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Evaluation of deﬂection in concrete members reinforced with ﬁbre reinforced polymer (FRP) bars H.A. Abdalla

*

Department of Structural Engineering, Faculty of Engineering, Cairo University, Cairo, Egypt

Abstract The use of ﬁbre reinforced polymer (FRP) reinforcements in concrete structures has increased rapidly in the last 10 years due to their excellent corrosion resistance, high tensile strength, and good non-magnetization properties. However, the low modulus of elasticity of the FRP materials and their non-yielding characteristics results in large deﬂection and wide cracks in FRP reinforced concrete members. Consequently, in many cases, serviceability requirements may govern the design of such members. This paper describes the development of simple approaches in estimating the deﬂection of FRP reinforced concrete members subjected to ﬂexural stresses. The predictions of these approaches are compared with the experimental results obtained by testing seven prototype concrete beams reinforced with glass ﬁbre reinforced polymer, GFRP, and carbon ﬁbre reinforced polymer, CFRP, bars. The proposed analytical methods are also substantiated by test results available in the literature from eight concrete slabs reinforced with conventional steel, GFRP, and CFRP bars. Good agreement was shown between the theoretical and the experimental results. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Deﬂection; Fibre reinforced polymers; FRP; Tension stiﬀening

1. Introduction The replacement of conventional steel reinforcement with FRP bars has been investigated to overcome the corrosion problem in bridge decks, parking garages, water and wastewater treatment facilities, marine structures and chemical plants. In addition to their excellent non-corrosive characteristics, FRP reinforcements have high strength-to-weigh ratio, good fatigue properties and electromagnetic resistance. Typical for these advanced composite materials is their relatively low modulus of elasticity and linear stress–strain diagram up to rupture with no discernible yield point and diﬀerent bond strength according to the type of FRP product. These properties result in large deﬂection and wide cracks. Many researchers [1–5] have found that design of concrete structures reinforced with FRP rods is primarily governed by serviceability criteria, particularly, deﬂection and cracking. This research examines the applicability of the various methods available for evaluation of deﬂection of concrete members reinforced with FRP bars. Modiﬁcations are in-

*

Fax: +202-266-4015. E-mail address: [email protected] (H.A. Abdalla).

troduced to these methods to account for the nature of crack pattern and propagation observed during the experimental program.

2. Research signiﬁcance Serviceability of FRP reinforced concrete members is one of the main issues that has to be examined due to the low modulus of elasticity and the linear stress–strain diagram of the FRP reinforcements. This paper provides detailed models to predict deﬂections of FRP reinforced concrete structures based on test observations. Eﬀect of tension stiﬀening on the deﬂection of such structures is examined. A simpliﬁed method to calculate deﬂection under short-term static load is introduced. Evaluation of the various methods for deﬂection predictions could be very useful in establishing design guidelines and future code for structures reinforced with FRP reinforcements.

3. Experimental program In this research, tests were conducted on concrete beams reinforced with diﬀerent types of FRP bars. The beams were tested under two-point loading to investigate

0263-8223/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 8 2 2 3 ( 0 1 ) 0 0 1 8 8 - X

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Nomenclature Af area of FRP tension reinforcement Afb area of FRP tension reinforcement for the balanced section As area of steel tension reinforcement b width of cross-section d depth to centre of reinforcements, measured from the extreme compression ﬁbre of concrete db bar diameter Ec elastic modulus of concrete Ef elastic modulus of FRP reinforcement in tension Es elastic modulus of steel reinforcement in tension fc0 compressive strength of concrete cylinders ff FRP stress at a speciﬁed load

their deﬂection, cracking, ultimate capacity and mode of failure. In addition, available experimental results [6–9] from testing of one way concrete slabs reinforced with FRP bars were also used for the veriﬁcation of the proposed analytical models. 3.1. Material characteristics Fig. 1 shows the material properties of the four types of reinforcement rods used in the experimental program. These include glass ﬁbre reinforced polymer, GFRP (Isorod), produced by Pultrall, Canada; GFRP (C-bar) produced by Marshall Industries Composites, USA; carbon ﬁbre reinforced polymers, CFRP (Leadline), produced by Mitsubishi Kasei, Japan; and conventional steel. The GFRP (Isorod) bars are manufactured by pultrusion of E-glass continuous ﬁbres and thermosetting polyester resin. To enhance the bond characteristics, the surface is wrapped by helical glass ﬁbre strands and covered by a mixture of a known grain size of sand and polyester resin [10]. The GFRP (C-bar) rod is manu-

