Shear and flexural strength of corroded R.C. beams Resistenza a flessione e taglio di travi in calcestruzzo armato corrose

Transcription

1 Sher n lexurl trength o orroe R.C. em Reitenz leione e tglio i tri in letruzzo rmto orroe G. Cmpione, F. Cnnell, L. Cleri, F. Di Trpni, G. inò Deprtment o Ciil, Enironmentl, erope n teril Engineering, Unierit o Plermo, Plermo, Itl BSTRCT: Simpliie eqution ime t eluting the lexurl n her pit o orroe R.C. em re preente n iue in thi pper, with reerene to orinr em reinore oth longituinll (with me-ize r) n trnerel (with tirrup). moel i eelope to tke re o iue n lolie orroion (pitting orroion), onrete e in ompreion n on-trength e t onrete-reinorement intere. irl innotie ontriution o thi tu i the introution into the propoe eqution o the min prmeter goerning the orroion proee. The propoe pproh i imple n eetie, n m e opte in the ement o mn mge truture () on the i o the ille experimentl inormtion (e.g., rontion epth, hlorie ontent, pit epth n ize in the r n m lo in the reinorement), n () utilizing nltil expreion lirte through the knowlege o the enit o the orroion urrent. / Nel preente loro engono preentte e iue equzioni empliite per eterminre l reitenz leione e tglio i tri on rmtur orro. Vengono nlizzte tri on letruzzo normle reitenz enti rmture longituinli e te. Nel moello engono onierti l riuzione ell reitenz el letruzzo, l orroione iu e pitting ulle rre i rmtur (onierno i le rre i ugule imetro he le te), e l riuzione ell tenione i erenz. Il ontriuto originle i queto loro è l introuzione ei prinipli prmetri he goernno il proeo orroio nelle epreioni per il lolo ell reitenz leionle e tglio elle tri in emento rmto. Queto pproio è emplie e può eere pplito ull e i inormzioni perimentli (ome eempio l pro i rontzione, il ontenuto i loruri, l miur el pit nell rr o il metoo grimetrio per l orroione generle) oppure utilizzno epreioni nlitihe lirte olmente ull onoenz ell intenità i orrente i orroione. KEYWORDS: her-moment intertion; orroion; on; pitting; lexurl repone / interzione tglio-momento; orroione; erenz; pitting; ripot leionle. INTRODUCTION Corroion o reinoring teel i one o the min ue o eteriortion o reinore onrete truture. It eet inlue rking n plling o the onrete oer, lo o on etween onrete n orroing reinorement, n reution o the roetionl re o the reinoring teel. Corroion et oth ultimte n erieilit onition o R.C. truture. Two tpe o orroion o reinorement orroion n et n R.C. truture: generl n pitting. Generl orroion et utntil re o longituinl n trnere reinorement with more or le uniorm metl lo oer the perimeter o reinoring r. It lo ue rking n poil plling n elmintion o the onrete oer n proue rut on the onrete ure. Pitting i lolize, eing limite to mll re o the reinorement. Both generl orroion n pitting ue onrete plling o the r oer. In numerou experimentl tuie the eet o orroion on the mteril he een throughl inetigte with reerene to riou topi, mong them r orroion (Ting & Nok, 99) n reinorement-onrete on (Coronelli ), et. Stuie t truturl leel he een rrie out well, or intne on the ening ehior o em (Roriguez et l. 997) n on the xil ore- ening moment intertion in olumn (Roriguez et l. 995). To erie the truturl ehior o orroe em, mot tuie re e on numeril nle rrie out with the inite element metho. Thee nle, howeer, re omplex n require etile inormtion on the ontitutie lw o the mge mteril. The min eort me in thi pper i to tr to introue the prmeter relte to the orroion proe (r-etion reution, n mehnil e o oth onrete in ompreion n reinorement-onrete on) into nltil expreion or the lultion o the lexurl n her trength o orroe R.C. em. The propoe moel gie reult tht it the ille experimentl reult. Sine mnul lultion re me poile, the propoe moel m e oniere n ueul tool or preliminr eriition o the et tte in eteriorte truture or or preiion o it reiul lie.

