MODELING OF FRP-CONFINEMENT OF LARGE-SCALE RECTANGULAR RC COLUMNS

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1 COMPDYN th ECCOMAS Themtic Conference on Computtionl Methods in Structurl Dynmics nd Erthquke Engineering M. Ppdrkkis, M. Frgidkis (eds.) Crete, Greece, June 2019 MODELING OF FRP-CONFINEMENT OF LARGE-SCALE RECTANGULAR RC COLUMNS Konstntinos G. Meglooikonomou 1 nd Georgios S. Ppvsileiou 2 1 Deprtment of Civil nd Environmentl Engineering University of Cyprus P.O. Box 20537, 1687 Nicosi, Cyprus e-mil: kmegl01@ucy.c.cy 2 Deprtment of Construction Technology Inverness College - University of the Highlnds nd Islnds 1 Inverness Cmpus, Inverness, IV2 5NA, UK e-mil: georgios.ppvsileiou.ic@uhi.c.uk Astrct One of the min pplictions of Fier Reinforced Polymers (FRPs) in construction is in the confinement of reinforced concrete (RC) columns. The performnce of FRP-confined concrete in circulr columns hs een extensively investigted nd the efficiency of models ville in literture is nowdys considered to e stisfctory. However, the cse of FRP-confinement of rectngulr RC sections is more complex prolem, the mechnism of which hs not yet een dequtely descried. The im of this work is to try nd simplify the prolem y proposing n itertive procedure sed on the outcome of 3D FEM nlysis run y the uthors. An interesting outcome is tht the so-clled rching effect is never oserved: indeed, the unconfined regions re prtilly confined nd provide certin contriution to the overll strength of the rectngulr RC sections. Bsed on system of generlized springs, well-known stress-strin lws nd filure criterion, simplified mechnicl model tht gives the stress-strin ehviour of rectngulr RC section confined y FRPs under concentric lod is proposed. The lgorithm tkes into ccount ll prmeters ville to designers, such s corner rounding rdius, stiffness of the FRP nd concrete strength, while it cn e esily understood nd implemented. Its results re found to correlte dequtely to recent experimentl dt yielded y lrge-scle tests on FRP-confined rectngulr RC columns. Finlly, in order to further evlute the performnce of this mteril model, it ws implemented in the simultion of series of experimentl tests of FRP-retrofitted squre RC columns under cyclic lterl loding simulting erthquke lods nd simultneous constnt xil compression, performed y Memon nd Sheikh [1]. In prticulr, ll specimens were simulted using nonliner fier elements, in which the FRP-confined concrete ws modelled using the forementioned mteril model. Comprison etween the numericl nd experimentl hysteresis of the column is indictive of the effectiveness of the implemented modelling. Keywords: Confinement, FRP, Concrete, Rectngulr, Model, Stress-Strin Behviour.

1 INTRODUCTION The ehviour of fier reinforced polymer (FRP) - confined concrete in circulr columns hs een widely studied, nd now the efforts of mny reserchers re directed towrds the comprehension of

In the literture, pst pproches hve concentrted on dividing the rectngulr section in confined nd n unconfined re, sed on the ide of possile rching effect etween corners.