Fig. 1. Material characteristics of FRP and steel reinforcements.

fs ft0 fu fy Icr Ie Ig Im M Ma Mcr t lm q qb

steel stress at a speciﬁed load tensile strength of concrete rupture stress of the FRP reinforcements yield stress of steel reinforcement moment of inertia of cracked section eﬀective moment of inertia gross moment of inertia mean moment of inertia applied bending moment maximum applied bending moment cracking moment total depth of cross-section bond strength of FRP reinforcement reinforcement ratio (Af or As =bd) balanced reinforcement ratio

factured by the hybrid pultrusion process [3]. C-bar rods are produced using four diﬀerent ﬁbre types, namely, E-glass, carbon, Aramid, and a hybrid of carbon and E-glass, designated as Type 1, Type 2, Type 3, and Type 4, respectively. Type 1 reinforcing bars are manufactured in two grades, Grade A and Grade B, according to the surface deformations and characteristics. Type 1– Grade B was used in this study. The CFRP (Leadline) rods are pultruded using linearly oriented coal tar pitchbased continuous ﬁbre epoxy resin [11]. Although GFRP bars possess the lowest tensile strength in comparison to other available FRP reinforcements, they have the advantage of being the least expensive, along with their non-corrosive, magnetically neutral and high strength to weight ratio characteristics. The measured average cylinder compressive strength of the concrete used for the beams ranged from 30 to 35 MPa at the time of testing, with a maximum aggregate size of 13 mm. The reinforcing steel was of Grade 400 (fy ¼ 435 MPa). 3.2. Beam tests Tests were carried out on seven concrete beams reinforced with diﬀerent types of FRP reinforcing bars. The beams with 500 mm 250 mm cross-section and 2300 mm clear span were simply supported and subjected to two concentrated static loads. Schematic view of the test set-up is shown in Fig. 2. A concrete clear cover of 38 mm was kept constant for all the test-beams. Steel stirrups of 9.5 mm diameter were used at 400 mm spacing along the tested length for all beams. Three of the test beams denoted as I.4, I.6, and I1.5 were reinforced with GFRP (Isorod) with reinforcement ratio of 0.4%, 0.6%, and 1.5%, respectively. Two beams, C.4 and C.8, were reinforced with GFRP (C-bar) with reinforcement ratio of 0.4% and 0.8%, respectively. The remaining two beams, L.2 and L.4, were reinforced with

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the lower modulus of elasticity of the FRP reinforcements relative to the conventional steel. For practical ratios of FRP reinforcements and in order to control deﬂection and cracking, most of the FRP reinforced concrete sections will be over-reinforced. It has to be noted that whether the FRP reinforced concrete section is under-reinforced or over-reinforced, the ﬂexural failure will be a brittle failure. This is due to the fact that the FRP reinforcements do not yield as in the case of steel reinforcement. Details of the seven prototype concrete beams tested in this program are given in Table 1. Fig. 2. Schematic view of the test setup.

CFRP (Leadline) with reinforcement ratio of 0.2% and 0.4%, respectively. The reinforcement ratios were chosen such that both the under-reinforced and over-reinforced conditions are achieved for each type of FRP reinforcements. The balanced reinforcement ratio, qb , was obtained by applying the equilibrium and compatibility conditions and using the equivalent rectangular stress block, as 0:85bfc0 0:003Ef qb ¼ ; ð1Þ fu 0:003Ef þ fu where qb ¼ Afb =bd; Afb is the area of FRP tension reinforcement for the balanced section; b and d are the width and the eﬀective depth of the cross-section, respectively; fc0 the concrete compressive strength; fu the rupture stress of the FRP reinforcement; Ef the modulus of elasticity of the FRP reinforcement; and b is the ratio of depth of equivalent rectangular stress block to depth of the neutral axis, which can be taken according to the ACI Code [12], in SI units, as 0 f 27:6 b ¼ 0:85 0:05 c : ð2Þ 6:7 It can be seen from Fig. 3 that the balanced reinforcement ratios for FRP reinforced concrete sections are much lower than those for steel reinforced concrete sections. This is due to the higher tensile strength and

