FRICTION INCREASE OF SPLICED BARS DUE TO FRP WRAPPING

Transcription

1 FRICTION INCREASE OF SPLICED BARS DUE TO FRP WRAPPING Vincenzo GIAMUNDO Ph.D. Suden Deparmen o Srucural Engineering Universiy o Naples Federico II Via Claudio, , Naples - Ialy vincenzo.giamundo@unina.i* Gian Piero LIGNOLA Assisan Proessor Deparmen o Srucural Engineering Universiy o Naples Federico II Via Claudio, , Naples - Ialy glignola@unina.i Andrea PROTA Assisan Proessor Deparmen o Srucural Engineering Universiy o Naples Federico II Via Claudio, , Naples - Ialy aproa@unina.i Gaeano MANFREDI Full Proessor Deparmen o Srucural Engineering Universiy o Naples Federico II Via Claudio, , Naples - Ialy gamanre@unina.i Absrac Exising concree srucures, and especially ypical old-ype reinorced concree columns, under seismic evens presen bond-criical regions where he reinorcemen is lap spliced (e.g. sarer bars going ou o he oundaion). Oen he regions o lap splice are he locaions o he ormaion o plasic hinges also, leading o even more criical consequences i hey are no designed according o seismic design provisions. FRP wrapping a lap spliced bars locaion provides coninemen o concree, which induces addiional laeral sress also, hereby increasing he bond sress o he spliced bars and prevening slippage. The evaluaion o he conining pressure a he bar locaion due o FRP wrapping is provided as a irs sep o evaluae he increase o ricion beween lap spliced bars and beneis in erms o duciliy and seismic behavior. Theoreical and parameric analyses show ha he FRP wrapping could enhance he bond srengh a lap splices locaions. Keywords: Bond srengh, FRP Coninemen, Columns, Lap splices, Reinorced concree, Seel bars, Analyical modeling. 1. Inroducion Many o he Reinorced Concree (RC) srucures buil in he pas do no saisy he modern seismic Design Codes. In previous codes he design key parameer was he srengh, and such codes did no give indicaion abou pos-elasic behavior o he srucures. The knowledge o srucure pos-elasic behavior is more imporan in he bond criical regions, or example a he base o he columns, where he reinorcemen is lap spliced wih sarer bars projecing above he oundaion (in hese locaions he ormaion o plasic hinges is expeced). Common Page 1 o 8

2 seismic reroiing echniques or RC columns are based on he increase o coninemen sress in he bond criical regions. The coninemen improves he RC perormance boh in erms o srengh and duciliy. Many sudies showed he enhancemen o he bond resisance due o iber reinorced polymer (FRP) coninemen o lap spliced regions [1]. A coninemen model proposed by Lignola e al [2], is based on he elasic ineracion beween he concree column and he conining FRP device. I is able o evaluae non uniorm conining sresses in each poin o noncircular secions. This model is he basis o evaluae he bond srengh increase due o coninemen pressure induced by FRP wrapping. 2. Mahemaical coninemen model To evaluae ricion increases due o FRP wrapping, he irs sep is o assess average coninemen pressure a he bars locaion. A irs model is presened o evaluae sresses in circular secions, while a second reers o boh recangular and square secions. 2.1 Circular secion I is well known ha FRP coninemen is paricularly eecive or circular secions. Laeral conining sresses are equal in circumerenial and radial direcions and uniorm all over he secion. The expression o laeral coninemen pressure l is given by he well know equaions: 1 4 E (a) (b) (2.1) 2 D l z where E is he FRP reinorcemen elasic modulus, ν is he dilaion raio (represening he raio beween ransversal srain, ε l, and axial srain, ε z, in concree) and ρ is he FRP reinorcemen geomeric raio. In he case o coninuous wrapping, ρ is compued according o eq. (2.1b) where is he oal hickness o he reinorcemen ply (or pli es) and D is he secion diameer. 2.2 Noncircular secion In square and recangular secions he laeral conining pressure is no uniorm. Inernaional Design Codes or noncircular secions usually assumes a convenional parabolic arching acion wihin which he concree is ully conined. In his paper, he coninemen model [2] provides σ x (and σ y exchanging he x wih y) and τ xy conining sresses by means o he ollowing expressions: A A x A y B L (a) () (b) A A xy (2.2) 2 x y x y y y xy x y where A x, A y and B y are he main parameers and x, y are he coordinaes o each poin o secion relaed o a reerence sysem wih origin a he cener o he secion. The expressions used o esimae he A x and B x (and A y and B y exchanging X wih Y) parameers are: EcE(21 Ly 21Lx 8)E LxLy 6(13 Ly c 7)(1)EL x Lx z Ax 4 E 6() L LE LE L 108(1)(2(10 3) 7 L7)E L L L c x y x y c x y x y in which: Θ=21L x 5 L y +8 L x 3 L y L x L y 5 and Ψ=63(L x 2+ L y 2 )+ L x L y (91ν-11) Page 2 o 8

