Accepted Manuscript. Reducing the seismic damage of reinforced concrete frames using FRP confinement. Vui Van Cao, Hamid Reza Ronagh

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1 Aepted Manusript Reduing the seismi damage of reinfored onrete frames using FRP onfinement Vui Van Cao, Hamid Reza Ronagh PII: S (14) DOI: Referene: COST 5813 To appear in: Composite Strutures Please ite this artile as: Cao, V.V., Ronagh, H.R., Reduing the seismi damage of reinfored onrete frames using FRP onfinement, Composite Strutures (2014), doi: This is a PDF file of an unedited manusript that has been aepted for publiation. As a servie to our ustomers we are providing this early version of the manusript. The manusript will undergo opyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the prodution proess errors may be disovered whih ould affet the ontent, and all legal dislaimers that apply to the journal pertain.

2 Reduing the seismi damage of reinfored onrete frames using FRP onfinement Vui Van Cao, Hamid Reza Ronagh* Shool of Civil Engineering, The University of Queensland, St. Luia, Australia * h.ronagh@uq.edu.au Abstrat The objetive of this study is to investigate the effet of FRP onfinement on reduing the damage of an 8-storey poorly-onfined reinfored onrete frame subjeted to different seismi intensities. Inelasti time history and damage analyses are performed for the poorly-onfined frame and its FRP retrofit. Analyses are also performed for a geometrially similar frame designed with the more restritive requirements of an intermediate frame for omparison with the poorly-onfined and retrofitted frames. The results onfirm the positive effet of FRP onfinement signifiantly reduing the damage of the poorly-onfined frame down one or two damage levels. The omparison reveals that the poorly-onfined frame has been essentially upgraded to the intermediate frame. The results are useful for strutural designers working in retrofitting area. The limitation of this study is also presented. Keywords: FRP; Confinement; Damage assessment; RC frame; Seismi load 1 Introdution Important roles of transverse reinforement in reinfored onrete (RC) strutures are 1) to prevent bukling of longitudinal bars; 2) to prevent shear failure and 3) to onfine the onrete [1]. A large number of buildings in different parts of the world are identified defiient with respet to their transverse reinforement when measured against the requirements of modern odes. Many of these had been designed and built based on older odes, in whih the earthquake loads were given a lower emphasis omparing to today s pratie while gravity loads were onsidered as the major design loads. Consequently, these strutures are not dutile enough to absorb the seismi energy demand and thus are vulnerable to earthquakes as has beome evident in the past reent earthquake events suh as Northridge (1994), Kobe (1995), Chi-Chi (1999), Bam (2003), Christhurh (2011). Mitigating the seismi hazards for these defiient strutures, instead of replaing, has been inreasingly looked at by the engineering ommunity due to eonomi reasons.

3 Fortunately, the availability of advaned building materials suh as Fibre reinfored polymer (FRP) at lower osts provides eonomial solutions to upgrade these defiient buildings. FRP with its distint harateristis suh as high strength, lightweight and ease of appliation has been inreasingly beoming the material of hoie. Numerous studies have been undertaken to evaluate the effets of FRP in upgrading defiient RC strutures. FRP an be used to inrease onfinement, a favourable situation for onrete. A great enhanement in the stress-strain behaviour of onrete onfined by FRP an be ahieved. This has been understood and proven in the past and a number of models for this behaviour, whih are later disussed in details in Setion 2.2, have been proposed by researhers [2-5]. FRP onfinement greatly enhanes the performane of olumns benefitting from the enhaned properties of onrete under onfinement. Harajli and Rteil [6] experimentally investigated the onfinement effet of FRP and ompared with that of steel stirrups on retangular RC olumns. Their results indiated that energy absorption and dissipation apability of the FRP onfined olumns was superior in omparison with that of the olumns onfined by steel stirrups. Sheikh and Yau [7] performed an experiment on 6 irular olumns retrofitted by FRP jaket subjeted to lateral yli displaements with a onstant axial load and showed enhanement of strength, dutility and energy absorption of these retrofitted olumns. Reently, Rahai and Akbarpour [8] onduted experimental and analytial studies on FRP onfined retangular RC olumns subjeted to axial and bending loads. Their results indiated a signifiant improvement of the strength and dutility of these onfined olumns. The FRP onfinement, in ombination with FRP flexural strengthening, was also investigated by Mukherjee and Joshi [9] in their experimental study on FRP retrofitted beam-olumn joints. They onluded that there were a onsiderable improvement of yield load, initial stiffness and energy dissipation apaity. At the maro level, Balsamo et al. [10] onduted a study on a 4-storey RC frame with olumns and beams wrapped by FRP. They onluded that the FRP retrofitted frame an withstand 1.5 times the intensity of the design earthquake. A few years later, Ludovio et al. [11, 12] performed experimental and analytial studies on gravity-load designed and retrofitted full sale three-storey RC strutures subjeted to seismi intensities of 0.2g and 0.3g. FRP onfinement was applied to the olumns while shear and flexural strengthening were applied to the beams. The Balsamo et al. s [10] onlusion was reaffirmed [11, 12]. They also onluded that the deformation apaity of the retrofitted struture inreased onsiderably and less damage of the retrofitted struture was observed in the experiments [12]. A similar study of retrofitting ombining onfinement and flexure was arried out by Garia et al. [13] for the original and FRP retrofitted damaged full sale 2-storey RC frames subjeted to different shaking levels. They onfirmed that the performane of the retrofitted

