Fourth International Conerence on FRP Composites in Civil Engineering (CICE008) -4July 008, Zurich, Switzerland Calibration o Bond Coeicient or Delection Control o FRP RC Members R. Fico, A. Prota & G. Manredi Department o Structural Engineering (DIST), University o Naples "Federico II", via Claudio, 805 Naples, Italy ABSTRACT: In 006 the Italian Research Council (CNR) published a Guide or the Design and Construction o Concrete Structures Reinorced with FRP Bars (CNR-DT 03/006); the approach ollowed is that o the limit states semi-probabilistic method; the model adopted or the design moment resistance o FRP RC sections is based on the design rules o Eurocode : it shall satisy both strength and serviceability requirements. The present work developed in this context assesses the ormulation suggested by the CNR-DT 03 or computing delections o FRP RC members depending on FRP bars-to-concrete bond, by taking into account the bond coeicient m. A calibration analysis was conducted in order to determine an optimum value or m, based on a large experimental database available in literature, made o FRP RC elements subjected to our-points bending tests. INTRODUCTION According to CNR-DT 03/006 and in compliance with the Eurocode (004), the computation o delections o FRP reinorced concrete (RC) members can be perormed by integration o the curvature diagram. Such diagram can be computed with non-linear analyses by taking into account both cracking and tension stiening o concrete. Alternatively, simpliied analyses are possible, similar to those used or traditional RC members. Experimental tests have shown that the model proposed by Eurocode when using traditional RC members can be deemed suitable or FRP RC elements too. Thereore, the ollowing equation to compute the delection can be considered: m M M = β β + β β cr cr M max M max where is the delection o the uncracked section; is the delection o the transormed cracked section; β = 0. 5 is a non-dimensional coeicient accounting or bond properties o FRP bars; β is a non-dimensional coeicient accounting or the duration o loading (.0 or short time loads, 0.5 or long time or cyclic loads); M max is the maximum moment acting on the examined element; M cr is the cracking moment calculated at the same cross section o M max ; m is a bond coeicient that CNR-DT 03 prescribes to be set equal to, unless speciic bond characterization o FRP bars or the investigation o delection is carried out by the manuacturer, by ollowing the procedure to determine a dierent value o m reported in Appendix E ; such procedure can be summarized as ollows: on the basis o a population o at least ive elements o concrete reinorced with FRP bars, that shall be subjected to our-points bending test, delections are measured or ixed load values, ensuring that or a single test there is a number o at least ive acquisitions over time interval between 0% and 60% o the ultimate load, P ult. The same load values are used to calculate the theoretical delections starting rom equation (). The exponent m is determined on the basis o the comparison between analytical and experimental results, using an appropriate statistical analysis, ater assigning the unitary value to β m () - -
and β. A similar approach was used herein to assess the accuracy o value m= on the basis o an extensive set o data available in literature. BOND The modulus o elasticity o glass and aramid FRP bars is about one-ith that o steel. Even though carbon FRP bars have a higher modulus o elasticity than glass FRP bars, their stiness is about two-thirds that o steel reinorcing bars. Lower stiness causes larger delections and crack widths or FRP reinorced members which can aect serviceability (Toutanji and Saai, 000). Since an important role is played by bond between FRP bar and concrete, the bond behavior o FRP reinorced specimens is o interest in this investigation. Bond between reinorcement and concrete is aected by many actors. The major actors inluencing the bond behavior o FRP reinorced concrete are as ollows (Pay, 005): Concrete cover and bar spacing; an increase o concrete cover and bar spacing enhances the bond capacity, although