SERVICEABILITY LIMIT STATE OF MF-FRP BEAMS

Transcription

1 SERVICEABILITY LIMIT STATE OF MF-FRP BEAMS Fabio NARDONE Post Dotoral Assoiate University o Naples Federio II via Claudio 21, Napoli abio.nardone@unina.it* Gian Piero LIGNOLA Assistant Proessor University o Naples Federio II via Claudio 21, Napoli glignola@unina.it Andrea PROTA Assistant Proessor University o Naples Federio II via Claudio 21, Napoli aprota@unina.it Gaeatano MANFREDI Full Proessor University o Naples Federio II via Claudio 21, Napoli gamanre@unina.it Antonio NANNI Full Proessor University o Miami 1251 Memorial Drive, Coral Gables, FL nanni@miami.edu Abstrat Reinored onrete (RC) strutura l members are usually strengthened with epoy bonded pre-ured FRP strips. An innovative strengthening tehnique appliation is based on the use o FRP strips, with enhaned bearing strength, attahed to onrete substrate by using mehanial asteners (MF-FRP) in plae o epoy adhesive. The MF-FRP method is a viable tehnique or strengthening onrete members, partiularly where speed o installation and immediay o use are imperative. Laboratory testing and a number o ield appliations have shown the eetiveness o suh method. An analytial model is disussed or RC beams strengthening using MF-FRP strips. The model aounts or equilibrium, ompatibility and onstitutive relationships o materials, in partiular, it aounts epliitly or the slip between the onrete substrate and the FRP strip due to the behavior o asteners. The proposed leural model, oupled with an appropriate omputation algorithm, is able to predit the undamentals o leural behavior o RC members strengthened with MF-FRP strips in terms o servieability limit state, suh as load vs. deletion urves, strain proiles and urvatures. A omparison between the analytial preditions and the eperimental results has been perormed to validate the proposed model. The omparison shows a good agreement between the analytial preditions and the eperimental results. Keywords: Mehanial astening, Fleure, Modeling, Slip, Reinored Conrete. Page 1 o 8

2 1. Introdution An aepted engineering pratie or repairing and strengthening onrete strutures is based on the use o FRP. Usually, FRP materials are eternally bonded (EB -FRP) to the onrete substrate with epoy. Today, an emerging tehnique or onneting FRP strip to the member substrate is based on the use o mehanial astening (MF -FRP). Prinipal beneits o this innovative tehnique ompared to EB-FRP are speed o installation, minimal or absent surae preparation under any meteorologial ondition and immediate use o the strengthened strutures. Conversely, some o the potential shortomings o this new tehnique are: brittle ailure modes; possible onrete damage during astener installation; and, diiulty o installation in the presene o ongested internal reinorement. The viability o this tehnology has been etensively tested in Missouri in a number o ield appliations [1, 2, 3]. Several researhers have investigated on the easibility o this tehnique or eternal strengthening o reinored onrete (RC) members. These eperimental studies have onirmed the eetiveness o this innovative tehnique. For eample, Bank et al. [4] showed that the load apaity inreased by up to 60% when using this strengthening tehnique. Lee et al. [5] perormed an investigation to evaluate the short-term eets o simultaneous environmental eposure and sustained load on RC beams. Ater observing and veriying the slip eet at the onnetion between FRP and onrete, they introdued a FRP strain redution ator, alibrated on the basis o the eperimental results, in order to aount or the slip eet. Similarly, an eperimental program arried out by Napoli et al. [6] has onirmed the neessity to onsider epliitly the slip between the FRP strip and the onrete substrate or a orret evaluation o the leural behavior. 2. Bearing models In order to onsider epliitly the slip between the onrete substrate and the FRP strip due to the presene o asteners, it is important to haraterize the shear apaity o the asteneronrete-frp onnetion [5]. Eperimental studies showed that the mehanial behavior o MF-FRP strengthened beams is pseudo-dutile due to the loal bearing ailure ourring in the FRP strips at the astener loations [4, 7, 8, 9]. Bearing tests on onrete bloks with FRP strips astened as per ASTM D5961 [10] provide the load vs. slip relationship and show that the behavior o the MF-FRP onnetion is linear-elasti up to the value o the bearing stress. The sustained bearing stress, b, is the stress at whih a progressive and sustained bearing ailure is attained and is a key design property or the MF-FRP system [9] along with the load vs. displaement plot or typial speimens tested in pin bearing. The bearing test data show that the FRP strip has a peretly plasti or hardening response one the sustained bearing ailure is initiated. Elsayed et al. [11] reported eperimental results rom 23 shear tests on speial hybrid glass/arbon MF-FRP. The FRP strip dimensions were mm and were attahed to onrete bloks with dimensions o mm. The strips were entered and lamped at the top o the onrete blok. The asteners were driven or hammered into the onrete in premarked loations. A onstant astened length o 250 mm was maintained or all the speimens. Both shot and srew-type asteners were used to install the FRP omposites on onrete bloks. Based on these eperimental results, the authors developed the bearing-slip model or both types o asteners by regression analysis. The mehanial behavior o the FRP/onrete interae was modeled as a relationship between the loal bearing stress,, and the relative displaement, s, between the FRP strip and the onrete. The -s relationship proposed by Elsayed et al. [11] is as shown in Eq. (1): Page 2 o 8