2 TERIL CHRCTERIZTION To lulte the lexurl n her trength o orroe R.C. em, knowing to wht extent the geometri n mehnil prmeter (relte to onrete etion n reinorement) re ete orroion i mut.. Conrete trength egrtion Crking, ue the expnion o orroe longituinl r in the ompree zone (rut eet) o the em, reue onrete ompreie trength. Thi eree in impliie mere rk moel n e relte to the rking w r inue the orroion proe (rut epoit). Thi rk with, n e expree, in Coronelli & Gmro 4, in the orm: w r uio π ( r ) X () i where ν r i the olume expnion rtio etween rut n teel. ν r i in the rnge.7 to 6.. In Eqution X i the thikne o the orroion ttk penetrtion, whih n e meure with the grimetri metho or lulte, uggete in Vl (7), in rerrnge orm o Fr lw o eletroli, : X. 6 i orr t () where i orr i the orroion urrent enit in the reinoring r expree in µ/m, D the imeter n t the time in er. The lterl trin, whih ue longituinl miro-rk, w ume to e mere on w r n reue the ompreie trength, n n e expree : nr wr π nr ( ν r ) X (3) eing the with o the em ter the orroion proe. The reue ompreie trength n e relte to, uggete in Vehio & Collin 986, men o the eqution: (4) * + k o with k. ume in in Coronelli & Gmro (4). Sutituting Eqution in Eqution 3 the expreion otine in Eqution 4 gie the ollowing: * ψ (5) π n ( ν ) X r r + k with ume to e equl to. or norml trength, norml weight onrete. The ψ tor gien Eqution 5 i inite the ompreie trength reution tor.. Generl-orroion moel For ontnt orroion rte, the reue re o the reinoring r n e etermine : ( t) n r π [ φ X ] 4 (6) I the lue o X gien Eqution i utitute in Eqution 6 we otin: ( t) n r π [ φ.6 i t] 4 orr.3 Pitting eet on re reution n lo o utilit (7) oring to Vl (7) the re reution in teel r ue to pitting epen on hlorie or rontion-inue orroion n hlorie m ue lolize reution o the etion. The epth o pit, p(t) whih i equilent to the mximum penetrtion o pitting t er ter the trt o orroion, n e elute : ( t). 6 i t R p orr (8) RP mx /P with P mx eing the mximum pitting penetrtion in the r n P orreponing to X gien Eqution. oring to Vl (7), the lue o R re etween 4 n or 5 n mm reinoring r o 5 3 mm length. Be on the moel gien in Vl (7), the ro-etionl re o pit, p, in reinoring r n e lulte. Conequentl, the re o min r n tirrup (i n) ete pitting i: π φ, pit ( t) n p ( t) 4 (9) The reution in ultimte trin i expree : ' α pit u + ( u ) mx i α pit mx α pit < α pit () The pplition o Eqution i relte to the prmeter α pit mx, whoe elution i ritil or the eription o r utilit. Dierent lue o α pit mx he een meure riou uthor, rng-

3 ing rom.5 to. (Cirn & illr, 999, Ctel et l., ). oreoer, one the oer o the top r rk eue o orroion, n oer plling our, the ompree r re likel to ukle. Finll, in the preene o generl orroion n pitting the whole reue re n e lulte :, re ( t) [ φ X ] π nr p ( t) 4.4 Bon egrtion ue to generl orroion () Seerl tuie preent in the literture he hown tht there i igniint rition in on trength with the lo o m o orroe teel r n eerl nltil expreion re propoe to preit thi phenomenon. The expreion utilize here i the one gien in Roriguez (994) in the orm: δ k ( λ ) µ t q re t X + () φ φ δ eing the oer thikne, t the re o leg o tirrup, the iel tre o tirrup, n t the tenile trength o onrete expree in CI 38 :. 