DESIGN MODELS FOR SHEAR STRENGTHENING OF REINFORCED CONCRETE BEAMS WITH EXTERNALLY BONDED FRP COMPOSITES: A STATISTICAL VS RELIABILITY APPROACH

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1 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 DESIGN MODELS FOR SHEAR STRENGTHENING OF REINFORCED CONCRETE BEAMS WITH EXTERNALLY BONDED FRP COMPOSITES: A STATISTICAL VS RELIABILITY APPROACH J.L.T. LIMA J.A.O BARROS MSc Student; Associate Pro., Department o Civil Engineering, University o Minho, Portugal Keyords: analytical, bonded, externally, FRP, models, shear, strengthening INTRODUCTION Experimental studies conducted orldide on reinorced concrete (RC) beams strengthened in shear ith externally bonded (EBR) iber-reinorced polymers (FRP) over the last years evince the reliability and eicacy o such technique or structural retroitting. For elements ith shear resistance deiciencies, an higher load carrying capacity may be achieved by bonding FRP reinorcement systems ith the ibers as orthogonal as practically possible to the critical shear crack plane or an optimal coniguration, or ith the ibers normal to the beam axis or a more practical setting. Common conigurations o strengthening (Fig.) include the ull rapping o the cross section (O), U jacketing along sides (U) and side bonding in the beam eb (S). Additional mechanical anchorage systems can be provided to enhance the behavior o U or S conigurations here the available bond length is short (U+ and S+). Fig. : Common externally bonded FRP strengthening conigurations Each o the aorementioned strengthening conigurations may be set in several possible arrangements (Fig. ) regarding the iber orientation, the use o discrete strips or continuous sheets, and the overlay o sheets ith dierent iber orientations, among others. Fig. : Possible arrangements or externally bonded FRP strengthening ANALYTICAL FORMULATIONS FOR FRP SHEAR REINFORCEMENT DESIGN As an outcome o the increasing demand stimulated by a continuous groth in ield applications, several proposed analytical ormulations [-] have been implemented into reerence design guidelines, providing the guidance or design, detailing, and installation o FRP based strengthening systems. The present study addresses the shear provisions included in ib [], ACI [], CNR [] and the Australian Standard [7] design guidelines. The later ollos an analytical model previously introduced by Chen and Teng (CT) [8, 9]. All o the aorementioned design models rely on the approach here shear strength o a strengthened member is attained by the sum o the contributions rom the reinorcing steel, V s, and concrete, V c, ith the one deriving rom the FRP,V, as ollos: Vr Vc + Vs + V ()

2 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 here V c and V s, may be calculated according to provisions existing on current design codes, independently o the FRP strengthening system adopted. The methodology to estimate the design value o the FRP contribution in shear, V d, according to each o the aorementioned design proposals is briely described in Table. Figure summarizes the adopted notation deining the geometric properties o a generic beam reinorced in shear ith externally bonded FRP. Fig. : Adopted notation to deine the main geometric properties o an FRP shear reinorcement Table : V d calculation methodology (cont.) ib design proposal: ACI design proposal: ( ) V.9 ε E ρ b d cotθ + cot β sin β d ed t ρ b s ε ed (strips) ; t sinβ ρ (cont.) b.8 ε e ; γ. /. /. γ i) Full rapping coniguration (O): cm εe.7 εu E ρ. ii) Side bonding or U jacketing coniguration (U, S):. cm. E ρ εe min. cm.7 εu E ρ Vd φψ t e (sinβ+ cos β) d s φ.8 ; ψ.9 (O) ; ψ.8 (U,S) E ε e e i) Full rapping coniguration (O): ε..7 ε e ii) Side bonding or U jacketing coniguration (U, S): k k e v u u ε k ε. v ck k 7 k k Le.7 9 ε ; L u e ( t E ).8 d L d L (U) ; k e e d d (S) Notation: εed - design value o eective FRP strain; ε e - mean value o eective FRP strain; ε u - FRP ultimate tensile strain; γ - partial actor or FRP reinorcement; ρ - FRP reinorcement ratio; E - elasticity modulus o FRP reinorcement; - concrete average compressive strength; cm φ - shear strength reduction actor []; ψ - additional reduction actor or FRP; kv - bond reduction coeicient; k - modi. actor regarding the concrete strength; k - modi. actor regarding the FRP coniguration; L e - eective bond length o FRP reinorcement; - concrete characteristic compressive strength; ck

