CRACKING BEHAVIOR AND CRACK WIDTH PREDICTIONS OF CONCRETE BEAMS PRESTRESSED WITH BONDED FRP TENDONS Weichen XUE Professor Tongji University Siping Road 1239#, Shanghai 200092, China xuewc@tongji.edu.cn* Yuan TAN PhD Candidate Tongji University Siping Road 1239#, Shanghai 200092, China 2009yuantan@tongji.edu.cn Abstract A total of six specimens were tested under four-point loading to examine the cracking behavior of prestressed concrete beams with a combination of bonded CFRP tendons and steel/gfrp reinforcements. The investigated parameters included the partial prestressing ratio (PPR), amount of prestressed CFRP tendons, types of nonprestressed reinforcements, and jacking stress levels. The characteristics of cracking propagation, cracking spacing and crack widths of specimens were presented. Test results indicated that the prestressed concrete beam reinforced with nonprestressed GFRP rebars exhibited wider crack width and larger crack spacing than those reinforced with nonprestressed steel rebars. Based on the correlative principles recommended by ACI 224R-01, a formula modified from the Frosh equation was provided for calculating the maximum crack width of concrete beams with a combination of bonded FRP tendons and steel/frp reinforcements. Keywords: bond CFRP tendon, concrete beam, crack behavior, crack width 1. Introduction Fiber-reinforced polymer (FRP) composites have been proposed for use as prestressing tendons in concrete structures due to their high-strength, lightweight and noncorrosive properties since 1970s [1]. Currently, remarkable progress has been made in field applications of FRP tendons in North America, Europe, Japan, China and several other countries [2]. FRP tendons and concrete are both brittle materials, so the classical ductility which requires plastic deformation is difficult to obtain in FRP prestressed concrete members. One possible technique to improve the ductile behavior of FRP prestressed concrete members is by partially prestressing the concrete beams with addition of nonprestressed reinforcements [3]. Herein, the nonprestressed reinforcements could be selected as the (anticorrosive) steel rebars with obvious yield plateaus or the GFRP rebars with relatively high strain capacity. Experimental work showed that the nonprestressed reinforcements could enhance the ductility and reduce the crack spacing and crack width of FRP prestressed beams [4]. Page 1 of 8
Extensive research work on concrete beams prestressed with bonded FRP tendons have been carried out by researchers all over the world [2], in which some experimental programs were conducted to examine the cracking behavior of FRP prestressed concrete beams. Abdelrahman and Rizkalla studied the serviceability of concrete beams prestressed with Carbon Fiber-reinforced polymer (CFRP) tendons or conventional steel strands (without nonprestressed reinforcements) [5]. Test results showed that the stabilized crack pattern for beams prestressed with CFRP tendons occurred at a much lower strain level than for beams prestressed with steel strands. The number of cracks of beams prestressed with CFRP was less than that of comparable beams prestressed with steel strands due to the lower flexural bond strength of the CFRP tendons. Consequently, the crack width and spacing were typically larger for a given load level. Meng et al. compared the cracking patterns and crack widths of concrete beams with a combination of bonded CFRP tendons and steel/frp reinforcements [3]. It was concluded that the remarkable reduce of crack width could be found in the concrete beams with combined reinforcements. The crack widths in the prestressed concrete beams reinforced with FRP reinforcements were larger than the corresponding values in prestressed concrete beams reinforced with steel reinforcements for a given load level. The ACI 440 Committee developed equations for calculating the crack widths in concrete beams reinforced with FRP bars [6], while limited studies focused on the crack width predictions of concrete beams with a combination of bonded CFRP tendons and steel/frp reinforcements. This paper presents the experimental program to investigate the cracking behavior of concrete beams with combined reinforcements. In addition, a modified formula was provided for predicting the maximum crack width of concrete beams with a combination of bonded FRP tendons and steel/frp reinforcements. 