CICE 2010 - The 5th International Conference on FRP Composites in Civil Engineering September 27-29, 2010, Beijing, China
Deflection Behaviour of Concrete Beams Reinforced with Different Types of GFRP Bars S. El-Gamal, B. AbdulRahman, & B. Benmokrane (
[email protected]) NSERC Research Chair, Department of Civil Eng., University of Sherbrooke, Sherbrooke, Quebec, Canada
ABSTRACT GFRP bars are non noncorrosive reinforcing materials having relatively lower tensile modulus compared to steel. The design of flexural concrete members reinforced with GFRP bars are usually governed by serviceability limits, deflection, and crack width. This paper describes an experimental study conducted to investigate the deflection behavior of concrete beams reinforced with GFRP bars. The bars came from three different manufacturers. A total of 8 beams measuring 4250 mm long ×200 mm wide×400 mm deep were built and tested up to failure under four-point bending. The study’s main parameters were reinforcement type (GFRP and steel) and amount (three reinforcement ratios). The midspan deflection of all the beams tested were recorded and compared. The test results were used to assess the equations in different FRP codes and guidelines. KEY WORDS
1
INTRODUCTION
GFRP reinforcing bars offer advantages not available with steel reinforcement due to their noncorrosive nature and magnetic transparency. Special considerations should be made in the design of GFRP reinforcing concrete members resulting from the relatively lower modulus of elasticity of GFRP bars compared to steel bars. As a result, GFRP-reinforced concrete members after cracking have relatively less stiffness than steelreinforced members. Consequently, deflection and crack width calculations under service loads usually govern the design. North American codes and guidelines for designing FRP-reinforced concrete require that deflection be computed. The deflection calculation of flexural members provided in these codes are mainly based on equations derived from linear elastic analysis using an effective moment of inertia, Ie, given by Branson’s formula, first published in 1965. Many researchers have suggested different modifications to Branson’s equation to make it more suitable for FRP- reinforced concrete members. This paper presents an experimental investigation into the deflection behavior of concrete beams reinforced with different types and ratios of FRP bars. In addition, the deflection equations provided in CSA S806-2002, ACI 440.1R-2006, and the ACI 440-2010 ballot were evaluated.
2 CURRENT DEFLECTION PROVISIONS 2.1
CAN/CSA S806-02
Clause 8.3.2 in the CAN/CSA S806-02 (CSA S806 2002) states that deflections that occur immediately on
application of load shall be computed by methods based on the integration of curvature at sections along the span. The moment–curvature relation of FRP reinforced concrete members shall be assumed to be tri-linear with the slope of the three segments being EcIg, zero, and EcIcr. For the case of two-point loading of P/2 on a simple span, L, with a shear span, a, the deflection is calculated according to Eq. 1. PL3 48 Ec I cr
G max
§ I cr ¨I © g
K 1 ¨
3 3 ª §a· §L · º §a· «3 ¨ ¸ 4 ¨ ¸ 8K ¨ g ¸ » © L¹ «¬ © L ¹ © L ¹ »¼
· ¸¸ ¹
(1a)
(1b)
where Gmax is the midspan deflection (mm), L is the span (mm), a is the shear span (mm), Ec is the modulus of elasticity of concrete (MPa), Icr is the moment of inertia of cracked section transformed to concrete (mm4), and Lg is the uncracked length (mm). 2.2
ACI 440.1R-06
ACI 440.1R-06 uses an effective moment of inertia formulation, Ie, to compute the deflection of cracked FRP-reinforced–concrete beams and one-way slabs based on an empirical expression originally developed for steel-reinforced concrete. The procedure entails calculating a uniform moment of inertia throughout the beam length and uses deflection equations derived from linear elastic analysis. The effective moment of inertia, Ie, is based on semi-empirical considerations and, despite some doubt about its applicability to conventional reinforced-concrete members subjected to complex
L. Ye et al. (eds.), Advances in FRP Composites in Civil Engineering © Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 2011
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loading and boundary conditions, it has yielded satisfactory results in most practical applications over the years. ACI 440.1R-06 uses Eq. 2 to calculate the deflection of FRP-reinforced concrete members: Ie
Ed
3 ª § M ·3 º § M cr · cr ¨ ¸ E d I g «1 ¨ ¸ » I cr M M « a © a ¹ © ¹ »¼ ¬
1§ Uf · ¨ ¸ d1 5 ¨© U fb ¸¹
ACI 440 2010 ballot
J
I cr 2
§M · ª I º 1 J ¨ cr ¸ «1 cr » © M a ¹ «¬ I g »¼
d Ig
1.72 0.72( M cr / M a )
(3a)
(3b)
All parameters are as in Eq. 2. 2.4 Materials Three different types of GFRP bars referred to as GFRP-1 (V-ROD Standard) (#5, #6, and #7), GFRP-2 (#5) (Aslan-100) and GFRP-3 (#5) (Combar), — manufactured by Pultrall, Hughes Brothers, and Schöck respectively—were used. Figure 1 shows the three types of GFRP bars used in this study. No. 15M steel bars were used in one beam for comparison.
