I-Beam Reinforced with Carbon Fiber Reinforced

THE 7TH ASIA PACIFIC YOUNG RESEARCHERS AND GRADUATES SYMPOSIUM “Innovations in Materials and Structural Engineering Practices”

Evaluation of Deflection in High Strength Concrete (HSC) I-Beam Reinforced with Carbon Fiber Reinforced Polymer (CFRP) Bars A.M.I. Said1, O.M. Abbas2 1 Professor, Dr., University of Baghdad, Iraq 2 Lecturer, Dr., University of Kufa, Iraq +964-7901423189, [email protected]

ABSTRACT In although many experimental investigations were conducted on FRP reinforced concrete beams with rectangular section, there has been very little research into the behavior of concrete flanged beams reinforced with FRP bars. This study aims at investigating the deflection of HSC I-beams reinforced with CFRP bars, both experimentally and analytically. At the service load level, most of the previous theoretical approaches underestimate the deflection. So, this paper reassess most of the previous models and propose a new approach for deflection prediction. A new equation for estimating the effective moment of inertia of CFRP reinforced concrete beam based on the analytical and experimental results was proposed. In the experimental part of the study, eight I-beam specimens were manufactured and tested. The effects of reinforcement ratio and the level of loading on the effective moment of inertia are taken into account. The proposed equations are compared with different code provisions and previous models for predicting the deflection of FRP reinforced concrete beams. Keywords CFRP, Deflection, Experimental, HSC, I beam, Strengthened

1. INTRODUCTION The Recently, composite materials made of fibers embedded in a polymeric resin, also known as FRPs, have become an alternative to steel reinforcement for concrete structures. Because FRP materials are nonmagnetic and noncorrosive, the problems of electromagnetic interference and steel corrosion can be avoided with FRP reinforcement. The most common types of fibers used in advanced composites for structural applications are the glass (GFRP), aramid (AFRP), and carbon (CFRP). The GFRP is the least expensive but has lower strength and significantly lower stiffness compared to other alternatives. CFRP is the stiffest, most durable, and the most expensive one. FPR bars present different surface conditions such as sand coated, ribbed, indented or braided. When FRP bars are used, different structural behavior is expected due to their different mechanical and bond properties compared with those of steel rebars, in particular, their relatively low modulus of elasticity and their linear stress-strain behavior until failure. The lower stiffness of FRP bars can yield to large strains being mobilized in the bars at low levels of external loads and lead to large crack widths and deflections. As a result, the design of concrete elements reinforced with FRP materials is often governed by the serviceability limit states (SLS). In the last two decades, a number of studies were carried out to investigate the flexural response of FRP RC beams. In the case of serviceability, and specifically for deflections of FRP RC elements, several authors propose coefficients to modify Branson’s equation used in concrete design codes (ACI Committee 318 2005), whereas other researchers suggest a modified equivalent moment of inertia derived from the integration of curvatures along the beam. These different approaches have been 519


adopted in the various design guideline proposals for FRP RC (ISIS Canada 2001, CAN/CSA 2002, ACI Committee 440 2006, fib 2007).

2. TEST SPECIMENS The beam types were identified using two terms. The first term, alphabetic term, of the identification corresponded to a beam group. CFB for beam group of CFRP rebars, and DCFB for beam group of double reinforced CFRP rebars. The ‘D’ letter of the beam notation stands for the double reinforcements. The ‘CF’ letters identify the type of longitudinal reinforcement: ‘CF’ for CFRP rbars. The ‘B’ letter refers to the type of the structural element, (Beam element). The second term, numerical term, represent beam series. For each beam group, beams of series 1 were designed to have a similar load-carrying capacity of approximately P=100 kN; while, beams of series 2,3, and 4 were designed to have load carrying capacities of approximately 130 kN, 150 kN, and 165 kN, respectively. A total of eight I-beams divided into two test groups (CFB, and DCFB group), were fabricated and tested under static loading conditions to determine the different limit state behavior including ultimate and mode of failure of HSC I-beams reinforced with CFRP bars, see (Fig. 1).