2. Experimental work 2.1 Test Specimens A total of six concrete beams (denoted as PB1 to PB6, correspondingly) were cast and tested. Each beam had a cross section of 150 300 mm and a span of 3700 mm. The main experimental parameters included partial prestressing ratio (PPR), amount of prestressing CFRP strands, types of nonprestressed reinforcements, and jacking stress levels. Details of the specimens are given in Table 1 and Figure 1. Table 1. Details of specimens Specimens PB1 PB2 PB3 PB4 PB5 PB6 Tendons 1M12.5CFRP 1M12.5CFRP 1M12.5CFRP 1M12.5CFRP 2M12.5CFRP 2M12.5CFRP Jacking stresses 0.55f u 0.55 f u 0.55 f u 0.65 f u 0.55 f u 0.55 f u PPR 0.74 0.52 0.34 0.52 0.54 0.73 Initial prestress level 50.0% 50.2% 50.0% 59.2% 49.7% 49.9% Bottom longitudinal 2M10 2M16 2M19 2M16 2M22 2M14 reinforcements (Steel bars) (A b) (Steel bars) (GFRP bars) (Steel bars) (Steel bars) (Steel bars) Top longitudinal reinforcements 2M8 (Steel bars) (A t) Note: f u represents the ultimate tensile strength of CFRP tendons. Page 2 of 8
8@100 8@200 1 8@100 At 250 1300 1100 1300 3700 Configuration of reinforcing bars 1 Ab Ap 250 102 63 50 42 40 42 50 350 300 300 300 300 300 300 300 3700 Arrangement of tendons 63 102 300 300 300 350 135 Figure 1. Reinforcing details of specimens (mm) The measured compressive strength of the concrete cubes was 57.7 MPa at the time of testing. The average elastic modulus of concrete was 33.7 GPa, and the average tensile strength was 4.5 MPa. Mechanical properties for reinforcements are listed in Table 2. Note that the high strength CFRP strands used in this experimental program are carbon fiber composite cables (CFCC) produced by Tokyo Rope Mfg. Co. Ltd, Japan with measured ultimate strength of 2400 MPa and guaranteed tensile strength of 1868 MPa. The high strength CFRP strands are made up of seven wires that are twisted to allow better stress distribution through the cross section. The GFRP bars used in the tests were provided by Aslan company. Table 2. Mechanical properties of reinforcements Mechanical properties Conventional steel reinforcements Page 3 of 8 FRP bars/tendons M8 M10 M14 M16 M22 M19GFRP M12.5CFRP Yielding strength f y(mpa) 418.0 318.0 341.0 321.0 324.5 Ultimate strength f u(mpa) Modulus of elasticity E s(mpa) 541.0 471.0 513.0 498.0 481.0 698.5 2400 1.81 10 5 1.68 10 5 1.81 10 5 1.71 10 5 1.82 10 5 4.15 10 4 1.43 10 5 Elongation ratio 24.5% 20.0% 23.0 % 20.0% 23.0% 6.0% 1.5% 2.2 Testing and Measurements All beams were tested under four-point loading. A schematic and a view of the testing setup are shown in Figure 2. The load was applied at mid-span by a hydraulic actuator acting against a reaction frame. All beams were initially loaded in increments of 1 kn and then reduced to increments of 0.5 kn as failure approached. A displacement transducer located on each beam at mid-span was used to monitor the deflection. Two displacement transducers (one at each supporting end of the beam) were used to measure the vertical displacements. Fourteen strain gauges (five on each side, two on the top, and two on the bottom of the beams) were used to measure the bending strains throughout the vertical sections of mid-span. Four strain gauges on the bottom nonprestressing bars and four on the CFRP strands were used to measure the longitudinal strains. The strains and deformation readings captured and monitored using an automatic data acquisition system, namely, process board type IMP 35951B SOLARTRON INSTRUMENTS Ltd., U.K..
P P 100 1200 1100 1200 100 3700 Figure 2. Loading of specimens 2.3 Test results All specimens exhibited elastic characteristics before initial cracking of concrete. With increase of the vertical loads, short and fine flexural cracks initiated at constant moment regions. For all the specimens, initial cracking could be observed as the applied load increased up to about 0.22 to 0.30P u (P u was the ultimate loads of specimens). Increase in the cracking loads of approximately 50% occurred in beams prestressed with two CFRP tendons. As the vertical loads continued increased, the existing fine vertical cracks extended longer and wider and meanwhile a few new cracks could be observed at constant moment regions as well as bending shear regions. As the nonprestressing steel bars yielded (except PB3), which corresponded to a load level of 0.58 to 0.90P u, the measured maximum crack width was in the range of 0.20 to 0.30 mm and the maximum crack spacing ranged between 90 and 120 mm. Figure 3 shows the development of maximum crack width of specimens under the loading. P/kN 60 40 20 PB1 PB2 PB3 PB4 PB5 PB6 0 0 0.1 0.2 0.3 0.4 0.5 w /mm Figure 3. Load versus maximum crack width of specimens After yielding of nonprestressing steel bars (except PB3), deflections of mid-span and strains of CFRP tendons increased dramatically with little vertical load gain. When reaching the peak loads, a sudden drop could be seen in the load versus deflection curves of PB1 and PB4 due to the rupture of CFRP tendons, which indicated that the specimens failed in tension. However, obvious descending stages were observed in the load versus deflection curves of PB2, PB5 Page 4 of 8