4 (3) t k, μ, λ eing empiril ontnt. k n μ re ume to e.6,. repetiel, while λ i etween.6 n.4. In the ene o tirrup, uming δd Eqution gie: q δ µ γ re k t ( λ X ) + (4).77 φ φ with X relte to X p whih i the orroion leel expree lo o m in % n lulte : X φ X p (5) 3 PREDICTION OF FLEXURL ND SHER STRENGTH OF CORRODED BES Commonl-eigne em re uner-reinore n the iel ore in the tenile teel ontrol their lexurl trength. B ontrt, or oer-reinore roetion, ruhing o ompree onrete oe not llow longituinl r to iel. The reerene moel or preition o lexurl trength i generll e on the hpothei tht the plne etion theor n e pplie eue o the peret on etween r n onrete. In the e o orroe r, lip etween onrete n teel r n our, reuing the ille utilit. The urrent moel reer to etionl nli. To reproue the wort onition, it w uppoe tht pitting n generl orroion our in ll r n in the me etion. In thi work, the lo o on trength ue to orroion i the onl prmeter ue to elute the trength lo o teel r. It h lo to e tree tht in the preene o tirrup the on reution i lower thn in the ene o tirrup. The reerene moel ue in thi work or preition o lexurl trength i the lil moel propoe in CI 38. In the e o orroe r it i oniere tht: - the oer o ompree r i plle o (i eere mge i eriie n when the urrent orroion intenit i higher thn μ/m n the rk with i higher thn mm); - the ompreie trength i reue the ψ tor (i moerte orroion i eriie ψ); - the re o the min r i reue, while the re o the ompree r (i n) i not oniere eue o the ukling eet; - the reution in ieling tre o r i proportionl to the oeiient γ (epening on the orroion proe). oreoer, ll r re ete me generl n pitting orroion n h me imeter. Thi i impliition whih i onertie when reer to ro-etion nli or to her trength mehnim long the her pn. The e reerre to here i tht o em ujete to lexure n her hing retngulr ro-etion with e, height H n eetie epth with oer δ. Uner thi hpothei, etion n till e ume to remin plin, n it i poile to ue the trnltion n rottion equilirium o internl ore to otin, repetiel, the poition o the neutrl xi n the lexurl trength. n e een in Figure, the poition o the neutrl xi x n the ultimte lexurl trength u re in the orm:, re γ xu α ψ β (6) φ u, re γ δ β x u (7) where α n β re the tre lok oeiient oring to CI 38, ume to e.85 n.8 or norml trength onrete, while i the teel ieling tre n,re the reue re gien Eqution.

4 Be on the preiou oniertion, with utitution o Eqution 6, Eqution 7 eome (or internl rm.9 ): u with ω δ φ γ ω.9 (8) re The lexurl trength houl lo not exee the moment pit u or ompreion ilure o orroe em lulte : u φ.5 ψ δ (9) For orroe em, utituting Eqution into Eqution 4 we otin: µ orr φ α α pit pit δ x φ + ( ) u mx (5) δ x u For the two preioul-exmine e, the timeeolution o the utilit i gien in Figure. Note tht n inree in the orroion leel in reinorement ring in eree in the utilit in thoe em exhiiting low reinorement rtio; ontrt, em with meium-high geometril rtio hnge it ehior rom utile to rittle. Figure. Flexurl etion moel or R.C. orroe etion. / oello leionle per ezioni in.. orroe. Coniering Eqution 9, the ultimte moment ue to ompreion ilure proe to e: δ.5 ψ + () u The ultimte ening moment i the minimum etween Eqution 8 n Eqution. The ieling (or liing) n the ultimte urture n e expree : φ () δ φ x u φu δ φ x u u < () u φ u u > (3) xu σ with E Finll, the ille utilit or non-orroe memer proe to e: δ x φ φu µ u φ δ xu φ (4) Figure. Reution o utilit with time. / Vrizione ell uttilità nel tempo. 3. Sher trength The ening moment n the her ore V t n gien ro-etion n e relte to the xil ore T in the longituinl r n to the internl rm j, men o: V x T j (6) x eing the itne etween the upport n the generi ro-etion o the em in the her pn. oreoer, the her ore V i relte to the rition in the reltionhip gien in Gregor (997): T ( j) V jo + T (7) x x x Eqution 7 gie the two unmentl reitne ontriution, well known in the literture em eet (j ontnt) n rh eet (j rile). From Eqution 7 it emerge tht the reitne ontriution ue to the em eet i eine : V T ( x) j (8) x

