Effects of Thermal Loads on Concrete Cover of FRP Reinforced Elements: Theoretical and Experimental Analysis

Transcription

1 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis Maia A. Aiello, Faneso Foai and Antonio Nanni 3 Depatment of Innovation Engineeing, Univesity of Lee, Via pe Anesano, 73, Lee, Italy Dipatimento di Costuzione dell Ahitettua (DCA), Istituto Univesitaio di Ahitettua di Venezia, Campo olentini 9, 335 Venie, Italy 3 Cente fo Infastutue Engineeing Studies, 4 Engineeing Reseah Lab 87 Mine Cile, Univesity of Missoui Rolla, Rolla, MO Abstat he pape is devoted to the analysis of FRP einfoed onete elements unde themal loads. As known, non metalli ebas pesent high values of tansvese oeffiients of the themal expansion (CE) with espet to onete; as a onsequene, when tempeatue ineases, tensile stesses take plae within the onete that may podue splitting aks and, eventually, the onete ove failue if the onfining ation is not suffiient. An analytial model is poposed to detemine the values of tempeatue inease ( ) oesponding to the fist appeaane of the aking phenomenon and to the onete ove failue. An expeimental investigation, aied out on onete speimens einfoed with FRP ebas, is desibed and obtained esults ae ompaed with theoetial peditions. Keywods: Coeffiient of themal expansion, Conete ove, Caking, FRP, ansvese CE, hemal load, Spalling.

2 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp M. A. Aiello, is an Assistant Pofesso in Stutual Engineeing, Depatment of Innovation Engineeing, Univesity of Lee, Italy. He main eseah inteests inlude the stutual analysis of FRP einfoed onete membes, the bond between FRP and onete, the adhesion systems between polymes and onete and the analysis of omposite laminated stutues. F. Foai is a Post Dotoal Reseahe in the Dipatimento di Costuzione dell Ahitettua (DCA), Univesity of Venie. His eseah deals with the stutual behavio of FRP einfoed onete membes, bond between FRP bas and onete and stutual ehabilitation using FRP. Antonio Nanni, FACI, is the V&M Jones Pofesso of Civil Engineeing and Dieto of the Univesity anspotation Cente (UC) at the Univesity of Missoui-Rolla. Pof. Nanni is inteested in onstution mateials, thei stutual pefomane, and field appliation. He is an ative membe in the tehnial ommittees of ACI, ASCE, ASM and MS. RESEARCH SIGNIFICANCE he pape is pat of a eseah wok on the influene of themal ations on stutual pefomane of FRP einfoed onete stutues. he diffeent tansvese oeffiients of themal expansion of onete and FRP ebas may ause splitting aks within the onete and, ultimately, the spalling of the onete ove. Suh phenomena, affeting the bond between the FRP ebas and onete, ould have a elevant influene on stutual esponse of the FRP einfoed onete membes both unde sevie and ultimate onditions. he pape pesents theoetial and expeimental analyses aimed at funishing design algoithms to avoid a degadation of the stutual esponse aused by themal loads and to povide appopiate onfining ation.

3 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Intodution he use of FRP ebas as einfoement fo onete elements seems to be an effetive solution fo oveoming duability poblems of taditional steel einfoed onete stutues, due to the oosion of metalli ebas. Fo this eason the eplaement of steel with nonmetalli ebas fo onstutions is gaining populaity woldwide. he numeous expeimental and theoetial studies aied out in the last yeas and many stutual appliations besides the geat effot done in many ounties to establish the guidelines of patial use of FRP einfoed onete stutues onfim the ineasing inteest in this field. Howeve, in ode to gain a deepe insight in the stutual behavio of suh new mateials and to guaantee thei safe appliation, futhe eseahes ae needed in speifi aeas as that onening the stutual pefomane and duability unde sevie onditions (Conad, Bakis, Bootby and Nanni, 995) and among all the effet of the tempeatue ineases. Unidietional FRP ods, geneally utilized in onete, pesent an anysotopi behavio. As a onsequene, the oeffiients of themal expansion ae diffeent in longitudinal and tansvese dietions. In patiula, the longitudinal CE, ontolled by fibes, is low and even negative (as in the ase of aamidi fibes), while the tansvese CE, ontolled by the esin, is up to 3-6 times that of the onete (Genty et al., 996). As a esult, a unifom inease in tempeatue podues busting stesses within the onete that may ause splitting aks. his fat involves a degadation of the bond between onete and einfoement (epfes, 998; epfes, 979), affeting the stutual esponse. Reent studies have evidened the influene of the themal load on onete elements einfoed with FRP ebas (Uijl, 995; Matthys et al., 996; Aiello, 999; Aiello et al. 999) and some tehnologial solutions have been onsideed to edue the themal inompatibility poblems between onete and omposite ods (De Sitte and olman 995; Genty and 3