3.3. Slab tests Tests [6–9] were carried out on eight prototype oneway concrete slabs reinforced with FRP and conventional steel reinforcements. The parameters considered were the depth of the slab, and the area and type of reinforcement. Five specimens were reinforced by GFRP (Isorod) bars, two specimens were reinforced by conventional steel bars and one specimen was reinforced with CFRP (Leadline), rods. The three slabs reinforced by CFRP and steel reinforcements are used as control specimens for comparison purposes. The length and width of all the slabs were 3500 and 1000 mm, respectively, with a clear span of 3000 mm. The thickness of the test-slabs was 150 mm according to the requirements of the Canadian Design Code, CAN3-A23.3-M94 [13], and the program was expanded to include 200 mm thick slabs. A concrete cover of 38 mm was used for the longitudinal reinforcements. The ratio of reinforcement area was changed to examine an under-reinforced concrete section, a balanced concrete section and an over-reinforced concrete section. Details of the eight prototype one-way concrete slabs, reinforced by three diﬀerent reinforcement materials, described in this program are given in Table 1. The tested beams and slabs were instrumented to measure the applied load, mid-span deﬂection, strains in the extreme compression ﬁbres of the concrete, strains in the reinforcements, strains in the concrete at the level of reinforcements, and crack widths within the constant moment zone. The objective of the test program was to investigate the performance of FRP reinforced concrete members in bending up to failure. This includes the behaviour at cracking, crack pattern, deﬂection, ultimate capacity, and mode of failure.

4. Experimental results

Fig. 3. Balanced reinforcement ratios for sections reinforced with GFRP, CFRP, and steel.

The load–deﬂection behaviour of the tested beams reinforced with diﬀerent ratios of FRP is shown in Fig. 4. During the experimental program, the concrete beams behaved linearly up to cracking. After cracking, the

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Table 1 Details of tested beams and slabs Specimen

Reinforcement material

Dimensions (mm) b

q (%)

q=qb

t

Beams I.4 I.6 I1.5 C.4 C.8 L.2 L.4

GFRP (Isorod) GFRP (Isorod) GFRP (Isorod) GFRP (C-bar) GFRP (C-bar) CFRP (Leadline) CFRP (Leadline)

500 500 500 500 500 500 500

250 250 250 250 250 250 250

0.38 0.63 1.52 0.45 0.88 0.20 0.47

0.78 1.26 3.00 1.05 2.05 0.95 2.24

Slabs [6–9] S-150-T I-150-A I-150-B I-150-C S-200-T I-200-A I-200-C LL-200-C

Steel GFRP (Isorod) GFRP (Isorod) GFRP (Isorod) Steel GFRP (Isorod) GFRP (Isorod) CFRP (Leadline)

1000 1000 1000 1000 1000 1000 1000 1000

150 150 150 150 200 200 200 200

0.96 0.49 0.76 0.96 0.39 0.23 0.77 0.30

0.23 0.66 0.99 1.25 0.09 0.31 1.01 0.87

q ¼ area of reinforcement/bd; qb ¼ balanced reinforcement ratio.