3 s i s s s ep() s s s i s s sb ; s b () srew type astener b i s sb () shot astener 2 2 osh( s /) sb sinh( /) s sb ; (1) where: b is the stress at sustained bearing in the FRP strip and s b is the orresponding slip; is the bearing yield stress o the FRP strip and s is the orresponding slip; and are alibration oeiients. In the model proposed by Elsayed et al. [11] ater an elasti branh (slip s lower than s ), there is a joining branh beore the sustained bearing slip, s b ; aterwards, the behavior is peretly plasti or srew-type asteners, while it is sotening or shot-type asteners. In Fig. 1, Eq. (1) is also ompared to a simpliied elasti-hardening model haraterized by the two stinesses, K /d t (equal to /s ) and K /d t, where s b* = b /K d t. [MPa] b Eq.(1) K''/dt K'/dt s sb* sb slip,s [mm] Figure 1. Stress vs. slip in double shear bearing test or MF-FRP strip (srew-type astener). 3. Numerial model at Servieability limit state The MF-FRP system is onsidered unbonded rom RC member and the mehanial asteners are onsidered in their atual position along the member (Fig. 2). This assumption implies that the mehanial astener ation onsists o an interation ore applied at a disrete number o loations [12]. The RC member is modeled on the lassial assumption that there is no slip between the reinoring bars and the onrete. The untion q() representing the distributed load or unit length ating on the RC beam an be onsidered as a step untion; onsequently, it is assumed onstant between two asteners. Three equations govern: global equilibrium o the ross setion; global equilibrium o the RC onrete member; and global equilibrium o the MF-FRP strip. Page 3 o 8

4 q() y N M V V +V M +M N +N M() V() V(+) M(+) N N h N +N Figure 2. Strutural model. Eq. (2) represents the global equilibrium at ross-setion,, evaluated with respet to the ontat between FRP and the RC beam. In this equations, M() and M are the global bending moments ating on global setion (RC member + FRP strip) and on the RC member only, respetively; N and N are the aial loads applied on the RC beam and FRP strip, respetively; and V is the shear ore ating on the RC beam orresponding to the global shear ore on the setion, V(), beause the FRP strip is assumed not to ontribute to shear apaity (Fig. 2). N N V V H t H t M N N M M N Similarly, the global equilibrium o the ross-setion, +, is represented by Eq. (3): N N N N V V V H t ()() M M N N M 2 Eq. (4) represents the global equilibrium o the RC member. In Eqs. (4)-(5), N and V are the variation o the aial and shear ores ating on the RC beam, respetively; M is the variation o the bending moment ating on the RC beam and N is the variation o the aial ore applied on the FRP strip. N N V q() M q() N H t h V 2 2 Eq. (5) represents the global equilibrium o the FRP strip: N N (5) h From Eq. (4) and Eq. (5), a new equation is obtained: N N N h (6) The slip between the RC beam and the FRP strip an be evaluated as: s w w (7),in. h (2) (3) (4) Page 4 o 8