4 frame was substantially improved; desirable beam-sway mehanism was ahieved and the deformability apaity of the olumns inreased signifiantly. In the same year, Mortezaei et al. [14] onduted a study on FRP retrofitted of different RC frames subjeted to near-fault ground motions with fling step. The FRP onfinement of olumns and flexural effet on beams were proved to result in inreases of 1.5 times and 2.3 times the shear apaity and the energy dissipation of the retrofitted frame, respetively. Eslami and Ronagh [15] used FRP to onfine olumns at the ritial zones of an 8-storey poorly-onfined frame. Their analytial results showed that the seismi performane and dutility inreased substantially. FRP onfinement demonstrates the above favourable effets; however, studies on the effets it an have on reduing the potential damage of multistorey RC frames subjeted to seismi loads are seldom found in literature. The objetive of this study is to explore the effet of FRP onfinement in terms of redution of potential damage expressed by a damage index. An 8-storey poorly-onfined (due to defiieny of transverse reinforement) RC struture is hosen for this purpose. A geometrially similar struture but with seismially adequate transverse reinforement aording to intermediate detailing requirements is designed. The poorly-onfined, the intermediate and the FRP retrofitted frames are modelled in SAP2000 [16] using nonlinear LINK elements. Inelasti time history analyses are onduted for different seismi intensities regulated in urrent seismi odes. The damage of poorly-onfined and retrofitted frames is ompared with one another and with that of the intermediate frame. The results show the favourable effet of FRP onfinement on reduing the potential damage. The omparison reveals that the poorly-onfined frame has been upgraded to the intermediate frame. For the numerial model to work properly, orret modelling of the material property is needed. This is explained below followed by the numerial model and the results. 2 Behaviour of onrete onfined by transverse reinforement and FRP 2.1 Behaviour of onrete onfined by transverse reinforement The stress-strain behaviour of onrete onfined by retangular stirrups has been extensively studied by researhers and different models have been proposed [17-21]. The features of these models were ombined in the model proposed by Kent and Park [22], in whih the stress strain relationship up to maximum stress is the same as that of unonfined model and the strain at the maximum stress remains unhanged at The differene between onfined and unonfined onrete is the desending branh after the maximum stress. Therefore, the Kent and Park [22] model is onservative in most ases as it does not take into aount the inrease in the maximum stress of onfined onrete [23]. In reognition of this issue, Park et al [24] modified the original Kent and Park [22] model taking into aount the enhanement of onrete strength due to

5 onfinement. This modified model is seleted for use in this paper. It is desribed by Equations 1-2, followed by Equations 3-6. f 2 '' 2ε 2ε = f εo ε o if ε ε o (1) ( ε ε ) '' '' f = f 1 Z o 0.2f if ε ε o (2) in whih f '' = Kf (3) ' ε = 0.002K (4) o Z 0.5 = '' + f b + ρs 0.002K s ' 3 ' f h (5) K ρ f = 1+ (6) s yh ' f where, f is stress, ε is the strain of onrete, ρ s is the ratio of the volume of retangular steel hoops to the volume of onrete ore measured to the outside of the peripheral hoop, ' f is the maximum stress in MPa, b is the width of the onrete ore measured to outside of the peripheral hoop, s h is the entre-to-entre spaing of hoop sets. 2.2 Behaviour of onrete onfined by FRP FRP an make the onrete onfined, resulting in a signifiant inrease of the strength and dutility of onrete. This has been proved by numerous researhers [2, 3, 25-28]. Their stress-strain models of FRP onfined onrete an be divided into two ategories: with and without internal transverse reinforement. For the ase with internal transverse reinforement, it would be appropriate if two separate models are simultaneously onsidered: one model is applied for the onrete ore surrounded by transverse reinforement, whih is onfined both internally by stirrups and externally by FRP; another model is applied for the outer part of the onrete (the over) whih is onfined only by FRP. However, this seems to be ompliated due to the interation of these internal and external onfinements. Additionally, the onfinement due to FRP is muh stronger than that due to transverse reinforement. This is expeted as the stress of onrete with a proper FRP onfinement inreases after the strain of around (Figure 1); however, after this strain, there is a desending branh in