3 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 Table (cont.): V d calculation methodology CNR design proposal: i) Full Wrapping coniguration (O).9 (cot cot ) Vd d ed t θ + β γ s ' ed L Rd Le sin β dd + min {.9 dh, } Le sin β + ( φr d dd) min{.9 dh, } e φ. + rc rc R. ;. b b E t ctm ; dd.8 E Gk γ t s ' Gk. kb ck ctm ; kb + b ii) U jacket coniguration (U) ed Le sin β dd min.9, iii) Side bonding coniguration (S) d { dh} sin V β d min{.9 d, h } ed t γ sin θ s ' Rd z. red, eq ed dd min{.9 dh, } Notation: z z + L red, eq red eq { } zred min.9 d, h Le sinβ su Leq sin β / E dd z L eq red, eq γ Rd - partial actor or the resistance model (.); - average concrete tensile strength; ctm ed - design value or the FRP eective stress; d - design value or the ultimate FRP stress; - design value or the FRP debonding stress; dd G - bonded joint speciic racture energy; k k b - covering / scale coeicient; s - FRP slip at debonding (.mm); u CIDAR (CT) design proposal: Vd ed t he (cotθ + cot β) sinβ s ' he zb zt ; zb.9 d db ; zt dt ed D d,max i) Failure by FRP rupture (O) z. t D + zb φr u, ε.% γ d,max φr E ε, ε >.% γ φ.8 ; γ. R ii) Failure by FRP debonding (U, S) - cos π λ sin π ( λ ) π ( λ), λ D π - λ > -, π λ he, (U) sin β Lmax ; L he, (S) sinβ d,max e ; λ Lmax Le φr u γ min E. βl β γ t λ, λ βl, λ > ; β E t ck ck, ( s β ) sin β, + s sin φr - reduction actor due to local stress in corners; λ - normalized maximum bond length; D - stress distribution actor; d,max - maximum design stress in FRP; u - ultimate FRP tensile stress; h - eective height o the bonded reinorcement; e β - bond length coeicient; L β - strip idth coeicient;

4 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 PERFORMANCE APPRAISAL OF THE ANALYTICAL FORMULATIONS. Database assembly To assess the accuracy o the theoretical predictions obtained ith the aorementioned analytical ormulations, a database (DB) containing the experimental results rom beams strengthened ith EBR as collected rom published literature, upgrading previous compiled databases [-]. The criteria adopted in this task as to collect the largest amount o data ith a ide spectrum o test results regarding the beams geometry, concrete properties, longitudinal steel reinorcement ratios, shear steel reinorcement ratios, FRP properties and strengthening conigurations. Aiming to reduce the inluence o erroneous and inconsistent data present in the DB, the analysis as perormed not only in the integral database (IDB), but also in partial subsets o the data reduced databases (RDB). Detailed inormation on the databases characteristics and the considered beams may be ound in [].. Results obtained using the integral database (IDB) For each described design model, the obtained values o V d are compared ith V,exp and a χ actor corresponding to the V,exp /V d ratio is evaluated. Figure plots the predicted against experimental values, here a º solid line establishes the division beteen the sae previsions rom the unconservative ones and a dashed line traces an ideal saety trend corresponding to χ.. χ χ ib design model Vd (kn) χ. ACI design model Vd (kn) χ. V,exp (kn) V,exp (kn) χ χ CNR design model Vd (kn) χ. CT design model Vd (kn) χ. V,exp (kn) V,exp (kn) Fig. - V,exp vs V d scatterplots regarding ib, ACI, CNR and CT design models A large scatter is observed in the experimental vs predicted design values or all o the considered analytical ormulations. Table summarizes the main descriptive statistical measures regarding the χ actor, namely minimum (MIN) and maximum (MAX) values, the average (AVG) that represents a global saety actor associated ith the design procedure, the standard deviation (STD) and the coeicient o variation (COV) that are indicators o accuracy. The irst quartile (Q) that cuts o the loest % o data, the median (MED) corresponding to the th percentile and the third quartile (Q) that cuts o the highest % o data are also included.