Figure 1. Eight HSC I-beams reinforced with CFRP bars The total length of each beam is 2440 mm, with an I- cross-section of bf = 150 mm (top and bottom flange width); H=300 mm (overall height); bw = 150 mm (width of the web); hf = 40 mm (top flange thickness); hfb = 50 mm (bottom flange thickness). The specimens were tested under two-point loading, with 2100 mm total span, and 800 mm shear span, the distance between loads being 500 mm, see (Fig.2).

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Figure 2. Beam tests layout and internal reinforcement details Each of the beams was instrumented with external strain gauges to measure strain at different level of beams height. In order to measure the deflection of the tested beams, a minimum of three vertical dial gauges were used: one at the mid-span section, and two more vertical dial gauges were added at the shear span, at 525 mm from the supports, see (Fig. 3).

Figure 3. Strain gauges on the concrete surface of the mid-span section The target concrete strength for all test specimens was 50 MPa. The shear span was reinforced with an amount of steel stirrups enough to avoid shear failure. The geometric characteristics of the different sections are summarized in (Fig. 4).

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Beam Designation Ratio of *

CFB1

CFB2

CFB3

CFB4

DCFB1 DCFB1 DCFB3 DCFB4

0.83 1.24 1.65 2.06 0.77 1.16 1.55 1.93 * is the ratio of (CFRP) reinforcement area to the balanced reinforcement area.

Figure 4. Geometric characteristics of specimen sections (Section at shear span) After some different concrete trial mixes, the used mixture was designed with the requirements of Silica Fume Association 2005. The mixture proportions and tested concrete cylinder results are listed in Table-1. For each group of specimens, cylinders, cubes, and prisms were cast, cured, and tested at the same time with the I-beam specimens to find mechanical properties of concrete.

Table 1. Mixture proportions and compressive test of cylinders for Used Mixture MATERIAL CONCRETE ( 1m3) TESTED AT 28 DAYS Cement (kg) Silica fume (kg) [Silica/Cement %] Water (Liter) HRWRA (Glenium 51) (Liter) Air content % Coarse Aggregate-12.5mm (kg) Fine Aggregate (kg) [ ]

495 79 [16%] 149 7.9 2 990

Compressive strength (MPa) 100x200mm cylinder test 59.02 MPa 57.92 MPa 65.45 MPa Average (MPa) 60.8 (MPa)

644 [39%]

According to ASTM C39

w/cm

0.26

522


3. TEST PROCEDURE All I-beam specimens were tested under a static two-point load test. A hydraulic jack with a capacity of 2000 kN was used to apply the load to the test beam through a spreader steel beam. The load was applied in load control mode at a load rate of 4 kN/min, and the strain gauges data were collected by a data acquisition system. The test was stopped every 5 kN to register the evolution of cracks, strains and the deflections along the beam.

4. PREDICTION MODELS FOR DEFLECTIONS Most of the prediction models to calculate the flexural deflection of a FRP RC element can be classified in those derived from Branson equation and from those where deflection is calculated as an interpolation between a cracked and an uncracked state of a deformation parameter (curvature or deflection). Some of the existing design guidelines for FRP RC adopted these approaches in their methodology to calculate deflections (ISIS Canada (2001), ACI Committee 440 (2006)). In this study, the experimental load-midspan deflection is compared to ACI440.1R-06, Hall and Ghali (2000), Mousavi and Esfahani (2012), EC2(CEN 1992), H.A. Abdalla (2002), ISIS Canada (2001) and Rafi and Nadjai (2009) equations. The formulation for the considered analytical approaches is presented in Table 2.

5. MODELS BASED ON BRANSON EQUATION In Figs.5-a to 5-h, an experimental versus theoretical load-midspan deflection response for the tested Ibeams reinforced with different reinforcement ratios is shown for the prediction models for FRP RC elements derived from Branson equation, (ACI 440.1R-06, Rafi and Nadjai (2009) and Mousavi and Esfahani (2012)). For comparison purposes, in each presented figure, two light center lines represent -Iun: uncracked-state deflection; -Icr: cracked-state deflection has been depicted. General forms of the effective moment of inertia are the same in the models suggested by ACI 440.1R-03, Yost et al. (2003) and ACI 440.1R-06. The parameter (d) accounts for the bond properties and modulus of elasticity of FRP bars in the ACI 440.1R-03 equation. In this parameter, (Ef) is the elastic modulus of the FRP bars; (Es) is the elastic modulus of the reinforcing steel bars and (b) is a bond-dependent coefficient. According to the ACI 440.1R-03 code, the value of (b) can be taken as 0.5 for all FRP bars. Based on the results of 48 GFRP reinforced concrete beam specimens tested by Yost et al. (2003), (b) must be significantly reduced to below the value of 0.5 recommended by ACI 440.1R-03. The results also show that this parameter depends on (f/fb); see Table 2.