Fig. 4. Load–deﬂection behaviour of the tested beams: (a) eﬀect of reinforcement ratio; (b) eﬀect of reinforcement type.

results showed a bilinear relationship with reduced stiﬀness. Comparing the results of beams I.4, I.6, and I1.5 reinforced with GFRP (Isorod), Fig. 4(a), it can be seen that increasing the reinforcement ratio greatly reduces the deﬂection after ﬁrst cracking. Fig. 4(b) shows the deﬂection behavior of beams I.4, C.4, and L.4 reinforced with similar reinforcement ratio of 0.4% using Isorod, C-bar, and Leadline, respectively. Comparing the results, it can be seen that beams reinforced with

GFRP bars exhibit a signiﬁcant reduction in stiﬀness after the initiation of the ﬁrst crack in comparison with the beam reinforced with CFRP reinforcement. This behaviour is attributed to the low elastic modulus of the GFRP bars compared to that of the Leadline. The low modulus of elasticity of the GFRP bars aﬀects the ability of these bars to control concrete cracking. This decreases the tension stiﬀening eﬀect for concrete between cracks leading to a reduced eﬀective moment of inertia and hence large deﬂections. Fig. 5 shows the crack pattern of beam I.6 reinforced with 0.6% Isorod, and Fig. 6 shows the cracking at failure of beam I.4 reinforced with 0.4% Isorod. A comparison between the experimental strain distributions at the same applied load (80 kN) for beam I.4 reinforced with GFRP and beam L.4, reinforced with CFRP, Leadline, is shown in Fig. 7. The theoretical strain of a reference beam reinforced with 0.4% steel ratio is also shown for comparison purposes. The results show that at the same load, the strains and hence the curvatures are higher in the beam reinforced with GFRP than in the beam reinforced with CFRP. Also the depth of the compression zone is always smaller in beams reinforced with GFRP than in those reinforced with CFRP. Beam C.4 reinforced with Cbar showed similar results to those of beam I.4, reinforced with Isorod. The eﬀect of low modulus of elasticity of reinforcement bars is also shown in Fig. 8 by comparing the results of slabs, S-150-T and I-150-C, reinforced with the same reinforcement ratio of steel and GFRP (Isorod), respectively. The results show that after ﬁrst crack, the stiﬀness of slab S-150-T was not signiﬁcantly reduced as in the case of slab I-150-C. The slope of the load

H.A. Abdalla / Composite Structures 56 (2002) 63–71

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Fig. 5. Crack pattern of beam I.6 reinforced with Isorod.

Fig. 6. Failure of beam I.4 reinforced with Isorod.

deﬂection relationship in slab S-150-T reinforced with steel started to be similar to that of slab I-150-C reinforced with GFRP after yielding of the steel bars.

5. Deﬂection prediction models Various methods available for predicting the deﬂection of concrete members reinforced with steel bars were found to underestimate deﬂection of concrete members reinforced with FRP bars [3,7,14]. According to the ACI Building Code [12] and the Canadian Building Code [13], the immediate deﬂection of a cracked member can be estimated using a constant eﬀective moment of inertia, Ie , given by the empirical equation

Ie ¼

Mcr Ma

3

" Ig þ 1:0

Mcr Ma

3 # Icr 6 Ig ;

ð3Þ

where Ma is the maximum applied bending moment at the load stage in which deﬂection is being calculated; Mcr is the cracking moment of the member cross-section; Ig is the gross moment of inertia of the crosssection neglecting reinforcement; and Icr is the moment of inertia of the cracked section transformed to concrete. Based on the experimental program described in this research, modiﬁcations are introduced to the current methods of deﬂection evaluation to account for the low modulus of elasticity of FRP reinforcements and the nature of crack pattern and crack propagation in

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Fig. 7. Strain distribution of beams reinforced with FRP rods (q ¼ 0:4%).

Ie ¼

Mcr Ma

"

3

bd Ig þ 1:0

Mcr Ma

3 # Icr 6 Ig ;

ð4Þ

where Ef b d ¼ ab 1 þ ; Es

Fig. 8. Load–deﬂection behaviour of test slabs S-150-T and I-150-C.

concrete members reinforced with FRP bars. A cracked member behaves, in general, as a member of variable cross-section since the rigidity is reduced at the cracked zone. At a crack there are no tensile stresses in concrete. However, between cracks, the concrete in tension contributes to the ﬂexural rigidity of the member resulting in stiﬀening of that member. Diﬀerent detailed models are presented to account for the tension stiﬀening in FRP reinforced concrete members. A simple design method for estimating the post-cracking deﬂection of these members is introduced along with a comparison between the measured deﬂections and the predicted values.