this aspect is less prominent or larger diameter bars. Concrete compressive strength. The eect o concrete strength is not ully understood or FRP reinorced specimens, since there is only limited data available or FRP bar reinorced specimens. Nanni et al. (995) investigated the eect o concrete strength on bond behavior using pullout specimens and ound that concrete strength does not have any inluence on pullout ailures. However Malvar (994) ound that, or splitting ailures, an increase in concrete strength results in an increase in bond strength. Development length; an increase in the development length o a reinorcing bar will increase the total bond orce transerred between the concrete and the reinorcement; as or steel, when the bonded length increases, the eectiveness o the bonded length decreases, thus the relative gain with increase in development length reduces. Further study is needed to quantiy this eect. Transverse reinorcement; the presence o transverse reinorcement in the development region prevents the progression o splitting cracks; thereore, the bond orce required to cause ailure o the bar increases (Orangun et al., 977, Tepers, 98, Darwin et al., 996 a, b). As the bond strength increases with an increase in transverse reinorcement, eventually the ailure mode changes rom splitting to pullout. Additional transverse reinorcement above that required to cause a pullout ailure is unlikely to increase the anchorage capacity o the section (Orangun et al., 977). Bar size; the bar size has a direct inluence on the bond strength o FRP reinorced beams. As the bar size increases or a given development and splice length, the total bond orce developed by the bar increases. However, the rate o increase in the bond orce is lower than the increase in bar area. Consequently, bond stresses are lower or larger diameter bars. Surace deormation o the reinorcement; the orce transer between FRP bars and concrete is mainly due to chemical adhesion and riction between the concrete and the reinorcement; bearing o concrete on the surace deormation is minimal. Makitani et al. (993), Malvar (994), and Nanni et al. (995) studied the eect o surace deormation on the bond strength o FRP reinorced specimens through pullout tests, concluding that the surace deormation o the bar has an inluence on the bond strength. 3 CALIBRATION OF BOND COEFFICIENT m 3. Test specimens and variables The data set consisted o sixty-seven concrete beam and slab specimens reinorced with continuous FRP bars, tested through our points bending tests and available in literature (Benmokrane et al., 996, Alsayed, 998, Masmoudi et al., 998, Theriault & Benmokrane, 998, Alsayed et al., 000, Pecce et al, 000, Toutanji & Deng, 003, Yost et al., 003, El Salakawy & Benmokrane, 004, Al Sunna et al., 006, Laoubi et al., 006, Rai et al, 006). Fig. shows the cross section and the test setup layout. - -
Figure. Cross Section and Test Setup Layout The cross section width, b, ranged between 0 and 000 mm; the height, H, ranged between 80 and 550 mm; the length, L, varied between 500 and 3400 mm; the distance between the support and the applied load, a, ranged between 500 and 450 mm; the constant moment zone, s, varied between 00 and 000 mm. As or the concrete used or casting the specimens, the mean compressive strength, c, ranged between 30 and 97 MPa; the mean tensile strength or lexure, ct,l, ranged between.9 and 5. MPa; and the compressive modulus o elasticity, E c, ranged between 3 and 46 GPa; in particular or E c also the corresponding theoretical values were computed (ranging between 3 and 4 GPa), using the ollowing relationship (ACI 38, 996): E c,the = 463 () c The FRP reinorcement included glass (6 specimens) and carbon bars (5 specimens) with dierent sizes and surace deormations. The bars tensile strength, u, varied rom 507 to 39 MPa; the modulus o elasticity, E, varied rom 36 to 36 GPa; and the diameter o bars in tension, φ, ranged between 9 and mm. All the geometrical characteristics and materials details related to the specimens considered are reported elsewhere (Fico, 007). 