Table 2. Different equations for the effective moment of inertia of FRP RC beams Reference Model Faza and Ganga Rao (1992) Al-Shaikh and Al-Zaid (1993) Benmokrane et al. (1996) Alsayed et al. (2000)Model B Hall and Ghali (2000)

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ISIS Canada (2001) H.A. Abdalla (2002)

ACI 440.1R-03

Yost et al. (2003)

ACI 440.1R-06 Bischoff (2005; 2007)

Rafi and Nadjai (2009)

Bischoff and Gross (2011a; 2011b)

S. Roohollah. Mousavi, and M. Reza. Esfahani (2012)

Based on an evaluation of experimental results from several studies, a new expression for (d), based on the relative reinforcement ratio, is given by ACI 440.1R-06 as shown in Table 2. A modification to the ACI 440.1R-06 method for calculating the effective moment of inertia was proposed by Rafi and Nadjai (2009) for all types of FRP bars. In this model, the coefficient (d) is similar to the expression used by the ACI 440.1R-06 code. The coefficient γ is a relation obtained by linear regression analysis of the test results. Mousavi, and Esfahani (2012) based on experimental results and Branson’s equation, proposed new equations for the effective moment of inertia in concrete beams reinforced with FRP bars. The equations were obtained so that the differences between the experimental responses and the calculated values are minimized by genetic algorithm optimization. For specimens which have a high relative reinforcement ratio, the results of the proposed model A, (see Table 2), were more reliable than those of model B. The results of model B were more accurate than those of model A in specimens having relative reinforcement ratios (f/fb) which are less than one. The three analytical approaches reduce (Ig) once the section attained the cracking load, and the interpolation between moments of inertia is consequently made between (Icr) and (d Ig) (ACI 440.1R-06), (Icr/) and (d Ig) (Rafi and Nadjai (2009)) and (0.89Icr) and (0.15Ig) (Mousavi and Esfahani (2012)). 524


It is observed that Mousavi and Esfahani and Rafi and Nadjai approaches give higher deflection than the experimental one, while ACI 440.1R-06 approach under-estimates the deflection when compared with the experimental deflection, especially for high reinforcement ratios.

6. MODELS BASED ON INTERPOLATION OF CURVATURES OR DEFLECTIONS In Figs.5-a to5-h, the approaches for the calculation of deflections based on interpolation of curvatures or deflections are compared to the experimental results, (Hall and Ghali (2000), EC2(CEN 1992), H.A. Abdalla (2002) and ISIS Canada (2001)). EC2 (CEN 2004) formulation evaluates deformations by interpolating between a cracked and an uncracked state. The deformations can be curvatures or directly deflections. According to EC2 (CEN 1992) approach, (1) is equal to 1.0 for high bond and (2) is equal to 1.0 for short-term loading. Hall and Ghali (2000) proposed an expression similar to that of ISIS Canada Design Manual 3 (2001). In these models, (IT) and (Icr) are the moments of inertia for un-cracked and full cracked transformed sections, respectively; (1) is the coefficient characterizing the bond properties of the reinforcing bars and is equal to 1.0 for ribbed bars, (0.5 for smooth bars) and (2) is the coefficient representing the type of loading and is equal to 0.8 for first loading., (0.5 for sustained or cyclic loading). ISIS Canada (2001) suggests a similar approach to Bischoff (2005) and EC2. The equation was originally intended for beams subjected to sustained or cyclic loading and includes a factor (=0.5) that shifts horizontally the deflection response just after the cracking load is attained.