2 1 INTRODUCTION The ehviour of fier reinforced polymer (FRP) - confined concrete in circulr columns hs een widely studied, nd now the efforts of mny reserchers re directed towrds the comprehension of the cse of FRP-confined rectngulr columns. Here, concrete is nonuniformly confined nd the confinement effectiveness is remrkly reduced. In the literture, pst pproches hve concentrted on dividing the rectngulr section in confined nd n unconfined re, sed on the ide of possile rching effect etween corners. Then, the confined zone is considered to e in stte of uniform ixil confinement, like in the circulr cross section, thus llowing the use of formuls derived for circulr columns, while the unconfined zone is considered unffected. This different ehviour is usully ccounted for through so-clled effectiveness coefficients, minly sed on geometricl considertions on the reltive size of the two different zones. In this study, n lterntive pproch is ttempted, which recognizes, through n itertive procedure sed on the outcome of 3D FEM nlysis, tht the rching effect does not relly exist. The unconfined regions re indeed prtilly confined nd contriute, though to lesser extent with respect to the core, to the totl strength of the rectngulr sections. 2 NUMERICAL ANALYSIS (FEM) In pper of Cmpione nd Mirgli [2] the picture elow (Fig. 1) is reported. The figure is relted to the cross-section of short squre column nd shows the effective concrete core fter FRP filure t the corner. Uneven dmge cn e oserved throughout the section nd two different regions cn e identified hving different confinement stress stte. In order to specify the pth of the confining stresses nd etter exmine the orders of those regions, 3D FEM in SAP 2000 [3] (liner rnge) hs een developed (Fig. 1). () () Fig. 1. Cross-section of short squre column: () experiment [2], () FEM model [4]. From the results otined from the progrm, 3D plots were drwn to study the stress field. The next four plots depict different stress fields in qurter section (100x100 mm). Stresses ner the rounded corner re not shown since they represent locl stress sttes. Firstly, the norml stresses prllel to the digonl re presented nd then those in the perpendiculr direction, so to etter recognize the direction of the confining forces. Fig. 2 illustrtes the confining stresses in qurtile of squre section.

Fig. 2. Confining stresses in qurtile of squre section 200 200mm: long digonl (top) nd orthogonl (ottom) direction. The round corner stresses re not included. Oserving the plots ove (Fig.

The centrl prts ner the sides re confined from forces coming from the corners nd moving prllel to the sides.

3 Fig. 2. Confining stresses in qurtile of squre section mm: long digonl (top) nd orthogonl (ottom) direction. The round corner stresses re not included. Oserving the plots ove (Fig. 2), the following importnt remrks cn e mde: No unconfined concrete regions re oserved, s ssumed in mny models. The centrl prts ner the sides re confined from forces coming from the corners nd moving prllel to the sides. The confining forces ner the perimeter hve strong directionlity (unixil confinement) nd on the other hnd ner the center there is more uniformity (ixil confinement) Within some tolernce, the regions where ixil nd unixil confinement exist cn esily e identified, sed on the rtio of the principl stresses of the two directions in the joints of the FEM (rtio of confining stresses less thn 15%). It hs een oserved tht the size of the ixil stress stte region is independent of the FRP stiffness; moreover, the rdius of the rounded corner is ffecting more the digonl dimension of this region, while prllel to the sides the size remins the sme. According to these results, the width of the unixilly confined peripherl region cn e simply clculted s 1/8 of the corresponding side (Figure 3). The dimensions of the regions re esily then relted nd determined ccording to this size. 3 SIMPLIFIED MECHANICAL MODEL A series of generlized springs (Fig. 3) is used to descrie the following confining ehviour. Compressed concrete expnds lterlly ccording to its confinement stte. Such expnsion ctivtes the confining device.

The confining forces re pplied t the section corners nd directed long the digonl (on pssing, the resultnt is lwys t 45 ngle, regrdless of the section spect rtio). The figure elow (Fig.

4 The confining forces re pplied t the section corners nd directed long the digonl (on pssing, the resultnt is lwys t 45 ngle, regrdless of the section spect rtio). The figure elow (Fig. 3) illustrtes how the springs re modelling the verticl nd the lterl ehviour of the section. In the verticl ehviour, the springs re experiencing the sme verticl displcements nd their strength is dded (prllel system). In the lterl ehviour, the springs re experiencing the sme force nd their displcements re dded (series system). Unixil Confinement Bixil Confinement Axil Behviour Lterl Behviour (Qurtile of rectngulr section) Fig. 3. FRP-confined rectngulr concrete section modelling using generlized springs. For the constitutive lw used to descrie the ehviour of these generlized springs, the model of Pntzopoulou nd Mills [5], which reltes volumetric strins εv to xil strins εc, hs een tken s sis. In order to comply with the mechnicl model of the generlized springs nd the differently confined regions, tht model hs een modified so to relte volumetric strins εv to xil stresses σc insted, ccording to the following eqution (the sme liner-prolic ehviour of volumetric strins versus xil strins hs een experimentlly oserved etween volumetric strins nd xil stresses, s well): 4 V (1 3v) 10 c c f co c 4 c c fco V ( 1 3v) 10 fco c fco fco fco fco (1) (1) The ove equtions descrie the following ehviour. Initilly, volume chnge is of compction nd is lmost liner up to the criticl stress of α fc0 (unconfined concrete strength, usully with α 0.7). Note tht for this xil stress level the Poisson s rtio ν remins in the rnge of (here, the initil Young s modulus of concrete is usully determined, s well). At this point, volume chnge is reversed resulting in volumetric expnsion, clled (ner- or t-pek-strength) diltncy. A point cn e found where the compression rte of the specimen equtes the expnsion rte, thus resulting in zero volumetric strin. This point is considered to pper when the ultimte strength of the unixilly confined region is reched (ixil stress stte, 1.2). After the deteriortion of this region, the expnsion rte increses more thn the compression rte (second order prol, c 2) due to less effective confinement. The expnsion ecomes unstle during the crushing phse eyond the pek strength. From volumetric strins, oth re strin εa nd side strins ε nd ε cn e esily clculted s follows (compressive xil strins re tken s negtive, nd nd re the sides length, relted y: / tnθ, with θ is the digonl ngle):