3 3 E E( 21 L 49L 8L L 28)E L L 6(7 L 8 L 21)(1)E B L L L x Lx 2E c 3() LxLyE LE x Ly 54(1) c 2(10 3) 7 L7 xly E Lx Ly c y x x y x y y c x x y y z where L x and L y are hal lenghs o he horizonal and verical sides o he secion respecively. E c (compued as 4700 co ) and co are he concree elasic modulus and srengh, respecively. FRP maximum iber srain along he sides o he secion is given by: A 3B A 3B max L ; L y y 3 x x 3 rp y x 3E 3E (2.3) 2.3 Nonlinear behavior Previous equaions are based on linear elasiciy, ha is exacly rue or he FRP bu no or concree, exhibiing a nonlinear behavior. Concree shows an increase in he dilaion raio wih ε z. To ake ino accoun he nonlinear behavior o concree a secan approach can be considered. An absolue value o he secan slope o he laeral o axial srain curve o FRP conined concree was proposed by Teng e al [3] in he orm: z 0.7 l l e zo co zo l 7 zo (2.4) Where zo is he unconined concree peak srain (usually i se equal o 0.002) and co is he corresponding sress. Laeral conining sress l is given by eq.(2.1a) or circular secions and or noncircular secions as he average o he wo orhogonal (and dieren) componen s provided by eq. (2.2a): l x y (2.5) 2 3. Bond srengh enhancemen due o coninemen Bond inluences perormance o concree in several ways [4]. In paricular i is responsible or srengh o reinorcemen overlapping. The main parameer inluencing he bond srengh beween concree and spliced bars is laeral conining sress divided by concree compressive srengh. Bond increases raio, Ω p,r a he bar locaion can be evaluaed according o wo dieren expressions. The irs one, repored in he ib Model Code 2010 inal dra, [4] is Ω p,r1, while a second expression is based on a Mohr Coulomb approach, Ω p,r2 : b, l b, l p, r1 1.0 anh 0.2 (a) p, r 2 1 (b) max 0.1c 0 max max (3.1) where µ is he ricion coeicien beween reinorcemen bars and concree (µ is assumed 0.3 [5]), τ b, is he eecive bond srengh and τ max is he peak value o he analyical bond sress- Page 3 o 8