6 the stress-strain urve of onrete onfined by stirrups as shown in Equation 2. Furthermore, FRP is often hosen to provide onfinement for poorly-onfined RC members. Thus, the poor onfinement of defiient stirrups an be negleted when the FRP beomes effetive. For simplifiation, together with the above reasons, models without internal transverse reinforement are onsidered for use. Amongst the available models, Lam and Teng [2, 25] model, whih was proven to be most suitable for irular and retangular olumns [29], and has been used in a number of studies [15, 29], is seleted in the urrent study. Figure 1 shows the Lam and Teng [2, 25] model, in whih, the stress-strain relationship of onrete onfined by FRP is desribed by two regions expressed by Equations 7 and 8, followed by Equations Stress (MPa) f u ' A FRP onfined B f ' Unonfined E = tan O 0 t u Strain (mm/mm) Figure 1. Lam and Teng [2, 25] model for FRP onfined onrete. Region OA ( 0 ε εt): Region AB ( ε t ε ε u ): where, ε t = E ' 2 f E 2 f ( E E ) 2 = E ε ε (7) 2 2 ' 4 f f = f + E ε (8) ' 2 (9) E 2 ' ' fu f = (10) ε u in whih, ' f u and ε u are the axial stress and orresponding axial strain at ultimate. For the general ase of retangular olumns, the ultimate strength taking into aount the redued effiieny of retangular setions as follows ' f u and strain ε u are expressed

7 ' ' f la fu = f ks1 ' f fla if 0.07 (11) ' f f ' u ' fla = f if < 0.07 (12) ' f ε ε k la hrup, u = o + s2 ' f ε o f ε 0.45 (13) f Et 2Et = ε = ε (14) R D f f f f la h, rup h, rup where, t f is the total thikness of the FRP jaket, ε hrup, is the rupture strain of FRP, E f is the modulus of FRP, and D as shown in Equation 15 is the diameter of equivalent irular olumn. 2 2 D= h + b (15) Shape fators: k s1 2 b = h Ae A (16) k s2 h = b 0.5 Ae A (17) Ae A (( b h)( h r) 2 ( h b)( b r) 2 ) ( Ag) 1 / 2 + / 2 / 3 ρs = 1 ρ s (18) in whih, b and h are the width and the depth of the ross setion, r is the radius of the orner, ρ s is the ratio of longitudinal steel reinforement in the setion. 3 Moment-rotation, hystereti behaviour and inelasti analysis 3.1 Moment-urvature and moment-rotation urves The models of onrete and steel are employed for the analysis of moment-urvature behaviour up to ultimate using the fibre model, in whih the ross setion is disretised into many fibres and the strain distribution is assumed to be linear while the stress in eah fibre is based on the material models with the strain defined at the entroid of that fibre. The iterative loops of strain distribution stop when the equilibrium onditions are ahieved. This proedure is ontinued until the urvature reahes its ultimate. This ultimate ondition is onsidered to be the attainment of the ultimate strain in the onrete or longitudinal steel whihever omes first. In ase of onfinement by stirrups, the

8 ultimate strain of onrete ε m and that of longitudinal steel ε sm, as shown in Equations 19 and 20 respetively [30, 31], are adopted. In ase of FRP onfinement, ε m is taken as ε u shown in Equation 13 in Lam and Teng [2, 25] model, in whih the rupture strain of the FRP ε hrup, is muh smaller than its ultimate tensile strain ε frp. Based on their experimental data, Lam and Teng [2] suggested ε, = 0.624ε for GFRP, whih is used in this paper. It is worth mentioning that the hrup frp ultimate strain of the longitudinal steel shown in Equation 20 is also applied for the ase of FRP onfinement. ρ f ε ε = (19) ε m sm s yh suh ' f = 0.6ε (20) su Ultimate of unonfined onrete Moment (Nmm) Crak Yield Ultimate based on onfined onrete and steel Ultimate based on FRP onfined onrete and steel RC setions without FRP onfinement RC setions with FRP onfinement O Cuvature (mm/mm) Figure 2. Moment-urvature urves of RC setions with and without FRP onfinement. Figure 2 shows typial moment-urvature urves of RC setions with and without FRP onfinement. These urves inlude the raking, yielding and ultimate points. The rak and yield points remain unhanged. The ultimate points are based on the lower of the two possible ultimates of the onfined onrete and steel. The ultimate of unonfined onrete is also inluded for the setions without FRP. The moment-urvature urve after the ultimate is assumed to drop to 0. After the moment-urvature urves are obtained, simple plasti hinge model with the plasti hinge length l p = h proposed by Sheikh and Khoury [32] is used to ompute moment-rotation urves, whih are used for the properties of the nonlinear LINK elements. 3.2 Hystereti behavior of RC members Hystereti models for RC members available in the literature an be lassified into two types: trilinear and bi-linear hystereti models. Tri-linear models inlude the raking of onrete in the