5 A V c (2) (1 + ( + ) ( + ) ( + side ) 2 dig dig 1 cos 1 sin side ) ( + side ) (1 + ) (1 + ) 1 (3) (4) (5) By the usul no-slip ssumption etween FRP jcket nd concrete, side strins ε, ε nd jcket strin cn e equted. Thus, the digonl force of the jcket pplied from the corners to the springs cn e determined s: F dig 2 E j R 1 k e side t j k e (6) (7) where ke is n efficiency fctor y Krm nd Tr [6], which considers tht confinement effectiveness increses s the corner rdius increses, nd decreses s the spect rtio of the section chnges from squre. Hving determined the digonl force pplied from the corners to the lterl springs in series, the lterl pressures (ssumed s uniform) for ech region cn e determined (Fig. 4). Two regions re identified: one with trixil stress stte nd one with ixil stress stte. Note tht no unconfined regions re to e found. Bsed on the lterl pressures clculted ove, the corresponding verticl stress cn e esily determined y the use of ixil or trixil stress-strin model corresponding to the confinement stress stte of ech region. The stress-strin model y Mnder et l. [7] is used to descrie the ehviour of the trixil stress-stte region. The model s eqution of mximum verticl stress fcc is not used in this cse due to the fct tht it descries the performnce of uniform ixil confining pressure. In order to comply with the ove modelling of the trixil stress-stte region where the confining pressures re different in two directions (they re equl only in squre sections), the filure criterion y Ottosen [8] is pplied. For the ixil stress-stte region, the model for concrete under ixil stress-stte of Liu et l. [9] is used. Finlly, sed on the res of the different regions, the totl verged verticl stress of the section is clculted. Fig. 4. Confining pressures in the regions Itertive procedure.

6 An itertive procedure is proposed in Fig. 4, where n ssumed vlue of xil stress σc corresponding to n imposed xil strin εc is rought to convergence. After convergence is reched etween the ssumed xil stress nd tht clculted with the ove considertions, the resulting sides strin through the itertive procedure should e compred to the ultimte rupture strin of the jcket. It hs een oserved from experimentl results [10] tht the verge filure strins of the FRP wrps re of the order of 50% - 80% of the filure strin of the tensile coupons mde from the sme mteril nd tested efore the ppliction of the mteril. The vlue of fctor k (rnging etween 50% - 80%) depends on the type of FRP used. 4 ASSESSMENT AGAINST EXPERIMENTAL RESULTS Recent experimentl dt collected y lrge-scle tests on FRP-confined rectngulr RC columns [11] were used for the simultion of monotonic loding. Zeng et l. [11] presented the test results of n experimentl study consisting of nine lrge-scle rectngulr RC columns with cross-section of 435mm in depth nd 290mm in width, including eight FRP-confined RC columns nd one RC column without FRP jcketing s the control specimen, tested under xil compression. The experimentl progrm exmined the sectionl corner rdius nd the FRP jcket thickness s the key test vriles. The proposed lgorithm ws ssessed ginst three of these specimens, i.e. the specimens with corner rdii 25mm or 45mm nd one or two lyers of Cron Fier Reinforced Polymer (CFRP) wrp. The corner rdius of 65mm ws not considered in the ssessment, since in uildings designed using osolete design codes the concrete cover thickness is typiclly smll. Hence, cover of t lest 65mm which would llow the formtion of the round corners in such column is highly unlikely to e found. Fig. 5 shows the correltion of the proposed mteril model with these experimentl results nd overll the numericl response cn e chrcterized s stisfctory. It should e noted tht for this comprison the itertive procedure ws terminted for FRP rupture strin equl to 50% of tht of the experimentlly tested tensile FRP coupons [11]. Fig. 5. Correltion of the proposed mteril model with experimentl results of lrge-scle CFRP-confined rectngulr RC columns under xil compression [11]. A further evlution of the model s performnce under cyclic lterl loding which simultes erthquke lods nd simultneous constnt xil compression ws performed. This ws