and PB6 and the specimens failed in compression. Cracks continued to propagate upwards, and the crack width increased quickly for all specimens. In contrast, due to the linear elastic stress-strain relationship of GFRP bars, PB3 exhibited marked differences in the loading process. No obvious yielding stage could be observed after cracking and it behaved linearly with reduced stiffness till crushing of top concrete, which resulted in the failure of the specimen. Moreover, once the cracks appeared, they extended quickly in both width and height. Eventually, the values of crack width and spacing in PB3 were found to be significantly larger than the corresponding values in other specimens. A comparison of the measured load versus mid-span deflection curves of the six specimens is given in Figure 4. P/kN 60 40 20 PB1 PB2 PB3 PB4 PB5 PB6 0-20 0 20 40 60 100 120 Δ/mm Figure 4. Load versus deflection curves of specimens The load versus strain curves of CFRP strands are given in Figure 5. Seen from the figure, the tendons in the five specimens reinforced with steel bars behaved in a similar manner that two obvious points, which corresponded to first concrete cracking and yielding of steel reinforcements, respectively, were found during testing. In contrast, only one point corresponding to first concrete cracking was observed in specimen PB3 reinforced with GFRP bars. The reason was that GFRP bars behaved linearly elastic up to failure and had no yield point under tension. At ultimate, the tendon strain increments of the six specimens ( PB1 to PB6) were 8242, 6003, 6014, 6099, 4509 and 5381, respectively. The ultimate tensile strains for both beams PB1 and PB4 were much higher than the others and reached the value of 14000, which was close to the nominal ultimate tensile strains of CFRP strands. The ultimate tensile strains of the remaining four specimens ranged between 10509 and 12609. This was consistent with the conclusion that PB1 and PB4 failed due to rupture of CFRP tendon prior to concrete crushing. P/kN 60 40 20 0 PB1 PB2 PB3 PB4 PB5 PB6 0 3000 6000 9000 12000 15000 Strain developed in CFRP/με Figure 5. Load versus strain curves of CFRP strands Page 5 of 8
3. Crack Width Predictions The ACI 440 Committee recommended the Frosch equation for calculating the crack width of concrete beams reinforced with FRP bars [6]. The Frosch equation was derived based on a physical model, rather than being empirically derived [7]. With considering the different bond behavior of FRP reinforcements compared with steel reinforcements, a corrective coefficient for the bond quality was introduced by ACI 440.1R-06. For predicting the maximum side face cracks in concrete beams reinforced with FRP bars, the equation is given as follows: f 2 2 w 2 f kb dc ds E (1) f where w is the maximum crack width (mm); f f is the reinforcing stress (MPa); E f is the reinforcement modulus of elasticity (MPa); is the ratio of distances to neutral axis from extreme tension fiber and from centroid of FRP reinforcements; d c is the bottom cover measured from center of lowest bar (mm); and d s is the side cover measured from center of outmost bar (mm). The kb term is a coefficient that accounts for the degree of bond between FRP bar and surrounding concrete. For FRP bars having bond behavior similar to uncoated steel bars, the bond coefficient k is assumed equal to 1. b According to ACI 224R-01 [8], the expressions given for crack prediction in nonprestressed beams can be used to estimate the cracks for prestressed beams with considering the load increase above the decompression moment, i.e. prestressed member could be treated as a reinforced concrete member and the stress increments in reinforcements were applied in the calculation. For the concrete beams with a combination of FRP tendons and steel/frp rebars, the flexural cracking was mainly controlled by the outmost layer of nonprestressed reinforcements. So the maximum crack width of concrete beams with combined reinforcements can be predicted by: fnp 2 2 w 2 kb dc ds E (2) np where fnp is the magnitude of the tensile stress in the outmost layer of nonprestressed reinforcement in which the decompression load is taken as the reference point (MPa); Enp is the modulus of elasticity of the outmost layer of nonprestressed reinforcement (MPa); kb is the bond coefficient corresponding to the outmost layer of nonprestressed reinforcement. When a specific value of kb is not known for FRP reinforcing bar with sand coating, indents, sand-blasted surface and molded ribs to enhance bond with concrete, it is recommended to use a conservative value of 1.4 [6]. The value of kb could be taken as 1.5 for the epoxy coated steel bars based on the bond behavior tests [4]. The flexural crack width experiments of concrete beams with a combination of FRP tendons and steel/frp reinforcements are summarized in Table 3. The maximum crack widths of specimens were predicted by Eq. (2), and comparisons of the measured and calculated maximum crack widths are illustrated in Figure 5. Page 6 of 8
Table 3. Summary of flexural crack width experiments References No. Specimens FRP tendon Nonprestressed reinforcement Beam width (mm) Beam depth (mm) Beam span (mm) PPR Initial prestress level PB1 CFRP uncoated steel 150 250 3500 0.74 50.1% Experimental work in this paper PB2 CFRP uncoated steel 150 250 3500 0.52 50.2% PB3 CFRP GFRP bars 150 250 3500 0.34 50.0% PB4 CFRP uncoated steel 150 250 3500 0.52 59.2% PB5 CFRP uncoated steel 150 250 3500 0.54 49.7% PB6 CFRP uncoated steel 150 250 3500 0.73 49.9% BAS1-210 AFRP epoxy coated steel 150 2 30 0.40 45.4% BAS2-210A AFRP epoxy coated steel 150 2 30 0.57 44.8% BAS2-210B AFRP epoxy coated steel 150 2 30 0.57 44.9% BAS2-214 AFRP epoxy coated steel 150 2 30 0.46 45.1% Ref. [4] BAS3-210A AFRP epoxy coated steel 150 2 30 0.66 42.6% BAS3-210B AFRP epoxy coated steel 150 2 30 0.66 42.9% BAS3-314 AFRP epoxy coated steel 150 2 30 0.46 43.2% BAS4-206 AFRP epoxy coated steel 150 2 30 0.92 45.1% BAS4-210 AFRP epoxy coated steel 150 2 30 0.72 45.3% BAS4-214 AFRP epoxy coated steel 150 2 30 0.63 44.9% B1 CFRP uncoated steel 148 307 2472 0.60 33.1% Ref. [3] B2 CFRP CFRP bars 150 305 2472 0.33 19.9% B9 CFRP uncoated steel 149 300 2472 0.70 12.4% B10 CFRP CFRP bars 149 306 2472 0.44 42.0% Calculated maximum crack widths (mm) 0.6 0.5 0.4 0.3 0.2 0.1 0 Perfect Correlation Ref.[4] Ref.[3] This paper 0 0.1 0.2 0.3 0.4 0.5 0.6 Measured maximum crack widths (mm) Figure5. Comparisons of the measured and calculated maximum crack widths As can be seen from Fig. 5, Eq. (2) provides good predictions for the maximum crack width of concrete beams with combined reinforcements, and the mean errors are within 10%. It should be noted that the theoretical formula should be further verified due to a lack of available test data. Page 7 of 8
4. Conclusions (1) Test results showed that remarkable reduce of crack width could be found in the concrete beams with combined reinforcements. The crack widths in the prestressed concrete beams reinforced with FRP reinforcements were larger than the corresponding values in prestressed concrete beams reinforced with steel reinforcements for a given load level. (2) Based on Frosh crack width equation, a modified formula was provided for calculating the maximum crack width of concrete beams with a combination of bonded FRP tendons and steel/frp reinforcements. Acknowledgements The authors acknowledge the supports of Fund of Western Communications Construction Scientific and Technological Project by the Ministry of Communications of the P.R. China (No.200631882244) and the Fund of National Natural Science Foundation of China (No. 50978193). References [1] REHM, G., FRANKE, L., Plastic Bonded Fiberglass Rods as Reinforcement for Concrete, Bautechnik, Ausgabe A, Vol. 51, No. 4, Apr. 1974, pp.115-120. [2] ACI COMMITTEE 440, Prestressing Concrete Structures with FRP Tendons (440. 4R-04), American Concrete Institute, Farmington Hills, Mich., 2004, 35 pp. [3] MENG, Y., GU, X. L., ANSARI, F., Calculation Method for the Bending Capacity of Concrete Beam Reinforced by CFRP Bars, Proceedings of the International Conference on FRP Composites in Civil Engineering, Vol. Ⅱ, CICE, Hong Kong, China, 2001, pp. 1161-1168. [4] MENG, L. X., TAO, X. K., GUAN, J. G., XU, F. Q., Experimental Study on Flexural Behavior of Partially Prestressed Concrete Beams with Bonded AFRP Tendons, China Civil Engineering Journal, Vol. 39, No. 3, Mar. 2006, pp.10-18, 36. (in Chinese) [5] ABDELRAHMAN, A., RIZKALLA, S., Serviceability of Concrete Beams Prestressed by Carbon Fiber-reinforced-plastic Bars, ACI Structural Journal, Vol. 94, No. 4, Jul.-Aug. 1997, pp. 447-457. [6] ACI COMMITTEE 440, Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06), American Concrete Institute, Farmington Hills, Mich., 2004, 44 pp. [7] FROSCH, R. J., Another Look at Cracking and Crack Control in Reinforced Concrete, ACI Structural Journal, Vol. 96, No. 3, May-June 1999, pp. 437-42. [8] ACI COMMITTEE 224, Control of Cracking in Concrete Structures (ACI 224R-01), American Concrete Institute, Farmington Hills, Mich., 2001, 46 pp. Page 8 of 8