Modulus of Elasticity (GPa)
Guaranteed Strength+ (MPa)
16
200
200
fy* = 453
#5
16
199
48.1
684
#6
19
284
47.6
656
#7
22
387
46.4
693
GFRP-2
#5
16
199
41.2
660
GFRP-3
#5
16
199
60.0
1130
*
fy is the yield strength of the steel bars. + Average tensile strength – 3 times the standard deviation.
2.5
Beam specimens and test setup
Eight full-scale concrete beams, measuring 4250 mm longu200 mm wide u 400 mm deep (see Figure 1), were constructed. All the beams were reinforced in the compression side with two steel bars (I 10 mm). On the tension side, the beams were reinforced with different types and numbers of reinforcing bars. The beams were divided into four groups. Each group was designed to investigate one parameter among 1) bar type, 2) reinforcement ratio with a similar bar diameter and different spacing, 3) reinforcement ratio with different diameters and similar spacing, and 4) beams of similar axial stiffness (see Table 2). Table 2 Test matrix Group 1
3
Figure 1 The three types of GFRP bars used in the study 4
No. of Area U Bars (mm2) (%)
Parameter
ID
Type of Bars
Type of reinf.
G-V-3#5
GFRP-1
3#5
594
0.84
G-A-3#5
GFRP-2
3#5
594
0.84
G-Co-3#5 GFRP-3
3#5
594
0.84
3#5
600
0.84
St-3#5 2
The mechanical properties of the FRP reinforcement bars were determined by tensile testing of representative specimens in accordance with ACI 440 3R-04. Table 1 summarizes these properties. Based on the values of modulus of elasticity, the three tested types of GFRP bars were classified as Grade I (GFRP-1 and GFRP-2) and Grade III (GFRP-3) according to the new CSA S807-09 (2010) specification for fibre-reinforced polymers. Grade I requires a minimum modulus of elasticity of 40 GPa, while Grade III requires 60 GPa.
Area
15M
GFRP-1
(2b)
db
(mm) (mm2)
(2a)
Based on the work of Bischoff and Scanlon (2007), a ballot taken by ACI 440 Committee (February 2010) proposed using Eq. 3 to calculate deflection: Ie
Bar Type
Steel
where Ie is the effective moment of inertia (mm4), Mcr is the cracking moment (N mm), Ma is the applied moment (N mm), Ig is the moment of inertia of gross section (mm4), and Uf and Ufb are the actual and balanced reinforcement ratio, respectively. 2.3
Table 1 Mechanical properties of the reinforcing bars
Steel
Reinf. Ratio G-V-2#5 (same G-V-3#5 diameter) G-V-4#5
GFRP-1
Reinf. Ratio G-V-2#5 (different G-V-2#6 diameters) G-V-2#7
GFRP-1
G-V-3#5
GFRP-1
Similar axial stiffness
2#5
396
0.56
3#5
594
0.84
4#5
792
1.12
2#5
396
0.56
2#6
570
0.81
2#7
776
1.11
3#5
594
0.84
G-V-2#6
2#6
570
0.81
G-V-4#5
4#5
792
1.12
G-V-2#7
2#7
776
1.11
Five linear variable displacement transducers (LVDTs) were installed on each beam to measure deflections at different beam locations (Figure 2). In addition, one high-accuracy LVDT was installed at the position of the first crack to measure crack width. Furthermore, several electrical-resistance strain gauges were used to measure
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strain in the reinforcing bars and at the top surface of the concrete. All beams were tested under four-point bending. The load was monotonically applied with a displacement control rate of 1.2 mm/min. During loading, crack formation on the side surface of the deck slabs were marked and recorded. Figure 2 illustrates the test setup, while Figure 3 is a photo of a beam during testing.
