn t xtrm omprion ibr an t rultant omprion or in onrt, = ara o omprion tl, = tr in omprion tl, = ara o tnion tl, an = tr in tnion tl.,max = u N. = α β t b (a =,max o N. α β t b Cro tion Strain itribution (b tual onrt tr itribution Equivalnt onrt tr itribution Figur. Strain an tr itribution - 3 -

4 .3 Latral mi-igt iplamnt T momnt, urvatur an ormation o an RC olumn unr ntri loaing ar own in Figur 3. T latral mi-igt ltion,, an b rlat to t mi-igt urvatur, φ, an t total lngt o t olumn, L, a ollow: φl = ( k T momnt o inrtia o a n orbl in t prnt tu wa 6 tim t inrtia o t olumn tion in t tt rgion, an n it an b aum tat k =..4 Moling prour T moling prour an b ummariz a ollow: For a givn /, u t unorm gomtr to trmin t tional or an urvatur at mi-igt o t olumn. U t mi-igt tional urvatur to alulat t latral mi-igt ltion. Moi t initial / to aount or t latral mi-igt ltion. U t moii / to ralulat t tional or an urvatur at t mi-igt. Rturn to tp i tr i a igniiant ang in t tional or. M = 0.9 L k = 4.8 L = 00 mm 0.4 L? M = ( M = (? φ k = L Unorm ap Dorm ap Momnt Curvatur Figur 3. Dorm ap an orrponing momnt an urvatur 3 MODEL VERIFICTION n xprimntal program wa arri out to xamin t mol aura. Dtail o tt pimn ar givn in Figur 4. total o twlv pimn wr tt. Tt paramtr inlu t oninmnt onition (No wrapping, ull FR-wrapping, an partial FR-wrapping wit w /S = 0.6, an t ntriit ratio (0.3, 0.43, 0.57, an T onrt trngt wa 8.5 Ma wra t longituinal tl a il an ultimat trngt o 550 an 75 Ma, rptivl. ur arbon ibr rinor polmr (CFR ompoit laminat u in t prnt tu a a tikn o 0.38 mm, a tnil trngt o 894 Ma, a tnil moulu o 65.4 Ga, an an ultimat longation o.33 % (inormation wa xtrat rom t manuaturr ata t. T olumn ornr wr roun to a raiu o about 0 mm

5 No. 70 mm No. 0 No. 0 No No. 4 B B x x No. 0 Long. bar Stainl tl tub Clar ovr o 5 mm Stion (B-B 5 Ø6 ti Stion (- 5 No No (ll im. ar in mm Figur 4. Spimn tail (all imnion ar in mm Exprimntal naltial Comprion trngt (kn No Wrapping Full FR-Wrapping artial FR-Wrapping Entriit ratio (/ Figur 5. naltial an xprimntal rult omparion btwn t analtial an t xprimntal rult ar givn in Figur 5. It an b n tat t trngt gain au b CFR wrapping ra a t ntriit ratio wa inra. On lar o ull CFR-wrapping rult in about 37 % trngt gain at a nominal / o 0.3 wra onl 3 % trngt gain wa ror at a nominal / o ll prit rult wr witin % rror ban wi onirm t abilit o t propo mol to auratl prit t trngt o unwrapp an FR-wrapp RC olumn unr ntri loaing. Figur 6 ow tpial intration urv or a quar olumn aving am ro tional imnion, tl rinormnt an matrial proprti a to o t pimn u in t prnt tu. Tr irnt wrapping m wr onir. T olumn wa itr ull wrapp wit on or two lar o CFR, or partiall wrapp wit on lar o CFR trip aving a lar paing lar = w. In t urv t olumn trngt unr onntri loaing, no, i prit b: 0.85 ( g t t o or unwrapp - olumn = (3 no o( g t t or CFR - wrapp olumn - 5 -

6 Wr t = total ara o tl, o = tl tr orrponing to a tl train o o, an = tl tr orrponing to a tl train o u but not gratr tan t tl ultimat tr. It i vint tat t trngt gain inra wit t amount o CFR. T CFR wrapping a a mor pronoun t on t trngt gain wn a omprion mo ailur i ominat. xila loa (kn No-wrapping artial-wrapping ( lar = w Full-wrapping ( lar Full-wrapping ( lar Bning momnt (kn.m Figur 6. Tpial intration urv 4 CONCLUSIONS n analtial mol tat an prit t trngt o ntriall loa RC olumn wrapp wit FR wa vlop an vrii againt tt rult. T mol aount or t oninmnt t o FR wrapping an t ang in gomtr au b t latral ormation unr ntri loaing. Rar ining iniat tat t trngt gain au b FR ra a t ntriit ratio i inra. CKNOWLEDGMENTS T autor woul lik to xpr i appriation to t Rar air at t UE-Univrit or t inanial upport o ti projt unr un grant # /06. REFERENCES Caallal, O., an Saaw, M rorman o ibr-rinor polmr-wrapp rinor onrt olumn unr ombin axial-lxural loaing. CI Strutural Journal, 97(4, Collin, M.., an Mitll, D rtr Conrt Bai. Canaian rtr Conrt Intitut (CCI, Ottawa, ON, Canaa. El Maaaw, T Bavior o orroion-amag RC olumn wrapp wit FR unr ombin lxural an axial loaing. Journal o Cmnt an Conrt Compoit, in pr. Fam,., Fliak, B., an Rizkalla, S Exprimntal an analtial moling o onrt-ill ibrrinor polmr tub ubjt to ombin bning an axial loa. CI Strutural Journal, 00(4, Mirmiran,., Saaw, M., an Samaan, M Strngt an utilit o bri FR-onrt bamolumn. Journal o Strutural Enginring-SCE, 5(0, arvin,., an Wang, W. 00. Bavior o FR jakt onrt olumn unr ntri loaing. Journal o Compoit or Contrution-SCE, 5(3, Samaan, M., Mirmiran,., an Saaw, M Mol o onrt onin b ibr ompoit. Journal o Strutural Enginring-SCE, 4(9, Tng, J., Cn, J., Smit, S., an Lam, L. 00. FR-trngtn RC Strutur, Jon Wil & Son Lt., Englan, 66 pp

Appendix XVI Cracked Section Properties of the Pier Cap Beams of the Steel Girder Bridge using the Moment Curvature Method and ACI Equation

Appendix XVI Cracked Section Properties of the Pier Cap Beams of the Steel Girder Bridge using the Moment Curvature Method and ACI Equation ppndix XV rakd Stion Proprti o th Pir ap Bam o th Stl Girdr Bridg ug th omnt urvatur thod and Equation Wt Bound Pir ap Bam Figur XV- Th atual pir ap bam ro tion [Brown, 99] Th ¾ - al i no longr orrt 5