Fig. 5-a Load-Deflection (CFB1)

Fig. 5-b Load-Deflection (CFB2)

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Fig. 5-c Load-Deflection (CFB3)

Fig. 5-d Load-Deflection (CFB4)

Fig. 5-e Load-Deflection (DCFB1)

Fig. 5-f Load-Deflection (DCFB2)

Fig. 5-g Load-Deflection (DCFB3)

Fig. 5-h Load-Deflection (DCFB4) 526


Abdalla (2002) tested 15 different concrete members (beams and slabs) reinforced with CFRP and two types of GFRP bars. Experimental deflections were used to evaluate various models of deflection calculation. According to Abdalla (2002), the ACI 440.1R-03 guidelines for design of FRP reinforced concrete members under estimate deflections when compared to the measured values, and this agrees with the results of the present study. In Figs.5-a to 5-h, results show that these approaches compare relatively well with the experimental data in the range of the serviceability loads. However, a tendency to underestimate deflections when the load increases is observed; this is similar to the behavior observed in ACI 440.1R-06. Abdalla (2002) has the closest results to the experimental results, and has little underestimation to the deflection.

7. PROPOSED MODEL BASED ON INTERPOLATION OF DEFLECTIONS In Figs.5-a to 5-h, especially for high reinforcement ratios ( >1.4fb), it is observed that the effective moment of inertial, (Ie) fall below the calculated cracked moment of inertia (Icr). Reducing the value of (Icr), however, implies obtaining more deformation than that calculated considering that the element is fully cracked. Therefore, it implicitly adds a percentage of deflection that may be justified because the materials lose their linearity, and this is observed by different researchers; (Benmokrane et al. (1996), Rasheed et al. (2004), and Rafi and Nadjai (2009)). Since Abdalla (2002) gives best prediction for deflections, comparing to other approaches, the proposed equation of (Ie) would follow the same steps followed by Abdalla, when he derived his formula, with some reasonable modifications. Abdalla modelis based on interpolation of deflections and starts with the following equation of deflection: (1) For simple bending, (2): deflection for fully cracked state, (1): deflection for uncracked state and the coefficient ( '') can be taken as 0.5 for most practical applications as was suggested by Hall and Ghali. It has to be noted that in Eq. (1), the expression represents the tension stiffening for concrete structures reinforced with conventional steel, Abdalla (2002). In ACI440.1R-06 and other approaches, the tension stiffening is assumed to be directly proportion to rather than

. Therefore, the first modification was replacing

by

to get;

(2) since, (3)

Where, (K) is a factor depending on loading and boundary conditions of the member and can be determined from elastic analysis; (L) is the span of the member; and (Ec) is the modulus of elasticity of concrete. Therefore, Eq. (2) can be rewritten in the following form:

(4)

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Therefore,

(5)

Since, (Ie) fall below the calculated cracked moment of inertia (Icr). The second modification was reducing the value of (Icr) to (Icr/j), and rearranging Eq.(5) leads to:

(6)

The experimental results of deflection show that the reduction in the value of (Icr) depends on the reinforcement ratio. Therefore, the (j) value should be calculated, for each reinforcement ratio (Af/Afb), so that it gives best agreement between experimental and theoretical deflection results. To do so, the experimental effective moment of inertia should be calculated from the following equation, (for beam in a two-point load system);

(7)

Where (L) is the span of the beam and (Pexp) is the total concentrated load divided into two concentrated loads (Pexp/2), each applied at a distance (La) from the support; (Ec) is the modulus of elasticity of concrete. The relations between the applied loads, (i.e. applied moments), and experimental effective moment of inertia (Ie,exp), for each tested specimen (i.e. different reinforcement ratio), were depicted in Figs. 6-a to 6-h. The best fit equation was Eq. (6) with the unknown coefficient (j), which should be determined. The coefficients of determination (R2), between the experimental data and the proposed equation of effective moment of inertia, were ranging from 82% to 98% with mean of 91%. The coefficient (j) is collected from each chart in Figs. 6-a to 6-h, and a new graph that represents the relation between (Af /Af b) and (j) values is drawn as shown in Fig.7. A linear equation is assumed to fit the data of (Af /Af b) vs. (j) coefficients. Therefore, the linear regression equation has the following form; (8)

Here, j is equal to 1.14 for all values of (Af /Af b) greater than 2, and is equal to 0.94 for the case of (Af/Af b) is less than 0.5.