5 in whih j i the rm leel in the loe etion, ume to e.9; the rition in the moment i ue to T. The ontriution ue to the em eet n e expree in term o plitting on tree q re trnmitte the longituinl r. Coniering em portion o length x, the equilirium o the internl ore (T n T+T) gie the ollowing: T x π n i q re φ (9) i D i eing the imeter o the i-th r elonging to the min reinorement o the re. Thereore, utilizing Eqution 8 n Eqution 9 it ollow tht: n T V jo jo π qre φ i (3) x i j o eing the rm o internl ore. The limit tte oniere here or her ilure re thoe hown in Figure 3. i φ eq φ (3) Thi gie, re φeq (33) π Sutituting Eqution 33 into Eqution 3 n tking Eqution (3) into ount gie: 3.9 δ, re q re (34) For limit tte goerne onrete ruhing, n upper limit or the her trength h to e tken into ount. B impoing the ilure o the rh in ompreion n relting the xil ore in the rh with the her ore t the upport it i poile to erie the ultimte her trength relte to ruhing o the onrete rh. With reerene to Figure 3 the ultimte xil ore in the onrete trut n e lulte : N υ x oθ (35) υ eing the otening oeiient ume in CI () in the orm: Figure 3. Limit tte or her-to-moment intertion. / Stti limite per l interzione tglio momento. The irt limit tte i relte to the em eet n orrepon to rehing o the reiul on trength long the r. The eon limit tte i ue to the ruhing o n inline onrete trut. The thir limit tte i relte to on ilure in the nhorge zone. I the limit tte i ue to on plitting ilure on the i o Eqution 9 n Eqution 3 the ollowing expreion i otine: ( δ φ ) jo π qre φi + (3) In Eqution (3) the term ( δ + φ ) tke into ount o the reution in eetie epth ue to oer plling in the ompree zone (ue to eere orroion tte). The equilent imeter o the longituinl r n e introue n eine :.33 3 υ.6 (36) n j θ rtn (37) The equilirium o the ore t the upport gie: V N inθ (38) n thereore the ultimte her tre relte to the rh ruhing i: υ x u in ( θ ) (39) Ltl, the her reitne gien Eqution 34 houl e lower thn the lue gien Eqution 39 to oi premture ruhing o the ompree rh. For the limit tte relte to the lo o on in the nhorge zone (e.g. in the upport) it i ume tht the T ore ore the longituinl r i relte to the her ore : V Tu tn θ n π φre ln qre (4)

6 Thereore, the her tre proe to e: n π φ l n q re (4) where l n i the nhorge length in the upport. In the preene o tirrup, the her trength ontriution i lulte, in CI 38, in the orm: t, re t ρ (4) where i the ieling tre o the tirrup, t,re the re o the two leg o one tirrup reue orroion (Eqution ) n ρ the geometril rtio o the tirrup n i the pith. Finll, the her trength ontriution i expree the um o the lowet lue etween em eet (Eqution 34), onrete ruhing (Eqution 39) n on ilure t upport (Eqution 4) n the tirrup ontriution (Eqution 4). ter the introution o Eqution 5 n into Eqution 34, 39 n 4 the expreion o the her trength proe to e: [ φ X ] 3.9 δ π nr t γ 4 n φ l n n γ p ( ) (43) π (44) Figure 4 how the eolution o the rtio etween lexurl n her trength with time. The / rtio oniere orrepon to L/4 whih etermine onition, in term o ening moment, equilent to the e o em with itriute lo. The ultimte moment i the lowet o the lue gien Eqution 5,8 n 48. The tirrup were ume to he ieling tre o 38 P n n initil imeter o 6 mm. The tirrup were ple t pithe o 5 (Figure 4 ) n 33 mm (Figure 4 ). It i importnt to unerline tht we ruhing in Figure 4 inite the her tre or the two ping tirrup (reult rom Eqution 47). The exmple in Figure 4 reproue tpil e o exiting ontrution rom the lt ew ee in the eiterrnen re expoe or lmot it er to eere enironmentl onition tht ue rontion, well generl n pitting