4 slip relaionship according o he ib Model Code 2010 inal dra [4]. On sae side, all oher bond condiions is assumed as reerence bond srengh, τ max =1.25 co. I is worh nohing ha maximum Ω p,r1 can be 2 hus leading o a maximum bond srengh τ b, =2τ max under high coninemen acions, ully compaible wih he value τ max =2.5 co provided in good bond condiions [4]. 4. Eecs o FRP wrapping on he bond sress I is expeced ha he eeciveness o coninemen acion, hus he increase o bond srengh, is greaer in circular secions compared o square and recangular. This is because, in circular secions, coninemen is uniorm and is eiciency is high. On he conrary in square and recangular secions, coninemen is no uniorm and conining sresses σ x, σ y and τ xy are highly variable over he secion. 4.1 FRP reinorcemen geomeric raio and side aspec raio The FRP reinorcemen geomeric raio ρ represens he raio beween he FRP reinorcemen volume and he concree volume. In he ollowing ρ is kep consan o compare resuls even or dieren secion shapes. For noncircular secions he FRP reinorcemen geomeric raio ρ, in he case o coninuous wrapping, is compued according o: () Lx Ly (4.1) L L x y he aspec raio, deined as A r =L x /L y, has been inroduced. Four secions have been chosen o make comparisons: one circular (reerence secion) and hree noncircular wih A r equal o 1, 1.5 and 2 respecively. For all he secions he value o he FRP reinorcemen geomeric raio ρ is he same. Assuming ρ equal o he main properies or parameric analysis are summarized in Tables 4.1 and 4.2 concerning wih geomeric and mechanical properies respecively. Eecive ulimae FRP srain,, has been inroduced. Table 4.1. Geomeric secion properies SECTION ID A r [-] MAIN PARAMETER VALUE [mm] C1 - D 400 S1 1.0 Ly 200 R1 1.5 Ly 167 R2 2.0 Ly 150 Table 4.2. Mechanical properies co [Mpa] ε zo E c [GPa] [mm] ε E [GPa] Sress sae over he secion The sress ield under coninemen or circular secions is well known and equal o l. For square secions, variaions o average laeral pressure, l, is negligible all over he secion, however i is worh nohing ha he dierence beween σ x and σ y is signiican. Thereore in he case o square secions, l seems o be no a signiican parameer, a leas in erms o concree coninemen. However, he sress sae in a recangular secion is signiicanly no uniorm in erms o σ x and σ y, bu more uniorm in erms o l. In paricular he recangular secion wih A r =1.5 (R1) has been chosen o be ploed in deail. Figure 4.1 shows conour diagrams o he conined concree sresses: σ x, σ y and l along wih he bond sress Page 4 o 8

5 enhancemen acor due o ransverse pressure, Ω p,r1. A reerence axial deormaion ε z =0.02% was chosen. This choice is crucial; i is an open issue o coninemen under debae wihin he research communiy. In ac, exacly he same issue arises when dealing wih he evaluaion o combined bending and axial load capaciy. The sress and srain sae as well as he behavior o concenrically conined cross secion is exended o he case o eccenrically loaded secions. On sae side, in his example, an average axial srain is chosen equal o unconined concree peak srain, however a high srain gradien characerizes real columns reaching higher srains in compression as well as srain levels in ension. Figure 4.1. Sress conour plo or R1 secion σ x (a), σ y (b), l (c) and Ω p,r1 (d). I is eviden ha he average laeral sress, l, is variable all over he secion or recangular secions. The mos conined regions are in he cener and diagonals o he secion while he leas conined regions are in he borders o he secion on he longes side. I is urher eviden, observing he conour map in igure 4.1d ha he bond sress enhancemen acor has almos he same rend. To sum up, i is possible o conclude ha he bar placed in he middle o he longes side o he secion has he leas beneis in erms o coninemen. All he ollowing consideraions reer o his bar. 4.3 Inluence o concree axial srain Figure 4.2 represens he variaion o l and l as a uncion o z; Ω p,r1 and Ω p,r2 as a uncion o l. Each o he our chars corresponds o a dieren secion, namely: circular (Figure 4.2a), square (Figure 4.2b), recangular wih A r =1.5 (Figure 4.2c) and recangular wih A r =2 (Figure 4.2d). For each char: in he irs quadran can be observed z - l curve, in he second quadran l - l curve and in he hird a comparison beween he bond increases Ω p,r1 and Ω p,r2. Each char can be read as shown in igure 4.3 saring orm he value o he axial srain parameer (e.g. z=0.02), he values o all oher parameers can be easily read ( l =0.02, l = [GPa], Ω p,r1 =1.39 and Ω p,r2 =1.25). The igure 4.2 clearly highligh ha or an assigned FRP reinorcemen geomeric raio, he greaer he aspec raio is he lower he enhancemen o bond srengh becomes; while he greaer he coninemen laeral sress is, he greaer he enhancemen o bond srengh becomes. Regarding he dieren resuls obained rom he wo dieren equaions or he bond srengh, as expeced, he bond increase evaluaed according o he Model Code [4] expression grows more quickly han he bond increase calculaed wih Mohr-Coulomb approach. However Ω p,r1 reaches a hreshold value when increasing l. Page 5 o 8

6 Figure 4.2. Axial and laeral srain, laeral sress and bond srengh increase: (a) C1, (b) S1, (c) R1, (d) R2 Figure 4.3. Usage o sress-srain char 4.4 Inluence o FRP siness Laeral coninemen sress, l, is srongly inluenced by FRP reinorcemen siness E or dieren axial srain levels. Figure 4.4 clearly shows a nonlinear rend o E - l curves or each secion. In paricular, each char corresponds o a secion: circular (Figure 4.4a), square (Figure 4.4b), recangular wih A r =1.5 (Figure 4.4c) and recangular wih A r =2 (Figure 4.4d). Page 6 o 8

7 Figure 4.4. FRP siness-conining laeral sress and bond increase raio: (a) C1, (b) S1, (c) R1, (d) R2 Increasing he value o he FRP reinorcemen siness he laeral coninemen sress l value does no increase proporionally, bu wih a lower rend. This rend is he same or all axial deormaions. Moreover, once FRP reinorcemen siness is assigned, he greaer he axial srain is, he greaer he conining laeral sress becomes. As shown in igure 4.5 each poin o he x-axis can be relaed o a cerain number o plies and FRP reinorcemen maerial. Figure 4.5. Usage o bond increase raio char Page 7 o 8

8 This analysis has shown ha here is a small dierence in erms o bond srengh increase beween recangular secions wih dieren aspec raio values. Insead greaer sensiiviy in erms o bond srengh increase has been highlighed in he ransiion rom circular o noncircular secion. This is due o available bond models relaing bond srengh increases o he average conining pressure l. More deailed models accouning or dieren conining sress conribuions, σ x and σ y, could lead o more reined resuls. I is worh noing ha 3D concree plasiciy suraces used in coninemen model [2] revealed signiican dierences in erms o behavior or he same S1, R1 and R2 secions. This resul was due o he remarkable dierences beween σ x and σ y, even i l was much more comparable 5. Conclusions A reined model has been proposed o evaluae he ricion increase a lap splice locaion in FRP wrapped concree secions. The ricion increase is he irs sep in he evaluaion o he bond srengh increase due o FRP coninemen and hus o he benei in erms o duciliy and seismic perormance. The model accouns or circular, square and recangular cross secion, evaluaing he average conining pressure a each bar locaion. The conining pressure is no uniorm over he secion and depends on FRP and concree mechanical and geomerical properies. The paper analyzed in deail he inluence o concree axial srain sae and FRP siness and i represen a irs sep owards he comprehension o eeciveness o FRP wrapping in prevening lap splice ailures in RC members. Fuure research should include he comprehension o he coninemen mechanisms o secions under non-concenrically axial load (i.e. under combined axial load and bending), or in oher erms, he selecion o a represenaive average axial concree srain o evaluae he FRP conining pressure. I is sill an open issue o coninemen under debae wihin he research communiy. Furhermore, available bond increase models are based on he average coninemen pressure around he bar, however in noncircular secions orhogonal sress componens o coninemen pressure presen remarkable dierences even i average pressure is quie uniorm. Fuure reined bond increase models should accoun or such dierences. Reerences [1] BOURNAS, D.A., TRIANTAFILLOU, T.C., ASCE, M. Bond srengh o Lap-Spliced Bars in Concree Conined wih Composie Jackes, ASCE Journal o Composies or Consrucion, Vol. 15, No. 2, March/April 2011, pp [2] LIGNOLA, G.P., PROTA, A., MANFREDI, G., COSENZA, E., Non linear reined modelling o FRP Coninemen on prismaic RC Columns, 14 h European Conerence on Earhquake Engineering, Ohrid, Republic o Macedonia, 29 Augus- 4 Sepember 2010, paper #1007. [3] TENG, J.G., HUANG, Y.L., LAM, L., YE, L.P., Theoreical model or iber reinorced polymer-conined concree, ASCE Journal o Composies or Consrucion, Vol. 11, No. 2, March/April 2007, pp [4] CEB-FIP Model Code (inal dra), Design Code, Comié Euro-Inernaional du Béon, Thomas Telord, Lausanne, Swizerland, 2010, pp [5] CORONELLI, D., Corrosion Cracking and Bond Srengh Modeling or Corroded Bars in Reinorced Concree, ACI Srucural Journal, Vol. 99, No. 3, May 2002, pp Page 8 o 8