Behavior of RC Columns Confined with CFRP Sheets and Subjected to Eccentric Loading

Lie Science Journal 2018;15(6) http:www.liesciencesite.com Behavior o RC Columns Conined with CFRP Sheets and Subjected to Eentric Loading Omar A. Farghal 1 and Mamdouh A. Kenawi 2 1 Civil Engineering Department, Faculty o Engineering, Assiut University, Egypt. 2 Civil Engineering Department, Faculty o Engineering, Sohag University, Egypt. e-mail: omar_arghal222@yahoo.com; mkenawi2@yahoo.com Abstract: Reinorced concrete (RC) rectangular columns with aspect ratio o approximately 1.5 and externally conined with bonded carbon iber reinorced polymers (CFRP) sheets were experimentally subjected to eentric compression loads up to ailure. The eect o the value o eentricity and coninement coniguration (ully conined (FC) and partially conined (PC)) on the behavior o the strengthened columns was studied. The experimental results showed that both strength and ductility o the strengthened columns had been improved with respect to the behavior o the reerence columns. The improvement in column compressive strength o both FRPconinement systems applied under eentric loading was so pronounced as or that under concentric loading. Furthermore, an analytical study was conducted aiming to apply models proposed by the ACI guidelines or strengthening concrete structures with FRP (ACI 440.2R-02 and ACI 440.2R-08) to evaluate the enhancement o the strengthened columns. To overcome the well-deined weaknesses o applying these models, a simpliied analytical orm is proposed to assess the enhancement in column strength under the eect o eentric loading. The proposed analytical model showed an agreement with the constructed theoretical axial orce-moment (P-M) interaction diagram or FRP-conined concrete using ACI 440.2R-08. Ultimately, the proposed model provides a reasonable approach or evaluating the increase in the strength o eentrically loaded ully or partially conined RC columns. [Omar A. Farghaland Mamdouh A. Kenawi. Behavior o RC Columns Conined with CFRP Sheets and Subjected to Eentric Loading. Lie Sci J 2018;15(6):22-39]. ISSN: 1097-8135 (Print) ISSN: 2372-613X (Online).http:www.liesciencesite.com. 4. doi:10.7537marslsj150618.04. Keywords:FRP sheets; Wrapping; Rectangular; P-M; Eentricity; Coninement. 1.Introduction Coninement o reinorced concrete columns by means o FRP jackets is commonly used to enhance their strength and ductility. An increase in capacity is an immediate outcome typically expressed in terms o improved peak load resistance. Concrete columns have important unction in the structural concept o structures. Oten these columns are vulnerable to load increase (change o structures unction, etc.), exceptional loads (such as: impact; explosion or seismic loads) and degradation (corrosion o steel reinorcement, alkali silica reaction, etc.). In practice, structural concrete columns axially compressed (i.e., concentrically) rarely our. Even in a column nominally carrying only axial compression, bending action is almost always present due to unintentional load eentricities andor possible construction error. However, research studies conducted so ar on external coninement o concrete columns have mainly concentrated (ocused) on concentric loading [1-8]. Few researches are known about the behavior o strengthened RC columns subjected to eentric loads [9-14]. Previous research studies showed that, when conined columns are subjected to axial loading, FRP composites could provide adequate lateral stresses. However, under eentric loading, some researches conirm that no signiicant eect is achieved, while others attested that conining columns with FRP composites can improve the structural perormance to some extent. Since the problem is quite complicated, very ew stress strain models have considered load eentricity. In act, some results contradict others. El Maaddawy[15] suggested that the stress strain curve or concentrically loaded columns may be used or eentrically loaded columns also, except that the inal point (ultimate ailure point) o the stress strain curve. This study presents experimental and analytical evaluation o the eectiveness o iber reinorced polymers (FRP) composites to strengthen RC columns subjected to eentric loading. The experimental program included eight rectangular RC columns tested under compression load with eentric ratios (eh = 0.0, 0.13, and 0.17). Three samples were ully conined (FC) with one layer o CFRP sheet, two samples were partially conined (PC) with two layers o CFRP sheet, and three columns served as reerences. To analytically evaluate the strength enhancement o FRP-conined RC columns, proposed models by ACI guidelines or strengthening concrete structures with FRPs (ACI 440.2R-02 [16] and ACI 440.2R-08 [17]) were examined. Moreover, a simple model based on linear and nonlinear geometrical properties o the transormed cross-section was 22