4 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Husain, 999). Howeve, futhe investigations ae needed fo a bette undestanding of the physial phenomenon in ode to develop models aiming to funish design povisions on the onfining ation needed to avoid the splitting aks within the onete at a given tempeatue inease. In this pape an analytial model is pesented; the analysis of the themal effets is pefomed onsideing the onete as a thik-walled pipe suounding the omposite eba. Analytial elationships ae detemined taking into aount diffeent states of stess within the onete. In patiula, two stages ae onsideed: that oesponding to the unaked onete, up to poduing the fist adial ak and that oesponding to the aked onete, up to sp poduing the spalling of the onete ove. heefoe, the model allows to detemine the themal loads and sp fo given geometial and themal popeties. Obtained esults ae ompaed with those fom an expeimental investigation esulting in the onsideation that the theoetial model pesented in this study allows to detemine a elationship between the ating themal load and the equied minimum onete ove value.. Analytial model he effet of themal loads on onete ove is analyzed by means of a theoetial appoah based on the following assumptions. FRP ebas ae teated independently, meaning that the lea spaing between two adjaent bas is suffiient to avoid the ouene of hoizontally splitting aks at the ba level (this assumption ould be easily emoved). Absene of bounday estaints at the ba teminations, aiming to fous the analysis on the effets of stesses inteation between FRP bas and onete podued by themal ations. 4

5 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Effet of tansvese einfoement is negleted in ode to evaluate the only ontibution of the onete ove to sustain the busting stesses podued fom the tempeatue vaiations. Conete and FRP bas pesent a linea elasti behavio. Some non-lineaity ould ou beause of the pesene of plasti defomations within the onete o a visous behavio of both the onete and the polymei matix within the bas. hese non-linea phenomena may lead to a diffeent edistibution of stesses between onete and einfoement. At pesent this influene is ignoed. he analytial investigation is aied out onsideing a ylindial FRP ba embedded in a onete ylinde as thik as the onete ove and subjeted to a tempeatue inease (Fig. ). Due to, a adial ompession ats at the ylindial sufae dividing onete and ba, it is defined by the ompatibility equation: = () b whee and is the vaiation of the adius of the ylindial hole in onete whee the od lies b is the vaiation of the ba adius, due to and, expessed as: () b = α b E b ( ν ). Behavio of the onete At the intenal sufae of the ylindial onete hole the adial ompession ats to inease the hole adius fom the initial value by a etain amount. 5

6 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp aking into aount the axial symmety of the system, in the hypothesis of plane elastiity, at a genei point in the onete with distane equal to fom the enteline of the ba, the following stesses an be detemined: ( ) ( ) + = = θ (3) being ( ) the stess in the adial dietion and ( ) θ the stess in the iumfeential dietion and the oute adius of the ylinde. he maximum value of the iumfeential tension in onete, ating at =, is:,max + = θ (4) At a etain, hee named, this stess eahes the onete tensile stength and splitting aks take plae. heefoe two ases must be onsideed, that is and >. he ase he stesses (3 give the following stains: ( ) ( ) ( ) ( ) ( ) ( ) ε ν ε ν θ = + = + E E E E (5)

7 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp As onsequene the initial adius of the hole, due to, ineases by the amount: + = + ν (6) E.3 he ase > When the tensile stength of onete is oveame, the fomation of a iula own of onete with adial aks is expeted (Fig. ), being and its inne and oute adius, espetively. Inside the own, iumfeential tension is not possible. It an be poved that the distibution of the adial ompession in the aked iula own is desibed by: ( ) = (7) It an be noted that in the unaked onete ( ) deeases popotionally to the invese of, while in the aked zone it deeases as the invese of, due to the absene of the iumfeential tension. he adial ompession (7) podues the adial stain: ε ( ) = (8) E he unaked zone, outside the iula own, is intenally delimited by a iumfeene with adius and extenally delimited by a iumfeene with adius. 7

8 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp At the intefae between aked and unaked zone, the adial ompession (equation (7) witten at = ) is given by:, ( ) = (9) Equation (3) at gives: θ ( ) = ( x, ) = + (a) (b) ϑ = f he ondition ( ) t, that is: + = f t ( x) () o: 3 + = f t + () f t allows to detemine as a funtion of. In onlusion, the inease of the adius is the sum of two ontibutions: the deease of the aked zone thikness (due to the adial ompession (7)) and the inease of the ile adius out of whih onete is unaked, that is: (note that fo the seond ontibution equation (6) an be used in whih and = ) is the ompession given by equation (9) 8

9 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp = + + ν ln (3) E he inement of the adius of the ylindial hole whee the able lies, due to is: = α (4) Fom equations (6) and (4) one obtains: + = + α E + ν (5) when onete does not ak. Fom equations (3) and (4) one obtains: + = ln E + + ν + α (6) when onete aks. Compatibility equation () an be witten as: E + + ν + α = α b E b ( ν ) (7) when onete does not ak and as: E ln ν + α = α b E b ( ν ) (8) when onete aks, being defined by equation () as a funtion of. 9

10 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Equilibium onfiguation afte adial aking he equilibium equation () imposes the adial ompession at = to be equal to the adial ompession assoiated to the iumfeential tension f t in the inne iumfeene of the unaked iula own. By setting: β = A = f t (9) it an be witten as: β 3 + Aβ β + A = () It an be poved that equation () has only one meaningful solution fo the atual poblem when A is in the ange A. 3. No solutions an be found fo A >. 3. he ondition A >. 3 means too high adial ompession o too small onete ove fo the unaked iula own of onete to be able to stop the adial aking, as an be seen in definition (9). he solution oesponding to A =. 3 is β =. 48. It s possible to onlude that the maximum adial ompession that onete an hold is given by: f =.3 t () being the oute adius of the aked iula own: =.48 ()

11 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp poduing the fist adial aks and the onete ove failue Fist adial aks appeas in onete when the iumfeential tension at =, given by equation (4) eahes the tensile stength of onete, that is when: γ = ft = f (3) t + γ + being: γ = (4) Coesponding is given by equation (7) as: f t γ ν f t f t ( α α ) = + + ( ν ) (5) E γ + E E b b he failue of the onete ove happens when the adial ompession is suh that the atio β eahes the value.48. By imposing this ondition in equation (), adial ompession is found as: =.3f γ (6) t Coesponding is given by equation (8) as:

12 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp f γ.3f γ α (7) t t ( α ) = [ ln(.48γ) ν ] + ( ν ) b sp E E b As the mehanial popeties of mateials and γ value ae known, it is possible to find value poduing the fist adial aks in onete and that ausing the onete ove failue, one the diffeene α α is speified. b 3. Expeimental investigation An expeimental investigation has been pefomed to analyze the effets of tempeatue ineases on onete elements einfoed with GFRP (Glass Fibe Reinfoed Polymes) ebas. Mateials popeties, test appaatus and obtained esults ae desibed in the following. 3. Mateials he GFRP defomed ods (C-BAR ) einfoing the tested speimens had a nominal diamete of 3 mm and wee supplied by Mashall Industies Composites, USA. Mehanial popeties of the einfoement and the onete utilized ae epoted in able. he aveage tensile stength f and the aveage tensile elasti modulus E of the einfoement wee those of the manufatue s speifiation, while the tansvese Young s modulus E tb and the Poisson atio ν of the utilized C-BAR was detemined by the invese ule of mixtues based on the peentage of fibes and matix. he aveage ompessive stength f of the onete was evaluated by standad ompession tests; elasti modulus E and tensile stength f t wee alulated aoding to (ACI 38). Effets of themal loads on FRP einfoed onete elements ae dependent on the tansvese CE of the mateials. In the pefomed analysis, CE s of the onete (α ) and GFRP bas (α b ) wee expeimentally evaluated testing six GFRP ods and fou onete elements unde an ineasing themal load and eoding the oesponding stains by means of a stain gage

13 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp attahed on the speimen s sufae. he aveage values and standad deviations wee evaluated as α b = 58-6 C -, SD = C - and α =. -6 C -, SD =.5-6 C -. he g (Glass ansition empeatue) of the esin utilized fo making C-BAR has been evaluated by the DMA tehnique; the obtained value is g = 3 C: aking into aount that the maximum tempeatue value eahed duing tests is almost C, it an be asseted that popeties of ebas would not have onsideable hanges duing test poedue. 3. Speimens Geomety and est Poedue Conete elements wee einfoed with an FRP ba without tansvese einfoement. wo shapes of oss setion, iula and etangula, wee onsideed to analyze the influene of the onete onfining ation on the stutual pefomane of the membes unde themal loading. In the fist ase, the onfining ation is axis-symmeti, as geneally onsideed in analytial models utilized fo studying the themal stess poblem. Fo etangula oss setions, the axis-symmety is emoved by plaing the ba lose to one side. Details of the speimens geomety ae epoted in Fig. 3 and able. he speimen s odes indiate the shape (fist lette, R: etangula, C: ylindial) followed by the onete ove value expessed in millimetes. Speimens wee subjeted to a themal loading by utilizing an oven. Holes wee dilled in the onete to plae themo-ouples fo deteting the tempeatue inside the speimen. he oven s tempeatue was ineased in steps of 5 to C, one the tempeatue in the onete had stabilized, up to a ak opening (Fig.4). Stain measuements wee obtained with stain gages plaed as shown in Fig. 3. 3

14 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Results and Disussion In the Figs. 5 to expeimental esults ae epoted. In patiula, eoded stains vesus tempeatue ineases ae dawn fo eah tested speimen; uves efe to the stain values measued by eah stain gage attahed on the speimens and indiated by a numbe. In addition, the aveage value of the stains is alulated and plotted in the figues. As one an see, uves pesent a simila tend, haateized geneally by two stages: the fist stage oesponds to the unaked situation, while a slope vaiation is obseved when a splitting ak is opening. Compaisons between expeimental and theoetial esults ae shown in Fig. 3. In patiula, the tempeatue ineases oesponding to the appeaane of a splitting ak ae epoted vesus the atio between the onete ove value and the ba diamete (/d). he theoetial pedition pesents an almost linea vaiation of the sp, poduing the spalling of the onete ove as a funtion of the atio /d. Expeimental esults ae in good ageement with the peditions. he figue illustates that values of /d> guaantee a good pefomane (i.e. no splitting aks) of the einfoed onete elements unde tempeatue vaiations typial of sevie onditions. 4. Paameti analysis Based on equation (7) a paameti analysis has been pefomed in ode to evaluate the needed onete ove fo a given design value of. Fo the analysis, thee onete types (f = 3, 4 and 5 MPa) wee onsideed; onsequent onete popeties E and f t wee estimated. Fo the pefomed analysis key paametes haateizing the einfoement ae the tansvese elasti modulus of the ebas, E b, and theis tansvese oeffiient of themal 4

15 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp expansion, α b ; theefoe diffeent values have been onsideed to evaluate the minimum equied onete ove unde the assigned. Figues 4 to 6 show the minimum onete ove (expessed by the atio /d) to be adopted in ode to avoid the onete ove spalling fo = 5 C in funtion of the mehanial popeties of the FRP eba and the onete utilized. It an be obseved that eithe the tansvese Young s modulus of the ba and the tansvese CE o the ba influene the spalling phenomenon, while the onete stength, in the onsideed ange, does not hange the ode of magnitude of the esults. his is beause an ineasing of f podues an ineasing of f t and onsequently a deeasing of /d ( sp = = 5 C is fixed) and at the same time an ineasing of E and onsequently an ineasing of /d. Diagams simila to those epoted in the figues an be dawn, with oesponding tables, fo all possible design situations. Using suh uves (o tables) designe an evaluate the equied minimum onete ove in ode to avoid the splitting phenomenon one the sevie tempeatue ineases ( ), the mehanial popeties of mateials (ompessive stength and CE of onete, adial elasti modulus and CE of the bas) ae known. 5. Conlusions On the basis of the theoetial and expeimental investigations, the following onluding emaks an be dawn: heoetial and expeimental esults evidene the effets of themal loads on FRP einfoed onete elements, that is the pesene of splitting aks and possible onete ove failue when the onfining ation is not suffiient. 5

16 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Results obtained onfim the need of an auate evaluation of the onete ove as funtion of the sevie tempeatue. Howeve, a onete ove value geate than two times the ba diamete seems avoid the ouene of the splitting aks. Analytial elationships have been shown to be useful fo design. In fat tables and diagams an be dawn fo an assigned themal load vaying popeties of onete and einfoement. One sevie tempeatue and popeties of mateials ae defined the designe ould easy evaluate the minimum equied onete ove to avoid the spalling phenomenon, utilizing diagams (o oesponding tables) simila to those epoted in the pape. wo shapes of oss setion, iula and etangula wee onsideed fo a onete ove value = 9 mm. Howeve, in ode to analyze the influene of the onete onfining ation, axis-symmeti o not fo iula and etangula oss-setion espetively, futhe tests ae needed. In patiula, etangula speimens with onete ove values =38 mm and =57 mm will be tested in ompaison with esults of ylindial speimens. Radial pessue fom anhoed ba add stess to the stess in onete ove aused fom themal expansion of ba. his stess supeposition may not be linea, beause the diamete of the ba deeases unde tensile load due to Poisson defomation, wih ounteats the themal diamete inease. Fo bas unde ompession the situation is moe unfavoable, beause both Poisson defomation and themal expansion inease the ba diamete. A suh ouene ould be futhe investigated fom a theoetial and expeimental point of view. A wide expeimental investigation would allow, moe oetly, to assess a theoetial model to funish, by simplified elationships, the minimum onete ove that must be adopted at design stage unde a given tempeatue gadient, one the mehanial and geometial popeties of the membes ae known. 6

17 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Refeenes Aiello, M. A.(999), Conete Cove Failue in FRP Reinfoed Beams unde hemal Loads. Jounal of Composites fo Constutions, Vol. 3, no., Aiello, M.A., Foai, F., Huang, P.C., Nanni, A. (999), Caking of Conete Cove in FRP Reinfoed Conete unde hemal Loads. Fouth Intenational Symposium on Fibe Reinfoed Polyme (FRP) fo Reinfoed Conete Stutues (FRPRCS-4), Baltimoe, Mayland, USA. Conad, J.O., Bakis C.E., Bootby,.E. and Nanni, A. (995), Duability of Bond of Vaious FRP Rods in Conete. CDCC-98, Shebooke, Canada, 99,3. Den Uijl, J. A. (995), Bond and fatigue popeties of Aapee. Non Metalli (FRP) Reinfoement fo onete stutues, L. aewe, ed., E & Spon, London, De Sitte, W. R., and olman, F. (995), J. A., Uni-dietional fibe petensioned onete elements. Non Metalli (FRP) Reinfoement fo onete stutues, L. aewe, ed., E & Spon, London, Genty,.R. (996). hemal ompatibility of Plasti Composite Reinfoement and Conete. Advaned Composite Mateials in Bidges and Stutues, M.M. El-Bady, ed., Canadian Soiety fo Civil Engineeing, Monteal, Quebe, Matthys, S., De Shutte, G., and aewe, L. (996). Influene of tansvese themal expansion of FRP einfoement on the itial onete ove. Advaned Composite Mateials in Bidges and Stutues, M.M. El-Bady, ed., Canadian Soiety fo Civil Engineeing, Monteal, Quebe, Genty, R.., and Husain, M. (999), hemal ompatibility of onete and omposite einfoements. Jounal of Composites fo Constutions, Vol. 3, no.,

18 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp epfes, R. (998). Bond between FRP-Bas and Conete. Division of Building ehnology, Chalmes Univesity of ehnology, Götebog, Publiation no. 98:3, Wok no., -6. epfes, R. (979). Caking of onete ove along anhoed defomed einfoing bas. Magazine of Conete Reseah, Vol. 3, no. 6, 3-. ACI Committee 38, Building Code Requiements fo Reinfoed Conete (ACI 38-95) and Commentay (ACI 38R-95, Ameian Conete Institute, Famington Hills, Mih. Appendix Notation he following notations ae used in the pape: = value of the onete ove; E = Young s modulus of the onete; E = elasti tensile modulus of the einfoement; E tb = Young s modulus of the ba in the tansvese dietion; f = ompessive stength of the onete; f t = tensile stength of the onete; f = tensile stength of the einfoement; L = speimen length; = b = adius of the ba; = = adius of the onete ylinde; = adius of the aked onete ylinde; α = oeffiient of themal expansion of onete; α b = oeffiient of themal expansion of the ba in the tansvesal dietion; 8

19 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp ε = stain value; = tempeatue inease; = tempeatue inease poduing the fist onete aking; sp = tempeatue inease poduing the spalling of the onete ove; ν = Poisson s atio of onete; ν = Poisson atio of the eba in the tansvese dietion; = stess at the intefae onete-eba; List of ables able : Mehanial popeties of mateials able : ested speimens List of Figues Fig. : a) Reinfoement and onete effetive aea; b) Dimensions; ) adial stess ating at the intefae eba-onete unde a tempeatue inease Fig. : Fist onete aking and onete spalling Fig. 3: Speimens Geomety a) Retangula oss-setion; b) Ciula oss-setion Fig. 4: Cak opening Fig. 5: Stains vesus tempeatue inease (Shape of the oss-setion: Ciula; Conete ove value=9 mm) Fig. 6: Stains vesus tempeatue inease (Shape of the oss-setion: Ciula; Conete ove value=9 mm) Fig. 7: Stains vesus tempeatue inease (Shape of the oss-setion: Retangula; Conete ove value=9 mm) Fig. 8: Stains vesus tempeatue inease (Shape of the oss-setion: Retangula; Conete ove value=9 mm) 9

20 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Fig. 9: Stains vesus tempeatue inease (Shape of the oss-setion: iula; Conete ove value=38 mm) Fig. : Stains vesus tempeatue inease (Shape of the oss-setion: Ciula; Conete ove value=38 mm) Fig. : Stains vesus tempeatue inease (Shape of the oss-setion: iula; Conete ove value=57 mm) Fig. : Stains vesus tempeatue inease (Shape of the oss-setion: Ciula; Conete ove value=57 mm) Fig. 3: Compaison between theoetial and expeimental esults fo GFRP ods Fig. 4: Needed onete ove fo = 5 C and f = 3 MPa Fig. 5: Needed onete ove fo = 5 C and f = 4 MPa Fig. 6: Needed onete ove fo = 5 C and f = 5 MPa able : Mehanial popeties of mateials Conete C-BAR M f (MPa) E * (MPa) f t * (MPa) f (MPa) E (MPa) E b * (MPa) ν * *theoetially evaluated Speimen able : ested speimens Ba Diamete d (mm) Conete ove (mm) Spe. Length Numbe L (mm) of speimens R9 3 (.5 ) 9 (.75 ) 76 (3. ) C9 3 (.5 ) 9 (.75 ) 457 (8. ) C38 3 (.5 ) 38 (.5 ) 457 (8. ) C57 3 (.5 ) 57 (.5 ) 457 (8. )

21 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp a) Reba Conete = d = +d/ b) ) =.48 f t = f t f t γ γ + θ = θ = =.3f t γ f t γ = f t ( )=.65f t = Fist aking = sp Limit situation > sp Conete spalling

22 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp Stain gage position Stain gage position A A a) L 76 mm mm Set A-A 3 b) A A L 4 5 mm Set A-A

23 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp C.9 Speimen ε (mio-stain) sp 3 4 av ( C) C.9 Speimen ε (mio-stain) sp 3 av ( C) 3

24 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp R.9 Speimen ε (mio-stain) sp av ( C) R.9 Speimen ε (mio-stains) sp av ( C) C3.8 Speimen 3 sp ε (mio-stains) av ( C) 4

25 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp ε (mio-stains) ε (mio-stains) C3.8 Speimen sp ( C) C5.7 Speimen sp av av ( C) 5

26 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp ( C) Analytial model R.9 C3.8 C5.7 C /d C5.7 Speimen 5 ε (mio-stains) 5 5 sp av ( C) ν.35 E 6 GPa f 3 MPa ν.8 f t 3.4 MPa α -6 C - E b = GPa E b = 9 GPa E b = 8 GPa E b = 7 GPa E b = 6 GPa E b = 5 GPa 5 E b = 4 GPa /d 4 E b = 3 GPa 3 E b = GPa sp = 5 C α b ( 6 C - ) 6

27 Aiello, M.A., F. Foai, and A. Nanni, Effets of hemal Loads on Conete Cove of FRP Reinfoed Elements: heoetial and Expeimental Analysis, ACI Mateials Jounal, Vol. 98, No. 4, July-Aug., pp /d /d ν.35 E 34 GPa f 5 MPa ν.8 f t 4.4 MPa α -6 C - sp = 5 C α b ( 6 C - ) ν.35 E 3 GPa f 4 MPa ν.8 f t 3.9 MPa α -6 C - E b = GPa E b = 9 GPa E b = 8 GPa E b = 7 GPa E b = 6 GPa E b = 5 GPa E b = 4 GPa E b = 3 GPa E b = GPa E b = GPa E b = 9 GPa E b = 8 GPa E b = 7 GPa E b = 6 GPa E b = 5 GPa E b = 4 GPa E b = 3 GPa 3 E b = GPa sp = 5 C α b ( 6 C - ) 7