orroion. Uner thee onition, urrent orroion intenit equl to μ/m i ue to lulte ll prmeter. u / Time (er) Bem eet We ruhing Flexurl trength Strength omin.33 3 x.66.6 u in( θ ).9 u in( θ ) (45) The trength ontriution ue to the tirrup i: x u / Bem eet We ruhing Flexurl trength Strength omin t π ( φ X ) t 4 p ( t ) (46) Time (er) Finll, the her tre proe to e: u (, ) t min, + (47) The ultimte imenionle ening moment oite with her ilure i: u u (48) Figure 4. Sher-to-moment intertion omin or ping tirrup: ) 5 mm; ) 33 mm. / Interzione tglio momento on po te: ) 5 mm; ) 33 mm. From the igrm o Figure 4 it ollow tht or low perentge o tirrup (pith 33 mm) n moerte perentge o longituinl teel, lexurl ilure i ttine t time zero. ter 4 er, her ilure ue to onrete we ruhing our with igniint e in lexurl trength. I low tirrup ping i opte (5 mm) her ilure i ele n lexurl ilure with eree in trength (epening minl on the geometr o the etion n on the reution in the re o the longituinl teel

7 r) i expete. ter out 6 er her ilure eome ominnt. 4 CLIBRTION ND EXPERIENTL VLIDTION OF THE ODEL In thi etion, the lirtion n the experimentl lition o the propoe moel re reporte on with reerene to the experimentl t gien in Roriguez (997). The e o lexurl n her ilure were exmine. For nltil lirtion the t gien in Roriguez (997) were utilize. In thi experimenttion, ll reinorement o ie et o impl upporte em, with ro-etion hing 5 mm, H mm n L3 mm, were orroe inluing lium hlorie in the mixing wter n ppling urrent o μ/m. The mount o orroion w etermine weight lo, while the pitting epth were meure. Two-point loing w pplie giing t n / rtio o 4.6. Figure 5 gie the preite lexurl trength eru experimentl lue. Ce o lexurl n her ilure ue to onrete ruhing ( u ) n teel ieling ( u ) n her ilure ue to on ilure ( u ) re gien. The omprion how tht the moel i urte n in mot e i onertie. urrent o μ/m w pplie to the mm r. Corroion w etermine weight lo. The e exmine re repreente in Figure 6, where omprion i me etween the reution in lexurl pit with the orroion leel etermine nltill n the experimentl lue. In thi e, the omprion i titor n, it i onirme experimentll tht the ilure moe rom ieling eome rittle with onrete ruhing. Reerring to her trength preition (Dl, 995), Figure 7 how the rition in the ultimte her trength with the leel o orroion (%) or oth e o em without tirrup n with tirrup. The min r were ontitute 4 eorme r with imeter mm. In thi e, the omprion etween experimentl n nltil preition i quite titor in term o oth pek lo n ilure moe; the ltter our minl ue to ieling o teel n eoning o min r. Flexurl trength reution Experimentl δ/φ δ/φ δ/φ3 Preite δ/φ δ/φ δ/φ Corroion leel 6 Preite (knm) 4 u Figure 6. Vrition in reution in lexurl pit with leel o orroion (lo o re) or t gien in Dl (994). / Riuzione ell pità leionle on i lielli i orroione (ti i Dl 995). u Experimentl (knm) Figure 5. Experimentl eru theoretil lexurl trength lue (lirtion o moel with t gien in Roriguez (997). / Conronto teorio-perimentle i lori i reitenz leione u Sher trength - V (kn) t o Dl t o Dl To rw more generl onluion other experimentl reerhe were utilize or omprion t o Dl (994) n Dl (995). Dl (994) reporte on 4 tet rrie out on impl upporte em to inetigte r tpe, oer n leel o orroion. The em h mm, H4 mm n L3 mm with pn o 6 mm. Two mm tenion r were proie with no tirrup or ompreion reinorement. Three ierent oer lue were nlze,, 4 n 36 mm repetiel, orreponing to δ/d, n Corroion leel (%) Figure 7. Sher trength reution or em with δ/φ untion o the orroion leel or em with δ/φ. / Riuzione ell reitenz tglio on lielli i perentule i orroione per tri enti δ/ϕ.