3. Cracking Moment In order to calibrate the bond coeicient m in ormula (), three dierent cases were analyzed, namely:. M, & E c,exp ;. M cr,the, & E c,exp ; 3. M, & E c,the, where M and M cr,the are the experimental and the theoretical value o the cracking moment, respectively. The deinition o the cracking moment is important since it inluences the evaluation o delection or FRP reinorced members (Pecce et al., 00); since M cr,the depends on the concrete strength in tension, that is a very uncertain parameter and usually can not be directly measured, but computed depending on the strength in compression, the introduction o the experimental value o the cracking moment M cr allows to examine the model eiciency disregarding the inluence o the uncertainties due to M cr,the ( st case); nevertheless, evaluating M cr,the is signiicant or the model application ( nd case); similarly, the signiicance o E c,the instead o E c,exp in the model application was taken into account (3 rd case). All values o the ultimate load, P ult, the moment o inertia o both the un-cracked (I ) and cracked section (I ), and o M and M cr,the relating to all specimens considered are reported elsewhere (Fico, 007). 3.3 Calibration Analysis For each o the three cases reported in 3., the calibration o the exponent m was carried out by computing the standard (e ) and the mean error (e ): e = n the test i= test i n ; e = n the test = i test i where the and test are the theoretical and the experimental value o the delection, respectively; i is the generic test, and n is the number o considered points; e can be considered as a n (3) - 3 -
measure o the reliability o equation, whereas e is a measure o the sae level o the model (e >0: the model is sae). The errors have been calculated in a load range which could be signiicant o serviceability conditions, namely 0 to 65% o ultimate load, P ult ; with load steps o 5%, 0 dierent delection values in correspondence o as many load values were measured or each test. Following a summary o the calibration analysis perormed is reported: Compute the theoretical delection corresponding to a percentage value α o the applied load (0%<α<65%), α the ; α Measure the corresponding experimental delection, test, on the plots available in literature (67 out o 80 specimens available in literature could be selected); Compute e and e. By varying the bond coeicient m the minimum value o e (with e >0) was ound or each o the three cases analyzed, as ollows.. M & E c,exp Fico (007) reports the values o theoretical delections computed or each load step when setting M cr =M and E c =E c,exp, according to equation (), and the corresponding experimental values measured. The bond coeicient corresponding to the minimum value e =0. is m=7. As or e, since the value derived is nearly zero (e =-6), it can be concluded that the analytical model is suiciently reliable. A dierent evaluation was perormed deriving m or each load step o every single test, ater setting exp = the, so that = γ + ( γ ). Thereore γ was derived: γ = exp exp (5), rom which: m (6) exp = log M cr M max Hence the ollowing quantities were plotted as shown in Fig -a: m= var 7 M M M M M M, ;, ;, (M a =αm max ). M a M a M a M a M a M a It can be noticed that points corresponding to m=7 approximate points with m=var. better than points corresponding to m=; thus, m=7 is suggested in replacement o m= in equation ().. M cr,the & E c,exp The signiicance o model was evaluated in the second case computing theoretical delections or each load step ater setting M cr =M cr,the and E c =E c,exp, according to equation (), and comparing the results with the corresponding experimental values measured. The same procedure already explained or the irst case was ollowed, computing e and e or each specimen tested. The bond coeicient corresponding to the minimum value e =0.38 is m=0.790. With respect to case ) it can be observed that the average standard error e in case ) is higher, and that the average mean error, e, is considerably lower than zero (i.e. e =-5), conirming that considering the analytical value o M cr instead o the corresponding experimental value decreases the model reliability. Similarly to case, the plot shown in Fig. -b was derived. None o the two lines (m= and m=0.79) approximates the points with m=var. properly, conirming that the m= line is not enough reliable and that considering M cr,the instead o M implies an accuracy reduction o the model proposed. 3. M & E c,the The signiicance o considering E c,the instead o E c,exp in the model application was taken into account in case 3). The theoretical delections were computed or each load step ater setting M cr =M and E c =E c,the, according to equation (), and comparing the results with the corresponding experimental delections already measured. The same procedure already explained or the irst two cases was ollowed, computing e and e or each specimen tested. The bond coeicient corresponding to the minimum value e =8 is m=0.70. Case 3) can be considered intermediate between cases ) and ), its average standard error e being higher than e o case ), but lower than e o case 3), yet quite reliable as it resulted or case ) (e =-59). - 4 -
As or case ) and ), the plot o Fig. -c was derived, that conirms the results already discussed: the line corresponding to m=0.79 approximates points with m=var. better than line with m=, conirming that the m= line is not enough reliable... (M/Ma).0 0. [m=] [m=var] [m=0,87] (Mcr,the/Ma).0 0. m= m=0,79 m=var. 0..0. (M /M a ) m 0..0. (M cr,the /M a ) m. (a) Case : M ;E c,exp. (b) Case : M cr,the ;E c,exp [m=0.79].0.0 (M/Ma) [m=0.7] [m=] 0. [m=var] 0..0. (M /M a ) m (c) Case 3: M ;E c,the Figure. (M cr /M a ) m vs (M cr /M a ) (Mcr/M a) [m=] [m=7] 0. [m=0.7] 0..0. (M cr /M a ) m (d) Summary o results 4 CONCLUSIONS Fig. -d shows the three lines obtained or the three values o m derived, compared to line relating to m=. It can be observed that the three lines corresponding to the three cases considered are very close and have concave trend, being m<, converse to the trend o m= line. From the comparison o the our lines with respect to the points obtained setting m=var., it can be concluded that the bond coeicient m= in equation () should be replaced by a value lower than unity. As or the three cases analyzed, Table shows a summary o the results obtained: Table. Summary o results Case: e e m ) M ; E c,exp 0, -0,06 0,87 ) M cr,the ; E c,exp 0,38-0,05 0,79 3) M ; E c,the 0,48-0,059 0,7 The irst value m =7 corresponds to the minimum value o the average standard error e with a suicient level o saety (e 0): this conirms that considering the experimental values o the cracking moment and o the modulus o elasticity o concrete instead o the theoretical values brings to more reliable predictions. Thereore the value m=7 to use as bond coeicient when computing delections o FRP RC elements in equation () o CNR-DT 03/006 is the one proposed. O the two other cases considered, case 3) where the theoretical value o E c replaced the experimental value, resulted to give better predictions than case ), where the theoretical value o M cr was used instead o the corresponding experimental value. The investigation o the available data collected allowed concluding that computing the cracking moment (rather than accounting or its experimental value) penalizes the reliability and the saety o delection calculations more than considering E c,the instead o E c,exp. Nevertheless, the values o m derived in case ) and in case 3) do not dier rom the value o case ) considerably, with a maximum - 5 -
variation o 7% o m 3 with respect to m. Hence, considering the theoretical aorementioned values rather than the corresponding experimental quantities does not penalize the reliability o results considerably. 