5.1. ACI Committee 440 [15] model Deﬂection of concrete members reinforced with FRP bars is currently estimated using the guidelines provided by the ACI Committee 440 [15] for the design and construction of concrete reinforced with FRP bars. According to these guidelines, the instantaneous deﬂection under service loads can be obtained using an eﬀective moment of inertia, Ie , given by

ð5Þ

where Ef is the modulus of elasticity of the FRP material; Es is the modulus of elasticity of the reinforcing steel; ab is a bond-dependent coeﬃcient; which can be taken as 0.5 for GFRP bars which is the same as for steel bars, value of 0.5 can also be used for other types of FRP bars [16,17]. The parameter bd given in Eq. (5) takes into account bond properties and modulus of elasticity of FRP bars. The long-term deﬂection, DðcpþshÞ , of FRP reinforced concrete members can be predicted using the ACI-440 [15] formula given by DðcpþshÞ ¼ dnDðinÞ ;

ð6Þ

where DðinÞ is the initial deﬂection; n is a time-dependent coeﬃcient which equals to 1.74 and 2.0 for loading duration periods of 12 months and 10 years, respectively; and parameter d varies between 0.46 for Aramid ﬁbre reinforced polymer, AFRP, bars and GFRP bars and 0.53 for CFRP bars and, for design considerations, can be conservatively taken as 0.6 [15]. Deﬂections calculated according to Eqs. (4) and (5) are compared to the experimental results in Fig. 9 for beams and in Fig. 10 for slabs, respectively. It can be seen from these ﬁgures that deﬂections estimated according to the ACI-440 [15] method are less than the experimental values especially for beams and slabs reinforced with GFRP bars. Fig. 10 shows that for slab S-150-T reinforced with steel, deﬂections estimated according to the ACI-440 [15] are in good agreement with the experimental results.

H.A. Abdalla / Composite Structures 56 (2002) 63–71

Fig. 9. Comparison of experimental and analytical deﬂection of FRP reinforced concrete beams.

69

Fig. 10. Comparison of experimental and analytical deﬂection of FRP and steel reinforced concrete slabs.

5.2. Hall and Ghali Model [18] This model was introduced by Hall and Ghali [18] to predict the post-cracking immediate and long term deﬂections of beams reinforced with GFRP bars. The model is based on integrating the mean curvatures at a number of sections along the member to determine the mid-span deﬂection. Similar integration method was also suggested by Razaqpur [19] and Razaqpur et al. [20]. The mean curvature at any section can be calculated from wm ¼

M ; EIm

ð7Þ

where M is the applied moment at the section, E is the modulus of elasticity, and Im is the mean moment of inertia given by [18]

Im ¼ I1 þ b1 b2

I1 I2 2 Mcr Ma

;

ð8Þ

ðI2 I1 Þ

where I1 and I2 are the moments of inertia for uncracked transformed sections and for full cracked transformed sections, respectively; b1 is the coeﬃcient characterizing the bond quality of the reinforcing bars and is equal to 1.0 for high bond bars and 0.5 for smooth bars; and b2 is the coeﬃcient representing the inﬂuence of the duration of application or of repetition of loading and is equal to 0.8 for ﬁrst loading and 0.5 for sustained or cyclic loading according to the CEB-FIP Code [21]. For simplicity, Hall and Ghali [18] suggested that the mid-span deﬂection could be calculated using only the curvature at the central section. Deﬂection of the tested

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H.A. Abdalla / Composite Structures 56 (2002) 63–71

beams and slabs was calculated using this method and compared to the experimental results in Figs. 9 and 10. It can be seen from these ﬁgures that using this method without integrating the curvatures at many sections of the member results in higher deﬂections than the experimental values. 5.3. ISIS Canada model [22] The draft of ISIS (Intelligent Sensing for Innovative Structures) Canada network design manual suggests that the eﬀective moment of inertia for deﬂection calculations of FRP reinforced concrete members can be taken as [22] Ie ¼