9 tension zone while the bilinear models exlude it. Amongst many available models, Takeda model [33] allows desription of the damage of RC strutures when the tension zone of onrete is raked as shown in Figure 3a, in whih the oordinates (D r, P r ) and (D y, P y ) represent the raking and yielding point, respetively; therefore, it is seleted to be used in this paper. Seven rules were developed by Takeda et al. [33] to apture the response of the strutures subjeted to yli loads as brieftly shown in Figure 3b and 3. The detail desription of these rules an be found in Ref [33]. Figure 3. Load-defletion relationship [33]. 3.3 Modelling tehnique for the inelasti time history analysis Figure 4 shows the theoretial bakground of the modelling for nonlinear analysis using the plasti hinge length tehnique. The beam with plasti hinge zone l p in Figure 4a orresponding to the idealized urvature in Figure 4b is modelled by ombining three types of elements: elasti, infinitely stiff and zero-length nonlinear LINK elements, whih are illustrated in Figure 4. The nonlinear LINK element allows for the inorporation of the moment-rotation property of the plasti hinge, whih behaves in aordane with the Takeda hystereti model [33] desribed in Setion 3.2. Therefore, the infinitely stiff elements an purely funtion as the onnetion.

10 plasti hinge a) p u y u b) y ) elasti element Link element infinite stiff element d) elasti element Link element elasti element Figure 4. Theoretial bakground of modelling with nonlinear LINK element. Stiffness is another important issue to be taken into aount for the elasti elements. ACI [34] uses the seant stiffness orresponding to yield point as the elasti stiffness; onsequently, the modifiation fators for EI g of beams and olumns an be taken as 0.35 and 0.7, respetively. However, the original stiffness should be used in ase the strutures work in the pre-raking range. To simplify, an approximation is made in this study: the infinitely stiff elements are replaed by the elasti elements shown in Figure 4. This is due to: 1) the elasti deformation of the assumed elasti elements with the length l p seems to be minor, and 2) the modified stiffness may result in underestimated deformations when strutures work in the plasti range beyond yield. This approximation provides some additional deformation from the assumed elasti elements whih may ompensate for the underestimation. As a result, the lumped plastiity model shown in Figure 4d is used in this study and the nonlinear LINK loations of beams and olumns in frames is shown in Figure 5.

11 h beam + l p /2 Nonlinear Link Elements h olumn+l p /2 Figure 5. Nonlinear LINK loations of beams and olumns in frames. 4 Damage models Damage models available an be lassified into two ategories: non-umulative and umulative. Using umulative damage models is a more rational hoie to evaluate damage states of strutures subjeted to earthquakes; hene, they are disussed here. Banon and Veneziano [35] simply used the normalised umulative rotation as a damage index (DI), whih is expressed by the ratio of the sum of inelasti rotations during half yles to the yield rotation. A few years later, Park and Ang [36] proposed a DI inorporating both deformation and hystereti energy as shown in Equation 21, where, u m is the maximum displaement of a single-degree-of-freedom (SDOF) system subjeted to earthquake, u u is the ultimate displaement under monotoni loading, E h is the hystereti energy dissipated by the SDOF system, F y is the yield fore and β is a parameter to inlude the effet of yli loading. DI u u E F u m h = + β (21) u y u Park and Ang [36] lassified damage states into the following five levels: DI < 0.1: No damage or loalized minor raking. 0.1 DI < 0.25: Minor damage: light raking throughout DI < 0.40: Moderate damage: severe raking, loalized spalling. 0.4 DI < 1.00: Severe damage: onrete rushing, reinforement exposed. DI 1.00: Collapse. DI 0.8 has been suggested to represent ollapse [37]. Park and Ang [36] also proposed DI for an individual storey and for an overall struture using the weighting fator based on the amount of