5 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 Table : Statistical values o the χ actor computed rom the IDB χ Min Q MED AVG Q MAX STD COV FIB ACI CNR CT The obtained results sho that the ib design model presents, in average, the loest saety actor hile the saest predictions are attained ith CNR. The largest scattering is attained by the CNR model (COV.7) hile the least scattered model is ib (COV.). The CT model globally presents a good perormance ith an average value o χ. and COV.8. Hoever, rom the structural saety point o vie, a classiication system based only on the main descriptive statistics measures regarding the behavior o the χ actor may not provide enough inormation to assess the reliability o a design proposal, considering that or structural purposes having χ. is orst than χ., hich is not taken into account on the statistical analysis. To overcome this limitation a eighed penalty classiication system as applied, based on the Demerit Points Classiication (DPC) model proposed by [], here a penalty (PEN) is assigned to each range o χ ratios according to Table, and the total o penalties determines the perormance o each design model. Table : Reliability analysis based on structural saety IBD χ Classiication PEN FIB ACI CNR CT <.7 Extr. Dangerous Dangerous. -. Reduced Saety Appropriate Saety Conservative 7 8 >. Extr. Conservative 8 PEN From Table it can be noticed that the ib design model presents the eakest perormance, ith the highest number o penalty points corresponding to % o Predictions Against Saety (PAS, χ<), hile the best results are attained by the CNR design proposal ith the loest o number o PAS (%). The CNR model also provides the highest number o extremely conservative values (%).. Results obtained using the RDB The high scattering ound in the previous analysis perormed over a DB ith beams ith highly dierentiated characteristics, proves that none o the studied design models simulates ith enough accuracy the generic behavior o RC beams strengthened in shear ith externally bonded CFRP. It as also ound that all the aorementioned design proposals provided a large amount o unsae values or V d, especially in the range < V,exp < kn. Such can be related ith a signiicant number o experimental results here, ithout a clear understanding, the load carrying increase due to the FRP reinorcement is either null or extremely small, disturbing the global perormance o the considered analytical models. From the above considerations, the consistence o results obtained ith the IDB as appraised by means o removing rom the analysis those observations, hich in the authors belie, lead into incoherent results. A reduced database (RDB) containing beams extracted rom the IDB as assembled. A beam as removed rom DB hen ulils one o the olloing conditions: i) statistical outliers; ii) beams reinorced ith bidirectional ibers; iii) reinorcement systems ith special anchorage mechanisms; iv) beams that sho poor perormance in all o the aorementioned design models (χ <.). Figure presents the obtained results ith the RDB, providing or each design model a scatterplot o the V d vs V,exp relationship, an histogram o the χ ratio distribution and a box and hiskers plot o the χ ratio variation related ith the reinorcement coniguration. The box plot diagram graphically depicts the statistical ive-number summary, hich consists o the smallest non-outlier observation, loer quartile (Q), median, upper quartile (Q), and largest non-outlier observation.

6 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 NLR - Linear Regression Model - Non Linear Regression Model χ.8 Normal Density Est. Desnsity ib design model Vd (kn) χ. Relative Frequency... χ ib. O S U NLR V,exp (kn) χ.8 χ ib Normal Density Est. Desnsity Rein. Coniguration ACI design model Vd (kn) χ. Relative Frequency... χ ACI. O S U NLR V,exp (kn) χ.8 χ ACI Normal Density Est. Desnsity Rein. Coniguration CNR design model Vd (kn) χ. Relative Frequency... χ CNR. O S U NLR V,exp (kn) χ.8 χ CNR Normal Density Est. Desnsity Rein. Coniguration CT design model Vd (kn) χ. Relative Frequency... χ CT. O S U V,exp (kn) χ CT Rein. Coniguration Fig. Analysis results ith the RDB (rom top to bottom: ib, ACI, CNR and CT design models)