8 5 CONCLUSIONS In the preent pper, impliie eqution to erie the lexurl n her trength o orroe em re preente n iue. Preliminr reerh on the eet o orroion on the propertie o mteril highlight tht the min eet ue to generl n pitting orroion re: - reution in teel re n utilit; - lo o on trength; - onrete ompreie trength egrtion. The expreion erie or lexure trength inlue lultion o ille utilit. The onier geometril prmeter (reution in roetion n teel r re) n mehnil prmeter (reution in ompreie trength). The expreion erie or her trength onier eerl poile limit tte, uh lo o on, nhorge ilure, onrete ruhing o ompree trut n ilure o tirrup n reution in the geometril n mehnil prmeter (ro-etionl re o etion, re o teel r n tirrup, on n ompreie trength). ll the expreion erie llow mnul lultion n he ler phil mening. Finll, omprion with exiting experimentl t turn out to e er titor in term o trength lue n ilure moe. Nel eguente loro ono tte preentte e iue equzioni empliite per eterminre l reitenz tglio e leione i tri orroe. Un rier preliminre h onentito i eterminre gli eetti ell orroione (lolizzt e pitting) ulle proprietà ei mterili: - riuzione ell re e ell uttilità elle rre; - perit i erenz iioletruzzo; - riuzione ell reitenz ompreione el letruzzo. Le epreioni erite per l reitenz leione inluono il lolo ell uttilità. Vengono onierti i prmetri geometrii (riuzione ell re elle rre) e menii (riuzione ell reitenz ompreione) per l erii i reitenz elle memrture. Le epreioni per l eterminzione ell reitenz tglio onierno i poiili tti limite, ome quello outo ll perit i erenz, rottur in zon i norggio, rottur el puntone i letruzzo, rottur elle te oltre onierre il eimento elle rtteritihe menihe e geometrihe (riuzione ell re elle rre, riuzione ell re ell ezione e riuzione ell tenione i erenz e ell reitenz ompreione). Tutte le epreioni erite onentono un lolo mnule e hnno un hiro igniito iio. Inine, un onronto on i ti perimentli iponiili riult eere oiente i in termini i preiione ell reitenz he elle molità i rottur. 6 CKNOWLEDGEENTS The reerh w perorme within the 4/8 Reerh Projet DPC ReLUIS (Diprtimento Protezione Ciile - Rete ei Lortori Unieritri i Ingegneri Simi), Line i Rier Cemento rmto. The relte innil upport w gretl ppreite. REFERENCES CI Committee 38.. Builing oe requirement or truturl onrete n ommentr, merin Conrete Intitute US P.O.BOX944-Frmington Hill, I Cirn, J. & illr, S Setion 3.: Reinorement orroion n it eet on reiul trength o onrete truture. Pro., 8th Int. Con. on Struture Fult n Repir,. Fore, e., Engineering Tehni Pre, Einurgh, U.K. ~CD-RO. Ctel,., Frnoi, R. & rliguie G.. ehnil ehior o orroe reinore onrete em. II: Bon n noth eet, ter. Strut., 33: Coronelli, D.. Corroion rking n on trength moeling or orroe r in reinore onrete, CI Strut. J., 99(3): Coronelli, D. & Gmro, P. 4. Struturl ement o orroe reinore onrete em: moeling guieline, SCE J. Strut. Eng., 4, 3(8): 4-4. Dl,. F. 994 Eet o elerte orroion on the lexurl trength o mll le em, TRL Reerh Report PR/CE/5/94, Crowthorne, Unpulihe. Dl,. F Eet o elerte orroion on the her ehior o mll le em, TRL Reerh Report PR/CE/97/95, Crowthorne, Unpulihe. Gonzle, J.., nre, C., lono, C. & Feliu, S Comprion o rte o generl orroion n mximum pitting penetrtion on onrete emee teel reinorement. Cem. Conr. Re., 5():, Gregor, J. G Reinore onrete: ehni n eign, 3r E., Prentie-Hll, Upper Sle Rier, N.J olin, F. J., lono & C., nre, C Coer rking untion o rer orroion: Prt Numeril moel, ter. Strut., 6: Prk, R. & Pul, T Reinore onrete truture, John Wile n on pulition. Pulett, P., Di Lu, D. & Ruo, G. 5. Exterior em olumn joint- Sher trength moel n eign ormul. Eng. Strut., 94: 7-8. Roriguez, J., Orteg, L. & Gri Corroion o reinoring r n erie lie o R/C truture: Corroion n on eteriortion, Pro., Int. Con. on Conrete ro Borer, 994; Vol. II, Roriguez, J., Orteg,. & Cl, J Lo ering pit o onrete olumn with orroe reinorement. Pro., 4th Int.Smp. on Corroion o Reinorement in Conrete Contrution, C. L.Pge, P. B. Bmorth, J. W. Figg, e., The Rol So o Chemitr, Cmrige, U.K.. Roriguez, J., Orteg, L.., Cl, J Lo rring pit o onrete truture with orroe reinorement, Contr. Buil. ter., (4): Ting, S. & Nowk,. 99. Eet o reinoring teel re lo on lexurl ehior o RC em, CI J. Strut Eng, 88(3): Vl, D. V. 7. Deteriortion o Strength o RC Bem ue to Corroion n It Inluene on Bem Reliilit, SCE J. Strut. Eng., 33(9): Vehio, F. & Collin. P The moiie ompreion iel theor or reinore onrete element ujete to her, Pro. CI, 83(): 9 3.