Figure 4 Load–midspan deflection of beams in group 1
Figure 2 Dimensions and instrumentation of tested beams
Figure 5 Load–midspan deflection of beams in group 2
Figure 6 Load–midspan deflection of beams in group 3 Figure 3 View of beam during testing (Beam G-V-2#7)
3 TEST RESULTS AND DISCUSSION 3.1
Load–deflection curves
The experimental load to midspan deflection curves of the steel and GFRP reinforced concrete beams are presented in Figures 4 to 7. Each curve represents the average of two deflection readings obtained from two LVDTs at beam midspan. The load–midspan deflections curves were bilinear for all FRP-reinforced beams. The first part of the curve up to cracking represents the behavior of the uncracked beams. The second part represents the behavior of the cracked beams with reduced stiffness. The cracking loads for all FRP-reinforced beams ranged from 15 to 20 kN. The value was slightly higher for the steel-reinforced beam: 26.3 kN. For the beams in group 1, the GFRP-reinforced
Figure 7 Load–midspan deflection of beams in group 4
concrete beams evidenced wider cracks than the steelreinforced concrete beam. Consequently they exhibited greater midspan deflections (see Figure 4). It can also be seen that, as the modulus of elasticity of the GFRP bars decreased, the reinforcement’s axial stiffness decreased, leading to increased midspan deflections. At 35 kN— about twice the cracking load—the midspan deflections
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were 3.6, 11.7, 10.6, and 8.8 mm for beams St-3#5, G-A-3#5, G-V-3#5, and G-Co-3#5, respectively. Figure 5 and 6 show that, for the same type of bars, the midspan deflection increased as the reinforcement ratio decreased. Increasing the reinforcement ratio, however, increased the ultimate capacity of the beams. At about twice the cracking load, increasing the tensile reinforcement from 2 #5 bars to 3 and 4 #5 bars decreased the midspan deflection from 12.5 to 10.6 and to 6.3 mm, respectively. For the beams in group 3, increasing the reinforcement from 2 #5 bars to 2 #6 and to 2 #7 bars decreased the midspan deflection from 12.5 to 9.5 and 8.2 mm, respectively. Figure 7 shows a comparison between midspan deflections of two pairs of beams whose tension reinforcement evidenced similar axial stiffness (G-V-3#5 and G-V-2#6) and (G-V-4#5 and G-V-2#7). Beams G-V-3#5 and G-V-2#6 had similar load–midspan deflection up to failure. Beam G-V-4#5, however, showed less midspan deflection than beam G-V-2#7. This indicates that using more bars of smaller diameter was more efficient than a smaller number of larger bars. This phenomenon could be explained by enhanced bond, better cracking performance by lowering reinforcement spacing, and the higher tension stiffening provided by FRP bars of smaller diameter. These factors contributed to beam stiffness, which was evidenced in lower mid-span deflection. 3.2 Predicted Deflections Table 3 shows a comparison between the midspan deflections of the tested beams and those predicted from Eqs. 1, 2, and 3. The accuracy of the calculated cracking moment, Mcr, is key to the accuracy of the deflection calculations. The controlling variable for predicting cracking moment is the modulus of rupture of concrete, fr. The modulus of rupture used to calculate the Mcr in Eqs. 1, 2, and 3 was taken from the corresponding code or guideline as given below in Eq. (4): For Eq. 1,
fr
For Eqs. 2 and 3,
0.6O f c' fr
(4a)
0.62O f c'
(4b) ' c
where fr is the modulus of rupture (MPa); f is the concrete compressive strength (MPa); and O is a factor accounting for concrete density. For normal-density concrete, O = 1. The moment due to beam self-weight (3.17 kN·m) was included in the analysis. Table 3 shows that, at 1.2 Mcr (applied moment right after cracking) and at 2.0 Mcr (around the service-load level), Eq. 1 (the CSA/S806 equation) gave very good yet conservative predictions of deflection compared to the measured values. Equations 2 and 3 (the current ACI 440.1R-06 equation and that proposed by ACI 440), however, underestimated deflection at 1.2 Mcr and 2.0 Mcr.