6 Φ 12 mm 1 φ 6 mm @ 125 mm Lie Science Journal 2018;15(6) http:www.liesciencesite.com proposed and evaluated in the light o both the available test results and the constructed P-M diagram using the stress-strain model o FRP-conined concrete adopted by ACI 440.2R-08 [17]. The obtained results concerning the maximum loads were also employed to study the applicability o the analytical model suggested by the authors to predict the nominal compressive strength o RC columns ully or partially conined with CFRP sheets and subjected to eentric loads. 2. Experimental Studies 2.1. Layout o Experiments and Materials The experimental program includes eight RC rectangular columns and tested under eentric loading, see Table 1. The cross-section o the tested columns has a dimension o 160 x 250 mm (b h) and the total height o column's specimens is 960 mm. These columns were reinorced with six high strength deormed bars, 6 12 mm, (Steel 360520 having proo stress, tensile strength, and Young s modulus o 386, 578, and 216000 MPa). These columns were provided with internal closed stirrups (Steel 240350 where their yield and tensile strengths are 280 and 410MPa) o 6mm in diameter and 125mm spacing (S). It is worth mentioning that each end zone o all studied columns was reinorced with 5 steel stirrups o 6mm in diameter (steel 240350), as shown in Fig. 1 and Table 1. The mean compressive strengths or the standard cylinder ( c ) and cube ( c ) ater 28 days or all tested columns were listed in Table 1. The wrapping reinorcement was a CFRP sheet o 0.16 mm eective iber thickness (t ). The tensile strength, maximum strain, and E-modulus o such CFRP sheet are (aording to the manuacturer) 3550 Nmm 2, 1.5%, and 230000MPa, respectively. The resin used to Table 1: Data o tested columns Column No. c (MPa) c (MPa) R.0 26.0 21.0 R.13 26.5 21.5 R.17 27.0 22.0 PC.0 26.0 21.0 PC.17 27.0 22.0 FC.0 26.0 21.0 FC.13 26.5 21.5 FC.17 27.0 22.0 Columns data A s Internal stirrups impregnate the CFRP sheets is a special one having tensile strength and lexural E-modulus (in aordance with the manuacturer) o 30 and 3800MPa, respectively. The designation o the tested columns R, FC, and PC indicate the reerence, ully-conined and partiallyconined, respectively, and0,13,17 denote the eentricity ratio to the column depth (eh = 0.0, 0.13, or 0.17). Three columns (R.0, R.13 and R.17)were tested without strengthening as control samples. Three columns (FC.0, FC.13 and FC.17) were conined with one ply o CFRP sheet applied over the total area in a circumerential way, as shown in Fig. 2. The last two columns PC.0 and PC.17were conined with two plies o CFRP strips each o 65-mm width (b ) and 65-mm ree spacing (S ). The discontinuous CFRP strips were distributed uniormly along the length (710-mm), as shown in Fig. 2. It isworthwhile to mention that the strengthened columns were conined with the same amount o iber reinorcement (ρ = volume ratio o wrapped CFRP sheet = 3.29 ). Moreover, to avoid local ailure o the ends o the tested columns, they were conined with two layers o CFRP sheet o 125- mm width, as shown in Fig. 2. The unidirectional CFRP sheets were bonded with a iber orientation perpendicular to the longitudinal axis o the columns, corresponding to the loading axis. When executing the CFRP wrapping system, an overlap length o 100-mm in the hoop direction was applied or the dierent columns (no overlap was provided in the longitudinal direction or ull wrapping). For the dierent tested columns, the cross-sectional cornershad been rounded in a curved shape o 50-mm diameterto avoid stress concentration at the corners' zones. Eentricity (e) e = 0.0 mm (eh = 0.00) e = 31.5 mm (eh = 0.13) e = 41.5 mm (eh = 0.17) e = 0.0 mm (eh = 0.00) e = 41.5 mm (eh = 0.17) e = 0.0 mm (eh = 0.00) e = 31.5 mm (eh = 0.13) e = 41.5 mm (eh = 0.17) Strengthening system Control column 1 Control column 2 Control column 3 Partially conined: 5 strips, each o 65-mm width & 65 mm ree spacing (two plies, μ 3.29 ) Fully conined (one ply, μ 3.29 ) 23

960 mm 710 mm 960 mm Lie Science Journal 2018;15(6) http:www.liesciencesite.com 168 Stirrups ϕ 6 mm 125 mm 125 125 125 A AA (As = 6 Φ 12 mm) b =160 mm 125 h=250 mm 125 Section A - A 168 Stirrups 5 φ 6 mm Figure 1.Details o internal reinorcement or tested columns. e P Two layers ocfrp Two layers o CFRP 63 65 65 65 65 65 65 Two layers ocfrp Full CFRP wrapping (one layer) S.G. 65 65 65 Two layers o CFRP 125 h = 250 mm (a) (b) (c) S.G. = Electrical strain gauge Figure 2.Details and arrangements o bonded CFRP sheets or tested columns:(a) Control ones, (b) Partialconinement, and (c) Full coninement. 2.2. Instrumentation The transverse strain induced in FRP sheets were measured using our electrical strain gauges which were aixed on the surace o the ibre sheets at the mid-height, as shown in Fig. 2. Also, the vertical strains induced in the concrete at the mid-height were measured using additional two electrical strain gauges aixed on the ibre sheets or FRP-conined columns and onthe surace o concrete in case o the control columns. Moreover, to measure the vertical shortening ourred in all tested samples, an LVDT (linear variable displacement transducer) was used.to record the dierent measurements regularly every optional interval (1 second), both the LVDT and strain gauges 24

Lie Science Journal 2018;15(6) http:www.liesciencesite.com were connected with data acquisition system (TDS- 150) which in turn was connected with a computer. 3. Experimental Results and Discussion A summary o the observed results o all tested columns is presented in Table 2, which includes: cracking load P cr ; maximum load(p max ); ratio o maximum load o the FRP-conined column to their corresponding control column (R); maximum mean normal stress (σ c,max = P max A g ), where A g is the gross sectional area; mean axial strain induced in the concrete (ε c,mean ) corresponding to ailure; h y and h ymax are the total axial shortening in the tested columncorresponding to both yielding and ailure, respectively; ductility actor μ D (= h ymax h y ); ailure modes o all columns; and transverse (hoop) strains o CFRP sheets (at mid-height) corresponding to ailure: (ε -X ) the average o the two transverse strains measured at the two opposite long directions and (ε - Y1&ε -Y2 ) the hoop strains measured at the two opposite short directions subjected to the maximum and minimum normal stresses, respectively. Table 2: Experimental results or tested columns Column No. Pcr [kn] Pmax [kn] R [-] Pcr Pmax [-] Max. normal stress & strains σc,mean εc,mean [MPa] [mmmm] Max. circumerential CFRP strains ε,max-x [με] ε,max-y1 [με] ε,min-y2 [με] Shortening & ductility hy [mm] hmax [mm] μd [-] Failure mode R.0 1075 1124 1.00 0.957 28.10 0.0037 ---- ---- ---- 2.51 3.89 1.55 F.M.1 R.13 1014 1061 1.00 0.956 26.53 0.0035 ---- ---- ---- 2.28 3.63 1.59 F.M.1 R.17 959 1004 1.00 0.955 25.10 0.0035 ---- ---- ---- 2.19 3.50 1.60 F.M.1 PC.0 1240 1331 1.18 0.932 33.28 0.0060 5560 5050 5355 2.52 6.53 2.59 F.M.2 PC.17 980 1118 1.11 0.877 27.95 0.0055 3452 3925 3343 2.19 6.15 2.81 F.M.2 FC.0 1285 1406 1.25 0.914 35.15 0.0062 >9193 (a) 8024 9918 2.54 7.01 2.76 F.M.3 FC.13 1099 1260 1.19 0.872 31.50 0.0057 4571 5154 4410 2.26 6.14 2.72 F.M.3 FC.17 1000 1218 1.21 0.821 30.45 0.0060 4119 3938 3287 2.21 6.24 2.84 F.M.3 Note: F.M.1, F.M.2, and F.M.3 are the irst, second, and third ailure modes, respectively. (a) One o the two strain gauges located at X-direction teared due sudden rupture o FRP sheet. 3.1. Cracking and Maximum Loads It is interesting to deine the cracking load to enrich the basic knowledge o design engineers with the perormance o eentrically loaded columns conined ully or partially with FRP sheets. Clearly, this will provide inormation about the end o uncracked stage. As a consequence, the cracking load or the reerence columns corresponded to observed-irstcrack on the column surace. For partially conined columns, the load corresponding to the irst noticed crack between the FRP strips deines the cracking load. However, or ully conined columns, the cracking load was deined based on a strong popping sound aompanied by bends on the bonded iber sheets. Aordingly, the cracking loads or all tested columns are deined and summarized in Table 2. Through this table, it is obvious that the strengthened columns showed an enhancement in comparison with their corresponding reerence columns, particularly in case o FC-columns regardless o the value o eentricity. However, the value o eentricity aected inversely the cracking load. For instance, in case o concentrically loaded columns (eh=0.0), the cracking load was 1075, 1240, and 1285 kn or R.0, PC.0, and FC.0, respectively; however, or the columns R.17, PC.17, and FC.17 subjected to eentric loading (eh = 0.17), the cracking load was 959, 980, and 1000 kn, respectively, as shown in Fig.3. For maximum load, in general, the eentricity was responsible or the decrease in the maximum carrying capacity o the tested columns compared with the axially loaded columns. In other words, axially loaded columns showed an improvement in the load carrying capacity higher than that o eentric loaded columns, as shown in Fig.4. This can be clearly ound in the results o ully conined columns, which showed improvement o 25, 19 and 21% when eentricities were 0.0, 31.5 and 41.5-mm respectively. In addition, or partially conined columns, the improvement was 18 and 11% in case o eentricities o 0.0 and 30-mm, respectively, as shown in Fig.5. As a consequence, 25

Lie Science Journal 2018;15(6) http:www.liesciencesite.com either in case o ully conined columns or partially conined columns, both cracking and maximum loads as well as strengthening eiciency are inversely proportional to the eentricity ratio (eh). Moreover, regardless o the value o eentricity, or the same strengthening degree (ρ 3.29 ), the FC-columns showed a higher eiciency than the corresponding PCcolumns; so ully conined system should be applied when it is possible. This conirms what was veriied by Farghal and Diab [18]. They concluded that to enhance the perormance o PC-columns, spacing between strips o FRP sheets should be minimized to conine the maximum possible area o the column. Figure 3. Cracking load (P cr ) or the dierent eentricity ratios (eh). Figure 4. Maximum normal load (P max ) or the dierent eentricity ratios (eh). Figure 5. Gain in strength or the dierent eentricity ratios (eh). Table 2 summarizes also the ratio o the cracking load to maximum load (P cr P max ), and it is remarkable that the strengthened columns had the smallest values compared with the reerence columns, mainly when load eentricity increased. That is, the irst crack initiated at a load level o about 0.96 times the maximum load in case o the control columns; however, it initiated at a load level smaller than 0.93 times the maximum load in case o strengthened columns depending mainly on the value o the eentricity and coninement coniguration. In case o the control columns, the value o eentricity showed approximately no clear eect on the ratio o cracking load to maximum load (P cr P max ): the ratio (P cr P max ) equal to 0.957, 0.956 and 0.955 when eh equal to 0.0, 0.13 and 0.17, respectively. However, or the 26

Lie Science Journal 2018;15(6) http:www.liesciencesite.com strengthened columns, the ratio (P cr P max ) decreased as the eentricity increased or both coninement conigurations used. The PC-columns showed cracking to maximum load ratios o 0.932, and 0.877 when (eh) equal to 0.0 and 0.17, respectively. Also, the FC-columns FC.0, FC.13, and FC.17showedP cr P max ratios o 0.914, 0.872 and 0.821, respectively, as shown in Fig.6. As a consequence, the ratio o cracking load to maximum load (P cr P max ) is inversely proportional to the eentricity ratio (eh). This could be attributed to the act that the ailure had not ourred until the coninement allowed the redistribution o normal stress along the entire column cross-section, and at that time rupture o wrapped CFRP sheets took place. As a result, the cracks o concrete propagated in the concrete section more than the control ones in which the ailure ourred when the crushing o concrete initiated in the extreme ibers o the section. This is clearly observed rom bends o the wrapped sheet ourred not only across the crosssection but also along the height o the columns. Figure 6. Cracking load to maximum load ratio (P cr P max ) or the dierent eentricity ratios (eh). 3.2. Failure Mode Three mechanisms o ailure were observed throughout the experimental tests carried out on FRPconined and un-strengthened rectangular RC columns. The irst mechanism was due to crushing o concrete ormed along the height o the columns. The second mechanism was also due to crushing o concrete which was seized at the unconined zones between CFRP strips. The third mechanism was due to rupture o CFRP sheet. The irst ailure mechanism ourred or both concentrically and eentrically loaded columns (R.0, R.13, and R.17), as shown infig.7(a). For the control column R.0 subjected to axial load (eh = 0.0), the crushing o concrete was due to somewhat an inclined crack initiated at the upper third zone and propagated suddenly causing ailure aompanied with a crushing o the concrete cover at that zone, as shown in Fig.7(a). For control columns R.13 and R.17 subjected to eentric loads (eh = 0.13 and 0.17, respectively), the crushing o concrete was or the concrete cover at the column zone o the highest compressive stresses (towards the side o higher compressive stress where the load was applied), as shown infig.7 (a). 27

Lie Science Journal 2018;15(6) http:www.liesciencesite.com Figure 7. Failure aspect o dierent columns:(a) Control R.-(b) Partially coninedpc., and(c) Fully coninedfc. The second ailure mechanism was observed or PC-columns subjected to either concentric or eentric loading PC.0 and PC.17 (eh = 0.00 and 0.17). These columns realized concrete crushing ormed at the unconined zones between CFRP strips, as shown infig.7(b). The concrete crushing in case o the PC.0 column was ormed in the middle third zone through approximately the whole cross-section; however, or PC.17 it was ormed in the upper third and located in side where the load was applied, as shown in Fig.7 (b). The third ailure mechanism was due to rupture o CFRP sheet and ourred or the ully FRPconined columns (FC.0, FC.13 and FC.17). When the load applied was concentric, (the columns FC.0 (eh = 0.0), the ailure was due to cut-oo the iber sheet bonded at the middle third o the column s height aompanied with a delamination o concrete cover along approximately the whole perimeter o the crosssection, as shown in Fig.7(c). However, or the FCcolumns subjected to eentric loading (eh = 0.13 and 0.17),the ailure detected was due to rupture o CFRP sheet located at the top third o the column s height aompanied with both a partial delamination o concrete cover and local concrete crushing, as shown in Fig.7(c). It is obvious that the concrete crushing located at the concrete zones o higher compressive stress close to the part o cross-section where the load was applied. It is worthwhile to mention that the rupture o CFRP sheet initiated at the long side o the cross-section (x-direction) in case o columns subjected to axially load (eh = 0.0), however or the columns subjected to eentric load (eh = 0.13 and 0.17) the rupture o CFRP sheet initiated at the short side o the cross-section (y-direction): the side exposed to the maximum compressive stresses. 3.3. Stress-Strain Behavior 3.3.1.Mean compressive stress-mean concrete strain relation The aixed vertical strain gauges to column surace at its mid-height cannot aurately represent the behaviour o the entire column, so the measured axial concrete shortening was used to determine the mean axial strain (= axial shorteningcolumn height) and plotted in Figs. 8 and 9 versus the nominal compressive stress level (P A g ) or all tested columns. In these igures, the FRP-conined columns displayed somewhat linear stress-strain relationship up to the cracking load level, which was then ollowed by a nonlinear behavior. No warning was observed beore ailure in case o the un-strengthened columns. However, in case o the FRP-conined columns, a reasonable ductility was noticed beore ailure, as shown in Figs. 8 and 9. The FRP-wrapping technique also showed a reasonable eect on the axial stinesses o the columns, particularly ater cracking. The ully coninement technique was able to decrease the column deormation in the longitudinal axis (shortening) showing the highest stiness compared with both PC-columns and un-strengthened samples, as shown in Figs. 8 and 9. Eects o load eentricity on mean compressive stress-strain relation were insigniicant up to the cracking level; however, ater exceeding the cracking load, the increase in load eentricity was associated with a considerable increase in column shortening which inversely aected its stiness. 28

Lie Science Journal 2018;15(6) http:www.liesciencesite.com (a) (b) Figure 8. Mean normal stress-axial strain diagrams or tested columns: (a) Control column R.-, and (b) Conined columnpc.-&fc.-. Figure 9. Mean normal stress-axial strain diagrams or tested columns:(a) Concentric loaded, and (b) Concentric loaded. 3.3.2.Mean compressive stress-cfrpcircumerentialstrainrelation The axial stress-cfrp transverse strain behavior or the conined columns is shown in Fig. 10. The CFRP transverse strain was recorded at the mid height or dierent directions: (ε -X ) the average o the two transverse strains measured at the two opposite long directions and (ε -Y1 &ε -Y2 ) the transversestrains measured at the two opposite short directions exposed to the maximum and minimum stresses, respectively. Throughout the nominal compressive stress- CFRP hoop strain behavior o the tested conined columns (Fig. 10), it is obvious that the normal stress- CFRP strain relation or the dierent measured strains (ε -X, ε -Y1 &ε -Y2 ) was approximately linear up to a certain normal stress level, which was dependent on the value o eentricity. Such normal stress was approximately 25, 18 and 15 MPaor FC- columns o eentricity ratio (eh) o 0.0, 0.13 and 0.17, (a) (b) respectively. However, or PC- columns such stress level has no obvious relation. Aterwards, once the columns are loaded beyond this stress level, a nonlinear relation was noticed. When considering the CFRP strain corresponding to the ailure, or conined columns (PC.0&FC.0) axially loaded (eh = 0.0) the CFRP strain ε -X was higher than ε -Y1 and ε -Y2. On the other side, as the eentricity increased ε -Y1 increased and both ε -Y2 and ε -X decreased. In the light o this, it is clear that the reason phenomena o the position o rupture initiation o CFRP sheet: the rupture initiated at the long direction (x-direction) or column FC.0, however it initiated at the short direction (y-direction) or column FC.17. This is attributed to the act that, the rupture o the bonded CFRP sheet ourred at the concrete zone in which the higher CFRP strain induced. For instance, in case o column FC.0 the rupture o CFRP initiated along the length o crosssection (x-direction) o higher CFRP horizontal strain: ε -X, ε -Y1 and ε -Y2 were > 9193 (one o the two strain 29

Lie Science Journal 2018;15(6) http:www.liesciencesite.com gauges located at X-direction (long side) teared due sudden rupture o FRP sheet), 8024 and 9918 microstrain (µɛ), respectively. However, in case o column FC.17 the rupture o CFRP initiated along the width o cross-section (y1-direction o maximum normal stress): ε -X, ε -Y1 and ε -Y2 at mid-height were 4119, 3938 and 3287µɛ, respectively. It is interesting to mention that in case o column FC.13 (ε -X, ε -Y1 and ε - Y2 were 4571,5154 and 4410µɛ, respectively) the CFRP strains induced in both directions "X&Y1" were somewhat close each other (4571 and5154µɛ). So the rupture o CFRP initiated along the corner o crosssection close considerably to tangency o the corner with length o cross-section (between X-and Y1- directions). Through Fig.10 and Table 2, it is obvious that the FC-columns ailed due to the rupture o the CFRP sheet showed a higher maximum hoop strain compared with those partially conined PC, which ailed due to concrete crushing at the ree zones (unconined zones). The values o hoop CFRP strain give an indication about the degree o taking advantage o the applied coninement technique. Hence, the eiciency o the applied strengthening technique is expressed by the ratio o the induced circumerential CFRP strain to the ultimate strain o the used CFRP sheets. As a consequence, the FC-columns satisied higher strengthening eiciency in comparison with the PCcolumns. Moreover, it is important to mention that, although a rupture o CFRP strips has ourred in case o FC-columns, the induced maximum CFRP strain had not reached the expected ultimate value o the CFRP strain (about 15000 µɛ). This is attributed to the act that the cut-o o CFRP jacket had not exactly ourred where the strain gauges used were installed. (a) (b) (c) Figure 10. Mean normal stress-circumerential CFRP strain diagrams or conined columns: (a) X-direction, (b)y1-direction&(c) Y2- direction. 3.4. Structural Ductility For any structural design, ductility is a required eature as an extra saety actor against unexpected overloading. Generally, or a structural member subjected to axial load, ductility may be measured by the ductility actor (μ D ) which is equal to the total axial shortening at ultimate load or ailure (Δh max ) to that at the beginning o yielding o main steel reinorcement (Δh y ). The total axial shortening generated in the structural member at ailure (Δh max ) is deined as the shortening ourred in the member at ailure, e.g. cuto o FRP sheets or crushing o concrete or when strength descends to 85 % o the maximum load. Careul scrutiny o the test results showed that the total vertical shortening corresponding to the irst yielding o internal main reinorcement (Δh y ) decreased as the eentricity increased without any clear eect or the type o coninement coniguration (PC or FC) on Δh y. For instance, the shortening corresponding to the irst yielding was more or less 2.50, 2.30 and 2.20 mm or eentricities o 0.0, 31.5 and 41.5 mm, respectively. This can be attributed to the local eect o the eentric loading which caused a signiicant increase 30

Lie Science Journal 2018;15(6) http:www.liesciencesite.com in the compressive stresses and strains in steel reinorcement as the eentricity increased. Figure 11. Ductility index μ D (= Δh max Δh y ) or the dierent eentricity ratios (eh). From the view point o the required gradual degradation o column strength ater achieving the maximum capacity, it is obvious that FRPconinedcolumns showed a reasonable deormation ater reaching the maximum load, but control columns ailed without suicient warning approximately at the maximum load level. It is worthwhile to note that, when compared with the control columns, the FRPconined columns showed a considerable enhancement in the obtained ductility μ D (= Δh max Δh y ), especially in case o FC- columns, as shown in Fig.11 and Table 2. For instance, in case o axial loading, the ductility index was 1.55, 2.59 and 2.76 or control, PC- and FC- columns. Also, or eentric loading (eh = 0.17), the ductility index μ D was 1.60, 2.81 and 2.84 or control, PC- and FC-columns respectively. It is worth to note that, in case o control- and FC-columns, eentricity has no obvious eect on the obtained ductility: the ully conined column FC.0, FC.13, and FC.17 had ductility indices o 2.76, 2.72 and 2.84, respectively; and un-strengthened columns R.0, R.13, and R.17, showed ductility indices o 1.55, 1.59 and 1.60, respectively. However, in case opc-columns, eentricity showed a reasonable eect on the obtained structural ductility: the ductility indices or the partially conined columns PC.0 and PC.17 were 2.59 and 2.81, respectively, see Table 2. 4. Analytical Modeling Conining RC columns with FRP sheets leads to improve the strength o concrete; namely conined concrete strength. As a consequence, the compressive strength o the concrete column is improved. The degree o coninement in terms o the amount o wrapping FRP inluences considerably the conined concrete strength. So, the compressive strength o non-slender RC FRP-coninedcolumns P max may be predicted in a similar way as that o unstrengthened RC members, using conined concrete strength aording to Eq. (1). A g A s s As Pmax k c (1) where A g is the gross area o concrete section, A s is the total area o main reinorcement, is the conined concrete compressive strength based on cylinder, k c is a actorwhich takes into aount the size eect (k c =0.85) and s is the stress generated in the main steel reinorcement at a load level equals the maximum load o the FRP-coninedcolumn P max. The ollowing section presents a summary o the models proposed by the ACI 440.2R-02 [16] and ACI 440.2R-08 [17] to predict the compressive strength o RC columns conined with FRP jackets. Ater that, in the light o the study conducted on these models, a simpliied analytical orm is proposed to evaluate the enhancement in the column capacity under the action o small eentricity (e < h6) ater strengthening with external FRP jacket using ull or partial wrapping conigurations. 4.1. Prediction o Nominal Compressive Strength ofrp-conined RC Columns under Eentric Loading Using ACI 440.2R-02 & ACI 440.2R-08. ACI 440.2R-02 [16] provided an analytical orm to predict the axial compressive strength o a nonslender, normal weight concrete member conined with an FRP jacket and with existing steel longitudinal reinorcement, Eq. (2). n A A A g s y s P 0.85 {ACI440.2R-02} (2) 31

Lie Science Journal 2018;15(6) http:www.liesciencesite.com Where y is the yield strength o the main steel reinorcement and is a actor equal to 0.95. ACI 440.2R-02 [16] adopted stress-strain model proposed by Mander et al. [5] or conined concrete. This model was originally developed or the coninement eect due to the steel jackets, Eq. (3). This equation has been shown to be applicable to FRPconined concrete (Spoelstra and Monti [7]). The conining pressure ( ) or ully wrapped columns, l however, must be considered to be linearly variable such that an increase in the strain in the FRP jacket results in a proportional increase in the conining pressure. The conined concrete strength can be computed rom Eq. (3) using a conining pressure given in Eq. (4) or ully wrapped columns, that is the result o the maximum eective strain that can be achieved in the FRP jacket as shown in Eqs. (4) through (6). requirement was included or evaluation o lateral pressure o partially conined columns. In the current design guidelines provision (ACI 440.2R-08 [17]), the axial compressive strength o short, normal-weight concrete member conined with an FRP jacket may be calculated using the conined concrete compressive strength, Eq. (8). The main dierence between Eq. (8) and Eq. (2) is the actor ψ, which is eliminated rom Eq. (2). P n A A A g s y s 0.85 {ACI 440.2R-08}(8) The stress-strain model proposed by Lam and Teng [8, 19] was adopted byaci code [17]. For circular and rectangular sections, this model describes the behavior o FRP-conined concrete subjected to concentric compression load. The actor ψ is presented in Eq. (9) to evaluate the maximum conined concrete compressive strength. l l 2.25 1.0 7.9 2 1. 25 c c c {ACI440.2R-02}(3) 3.30 k {ACI 440.2R-08} (9) c where, a l l k a E e {ACI 440.2R-02} (4) 2 2 n t ( b h ) bh {ACI 440.2R-02} (5) k a 1 2 b 2 r h 2 r Where 3bh c 1 unconined concrete cylinder, l s 2 {ACI 440.2R-02} (6) is the compressive strength o stress due to wrapping iber sheets, is the lateral conining e is the eective strain induced in FRP reinorcement corresponding to ailure (mmmm), E is the modulus o elasticity o FRP (MPa), ρ is the FRP reinorcement ratio, and k a is the eiciency actor which takes into aount the geometry o the section (k a = 1.0 or circular sections). I the member is subjected to I the member is subjected to combined compression and shear, the eective strain in the FRP jacket should be limited based on the criteria given in Eq. (7). 0.75 0.004 (7) e u In reality, ACI 440.2R-02 [16] did not report any clear recommendation or prediction o the strength o FRP-conined RC columns under eentric loading or both circular and rectangular sections. In addition, no k a c A e A c 2 b h {ACI 440.2R-08}(10) b 2 h 2 h 2 r b 2 r c c h b 1 s A e 3bh {ACI 440.2R-08} (11) A (1 ) l 2 E n t e 2 2 b h s {ACI 440.2R-08} (12) In Eq. (12), the eective strain level in the FRP at ailureε e is given by: k (13) e u The FRP strain eiciency actor k takes into aount the premature ailure o the FRP system. ACI 440.2R-08 [17] recommends that a strain eiciency actor o 0.55 and a minimum coninement ratio l c o 0.08 should be used. Furthermore, the eective strain in the FRP jacket should be limited to the value given in Eq. (14) to ensure the shear integrity o the conined concrete or the members subjected to combined axial compression and bending. 0. 004 k (14) e u For the purpose o predicting the eect o FRPconinement on strength enhancement o RC columns under the action o eentric loading, the current version o ACI guidelines or strengthening concrete 32

Lie Science Journal 2018;15(6) http:www.liesciencesite.com structures with FRPs (ACI440.2R-08 [17]) presents Eqs. (9-14) or prediction o column strength when eentricity is less than or equal to 0.1h. When the eentricity is larger than 0.1h, the P-M diagram or the FRP-conined member should be constructed using the concrete material properties o the member crosssection under compressive strength. That is to say that P-M diagrams should be developed by satisying strain compatibility and orce equilibrium using the proposed model or stress-strain behavior o FRP-conined concrete. ACI 440.2R-08 [17] assumed a negligible eect or the conining FRP jackets when aspect ratio (hb) exceeds 2.0 (limited to 1.5 in ACI 440.2R-02 [16]) or ace dimensions b or h exceeds 900-mm. Based on the recommendations o the early version o ACI guidelines, the enhancement in the strength o the tested columns in this study is insigniicant to be considered, which is in contrary to the experimental indings. On the other hand, the approach incorporated by ACI 440.2R-08 [17] to evaluate the enhancement in column strength ater wrapping with CFRP sheets can only evaluate the compressive strength o the ully FRP-conined columns. Nonetheless, in case o circular and non-circular sections, both ACI 440.2R- 02 [16] and ACI 440.2R-08 [17] guidelines have not introduced any analytical models to predict the strength o RC columns conined with partiallywrapped FRP sheets. Strength enhancement o the ully-wrapped columns is evaluated using Eqs. (9-14). Since these equations should be applied or columns subjected to eentric loading at a distance (e) < 0.1h, the P-M diagram or the FRP-conined member is constructed or higher eentricities, as shown in Fig.12. This diagram is developed by satisying strain compatibility and orce equilibrium using Lam and Teng model [8, 19] which was adopted by the ACI 440.2R-08 [17]. Predicted values using Eqs. (9-14) are superimposed on Fig.12. Also the experimental envelope o P-M diagram is plotted on the same igure or comparison. It is remarkable that the applied Eqs. (9-14) overestimate the eect o eentricity compared with the P-M diagram constructed based on the same code provisions (ACI 440.2R-08 [17]). However, in general, both Eqs. (9-14) and P-M diagram underestimate the enhancement in the compressive strength o the tested FRP-conined columns. Compared with the constructed P-M diagram, the error P n,model P n,exp P n,exp was around -27% or axially loaded columns, but it increased to -41% and -44% when the applied load is located at eentricity o 31.5-mm and 41.5-mm, respectively (Fig.12). This underestimation can be attributed to the auracy o the applied stressstain model to determine the concrete material properties o the member cross-section. Lam and Teng stress-strain model [8, 19] was based on a ew test results o rectangular columns with aspect ratio >1.0. Eight samples were collected by Lam and Teng [19] rom which only two samples exhibited enhancement in axial strength capacity. To develop a model with a reasonable auracy, Lam and Teng [19] tested a new series o ourteen samples; in which, two columns with aspect ratio o 1.5 showed an increase in the axial strength capacity.despite the well-established auracy o FRP-conined model proposed by the ACI 440.2R-08 [17] to evaluate the stress-stain behavior or circular sections, it should be ocusedin uture research or urther development to predict the stressstrain behavior o noncircular columns conined with FRP. Also, it is obvious that comprehensive calculations are necessary to construct an aurate P- M diagram, corresponding to compression-controlled ailure, to evaluate column strength when eentricity is larger than 0.1h. In the ollowing sections, the eect o partial coninement on evaluation o column compressive strength is considered without any urther modiication o the stress-strain models. diagramexperimental envelope o ACI 440.2R-08 envelope o P-M Figure 12.P-M diagram or ully FRP-conined columns using ACI 440.2R-08. 33

Lie Science Journal 2018;15(6) http:www.liesciencesite.com For FRP-conined columns partially wrapped, the eiciency o the wrapping system decreases due to existing o both conined and unconined zones [6], as shown in Fig.13. In a similar way as circular columns, a modiication actor to Eqs. (4) and (12) was introduced to deal with RC rectangular FRP-conined columns which are partially wrapped. Equation (15) identiies the coninement eectiveness coeicient k p, which takes into aount the eectiveness o the hoopstress rom the wrapping system on part o the concrete where the conining stress has ully generated as a result o the arch action. The eect o the arch action is proposed as a parabola with an initial inclination o 45 o [6], as shown in Fig.13. Consequently, at the mid-distance between two suessive iber strips, the eectiveconined concrete area A e is to be taken into aount. So that, the coeicient k p is calculated by considering the ratio (A e A c ) [20], where A c is the area o concrete (= the gross cross-sectional area (A g )- the area o longitudinal steel (A s ): A c = A g A s ).In addition, a deinition (ρ p ) is given or the FRP reinorcement ratio o partially conined columns, Eq. (16). k p A A e c 1 2 s 1 h 2 r 2 b 2 r c 1 2 n b h b t (16) b h s s s c 1.0(15) where b is the width o the FRP strips, s is spacing between center to center o the CFRP strips (s = b in case o ully wrapping), s (= s - b ) is the clear spacing between two suessive wrapped CFRP strips, ρ s is the reinorcement ratio o the longitudinal steel reinorcement with respect to the gross cross-sectional area (= A s A g ). b r b b s s h = h 2r c Figure 13. Conining pressure exerted by wrapping FRP sheet on a rectangular column [6] 4.2. Proposed Analytical Modelor Nominal Compressive Strength o FRP-Conined RC Columns under Eentric Loading For columns strengthened with iber reinorcement jackets and subjected to eentric loading, the available code provisions have not introduced a direct analytical model or quantitative prediction o the column strength. However, charts or analytical orms are used by engineers as design tools or the evaluation o design strength. This gives a rise to a need or analytical orms to evaluate the design strength o eentrically loaded columns. Hence, an expression, Eq. (17),is usedto predict the nominal compressive load P n or columnssubjected to loading at eentricity e x rom column center o gravity: section subjected to combined eect o axial compression P h Cross- section h = h s2 h Partial wrapping and bending M x (= P e x ), as shown in Fig.14. The suggested orm is dependent on that the sum o the induced stresses on the column cross-section due to axial orce and bending moment (б max ) should be in equilibrium with the maximum compressive strength o the cross-section ater applying the FRPconinement system. To relect the impact o mechanical characteristics o the column materials on the evaluated column strength, a modular ratio is deined. For un-cracked section, the modular ratio o elasticity between steel and concrete (n = E s E c : E c = 4700 c or ACI 318-08 [21]) is used to deine both the equivalent column cross-sectional area ( h Full wrapping A eq ) and the second moment o inertia about Y- axis ( I ). However, when cracked section is the case, the modular ratio o elasticity nshould be measured or eq y 34

b Lie Science Journal 2018;15(6) http:www.liesciencesite.com approximately taken as 1.5 times that o un-cracked section or normal strength concrete [21]. Figure 14. Distribution o normal stresses along the cross-section. max 1 P n A eq h e x 2 I eq y (17) I eq y b h 12 б 3 X n A bh ( n 1) s ( n 1) d 64 eq A s 4 n s 1 ( n 1) A x (19) Y Y h 2 (18) where x is the horizontal distancebetween the steel bar and Y-axis, n s is the number o longitudinal bars, A s and y are the total areaand yieldproo stress o the longitudinal reinorcement respectively, d anda ϕ are the diameter and cross-sectional area o e. P б X longitudinal bar, respectively, and n is the modular ratio o elasticity between steel and concrete. It should be clear that the evaluation o the proposed equation depends on the auracy o the adopted FRP-conined concrete stress-strain model: that is Eq. (17) relies on the value o. Although the model proposed by ACI 440.2R-08 [17] is in need or urther improvement as discussed in the preceding sections, one o the aims o this work to examine validity o the proposed equations to predict the eect o eentricity on column strength in comparison with the constructed P-M diagram, as shown in Figs.15 and 16. These igures present the constructed P-M diagram or both FC and PC concrete columns, respectively. The proposed modiication or the coninement coniguration eect (Eqs. (15 and 16)) was considered in the development o P-M diagrams. These igures show that Eqs. (17-19) can relect the eect o eentricity on the column strength with a sound auracy in regard to the P-M diagrams. But, these equations cannot be urther applied when the minimum stress (б min ) in the opposite extreme iber o the cross-section is tension, as shown in Fig.14. This means that the proposed model is applicable or small eentricity ratio. Additionally, the compressive strength o the tested columns were predicted using the proposed model, in which was determined based on stress-strain model o FRP-conined concrete by ACI 440.2R-02 [16]; the results are summarized in Table 3. The proposed modiication on the lateral coninement pressure using Eqs. (15 and 16) was considered or the evaluation o partial coninement eect. Table 3: Evaluation o the proposed model (Eq. 17) using the FRP-conined concretecompressive strength models given by ACI 440.2R-02 (Eq.2) and ACI 440.2R-08 (Eq.8). Eq.17 Eq.17 Experimental Column &ACI-02*(Eq.2) &ACI-08**(Eq.8) P No. max P (kn) n Error P n Error (kn) (%) (kn) (%) R.0 1124 964-14 964-14 R.13 1061 766-28 766-28 R.17 1004 690-31 690-31 PC.0 1331 1211-9 1022-23 PC.17 1118 757-32 715-36 FC.0 1406 1315-7 1029-27 FC.13 1260 891-29 816-35 FC.17 1218 820-33 722-41 Note: *ACI-02 means the ACI 440.2R-02; ** ACI-08 means the ACI 440.2R-08; Error = P n,model P n,exp P n,exp 35

Lie Science Journal 2018;15(6) http:www.liesciencesite.com The combined application o the FRP-conined concrete strength models and the proposed model or the evaluation o column strength shows that Eq. (9) "ACI 440.2R-08 [17]" has inerior eect on the evaluation o column strength than Eq. (3) (ACI 440.2R-02 [16]) or both applied coninement conigurations (FC and PC). For instance, when applying Eq. (9) (ACI 440.2R-08 [17]), the proposed model underestimates the compressive strengths o the concentric loaded columns"r.0, PC.0 and FC.0" with values ranged between -14% and -27%. However, or eentric loaded columns"r.13, R.17, PC.17, FC.13&FC.17" the errors ranged between -28% and - 41% aording to the value o eentricity ratio (eh): the errors increased as eentricity ratio increased. On the other hand, when applying Eq. (3) (ACI 440.2R-02 [16]), the proposed model underestimates the compressive strengths o the concentric loaded columns"r.0, PC.0&FC.0" with values ranged between -7% and -14%. However, or eentric loaded columns"r.13, R.17, PC.17, FC.13&FC.17" the errors ranged between -28% and -33% aording to the value o eentricity ratio (eh): the errors increase as eentricity ratio increases. Experimental envelope o P-M diagram ACI 440.2R-08 envelope o P-M diagram Figure 15. P-M diagram or ully FRP-conined columns using ACI 440.2R-08 in comparison with proposed analytical model. Experimental envelope o P-M ACI 440.2R-08 envelope o P-M diagram Include reduction actors Balance line Figure 16.P-M diagram or the partially FRP-conined columns using ACI 440.2R-08 in comparison with proposed analytical model. 36

Lie Science Journal 2018;15(6) http:www.liesciencesite.com The previous discussion demonstrates the proposed model validity in predicting the load carrying capacity o the concentrically loaded columns "unstrengthened and FRP-conined columns", particularly when Eq. (3) (ACI 440.2R-02 [16] is adopted. On the contrary, the validity o proposed model to predict the load carrying capacity o the eentrically loaded columns needs to be modiied and adjusted. Again, the author emphasizes on that a much better estimation o column compressive strength could be obtained when the auracy o the model in predicting the FRPconined concrete compressive strength is highly improved. 4.3. Evaluation and Modiication o the Proposed Analytical Model The combined application o the analytical model proposed by the author and both ACI models (ACI 440.2R-02 and ACI 440.2R-08) showed under estimation to predict the strength o FRP-conined RC columns under eentric loading. However, theproposedanalytical model proved somewhat an aeptable approach to the obtained experimental results when using the modelby ACI 440.2R-02[16] compared with thatwhen using that by ACI 440.2R-08 [17].Such inaurate prediction is attributed, rom the author s point o view, to the act that the proposed model equates б max with regardless the state o loading, eentric or concentric, see Eqs. (3), (9) and (17).Thereore, modiication in the proposed model deals with the adjusted value o the maximum FRPconined concrete strength under eentric loading,e should be taken into aount when calculating the nominal compressive load P n o RC columns conined with wrapped FRP sheets. On the basis o the obtained test results, the concrete strength (maximum stress) under eentric loading,e is higher than that under concentric loading,o (=, see Eq.3). The developed concrete strength depends mainly on the eentricity ratio eh. Based on the suggested expression (Eq.17) and the obtained experimental load carrying capacity o the dierent columns and in a contrary manner, the actual conined concrete strength,e were derived and compared with the predicted conined concrete strength o the corresponding columns subjected to concentric loading,o (= ). In other words, the conined concrete strength o the columns under eentric loading was calculated in similar way as the corresponding ones under concentric loading. Aording to the obtained calculations, it was obvious that the obtained,o is approaching considerably the in case o columns under concentric loading;,e however,,e is higher or columns under eentric loading, particularly or higher eh, see Fig.17. As a result, a modiication in predicting,e should be considered. As the conined concrete strength under eentric loading depends on various aspects and parameters, or which the inluence and interaction are diicult to be quantiied analytically, the author proposed a modiied relationship among,e,,o, and eh. The modiied expression is based on perorming a curve itting which in turn depends on the (,e,o ) and (eh) data points, see Fig.17 and Eq. (20). So, the FRP-conined concrete strength under eentric loading,e may be obtained aording to Eq. (20).,e =,o 1.0 + 2.10 e h (20) Figure 17. The ratio,e,o or dierent eentricity ratios (eh). When the above modiication was taken into aount in calculating the nominal compressive load P n o RC columns conined with wrapped FRP sheets, the predicted values showed a better estimation and an aeptable approach to the experimental results, 37

Lie Science Journal 2018;15(6) http:www.liesciencesite.com particularly when using ACI 440.2R-02 [16] model, as or ully and partially FRP-conined columns, shown in Table 4. The percentage o errors respectively. What was mentioned beore P n,model P n,exp demonstrates well thevalidity o the proposed model in ranged rom -11% to -15% in case o P n,exp predicting the load carrying capacity o RC FRPconined columns. the control columns. However; the percentage o errors ranged rom -7% to -10% and rom -8% to -9% Table 4: Evaluation o the proposed model (Eq. 17) using the FRP-conined concrete compressive strength models given by ACI 440.2R-02 (Eq.2) and the modiication,e (Eq. 20). Column No. Conclusions Experimental P max (kn) Eq.17 & ACI-02 (Eq.2) P n Error (%) Eq.17, Eq.20 & ACI-02 (Eq.2) P n Error (%) (kn) (kn) R.0 1124 964-14 964-14 R.13 1061 766-28 903-15 R.17 1004 690-31 890-11 PC.0 1331 1211-9 1211-9 PC.17 1118 757-32 1028-8 FC.0 1406 1315-7 1315-7 FC.13 1260 891-29 1134-10 FC.17 1218 820-33 1113-9 Based on the conducted experimental study on FRP-wrapped rectangular RC columns under the eect o small eentricity loading as well as the perormed analytical veriications, the ollowing conclusions may be drawn: 1- Coninement o rectangular columns using CFRP sheets is an eicient technique to improve the strength and axial stiness o RC columns subjected to eentric loading, particularly in case o ully coninement coniguration. 2- The applied strengthening technique enhances bothcracking and maximum loads. The enhancement was higher in case o FC-columns in comparison with their counterparts o PC-columns. However, the value o eentricity showed inverse eect on bothcracking and maximum loads. 3- A decrease in the ratio o cracking load to maximum load (P cr P max ) was noticed with the increase in eentricity or the conined columns; however, this is not really detected or the reerence columns. 4- The conined columns showed reasonable strains beore ailure, but the control columns approximately ailed at the maximum stress. As a result, the structural ductility o RC columns improved considerably when conined with CFRP sheets, particularly in case o FC-columns. Regardless the coninement coniguration, the improvement slightly increases as the eentricity ratio (eh) increases. 5- The ailure mechanism is aected by the applied FRP-wrapping technique. However, the eentricity ratio has no inluence on the ourred ailure mode. 6- Comparison between experimental results o FRP-conined columns with the constructed P-M diagram based on ACI 440.2R-08, the error P n,model P n,exp P n,exp was around -27% or axially loaded columns, but it increased to -41% and -44% when the applied load is located at eentricity o 31.5-mm and 41.5-mm, respectively. 7- The authors presents a simple approach (Proposed Analytical Model) that can be applied to ind out the eect o FRP-coninement on the compressive strength o concentrically or eentrically loaded column. This approach depends on the transormed section, considering the linear and nonlinear geometrical properties o the cross-section. 8- The combined application o the analytical model proposed by author and ACI 440.2R- 02modelshowed a good estimation to predict the strength o FRP-conined RC columns under eentric loading, particularly when the modiication in the proposed model deals with the adjusted value o the maximum FRP- conined concrete strength under eentric loading,e is taken into aount. The errors P n,model P n,exp P n,exp ranged rom -11% to -15%, rom -7% to -10% and rom -8% to -9% in case o the control, ully and partially FRP-conined columns respectively. 38