12 hystereti energy (E i ) absorbed by the element or the omponent. Park and Ang [36] is the best known and the most widely used DI [38], largely due to its general appliability and the lear definition of different damage states provided in terms of DI. However, the following limitations are worth noting: DI > 0 when a struture works within elasti range and DI > 1 when the struture ollapses with no speified upper limit for DI. Due to these limitations, Park and Ang s [36] onept has been modified by researhers suh as Fardis et al. [39], Ghobarah and Aly [40] and Bozorgnia and Bertero [41]. However, the most signifiant modifiation was made by Kunnath et al. [42] who used the moment-rotation behaviour to replae the deformation terms used by Park and Ang [36] and subtrated the reoverable rotation as shown in Equation 22, where, m θ is the maximum rotation in loading history, u θ is the ultimate rotation apaity, r θ is the reoverable rotation when unloading and M y is the yield moment. The merit of this modifiation is that DI will be 0 when strutures work within elasti range. The major limitation to this proposal is, however, that the DI > 1 when the struture fails. θm θr Eh DI = + β θ θ M θ u r y u (22) The amount of energy absorbed by a struture is losely related to its orresponding damage state. Hene, DI may be expressed as the ratio of the hystereti energy demand E h to the absorbed energy apaity of a struture under monotoni loading E h,u [43-45]. However, this proposed DI has no speifi upper limit to define the state of ollapse. In reognition of the energy parameter, whih takes into aount a number of parameters suh as fore, deformation and the number of yles, Cao et al. [46] proposed a model whih was later modified by the authors as shown in Equations DI E h = Eh + Ere α ( N i) (23) N i E h,1ollapse = (24) E E E h,1y h,1y h = (25) where E h,1ollapse and E h,1y are the hystereti energy of one omplete ultimate and yielding yle, respetively. Equations 24 and 25 define the proposed parameters N and i. N is the equivalent number of yielding yles to ollapse whilst i is the equivalent number of yielding yles at the urrent time of loading (i N). α is a modifiation fator and is proposed as 0.06 and the damage

13 levels are shown in Table 1, in whih the legends in the first olumn orresponding to the damage levels are used to express the damage in the studied ases presented in Setions 5 and 7. Table 1. Damage levels. Legend Damage index Desription. > No or minor Light x Moderate Severe Collapse 5 Verifiation of the modelling tehnique In order to validate the modelling tehnique mentioned above, a tested three-storey frame [47] is seleted. Its details, and inelasti time history and damage analyses of the frame are desribed as follows. 5.1 Desription of a tested three-storey frame [47] The frame shown in Figure 6 is a one-third sale three-storey RC frame designed only for gravity loads. Its dimensions and reinforing details are presented in Figure 7. Conrete strength varied from 20.2 to 34.2 MPa (the average an be taken as f = 27.2 MPa), and the average modulus of elastiity was taken as E = MPa. Four types of reinforement were used, and their properties are shown Table 2. Reinforement Diameter (mm) Table 2. Properties of reinforement. Yield strength (MPa) Ultimate strength (MPa) Modulus (MPa) Ultimate strain D D ga ga The Dead Loads were alulated from the self-weight of beams, olumns, slabs and additional weights attahed to the frame, as shown in Figure 6. The total weight of eah floor was found to be approximately 120 kn. Further details of this frame an be found in [47] and [48]. The seismi reord seleted for simulation was the N21E ground aeleration omponent of Taft earthquake ourred on 21 July 1952 at the Linoln Shool Tunnel site in California. The peak ground aelerations (PGA) are 0.05g, 0.20g and 0.30g representing minor, moderate and severe shaking, respetively.

14 Figure 6. Three storey frame [48]. Figure 7. Dimensions and reinforement arrangement of three storey frame [48]. 5.2 Modelling and verifiation The axial loads in olumns are assumed to be onstant during exitations and are shown in Table 3. Moment-rotations for all beams and olumns were omputed as desribed in Setion 3.1. Axial loads on olumns were taken into aount; however, the effet of onfinement was ignored due to

15 relatively large stirrup spaing. Figure 8 shows the model with nonlinear LINK elements in SAP2000. The hystereti behaviour of these nonlinear elements follow the Takeda model [33]. The strutural frequenies of the first three mode shapes are determined in Table 4 in omparison with the experimental results. They are very lose in the first and seond modes, but there is little differene in the third mode. However, the first mode plays the most important role. Table 3. Axial load in olumns. Storey Axial load (kn) External olumn Internal olumn Figure 8. Modelling of the three-storey frame with nonlinear LINK elements. Table 4. Modal frequenies (Hz). Mode Experiment [48] Model Inelasti time history analyses of the SAP2000 model subjeted to the Taft earthquake ground motions are performed. The results in terms of maximum inter-storey drift and maximum storey displaement are presented in Table 5 in omparison with those obtained from experiment [48]. Though not an exat math, the model provides an overall good approximation.

16 Table 5. Comparison between experimental [48] and analytial results. PGA Storey Maximum inter-storey drift (%) Maximum storey displaement (mm) Experiment Model Experiment Model 0.05g g g Damage analyses and omparison The seleted damage model is employed to identify, loate and quantify the damage imparted to the struture during the exitation. Figure 9a, 10a and 11a present the experimental damage states taken from [47] while Figure 9b, 10b and 11b show the analytial damage states for the Taft PGAs of 0.05g, 0.20g and 0.30g, respetively. It should be noted that the analytial damage states are plotted for different damage index levels as desribed in Table 1. The damage states obtained from analyses are lose to those obtained from experiment. a) b) Figure 9. Damage states Taft 0.05g: a) Experiment [47]; b) Analysis.

17 a) b) Figure 10. Damage states Taft 0.20g: a) Experiment [47]; b) Analysis. a) b) Figure 11. Damage states Taft 0.30g: a) Experiment [47]; b) Analysis. 6 Eight-storey frames 6.1 Desription of eight-storey frames An 8-storey RC frame [15, 49] shown in Figure 12 with its typial olumn and beam setions shown in Figure 13 is revisited. Its dimensions in millimetres and reinforing details are shown in Table 6 with different shear steel spaing for intermediate and poorly-onfined frames. Grade 60 (f y = 420 MPa) steel and the onrete ompressive strength of 25 MPa were used. The deformed steel bars of Φ10mm were used for transverse reinforement.

18 Figure 12. Eight-storey frame [15, 49]. Figure 13. Typial olumn and beam setions [15, 49]. Table 6. Reinforement details of the 8-storey intermediate and poorly-onfined frames [15]. Setion b h d d' A st A s A' s Shear steel spaing Intermediate Poorly-onfined A-A Φ B-B Φ C-C Φ D-D Φ25 4Φ E-E Φ22 4Φ F-F Φ18 3Φ The design Live Load was 10 kn/m and the Dead Load was 30 kn/m in addition to the self-weight of the struture. The design seismi load was determined based on UBC 1994 [50]. The design aeleration of 0.3g representing for a high level of seismi hazard, and soil profile type III whih is

19 similar to lass D in FEMA 356 [51] was used for the alulation of the design base shear. The orresponding design response spetrum divided by PGA is established as shown in Figure Spetral aeleration PGA T (se) Figure 14. Spetral aeleration/pga. 6.2 Modelling and verifiation The total Dead Load and 25% Live Load as reommended by many seismi odes are used for the inelasti time history analyses. The 8-storey frame is modelled using the modelling tehnique with SAP2000 nonlinear LINK elements desribed in Setion 3.3. The properties of nonlinear LINK elements were determined based on moment-urvature and moment-rotation analyses presented in Setion 3.1. The elasti modulus of onrete was taken as E = 4700 f [34], in whih ' f is the ompressive strength of onrete. It is worth noting that the onfinement effet is taken into aount in this study ase. The moment-urvature urves for olumns and beams are omputed using the average axial loads on them during an earthquake, whih are orresponding to the axial loads determined from the stati load ase. The fundamental period (T) of the struture orresponding the full Dead Load and 25% Live Load is determined as 1.24s whih is lose to the period 1.28s modelled by Ronagh and Eslami [49]. 6.3 Validation of the model using pushover analysis The vertial distribution of the equivalent horizontal stati seismi loads are omputed in aordane with the Equation 26 [50]. An additional fore F t as shown in Equation 27 is applied for the top storey. i ( ) i i F = V F t Wh Wh i i (26) F = 0.07TV 0.25V (27) t in whih, F i is the lateral fore at storey i, W i is the seismi weight of storey i, whih inludes the

20 Dead Load and 25% Live Load, h i is the height of storey i, F t is the additional fore on the top storey, V is the shear fore. The above lateral loads are applied to the model with SAP2000 nonlinear LINK elements and nonlinear stati (pushover) analysis is performed. The obtained pushover urve is plotted in omparison with that performed by Ronagh and Eslami [49] as shown in Figure 15. It shows a good overall approximation Base shear (kn) Roof displaement (mm) Figure 15. Comparison of pushover urves. SAP 2000 pushover urve using LINK elements Ronagh and Eslami (2013) 6.4 Seletion of seismi reords The intensities equal or larger than the design PGA of 0.3g are seleted for damage analyses. They are seleted as 0.3g, 0.45g and 0.6g whih are used to establish the orresponding spetra. These spetra are used as the target for saling ground motions. The saling riterion is based on ASCE [52] whih requires that the mean value of the 5%-damped response spetra for the set of saled ground motions is not less than the target response spetrum over the range of periods from 0.2T to 1.5T, where T=1.24s is the fundamental period of the struture. In addition, the demand parameter suh as drift, fore and deformation an be alulated in different ways, depending on the number of ground motions in eah set. If eah set ontains 7 ground motions or more, the demand parameter is the average value; otherwise, the maximum an be used for the demand parameter.

21 Figure 16. Saling reords to math the target spetrum. In this paper, ground motions used in this study are seleted using the Paifi Earthquake Engineering Researh Center database software [53]. The seleted reords are saled to math the target spetrum in a range of periods from 0.2T=0.248s to 1.5T=1.86s. Figure 16 is an example of saling results. Three sets of reords with different intensities representing by PGAs 0.3g, 0.45g and 0.6g are used. The effet of near-fault ground motions was not onsidered for the design; hene, pulse-type motions are not seleted. Eah set inludes 14 saled fault-normal and fault-parallel ground motion reords of seven stations; therefore, the average value of the demand parameter is used. Table 7 shows the earthquake reords with different Next Generation Attenuation number (NGA#) and saling fators for three intensities obtained from the Paifi Earthquake Engineering Researh Center database software [53].

22 Table 7. Ordinary reords with saling fators for the seismi intensities of 0.3g, 0.45g and 0.6g. No. NGA# Sale Fator for intensity of 0.3g 0.45g 0.6g Event Year Station Magnitude Chi-Chi, Taiwan 1999 TCU Chi-Chi, Taiwan 1999 CHY Chi-Chi, Taiwan 1999 TCU Chi-Chi, Taiwan TCU Chi-Chi, Taiwan KAU Chi-Chi, Taiwan TTN Chi-Chi, Taiwan 1999 CHY Designing and modelling of the retrofitted frame Due to its muh lower modulus whih results in higher displaement dutility, and its omparatively lower ost in omparison to CFRP, GFRP is a better hoie for the onfinement purpose; therefore, it is seleted in this paper. Table 8 shows the properties of GFRP materials provided by the manufaturer. Tensile strength, f fr (MPa) Table 8. Properties of GFRP [54]. Tensile modulus, E f (MPa) Thikness, t f (mm) As stated, the objetive of this study is to investigate the FRP onfinement effet on the potential damage of RC strutures subjeted to earthquakes, the GFRP retrofitting design is presented in Figure 17. The olumns are rounded at the orners with a radius of 50mm and then wrapped by two layers of GFRP to provide external onfinement. With the rounded orners, the GFRP onfinement beomes more effetive omparing to without rounding [55].

23 FRP wraps r=50mm GFRP wraps A st a) GFRP wraps of olumns b) A ross setion of olumns retrofitted by GFRP wraps Figure 17. Design of GFRP wrap to onfine onrete. It is worth noting that the plasti hinge loation is not affeted by the GFRP onfinement as evident in the olumns retrofitted by GFRP wrap [7]. Hene, the loations of plasti hinges in the retrofitted frame are similar to those of the original frame. At the presene of GFRP onfinement, the yield stiffness remains unhanged as the longitudinal reinforement has not hanged. This is also evident from the authors analytial results shown in Figure 2; therefore, the stiffness of the elasti olumn elements is unhanged. The properties of nonlinear LINK elements of beams are also unhanged as FRP is not applied to beams; however, these of olumns are hanged. 7 Results and disussions Inelasti time history analyses are performed for the poorly-onfined, intermediate frames and the FRP retrofitted frame subjeted to the saled ground motions orresponding to seismi intensities of 0.3g, 0.45g and 0.6g as seleted in Setion 6.4. The results from inelasti time history analyses are used to ondut damage analyses and damage indies are obtained for all nonlinear LINK elements in aordane with 14 ground motions of eah seismi intensity. Then, for every LINK element, the average damage index (from 14 damage indies) orresponding to a seismi intensity is omputed. The distribution of damage indies around the frames are plotted in Figures 18, 20 and 22. It should be noted that the damage levels presented in these Figures are provided in Table 1. The maximum damage indies in eah storey are determined and plotted in Figures 19, 21 and 23.

24 a) Poorly-onfined frame b) Intermediate frame ) Retrofit of the poorly-onfined frame Figure 18. Damage modes of the 8-storey frames subjeted to seismi intensity 0.3g.

25 Storey Poorly-onfined frame FRP retrofit of the poorlyonfined frame Intermediate frame Maximum damage index Figure 19. Distribution of maximum damage indies of the 8-storey frames subjeted to seismi intensity 0.3g.

26 a) Poorly-onfined frame b) Intermediate frame ) Retrofit of the poorly-onfined frame Figure 20. Damage modes of the 8-storey frames subjeted to seismi intensity 0.45g.

27 Poorly-onfined frame FRP retrofit of the poorly-onfined frame Intermediate frame Storey Maximum damage index Figure 21. Distribution of maximum damage indies of the 8-storey frames subjeted to seismi intensity 0.45g.

28 a) Poorly-onfined frame b) Intermediate frame ) Retrofit of the poorly-onfined frame Figure 22. Damage modes of the 8-storey frames subjeted to seismi intensity 0.6g.