528


6.a)

vs.

(CFB1); coefficient j=0.951

6.b)

vs.


6.c)

vs.


6.d)

vs.


6.e)

vs.

(DCFB1); coefficient j=0.980

6.f)

vs.

(DCFB2); coefficient j=1.046 529


6.g)

vs.


Figs. (6.a to 6.h) Best fit for

6.h)

vs.

vs.


to determine j coefficient.

The mid-span deflections of CFRP reinforced specimens were calculated using proposed effective moment of inertia in Eq. (6) and with j coefficient in Eq. (8). The results were compared with the experimental one, as shown in Figs. 5-a to 5-h, which show very good agreement between them.

Fig. 7 Linear regression of reinforcement ratios vs. j-coefficients.

530


8. ANALYSIS OF THE EXPERIMENTAL VERSUS THEORETICAL MODELS In this section, a measure of the relative fitting between the experimental and the theoretical deflections is presented. The ratio theoretical vs. experimental deflection ( ) is depicted depending on the (Af /Af b) parameter for the different studied theoretical approaches in Fig. 8-a to 8-d. The outcome is depicted for a moment ratio of 1.6, 3 and 4.2. This last value is considered a reasonable upper bound limit of the serviceability conditions.

a)

c)

ACI440.1R-06.

b)

ISIS (2001).

Fig. 8 Ratio

d)

depending on

EC2 (CEN 1992).

Proposed.

for different approaches

Results show that at the moment ratio of =1.6 ACI440.1R-06, ISIS (2001) and EC2 (CEN 1992) approaches clearly underestimate the experimental deflection. This behavior is especially observed for EC2 (CEN 1992) prediction model. As the ratio approaches to 3 and 4.2, the ratio gets closer to the unity for all the studies, showing a better fit to the experimental data at these stages of loading. 531


9. SUMMARY AND CONCLUSIONS FRPs present different mechanical properties than that of steel. FRP characteristics have a direct effect on the flexural behavior of FRP RC under flexural stresses, generally leading to higher deflections and crack widths than that of steel RC. Thus, serviceability criteria may govern the design of FRP RC and needs to be reassessed. The short-term deflection behavior of CFRP RC I-beams has been investigated through theoretical analysis and experiments. The most relevant experimental and analytical studies on deflections of FRP RC elements have been presented and discussed. Different prediction models for the evaluation of deflections have been analyzed and compared. Most of these approaches propose coefficients that adjust a limited number of experimental data to existing design equations for steel RC. Because SLS result, specifically the deflection, determining for the design of FRP RC elements, a new equation for calculating the effective moment of inertia was proposed. The most relevant conclusions of the present work can be summarized as follows: 1. 2.

All the CFRP RC beam specimens behaved linearly until cracking and, due to lack of plasticity in the reinforcement, almost linearly between cracking and failure, with a greatly reduced slope. At the service load level, most of the theoretical approaches underestimate the deflection. So, it is worth to reassess all of the theoretical approaches and propose a new approach for deflection prediction. Thus, a new proposed equation for calculating effective moment of inertia, and subsequently calculating deflection, was developed.

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Rasheed, H. A., Nayal, R., and Melhem, H. (2004). “Response Prediction of Concrete Beams Reinforced with FRP Bars.” Compos. Struct., 65, 193-204. Silica Fume Association, 2005, “Silica Fume User’s Manual,” Publication No. FHWA-IF-05-016, Federal Highway Administration, Washington, DC. S. Roohollah. Mousavi, and M. Reza. Esfahani (2012), “Effective Moment of Inertia prediction of FRP Reinforced Concrete Beams based on Experimental Results”, Journal of Composites for Construction, ASCE. Vol.16, No.5, pp. 490-498. Yost, J. R., Gross, S. P., and Dinehart, D. W. (2003). “Effective Moment of Inertia for Glass FiberReinforced Polymer-Reinforced Concrete Beams.”ACI Struct. J., 100(6), 732-739.

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