Table 3 Experimental and predicted deflections Beam ID
G-V-3#5 G-A-3#5 G-Co-3#5 G-V-2#5
Measured Midspan Deflection, (mm)
Predicted Midspan Deflection, (mm) Eq.1 Eq.2 Eq.3 (Pred./Exp.) (Pred./Exp.) (Pred./Exp.)
2 1.2 1.2 Mcr* Mcr* Mcr*
2 Mcr*
1.2 Mcr*
2 Mcr*
8.5
17.2
17.5
5.9
15.3 3.95 13.17
8.7
19.3 10.1 19.5
9.1
1.2 Mcr*
2 Mcr*
(1.07) (1.02) (0.69) (0.89) (0.46) (0.77) 5.6
16.2 4.31 14.6
(1.16) (1.01) (0.64) (0.83) (0.50) (0.76) 6.6
13.7
6.9 13.3 3.3 10.4 3.18 10.12 (1.05) (0.97) (0.5) (0.76) (0.48) (0.74)
9.7
21.5 13.0 25.2
8.7
22.3 5.36 18.73
(1.34) (1.17) (0.90) (1.04) (0.55) (0.87) G-V-4#5
4.6
11.1
G-V-2#6
6.9
17.3
6.1 13.3 3.9 11.2 4.31 9.53 (1.32) (1.20) (0.85) (1.01) (0.94) (0.86) 8.6
17.8
5.3
15.0 2.71 12.47
(1.24) (1.03) (0.77) (0.87) (0.39) (0.72) G-V-2#7
5.6
15.0
Average (Pred./Exp.)
6.7
13.7 3.9 11.5 2.27 9.73 (1.19) (0.91) (0.70) (0.77) (0.41) (0.65) 1.19 1.04 0.72 0.88 0.53 0.77
* For comparison, Mcr was taken as the average experimental value from all beams (17 kN·m – without Mself weight).
4 CONCLUSIONS The use of smaller-diameter GFRP bars yielded better deflection enhancement than larger-diameter bars for the same reinforcement ratio. Higher beam stiffness was observed when increasing the reinforcement ratio, either by using more bars or larger-diameter bars. In terms of deflection prediction, CAN/CSA S806-02 showed very good agreement with the experimental results for the three types of GFRP bars. Based on the comparison at 1.2 Mcr and 2.0 Mcr, both ACI.440.1R-06 and ACI 440 ballot underestimated the deflection values, although the former gave a better prediction.
REFERENCES ACI 2006. ACI 440.1R-06: Guide for the design and construction of concrete reinforced with FRP bars, American Concrete Institute, Farmington Hills, Michigan, USA. CSA 2002. Standard CAN/CSA-S806-02: Design and Construction of Building Components with Fibre-Reinforced Polymers, Canadian Standards Association, Toronto, Ontario. CSA 2010. Standard CAN/CSA-S807-09: Specification for FibreReinforced Polymers, Canadian Standards Association, Toronto, Ontario. Bischoff, P.H., and Scanlon, A. 2007. Effective Moment of Inertia for Calculating Deflections of Concrete Members Containing Steel Reinforcement and FRP Reinforcement, ACI Structural Journal, V. 104, No. 1, pp. 68–75.