Ig Icr : 2

Icr þ 1 0:5 MMcra Ig Icr

ð9Þ

5.4. Proposed method for estimating deﬂection Favre and Charif [23] introduced a method for deﬂection calculations according to the CEB-FIP Model Code 1990 [21] for concrete structures reinforced with conventional steel. According to this method, the immediate deﬂection, D, can be estimated from Mcr ; Ma

ð10Þ

where D1 and D2 are deﬂections in states 1 and 2, respectively, for simple bending; where a non-cracked section is said to be in state 1 and a cracked section with the concrete in tension is ignored is said to be in state 2; in state 1 the transformed moment of inertia is used to calculate D1 , and in state 2 the cracked moment of inertia is used to calculate D2 ; and the factor b0 is equal to ðb1 b2 Þ. It has to be noted that in Eq. (10) the expression ½ðD2 D1 Þ b0 ðMcr =Ma Þ represents the tension stiﬀening for concrete structures reinforced with conventional steel. Eq. (10) can be simpliﬁed for the case of FRP reinforced concrete members by replacing the transformed moment of inertia used in state 1 by the gross moment of inertia Ig , neglecting the inertia of reinforcement. This is due to the typical low modulus of elasticity of the FRP reinforcement. Also, the coeﬃcient b0 can be taken as 0.5 for most practical applications as was suggested by Ghali [24]. Therefore, Eq. (10) can be rewritten in the following form:

0:5Mcr Ma 0:5Mcr þ ; Ig Icr

ð11Þ

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. To account for the reduction in tension stiﬀening in fully cracked FRP concrete section, second term in the right-hand side of Eq. (11) will be multiplied by a factor of 1/0.85. Hence, deﬂection of FRP reinforced concrete members can be estimated from D¼

KL2 Ma ; Ec I e

ð12Þ

where Ie ¼

The eﬀective moment of inertia given by Eq. (9) was used to estimate the immediate deﬂection of the tested beams and slabs. Figs. 9 and 10 show good agreement between the experimental deﬂections and those calculated using ISIS Canada model.

D ¼ D2 ðD2 D1 Þ b0

KL2 D¼ Ec

Ig Icr Icr f þ 1:15Ig ð1 fÞ

ð13Þ

0:5Mcr : Ma

ð14Þ

and f¼

Deﬂections of the tested beams and slabs were estimated using Eqs. (12)–(14) and compared to the measured values. Good agreement was found between the experimental and the theoretical results as shown in Fig. 9 for beams I.6, C.4, and L.2 and in Fig. 10 for slabs I150-A and LL-200-C. In Fig 10, experimental deﬂection of slab S-150-T reinforced with steel was compared to the diﬀerent analytical methods described above. It can be seen from that ﬁgure that the proposed method for predicting deﬂection of FRP reinforced concrete members overestimates the deﬂection of steel reinforced concrete members up to yielding of steel. For loads greater than the load causing steel yielding, deﬂections predicted by the proposed method are much lower than the measured values.

6. Summary and conclusions Measured deﬂections of 15 simply supported FRP reinforced concrete beams and slabs were used to evaluate the deﬂection of members in bending. Based on the results of this investigation, the following conclusions can be made. Concrete members reinforced with FRP and subjected to bending moments behave linearly up to cracking, and linearly after cracking with greatly reduced stiﬀness. Deﬂections and strains of concrete members reinforced with FRP rods are generally larger than those reinforced with steel rods. This is due to the low modulus of elasticity and the diﬀerent bond characteristics of the FRP reinforcements.

H.A. Abdalla / Composite Structures 56 (2002) 63–71

The balanced reinforcement ratios for concrete sections reinforced with FRP rods are much lower than those for sections reinforced with steel. For practical ratios of FRP reinforcements and in order to control deﬂection and cracking, most of the FRP reinforced concrete sections will be over-reinforced. The ACI-440 guidelines for design of FRP reinforced concrete members gave lower estimate for deﬂections of the tested members than the measured values at loads higher than the cracking load. Deﬂections estimated according to the proposed method in this research or ISIS Canada approach are in good agreement with the experimental results.

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[13] [14]

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