29 Poorly-onfined frame FRP retrofit of the poorly-onfined frame Intermediate frame 0.93 Storey Maximum damage index Figure 23. Distribution of maximum damage indies of the 8-storey frames subjeted to seismi intensity 0.60g. Figures 18 to 23 show the damage in terms of damage index of the poorly-onfined and FRP retrofitted frames in omparison to the intermediate frame when subjeted to different seismi intensities. As is seen, the storey 5 suffers the most severe damage while the top storey experienes the least damage. Also, the damage in the two inner olumns is more severe than that in the outer olumns of the same storey. More damage in storey 1 omparing to storey 2 is due to higher axial fores and moments on the olumns of the first storey. Notieably, the damage of FRP retrofitted frame is signifiantly less than that of the original poorly-onfined frame and is almost similar to or less than that of the intermediate frame. For the seismi intensity of 0.3g, the poorly-onfined frame suffers moderate damage while the retrofitted frame experienes light damage whih is similar to the damage state of the intermediate frame. There is no damage in beams of these frames. For the seismi intensity of 0.45g, the storey 5 of the poorly-onfined frame reahes the ollapse state while the retrofitted frame experienes moderate damage that is similar to the damage of the intermediate frame. There is no or minor damage in beams of the poorly-onfined and the retrofitted frames; though some minor damage is developed in beams of the intermediate frame. The FRP onfinement effet brings the state of the poorly-onfined frame down two damage levels from ollapse to moderate. For the seismi

30 intensity of 0.6g, the poorly-onfined frame ollapses while the retrofitted frame suffers a severe damage state whih is almost the same as the damage state of the intermediate frame. Generally, due to the FRP onfinement effet, the damage state of the retrofitted frame is redued one or two damage levels omparing to that of the poorly-onfined frame; also the retrofitted frame suffers less damage in omparison to the intermediate frame as an be seen from Figure Poorly-onfined frame 0.98 Maximum damage index Intermediate frame FRP retrofit of the poorly-onfined frame Collapse Severe Moderate Light g 0.45 g 0.60 g Seismi intensity Figure 24. Maximum damage indies of the poorly-onfined, intermediate and the FRP retrofit of the poorly-onfined frame. The redution of damage indies of the retrofitted frame is signifiant as shown in Figure 24 and Table 9. The damage index of the retrofitted frame redues by 0.33, 0.51 and 0.42 ompared to that of the original poorly-onfined frame when subjeted to the seismi intensities of 0.30g, 0.45g and 0.60g, respetively. This leads to signifiantly positive hanges on damage states and demonstrates the effetiveness of the FRP onfinement retrofit of the poorly-onfined RC frames.

31 Table 9. Redution of damage indies. Seismi intensity MaxDI original - MaxDI retrofitted 0.30 g g g Conlusions Inelasti time history and damage analyses of an 8-storey frame designed for 3 different onditions as 1) poorly-onfined, 2) seismially detailed to the intermediate and 3) retrofitted by FRP onfinement were performed at different seismi intensities. The onfinement effet of FRP on the damage of the poorly-onfined frame was investigated with the referene to the intermediate frame. Although the poor onfinement of the transverse reinforement is negleted, the effet of FRP onfinement is onfirmed to signifiantly redue the damage index of the retrofitted frame by 0.33, 0.51 and 0.42 in omparison to that of the original if subjeted to the seismi intensities of 0.30g, 0.45g and 0.60g, respetively. Consequently, the damage of the poorly-onfined frame is brought down one or two damage levels. The retrofitted frame suffers less damage than the intermediate frame also onfirms the signifiant effet of FRP onfinement. These demonstrate the FRP external onfinement as an appropriate retrofitting solution for RC strutures poorlyonfined by the internal transverse reinforement. With this retrofitting solution, poorly-onfined RC frames an be upgraded to seismially designed frames. This signifiant effet of FRP onfinement is worth taking into aount when retrofitting RC frames with the defiieny of transverse reinforement. 9 Referenes [1] Paultre P, Légeron F. Confinement reinforement design for reinfored onrete olumns. Journal of Strutural Engineering. 2008;134(5): [2] Lam L, Teng JG. Design-oriented stress strain model for FRP-onfined onrete. Constrution and Building Materials. 2003;17: [3] Wei Y-Y, Wu Y-F. Unified stress strain model of onrete for FRP-onfined olumns. Constrution and Building Materials. 2012;26: [4] Samaan M, Mirmiran A, Shahawy M. Model of onrete onfined by fiber omposites. Journal of Strutural Engineering. 1998;124(9): [5] Pellegrino C, Modena C. Analytial model for FRP onfinement of onrete olumns with and without internal steel reinforement. Journal of Composites for Constrution. 2010;14(6): [6] Harajli MH, Rteil AA. Effet of onfinement using fiber-reinfored polymer or fiber-reinfored onrete on seismi performane of gravity load-designed olumns. ACI Strutural Journal. 2004;101(1): [7] Sheikh SA, Yau G. Seismi behavior of onrete olumns onfined with steel and fiberreinfored polymers. ACI Strutural Journal. 2002;99(1): [8] Rahai A, Akbarpour H. Experimental investigation on retangular RC olumns strengthened with CFRP omposites under axial load and biaxial bending. Composite Strutures.

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