7 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 Table : Statistical values o the χ actor computed rom the RDB χ MIN Q MED AVG Q MAX STD COV PEN FIB ACI CNR CT The values in Table sho that, despite the global improvement in the design models perormance ith the RDB, the results ollo the same trend as or the IDB analysis, thus ratiying the consistency o the collected data. Figure plots the sae (PSS) vs unsae (PAS) predictions diagrams or both the IDB (a) and the RDB (b). From their analysis, it is mandatory to emphasize that all the studied design models sho a poor perormance taking into account the large amount o unsae predictions or the design value o the FRP contribution in shear. PAS PSS PAS PSS FIB ACI CNR CT FIB ACI CNR CT a) b) Fig. PAS and PSS ratios ith the: a) IDB, b) RDB. Inluence o other parameters not explicitly considered in the analytical ormulations Such poor perormance shoed by the aorementioned analytical ormulations indicates that the relative inluence o the considered parameters is simulated deiciently and the eect o others, not explicitly taken into account, should not be neglected. Figure 7 presents some relationships that are supposed to aect the perormance o the analytical models namely, the shear orce gain ratio, V,exp (V r,exp V,exp ), the inluence o the longitudinal reinorcement percentage, ρ sl, and the inluence o shear steel reinorcement presence are investigated. All the studied analytical ormulations seem to sho an increase o the χ actor ith beams here the global shear orce gain is higher. Such trend is observed or both discrete (DISC) and continuous (CONT) reinorcement arrangements, being more obvious or the ib and CT models hile a more diuse pattern is observed ithin the ACI and CNR models. From the interaction beteen the χ actor and the longitudinal steel reinorcement it is ound that χ tends increase ith the increment o the E s ρ s E ρ ratio suggesting a major interaction beteen the FRP and longitudinal reinorcement. On the plotted diagrams, beams ith conventional shear reinorcement are set aside rom those ithout stirrups decoupling the interactions beteen these to phenomena. It proved that both kinds o beams (ith and ithout stirrups) ollo the same trend regarding the χ vs E s ρ s E ρ relationship. The plots o the χ vs E s ρ s E ρ relation suggest that beams ithout stirrups may have higher χ actors ith the studied analytical models than those ith higher shear reinorcement ratio. Nevertheless it is the authors belie that the pattern ound in the χ vs E s ρ s E ρ scatter hen A s > may also be inluenced by the longitudinal reinorcement ratio. In a uture approach these phenomena should be investigated, making several analysis o χ vs E s ρ s E ρ or dierent clusters o ρ sl. 7

8 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 CONT DISC As As> χ ib χ ib χ ib Shear Force Gain Esl ρsl / E ρ Es ρs / E ρ CONT DISC As As> χ ACI χ ACI χ ACI Shear Force Gain Esl ρsl / E ρ Es ρs / E ρ CONT DISC As As> χ CNR χ CNR χ CNR Shear Force Gain Esl ρsl / E ρ Es ρs / E ρ CONT DISC As As> χ CT χ CT χ CT Shear Force Gain 8 Esl ρsl / E ρ 8 Es ρs / E ρ Fig. 7 Inluence o shear gain, longitudinal and shear reinorcement on the models perormance 8