5 In Eq. (7), w, in. is the displaement o the lower iber o the RC beam, while w is the displaement o the FRP strip. Eq. (7) an be derived with respet to, providing an epression, Eq. (8), ontaining: the urvature, and the strains,,in. and rp, at the soit o the RC beam and at FRP strip level, respetively: ds M N H 2 N,in. H H (8) d I E E A n with E the Young s modulus o onrete and I n the moment o inertia o the RC setion with respet to neutral ais depth,. Using Eq. (2), Eq. (8) an be written as: ds M () 2H t 2H 1 H N (9) d InE 2InE E A The ondition o ompatibility is represented by Eqs. (7)-(9), whih must be satisied at the interae between the two parts o the ross setion. Eq. (9) an be derived with respet to, taking into aount that dn /d=0 beause N is onstant between two asteners and the laminate is ully unbonded (the shear stress is equal to zero =0): d ds V () H (10) d d InE Eq. (10) derived again provides: d d ds q() H d d d (11) InE The slip untion s() an be written (realling the assumption that q() is a step untion) as: s()= A 3 +B 2 +C+D (12) and an be easily solved through Eqs. (8)-(11) given proper boundary onditions disussed in the ollowing. Aording to previous equations, oeiients A to D are: q() A H 6I E n V () 3() q B () H H 2I E I E n n 2H t 2H M () 1 2 C H N 3A 2B InE 2InE E A 3 2 D s A B C 4. Computational aspets o proposed numerial model In the numerial proedure, the length L between the outmost astener and the ais o symmetry is divided into n parts, deined by a spaing, not neessarily onstant, o the nodes equal to i, in whih eah slip untion, s i (), is deined. In the n-1 internal nodes, the slip untions are ontinuous, while disontinuities o their derivatives are due to the presene o asteners or eternal ations. The numerial proedure onsists o assigning a trial value, s ma, in the irst node at the outmost astener (irst boundary ondition), in order to deine the orresponding value o N h = d t through Eq. (1) or the proposed simpliied bilinear model (Fig. 1). In this numerial proedure the simpliied proposed bilinear model does not provide useul simpliiation and or this reason it is suggested to use more reined nonlinear Eq. (1) or the Servieability Limit State. (13) Page 5 o 8

6 From equilibrium (Eqs. ( 2)-(6)) and ompatibility (Eqs. ( 7)-(11)) onditions, it is possible to deine s 1 () in the irst spaing, 1, in whih the member has been divided. Following the same approah, it is possible to deine the slip untion in all other i spaings. In general, or the boundary onditions between onseutive parts, two situations may our: a astener or a onentrated load is present. In the irst ase the slip and the interation ore, N h, must satisy the Eq. (1), while in the seond ase the interation ore is equal to zero. Continuity o slip untions must granted at the boundary i (i.e. s i-1 (i)=s i ( i )). The our onstants (Eq. ( 13)) in the generi slip untion s i () an be determined in the node i evaluating the values o q( i ), V( i ), M( i ) and N aording to Eq. (3). The proedure is iterative. The goal is to have a zero value o s n (L) at the ais o symmetry o the member (last boundary ondition) hanging the trial value, s ma. Details about omputational aspets o the proposed numerial models are reported in Nardone et al. [13]. 5. Eperimental vs. theoretial results at servieability limit state (SLS) The robustness o the proposed numerial model was veriied by omparing the predited values in terms o strains in the MF-FRP strip and displaement at midspan ross-setion, with eperimental data. The omparisons were perormed or leural moments up to yielding o the steel. Elsayed et al. [11] perormed shear tests on the same type o FRP strip used in all the eperimental programs herein used or omparison. Coeiients or Eq. (1) obtained by best itting the eperimental urves were proposed in their work and here adopted. Borowiz [14] tested a series o ,657.6 mm 3 reinored onrete beams. One RC member was used as benhmark. The average 28-day onrete ompressive strength (based on 6 ylinder tests) was 45 MPa. The members were reinored with 2D25 and 2D9 Grade 60 ( y =420 MPa) longitudinal deormed steel bars as tensile and ompressive reinorement, respetively, and D13 Grade 60 deormed steel stirrups at a spaing o 102 mm on-enter in the shear spans. For MF-FRP members (with a astener spaing o 51 mm) the FRP strain omparison o the strip and the ompanion moment-midspan displaement urve are shown in Figs. 3a and 3b, respetively Moment [kn-m] UW2 UW4 UW5 UW6 UW7 UW8 UW9 Moment [kn-m] UW2 UW4 UW5 UW6 UW7 UW8 UW FRP midspan [me] (a) Displaement [mm] Figure 3. Theoretial vs. eperimental: (a) FRP strain; (b) displaement, at midspan (b) [14]. (b) RC beams 2440 mm long with nominal ross-setion measurements o mm 2 were abriated and tested by Marks et al. [15]. The members (with a onrete strength o 28 MPa) were reinored with 2D13 Grade 60 deormed bars as tensile reinorement. Beams were designed suh that no shear reinorement was required. In eah strip, two rows o asteners at 102 mm spaing along the length were used. The members were tested under our-point bending over a span o 2290 mm with a shear span o 1070 mm. The leural reinorement onsisted o two D13 Grade 60 deormed steel bars. In Figs. 4a and 4b are shown the omparison o moment-midspan FRP strains and the ompanion moment-midspan Page 6 o 8

7 displaement urve, respetively, or speimens tested by Marks et al. [15]. For this seond data set, the higher satter between theoretial predition and eperimental outomes an be due to a lower value o onrete elasti modulus ehibited by tested speimens with respet to the outomes o ylindrial onrete samples used in the model Moment [kn-m] Moment [kn-m] FRP midspan [me] Displaement [mm] (a) Figure 4. Theoretial vs. eperimental: (a) FRP strain; (b) displaement, at midspan (b) [15]. (b) 6. Conlusions A numerial model was proposed or the analysis o the leural behavior o RC members strengthened with MF-FRP strips at servieability limit state aounting epliitly or the slip between the substrate surae and the FRP strip. The omparison between the analytial preditions and eperimental results available in literature shows a good agreement in terms o strain values in MF-FRP strip and moment deletion urves. The knowledge o the relationship between the ore ating on the astener and the slip is undamental in order to apply the proposed model. 7. Aknowledgement The authors aknowledge the inanial support provided by ReLUIS or the researh program unded by the Department o Civil Protetion Eeutive Projet and the work o Viki L. Brown at Widener University, Chester (PA). 8. Reerenes [1] RIZZO, A., Appliation o mehanially astened FRP (MF-FRP)-Pre-ured laminates in O- System Bridges, M.S. Thesis, University o Missouri-Rolla, [2] RIZZO, A., GALATI, N., NANNI, A., DHARANI, L.R., Material haraterization o FRP pre-ured laminates used in the mehanially astened FRP strengthening o RC strutures, IN: Pro FRPRCS-7, New Orleans, USA, 2005; 230: [3] RIZZO, A., GALATI, N., NANNI, A., BANK, L.C., Strengthening onrete strutures with mehanially astened pultruded strips, IN Pro. COMPOSITES, Columbus, Ohio, [4] BANK, L.C., OLIVA, M,G,, ARORA, D., BOROWICZ, D.T., Rapid strengthening o reinored onrete bridges, Wisonsin Highway Researh Program, Report No Wisonsin Department o Transportation, Madison, WI, [5] LEE, J.H., LOPEZ, M.M., BAKIS, C.E., Slip eets in reinored onrete members with mehanially astened FRP strip, Cement & Conrete Composites, Vol. 31, No. 7, 2009, pp [6] NAPOLI, A., MATTA, F., MARTINELLI, E., NANNI, A., REALFONZO, R Page 7 o 8

8 Modelling and veriiation o response o RC slabs strengthened in leure with mehanially astened FRP laminates, Magazine o onrete researh, Vol. 62, No. 8, 2010, pp [7] BANK, L.C., Mehanially asyened FRP (MF -FRP)- A viable alternative or strengthening RC members, In Pro. FRP Composites in Civil Engineering, CICE; Adelaide, AU, 2004, pp [8] LAMANNA, A.J., BANK, L.C., SCOTT, D.W., Fleural strengthening o reinored onrete members by mehanially attahing iber-reinored polymer strips, Journal o Composites or Constrution, Vol. 28, No. 3, 2004, pp [9] BANK, L.C., ARORA. D., Analysis o RC beams strengthened with mehanially astened FRP (MF-FRP) Strips, Composite Strutures, Vol. 79, No. 2, 2007, pp [10] ASTM D5961/D 5961M. Standard test method or bearing response o polymer matri omposite laminates, Amerian West Conshohoken, PA: Soiety or testing and Materials, [11] ELSAYED, W.E., EBEAD, U.A., NEALE, K.W., Studies on mehanially astened iber-reinored polymer strengthening systems, ACI Strutural Journal, Vol. 106, No. 1, 2009, pp [12] FABBROCINO, G., MANFREDI, G., COSENZA, E., Non linear analysis o omposite beams under posistive bending moment, Computers & Strutures, Vol. 70, No. 1, 1999, pp [13] NARDONE, F., LIGNOLA, G.P., PROTA, A, MANFREDI, G., NANNI, A., Modeling o leural behavior o RC beams strength-ened with mehanially astened FRP strips, Composite Strutures, Vol. 93, No. 8, 2011, pp [14] BOROWICZ, D.T., "Rapid Strengthening o Conrete Beams with PAF Systems andfrp Composite Materials", MS Thesis, Univ. o Wisonsin Madison, [15] MARKS, J.J.; IACONO, G.; MORTENSEN, M.; WATTS, J.; BROWN, V.L.; Strengthening Reinored Conrete Beams with Mehanially Fastened Fiber- Reinored Polymer (MFFRP) Strips, Senior Projet Group #4 Report, Widener University, Chester, PA, Page 8 o 8