7 chieved y comprison ginst the experimentl tests of FRP-retrofitted squre RC columns performed y Memon nd Sheikh [1]. This experimentl study evlutes the effectiveness of Glss Fier Reinforced Polymer (GFRP) wrps in strengthening deficient nd repiring dmged squre RC columns. Ech of the eight specimens tested, representing columns of uildings nd ridges constructed efore 1971, consisted of mm column connected to mm stu. Specimens were tested under constnt xil compression nd cyclic lterl displcement excursions simulting erthquke lods. The modelling of these FRP-confined squre RC columns hs een performed using the MtL toolox FEDEAS l Finite Elements for Design Evlution nd Anlysis of Structures [12]. The experimentl moment-curvture responses within the plstic hinge regions re reported long with the numericl results in Fig. 6. The simultion of the cntilever columns hs een pplied using unique fier em-column element [13] with force formultion for the entire column, in which the FRP-confined concrete ws modelled using the proposed mteril model with degrded liner unloding/reloding stiffness ccording to the work of Krsn nd Jirs [14] nd no tensile strength. The constitutive model y Menegotto nd Pinto [15] is used to model the longitudinl steel ehviour. The moment-curvture response of the most criticl fier section of the pplied nonliner fier element ws then reported. It cn e seen tht the greement is very close to the experimentl one, with some devition concentrted on the prts of reloding fter reversl of the imposed displcement. This difference in response in terms of modelling cn e explined sed on the wy the crcks on the concrete surfce re descried in the level of the mteril model. Becuse the crck is descried s two-event phenomenon (open or closed crcks), when the longitudinl steel reinforcement is in compression nd the crck is closing, the concrete contriutes to the totl strength of the column, creting this devition in the response. In relity, this is not the cse due to imperfect crck closure.

Fig. 6. Correltion of the proposed mteril model with experimentl results of lrge-scle GFRP-confined squre RC columns under cyclic excittion y Memon nd Sheikh (2005) [1].

8 Fig. 6. Correltion of the proposed mteril model with experimentl results of lrge-scle GFRP-confined squre RC columns under cyclic excittion y Memon nd Sheikh (2005) [1]. 5 CONCLUSIONS An itertive pproch ws proposed to model oth the xil nd lterl stress-strin response of xilly loded FRP-confined rectngulr nd squre reinforced concrete columns. In FRP-confined squre or rectngulr sections, no unconfined concrete regions re oserved, s ssumed in mny models. These sectors long the sides etween djcent corners re confined from forces coming from the corners nd moving prllel to the sides. Therefore, the res where rching effect is ssumed in the section re ctully prtilly confined, so they contriute to the column s totl strength until their mximum strength (which is lower thn the inner prt of the section). Thus, two different regions with different confining stress-sttes re identified. The two regions re unixilly nd ixilly confined (ixil nd trixil stress-stte, respectively). Therefore, the contriution of ech region to the totl section strength cn e modelled s system of prllel springs, whose xil stresses re dded sed on the corresponding constitutive lw under ixil or trixil stress stte. The lterl ehviour develops long the digonls of the section nd cn e represented y system of springs in series. It ws shown tht oth sides lterl strins in the rectngulr sections re equl, regrdless of their spect rtio. The recting force of the confining device pplied from the corners cn e shred mong the regions sed on the defined pth of the confining forces nd the geometry of the regions. The resulting lterl uniform pressures led to the corresponding xil strength of the regions. The lgorithm tkes into ccount ll prmeters ville to designers, such s corner rounding rdius, stiffness of the FRP nd concrete strength, while it cn e esily understood nd implemented. Its results re found to correlte dequtely to recent experimentl dt yielded y lrge-scle tests on FRP-confined rectngulr RC columns. Finlly, the performnce of this mteril model ws further investigted y its implementtion to the simultion of series of experimentl tests of FRP-retrofitted squre RC columns under cyclic lterl loding simulting erthquke lods nd simultneous constnt xil compression. In prticulr, ll specimens were simulted using nonliner fier elements, in which the FRP-confined concrete ws modelled using the developed mteril model. Comprison etween the numericl nd experimentl hysteresis of the column is indictive of the effectiveness of the implemented modelling.