9 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 CONCLUSIONS Based on the inormation available in the literature regarding the shear strengthening o RC beams ith externally bonded CFRP, a comprehensive database as assembled containing experimental results o beams. The results obtained rom a statistical analysis carried out on such database demonstrate that none o the analytical ormulations predicts ith enough accuracy the contribution o the EBR CFRP systems or the shear strengthening o RC beams. A large scatter o the χv,exp /V d as ound ithin all the design models, even hen a reduced database (RDB) as used in the analysis. Using the RDB the average o the χ actor varies beteen. (ib) and.9 (CNR) and the coeicient o variation is comprehended beteen % (ib) and 7% (CNR). From a statistical point o vie the CT model can be pointed as the one ith the best perormance since it alays combines an appropriate global saety actor (AVG χ.7) ith the one o most least scattered behaviors (COV χ 7%). Although the large amount o calculated V d values that are against saety suggest that all o the aorementioned models are still not robust enough or generalized practical design purposes. A reliability analysis and classiication based on structural saety as also implemented. Among the studied ormulations, the ib design model presented the most unsae results rom all, hile the saest results ere attained ith the CNR design code provisions. CNR also provided the largest amount o extremely conservative predictions especially or the S type strengthening coniguration. The inluence o some parameters not explicitly considered on the analytical models as assessed, proving that the perormance o the aorementioned design models is subordinated to the global attained shear orce gain. Furthermore, the inluence o conventional steel reinorcement (longitudinal and transversal) proved to be signiicant, and none o the studied analytical models explicitly considers these parameters to determine the FRP contribution to shear. Other parameters not taken into account in the analytical ormulations may also inluence the behavior o strengthened beam. The collected database provides a signiicant source or data mining techniques in order to decouple the interactions beteen all the phenomena involved. Thus, more investigation in this ield is needed in order to improve the existing design models. ACKNOWLEDGEMENTS The study reported in this paper orms a part o the research program CUTINSHEAR - Perormance assessment o an innovative structural FRP strengthening technique using an integrated system based on optical iber sensors supported by FCT, POCTI/ECM/9/. The irst author acknoledges the support provided by the grant in the ambit o this research project. REFERENCES [] Triantaillou, T. Shear strengthening o reinorced concrete beams using epoxy bonded FRP composites ACI Structural Journal, 9 (March-April 998), 7-. [] Khalia et al Contribution o externally bonded FRP to shear capacity o RC lexural member Journal o Composites or Construction ASCE, (998), 9-. [] Monti, G., and Liotta, M. FRP-strengthening in shear: tests and design equations. em 7th International Symposium on Fiber Reinorced Polymer (FRP) Reinorcement or Concrete Structures (FRP7RCS),, ACI Symposium Publication. [] ib Bulletin - Externally Bonded FRP reinorcement or RC structures Technical report,, Task Group 9. FRP (ibre reinorced polymer) reinorcement or concrete structures. [] ACI.R-: Guide or the design and construction o externally bonded FRP systems or strengthening o concrete structures,, Reported by ACI Committee. [] CNR-DT Guidelines or design, execution and control o strengthening interventions by means o ibre reinorced composites,, National Research Council. [7] CIDAR - Design guideline or RC structures retroitted ith FRP and metal plates: beams and slabs Drat - submitted to Standards Australia,, The University o Adelaide. [8] Chen, J.F. e Teng, J.G. - Shear Capacity o FRP Strengthened RC Beams: FRP Rupture Journal o Structural Engineering, ASCE : 9():. 9

10 FRPRCS-8 University o Patras, Patras, Greece, July -8, 7 [9] Chen, J.F. e Teng, J.G. - Shear Capacity o FRP Strengthened RC Beams: FRP Debonding Construction and Building Materials : 7(): 7. [] ACI 8 8-/8R-: Building code requirements or structural concrete and commentary,, Reported by ACI Committee 8. [] Bousselham, A., and Chaallal, O. Shear strengthening reinorced concrete beams ith iber reinorced polymer: assessment o inluencing parameters and required research''. ACI Structural Journal, (March-April ), 9-7. [] Aprile, A., and Benedetti, A. Coupled lexural-shear design o R/C beams strengthened ith FRP Composites Part B: Engineering, (January ), -. [] Lima, J.L.T. Assessment o the eective strain in FRP laminates used in shear strengthening o reinorced concrete beams, MSc thesis (in preparation), Univ. Minho, Portugal. [] Collins, M.P. - Evaluation o shear design procedures or concrete structures,, A Report prepared or the CSA technical committee on reinorced concrete design.