5 REFERENCES American Concrete Institute (ACI), 996, Building code requirements or reinorced concrete and commentary, ACI 38-95, Detroit. Alsayed, S.H., 998, Flexural Behaviour o Concrete Beams Reinorced with FRP Bars, Cement and Concrete Composites, No. 0, pp. -; Alsayed, S.H., Al-Salloum, Y.A., and Almusallam, T.H., 000, Perormance o glass iber reinorced plastic bars as a reinorcing material or concrete structures, Department o Civil Engineering, King Saud University, P.O. Box 800, Riyadh 4, Saudi Arabia Composites: Part B 3, pp 555 567; Al-Sunna, R., Pilakoutas, K., Waldron, P., Guadagnini, M, 006, Delection o GFRP Reinorced Concrete Beams, Fédération Internationale du Béton Proceedings o the International Congress, June 5-8, 006, Naples, Italy; Benmokrane, B., Tighiouart, B., and Chaallal, O., 996, Bond Strength and Load Distribution o Composite GFRP Reinorcing Bars in Concrete, ACI Materials Journal, V. 93, No. 3, pp. 46-53; CNR-DT 03/006. Guide or the Design and Construction o Concrete Structures Reinorced with Fiber-Reinorced Polymer Bars National Research Council, Rome, Italy, 006; Darwin, D., Tholen, M. L., Idun, E. K., and Zuo, J., Splice Strength o High Relative Rib Area Reinorcing Bars, ACI Structural Journal, V. 93, No., Jan.-Feb. 996, pp. 95-07; Darwin, D., Zuo, J., Tholen, M. L., and Idun, E. K., Development Length Criteria or Conventional and High Relative Rib Area Reinorcing Bars, ACI Structural Journal, V. 93, No. 3, May-June 996, pp. 347-359; El-Salakawy, E. and Benmokrane, B., 004, Serviceability o Concrete Bridge Deck Slabs Reinorced with Fiber-Reinorced Polymer Composite Bars, ACI Structural Journal, V.0, No 5, pp. 77-736; EN 99-- Eurocode Design o concrete structures - Part -: General rules and rules or buildings, 004; Fico, R., 007, Limit States Design o Concrete Structures Reinorced with FRP Bars, PhD Thesis, Univ. o Naples, Italy, 67 p.; Laoubi, L., El-Salakay, E., and Benmokrane, B., 006, Creep and durability o sand-coated glass FRP bars in concrete elements under reeze/thaw cycling and sustained loads, Cement & Concrete Composites 8 (006) 869 878; Makitani, E., Irisawa, I., and Nishiura, N., Investigation o Bond in Concrete Members with Fiber Reinorced Plastic Bars, International Symposium: Fiber-Reinorced Plastic Reinorcement or Concrete Structures, ACI Proceedings, SP-38, Nov. 993, pp. 35-33. Malvar, J. L., Technical Report: Bond Stress Slip Characteristics o FRP Bars, Naval Facilities Engineering Service Center, Port Hueneme, CA, Feb. 994, 45 pp; Masmoudi, R., Theriault, M., and Benmokrane, B., 998, Flexural Behavior o Concrete Beams Reinorced with Deormed Fiber Reinorced Plastic Reinorcing Rods, ACI Structural Journal, V. 95, No. 6, pp. 665-676; Nanni, A., Al-Zahrani, M. M., Al-Duajani, S. U., Bakis, C. E., and Boothby, T. E., Bond o FRP Reinorcement to Concrete- Experimental Results, Non-Metallic Reinorcement (FRP) or Concrete Structures, Proceedings o the Second International Symposium, 995, L. Taerwe, Editor, pp. 35-45; Orangun, C. O., Jirsa, J. O., and Breen, J. E., A Revaluation o Test Data on Development Length and Splices, ACI Journal, Proceedings V.74, No.3, Mar. 977, pp. 4-; Pecce M, Manredi G, and Cosenza E, 000, Experimental Response and Code Models o GFRP RC Beams in Bending, Journal o Composites or Costruction, Vol. 4, No. 4, November 000, pp. 8-90; Pay, A.C., 005, Bond Behavior o Unconined Steel and FRP Bar Splices in Concrete Beams, Purdue University, PhD Thesis; Pecce M., Manredi G., Cosenza E., A Probabilistic Assessment o Delections in FRP RC Beams, Proceedings o the Fith Conerence on Non-Metallic Reinorcement or Concrete Structures, FRPRCS5, Cambridge, UK, 6-8 July 00; Rai M. M, Nadjai, F. A., and Talamona, D., 006, Aspects o behaviour o CFRP reinorced concrete beams in bending, Construction and Building Materials, article in press; Tepers, R., Tensile lap splices with conining reinorcement, Contribution to the International Conerence on Bond in Concrete, Paisley, Scotland, June 4th-l6th 98, pp. 38-330; Theriault, M., and Benmokrane, B., 998, Eects o FRP Reinorcement Ratio and Concrete Strength on Flexural Behavior o Concrete Beams, Journal o Composites or Construction, Vol., No., pp.7-6; Toutanji H. A., M. Saai, Flexural Behavior o Concrete Beams Reinorced with Glass Fiber-Reinorced Polymer (GFRP) Bars, ACI Structural Journal/September-October 000; Toutanji H., and Deng, Y., 003, Delection and crack-width prediction o concrete beams reinorced with glass FRP rods, Construction and Building Materials, 7, pp. 69-74; Yost, J. R., Gross, S. P., and Dinehart, D. W., 003, Eective Moment o Inertia or Glass Fiber-Reinorced Polymer-Reinorced Concrete Beams, ACI Structural Journal, V. 00, No. 6; - 6 -