9 REFERENCES [1] Memon, M. S., Sheikh, S. A. (2005). Seismic resistnce of squre concrete columns retrofitted with glss fier-reinforced polymer. ACI structurl journl, 102(5), DOI: /14673 [2] Cmpione, G., Mirgli, N. (2003). Strength nd strin cpcities of concrete compression memers reinforced with FRP. Cement nd Concrete Composites, 25(1), DOI: /S (01) [3] Computers nd Structures, Inc CSI Anlysis Reference Mnul. Berkeley, CA: Tylor & Frncis. [4] Meglooikonomou K.G. & Ppvsileiou, G.S. (In press). Anlyticl Stress-Strin Model for FRP-Confined Rectngulr RC Columns. Sumitted to Frontiers in Built Environment Erthquke Engineering. [5] Pntzopoulou, S. J., Mills, R. H. (1995). Microstructurl spects of the mechnicl response of plin concrete. Mterils Journl, 92(6), DOI: /9780 [6] Krm, G., Tr, M. (2005). Confinement effectiveness in rectngulr concrete columns with fier reinforced polymer wrps. Journl of composites for construction, 9(5), DOI: /(ASCE) (2005)9:5(388) [7] Mnder, J. B., Priestley, M. J. N., Prk, R. (1988). Oserved stress-strin ehvior of confined concrete. Journl of structurl engineering, 114(8), DOI: /(ASCE) (1988)114:8(1827) [8] Ottosen, N. S. (1977). A filure criterion for concrete. Americn Society of Civil Engineers. Engineering Mechnics Division. Journl, 103(4), [9] Liu, T. C., Nilson, A. H., & Slte, F. O. (1972). Bixil stress-strin reltions for concrete. Journl of the Structurl Division, 98(5), [10] Lm, L., Teng, J. G. (2003). Design-oriented stress-strin model for FRP-confined concrete in rectngulr columns. Journl of reinforced plstics nd composites, 22(13), DOI: / [11] Zeng, J. J., Lin, G., Teng, J. G., Li, L. J. (2018). Behvior of lrge-scle FRP-confined rectngulr RC columns under xil compression. Engineering Structures, 174, DOI: /j.engstruct [12] Filippou, F. C., Constntinides, M. (2004). FEDEASL getting strted guide nd simultion exmples. NEESgrid Report, 22, [13] Spcone, E., Filippou, F. C., Tucer, F. F. (1996). Fire em column model for non liner nlysis of R/C frmes: Prt I. Formultion. Erthquke Engineering & Structurl Dynmics, 25(7), DOI: /(SICI) (199607)25:7<711::AID-EQE576>3.0.CO;2-9 [14] Krsn, I. D., Jirs, J. O. (1969). Behvior of concrete under compressive lodings. Journl of the Structurl Division. 95(12): [15] Menengotto, M. (1973). Method of Anlysis for Cycliclly Loded Reinforced Concrete Plne Frmes Including Chnges in Geometry nd Nonelstic Behvior of Elements under Comined Norml Force nd Bending. In IABSE Symposium on Resistnce nd Ul-

10 timte Deformility of Structures Acted on y Well-Defined Repeted Lods, Finl Report, Lison, Portugl.

1 Bending of a beam with a rectangular section

1 Bending of a beam with a rectangular section 1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure