Numerical Simulation of Thermal Stresses in Prismatic Concrete Beams Reinforced with FRP Bars under Low Temperatures

Transcription

1 Cemisry and Maerials Resear, Vol Speial Issue for Inernaional Congress on Maerials & Sruural Sabiliy, Raba, Moroo, 7-30 November 013 Numerial Simulaion of Termal Sresses in Prismai Conree Beams Reinfored wi FRP Bars under Low Temperaures A. Zaidi 1, R. Masmoudi, S. Amara 1, M. Laidi 1 and S. Sai 1 1 Sruures Reabiliaion and Maerials Laboraory (SREML), Universiy of Lagoua, Algeria Deparmen of Civil Engineering, Universiy of Serbrooke, QC., Canada Absra. Te ermal properies of fiber reinfored polymer (FRP) bars pariularly in e ransverse direion are iger an ose of ardened onree and seel bars. Te differene in ransverse ermal araerisis beween FRP bar and onree generaes radial ensile sresses wiin onree a e inerfae of FRP bars/onree under low emperaures. Tese ermal sresses may ause irumferenial raks in onree a e inerfae and evenually e reduion of e bond a an affe signifianly e servieabiliy of reinfored onree sruures. Tis paper presens a nonlinear numerial simulaion of ermal sresses in prismai onree beams reinfored wi glass FRP (GFRP) bars submied o low emperaures wen e onfining aion of onree is asymmeri. Te non linear numerial analysis sows a e firs irumferenial raks sar o develop wiin onree a FRP bar/onree inerfae a a emperaure derease T r varied beween -30 C and -5 C for prismai onree beams reinfored wi GFRP bars aving a raio of onree over ikness o FRP bar diameer (/d b ) varied from 1.0 o 3.. Furermore, e deps of irumferenial raks propagaed from e inerfae roug e onree over inrease wi e derease of e ermal load T (from -5 C o -50 C). Tese deps did no rea e ouer surfae of e onree over under low emperaures up o -50 C. Also, e radial ensile sress a FRP bar/onree inerfae inreases wi e inrease in e raio /d b. Te raking ermal loads and ermal sresses predied from nonlinear finie elemen model are ompared o ose evaluaed wi analyial models. Comparisons beween numerial and analyial resuls in erms of raking ermal loads and ermal sresses are presened. 1 Inroduion Te use of fiber reinfored polymer (FRP) maerials as a reinforemen in onree sruures as inreased remarkably in reen years, beause of eir exellen resisane o orrosion, ig ensile sreng, low weig, eleromagnei neuraliy, and ig siffness. Nevereless, e ermal expansion of FRP bars in e ransverse direion is iger an a of e ardened onree. Tis differene in ransverse ermal expansion beween FRP bars and onree may ause irumferenial raks wiin onree a FRP bar/onree inerfae under low emperaures. As a onsequene, e servieabiliy of reinfored onree sruures an be redued. Many experimenal works were arried ou on ermal effe on onree sruures reinfored wi FRP bars [1-4]. However, numerial sudies in is opi need more invesigaion pariularly e effe of low emperaures on sress and srain disribuions in onree over a e inerfae of FRP bar/onree. Tis paper presens a nonlinear numerial simulaion using ADINA sofware o invesigae ermal sress disribuions a e inerfae of onree/frp bars wen e onfining aion of onree surrounding FRP bar is asymmeri. Tis invesigaion as been arried ou on prismai onree beams reinfored wi glass FRP (GFRP) bars subjeed o low emperaures (T) up o -50 C. Te nonlinear finie elemen analysis allows o deermine e ermal loads (T r ) produing e firs irumferenial raks wiin onree a e inerfae of FRP bar/conree as a funion of e raio of onree over ikness o FRP bar diameer for reinfored prismai onree beams used. Te ermal sresses and raking ermal loads predied from e numerial model are ompared wi ose obained from analyial models. 16 Non-linear finie elemen analysis.1 Finie elemen model A nonlinear numerial simulaion was arried ou uilizing ADINA sofware o analyse ermal sress disribuions in prismai onree beams reinfored wi glass FRP (GFRP) bars submied o a emperaure derease (T) varied from 0 o -50 C wi an inremen of -5 C. Te raio of onree over ikness o FRP bars (/d b ) used is varied from 1 o 3., as sown in figure 1 and Table 1. Te prismai onree beam was modeled by means of wo dimensional plane sress elemens beause of e onsan of axial deformaions. Te sudy was arried ou only for e alf of e ross seion beause of e symmeri of e ross-seion of e prismai onree beam wi respe o z-z axis, as sown in figure 1a and 1. Te mesing of e bo

2 Cemisry and Maerials Resear, Vol Speial Issue for Inernaional Congress on Maerials & Sruural Sabiliy, Raba, Moroo, 7-30 November 013 GFRP bar and onree (Figure ) was arried ou using riangular elemens wi 6 nodes. GFRP bars used in is sudy ad a linear elasi beavior. Te meanial properies of GFRP bars deermined experimenally [3] are presened in Table. Te modulus of elasiiy (E ) and Poisson s raio ( ) of GFRP bars in e ransverse direion evaluaed eoreially using e rule of mixure were found o be equal o 7.1 GPa and 0.38, respeively. Te ransverse and e longiudinal oeffiiens of ermal expansion (CTE) of GFRP bars for e five FRP bar diameers esed were found o be equal o = 33 ± 4 x10 6 / C and l = 8 ± / C in average, respeively. Te onree used in is sudy was onsidered o ave a non-linear beavior. Te meanial properies of e onree are repored in Table 3. Te average ensile sreng (f ) of onree was deermined by spliing ess and e average ompressive sreng (f ) was evaluaed by sandard ompression ess. Te modulus of elasiiy of onree (E ) was deermined aording o CAN/CSA- S806-0 guidelines [5], wile e Poisson s raio of onree ( ) was assumed Te oeffiien of ermal expansion (CTE) of onree was deermined by experimenal ess and was found o be equal o 11.6 ±.1 x10-6 / C. Z A-A (a) GFRP bar Conree b 1 a = d b / b = d b /+ Y 380 mm mm (b) Fig.1. Prismai onree beam reinfored wi GFRP bar modeled Z b 1 / () d b A A Y Fig.. Mesing of e bo onree and GFRP bar Table 1. Deail of prismai onree beams reinfored wi GFRP bars. Speimens Spe. wid b 1 [mm] Spe. Heig [mm] Bar diameer d b [mm] Conree over ikness [mm] /d b P.#10.0 * P.# P.# P.# P.# P.# P.# P.# P.# P.# P.# P.# P.# P.# P.# *P : Prismai onree beam ; #10 : Nominal diameer GFRP bar; 0 : Conree over ikness in mm Table. Meanial properies of e GFRP bars Bar diameer d b, mm Ulimae ensile sreng f fu, MPa Longiudinal modulus of elasiiy E l, GPa Longiudinal Poisson s raio l ± ± ± ± N/a N/a 0.8 ±

3 Cemisry and Maerials Resear, Vol Speial Issue for Inernaional Congress on Maerials & Sruural Sabiliy, Raba, Moroo, 7-30 November 013 Table 3. Meanial properies of onree Compressive sreng f 8, MPa Tensile sreng f 8, MPa Modulus of elasiiy E, GPa Firs irumferenial raks Numerial Resuls Figures 3 sows ypial urves of radial ensile ermal sresses wiin onree a FRP bar/onree inerfae for prismai onree beams reinfored wi GFRP bars, under low emperaures, aving a raio of onree over ikness o FRP bar diameer (/d b ) equal o 1. and.5. I an be seen a e ensile sress inreases wi e derease in e emperaure variaion (T r ) unil -5 C and -30 C orresponding o raios of /d b equal o.5 and 1., respeively. From ese ermal loads T r e radial ensile sress dereases abruply beause of e appearane of e firs irumferenial raks wiin onree a e inerfae, as sown in figure 4. I is noed a e deps of irumferenial raks propagaed from e inerfae roug e onree over inrease wi e derease of e ermal load T (from -5 C o -50 C). Tese deps did no rea e exernal surfae of onree over for emperaure variaions up o -50 C (Figure 5). Table 4 presens e ermal loads T r produing e firs irumferenial raks wiin onree a FRP bar/onree inerfae versus e raio of /d b varied from 1 o 3. for prismai onree beams reinfored wi GFRP bars aving asymmeri onree onfining aion. I is observed a e irumferenial raking onree appeared in onree over a ermal loads of -5 C for /d b varied from 3. o 1.9 and -30 C for /d b varied from 1.9 o 1. Fig. 4. Appearane of e firs irumferenial raks wiin onree a FRP bar/onree inerfae a ermal load ΔT r (for onree beams aving /d b =.5, ΔT r = -5 C) (a) ΔT = -30 C FRP bar/onree inerfae l r =Craking onree dep (b) ΔT = -50 C Fig. 5. Cirular rown of irumferenial raked onree formed a ermal loads -30 and -50 C (for onree beam aving /d b =.5) Table 4. Non linear numerial ermal loads (T r ) produing e firs irumferenial raks wiin onree a FRP bar/onree inerfae for prismai onree beams /d b T r ( C) 1.9 < /d b /d b Linear analyial analysis of ermal sresses Fig. 3. Radial ensile sresses in onree a onree/frp bar inerfae for prismai onree beams aving /d b =1. and.5 Te ermal expansion of FRP bars in e ransverse direion is iger an a of ardened onree. Tis differene in ransverse ermal expansion 18

4 Cemisry and Maerials Resear, Vol Speial Issue for Inernaional Congress on Maerials & Sruural Sabiliy, Raba, Moroo, 7-30 November 013 generaes radial pressure (P) a e inerfae of FRP bar/onree under low emperaures (T).Tis radial pressure reaes ensile sresses wiin onree. From e analyial models arried ou by Raman e al. (1995) [6] and Masmoudi e al. (005) [3], e radial ensile sress (σ ) in a onree elemen siuaed a a radius from e ener of onree ylinder reinfored wi FRP bar due o radial pressure P, is given by: P b 1 (1) r 1 Were r = b/a is e raio of onree ylinder radius (b=+d b /) o FRP bar radius (a=d b /), as sown in figure 1; P is e radial pressure a FRP bar/onree inerfae wi is given by: P ) T () 1 r² E r² 1 E Were E is e modulus of elasiiy of onree ; is Poisson s raio of onree ; is e oeffiien of ermal expansion of onree ; E is e modulus of elasiiy of e FRP bar in e ransverse direion ; is Poisson s raio of e FRP bar in e ransverse direion and is e ransverse oeffiien of ermal expansion of FRP bar. Te maximum value of e radial ensile sress in onree a e inerfae, a ρ=a, obained by Eq.(1), is given by: ose deermined from analyial model beause of e non-linear beavior of onree onsidered in e numerial model. Table 5. Termal load T r produing e firs irumferenial raks in onree a FRP bar/onree inerfae of prismai onree beams - omparison beween analyial and numerial models /d b Analyial model Numerial model T r, C T r, C 1.9< /d b /d b Termal sresses Figures 6 and 7 ompare ypial urves of radial ensile sresses predied from analyial model wi ose obained from numerial model a FRP bar/onree inerfae of prismai onree beams reinfored wi GFRP bars a ave a raio of onree over ikness o FRP bar diameer (/d b ) equal o 1. and.5. I an be seen a e numerial resuls predied from e nonlinear numerial model are in good agreemen wi analyial resuls unil -5 C and -30 C from wi numerial urves derease suddenly beause of e appearane of irumferenial raks in onree wi are no onsidered in e analyial model. P (3) max f Te firs irumferenial raks appear in onree a e FRP bar/onree inerfae wen e radial sress reaes e ensile sreng of onree f a e ermal load (T r ) obained from Eqs. and 3, as follows: f 1 r 1 1 T r E r 1 E 1 (4) 4 Comparison beween analyial and numerial resuls 4.1 Craking ermal loadings Table 5 presens omparison beween ermal loads (ΔT r ) a produe e firs irumferenial raks in onree a e inerfae of FRP bar/onree obained from analyial and numerial models for prismai onree beams reinfored wi GFRP bars a ave a ensile sreng of onree f = 4.1 MPa. I an be observed a e algebrai values of ermal loads ΔT r predied from numerial model are generally lower an 19 Fig. 6. Radial ensile onree sress versus emperaure variaion a FRP bar/onree inerfae of onree beam aving a raio /d b = 1. - Comparison beween numerial and analyial models

5 Radial ensile sress (MPa) Cemisry and Maerials Resear, Vol Speial Issue for Inernaional Congress on Maerials & Sruural Sabiliy, Raba, Moroo, 7-30 November 013 /d b =.5 Numerial model Analyial model Temperaure variaion ( C) Fig.7. Radial ensile onree sress versus emperaure variaion a FRP bar/onree inerfae of onree beam aving a raio /d b =.5 - Comparison beween numerial and analyial models 5. Conlusions Reabiliaion, CDCC-11, (Quebe Ciy, Quebe, Canada, 011).. A. Zaidi and R. Masmoudi, Effe of Conree Cover Tikness and FRP-Bars Spaing on e Transverse Termal Expansion of FRP Bars, 8 Inernaional Symposium on Fiber Reinfored Polymer Reinforemen for Conree Sruures, (Universiy of Paras, Deparmen of Civil Engineering, Paras, Greee, 007). 3. R. Masmoudi, A. Zaidi, and P. Gérard, Transverse ermal expansion of FRP bars embedded in Conree, Journal of Composies for Consruion, ASCE, 9 (005), Genry, T.R., and Husain, M., Termal ompaibiliy of onree and omposie reinforemens, Journal of Composies for Consruion, 3 (1999), Canadian Sandards Assoiaion, Design and Consruion of Building Componens wi Fiber Reinfored Polymers, CAN/CSA S806 0, Torono, Onario, Canada, (00). 6. Raman, H.A., Kingsley, C.Y., and Taylor, D.A., Termal sress in FRP reinfored onree, Proeedings, Annual Conferene of e Canadian Soiey for Civil Engineering, Oawa, (1995), Firs irumferenial raks appear in onree a FRP bar/onree inerfae a emperaure derease T r varied beween -30 C and -5 C for prismai onree beams reinfored wi GFRP bars aving a raio of onree over ikness o FRP bar diameer (/d b ) varied from 1.0 o 3. and a onree ensile sreng of 4.1 MPa. - Te radial ermal sresses predied from nonlinear numerial model, a FRP bar/onree inerfae of prismai onree beams reinfored glass FRP bars aving raio /d b varied beween 1.0 and 3., are in good agreemen wi ose deermined from e linear analyial model unil a emperaure variaion ΔT r around -5 C from wi e numerial resuls derease abruply beause of e appearane of irumferenial raks wi are no onsidered in e linear analyial model. - A low emperaure, e non-linear numerial analysis sows a e deps of irumferenial raks propagaed from e inerfae roug e onree over inrease wi e derease of e ermal load T (from -5 C o -50 C). Tese deps did no rea e ouer surfae of e onree over under low emperaures up o -50 C. Also, e radial ensile sress a FRP bar/onree inerfae inreases wi e inrease in e raio /d b. Referenes 1. B. Benmokrane, E. El-Salakawy, and E. Amed, Proeedings of e Four Inernaional Conferene on Durabiliy & Susainabiliy of Fibre Reinfored Polymer Composies for Consruion and 0