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Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures
Composites: Part B 31 (2000) 555±567
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Performance of glass ®ber reinforced plastic bars as a reinforcing material for concrete structures S.H. Alsayed*, Y.A. Al-Salloum, T.H. Almusallam Department of Civil Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
Abstract The increasing use of ®ber reinforced plastic (FRP) bars to reinforce concrete structures necessitates the need for either developing a new design code or adopt the current one to account for the engineering characteristics of FRP materials. This paper suggests some modi®cations to the currently used ACI model for computing ¯exural strength, service load de¯ection, and the minimum reinforcement needed to avoid rupturing of the tensile reinforcement. Two series of tests were conducted to check the validity of the suggested modi®cations. The ®rst series was used to check the validity of the modi®cations made into the ¯exural and service load de¯ection models. The test results of the ®rst series were also analyzed to develop two simple models for computing the service load de¯ection for beams reinforced with glass FRP (GFRP) bars. The second series was used to check the accuracy of the modi®cation suggested into minimum reinforcement model. Test results of the ®rst series indicate that the ¯exural capacity of the beams reinforced by GFRP bars can be accurately predicted using the ultimate design theory. They also show that the current ACI model for computing the service load de¯ection underestimates the actual de¯ection of these beams. The two suggested models for predicting service load de¯ection accurately estimated the measured de¯ection under service load, and the simpler of the two pertains better predictions than those of the models available in the literature. Test results of the second series reveal that there is an excellent agreement between the predicted and recorded behavior of the test specimens, which suggests the validity of the proposed model for calculating the required minimum reinforcement for beams reinforced by GFRP bars. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Glass ®bers; Reinforced concrete structures
1. Introduction Lately, ®ber reinforced plastic (FRP) materials such as glass ®ber reinforced plastic (GFRP) rebars, as a reinforcing material for concrete structures, have received a great deal of attention among many engineering societies worldwide. Many engineers consider FRP as one of the most innovative material that may overcome the inherited de®ciency of reinforcing concrete structures by steel rebars in harsh environments due to corrosion. In comparison with steel, FRP have higher resistance to corrosion, higher tensile capacity, and lower weight. They are also non-conductive for electricity and non-magnetic. Thus, for structures built in or close to seawater or at similar corrosive environment, where electromagnetic neutrality and/or electric insulation are required, or exposed to deicing salts, FRP may become invaluable. Unfortunately, FRP are not free from hindrances that need to be resolved before they can be prescribed as a * Corresponding author. Tel.: 196614676925; fax: 196614677008. E-mail address: [email protected] (S.H. Alsayed).
reinforcing material for concrete structures. The major obstacles are the high initial cost, low modulus of elasticity, lack of ductility and absence of design guidelines. The ®rst of these obstacles is greatly in¯uenced by the manufacturing process. However, different low cost techniques are currently under development by many fabricators. The second and third obstacles (low modulus of elasticity and lack of ductility) are considered the major engineering drawbacks of the FRP materials. This is because when a concrete element is reinforced by FRP rebars, it may undergo larger de¯ection and suffer less margin of safety in comparison to that of its counterpart concrete element reinforced by steel bars. To overcome the fourth obstacle, a bulk of laboratory and ®eld data is needed. It is worth mentioning that the currently available design formulae for designing reinforced concrete (RC) elements as adopted by many design codes were originally developed with regard to that reinforcement is provided by steel. Thus, they may not be equally applicable to design concrete element reinforced by FRP rebars. On account of that, and to bene®t from the advantages of FRP materials, currently utilized design formulae must be reviewed considering the
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properties of FRP materials. Then, the formulae can be modi®ed, if necessary, to assure adequate safety and serviceability of the FRP concrete structures. The aim of this paper is to present the major results of an extensive research project that was carried out to study the actual behavior of concrete beams reinforced by GFRP bars and subjected to transverse (¯exure) loading. The work checks the suitability of using the existing ACI beam design equations for ¯exure and de¯ection when reinforcement is provided with GFRP bars and suggests the needed modi®cations to the equations in order to account for the engineering properties of GFRP bars. The study also investigates the condition of the required minimum GFRP reinforcement to avoid the catastrophic tensile failure of the beams. Modi®cations to the currently used models are suggested based on the test results of full size beams along with the equivalent data from the literature, whenever available. Further, the predicted service load de¯ections using the suggested models are compared with the measured de¯ections at midspan for these beams and their corresponding predicted values using the ACI model as well as those models available in the literature. It is hoped that the output of this study will help in paving the road for a design code for FRP material, which will help practitioners in designing and constructing concrete structures with FRP material that will ful®ll the strength and serviceability requirements and extend the useful service life of the infrastructure. 2. Flexural strength Before incorporating the GFRP bars into the design codes and standards, extensive research is needed to determine the values and limitations of design parameters. However, to minimize the possibility of having failure due to breakage of the GFRP bars, which is more brittle than failure due to crushing of concrete [1], researchers recommended some reduction factors to be applied to the GFRP ultimate tensile strength, fpu. Faza et al. [2] recommended that the maximum permissible strength, fpy, to be 0.80 of the ultimate strength. Nanni [3] suggested that the strength reduction factor, f , to be taken as 0.70 and the minimum ®ber plastic reinforcement ratio, r pmin, to be the larger of 1.33r pbal (rppbal is the balanced ®ber plastic reinforcement ratio) or 0:24 f 0c =fpu (to assure that fM n . M cr )Ðin general, researchers [2±6] recommended the use of some allowance (reduction factor) ranging from 0.70 to 0.80, that is to account for the possibility of experiencing undesired tensile failure type of GFRP bars. In other words, they have de®ned a pseudo yield point of fpy ranging from 0.70 to 0.80fpu for the FRP reinforcement. The ¯exural strength of a singly-reinforced beam section according to the ACI-Code provisions [7] requires Mu , fMn in which Mu is the required factored moment strength, Mn is the nominal moment strength of
the beam section, and f is the strength reduction factor (f 0:90 for ¯exure). For GFRP-RC beams, the ¯exural strength equation can be written as: fpy 1 Mn Ap fpy d 1 2 0:59rp 0 fc where, Mn nominal moment capacity of a section, N mm Ap area of GFRP rebars in tension region, mm 2 fpy pseudo yield tensile strength of GFRP rebars, MPa d distance from extreme comp. ®ber to centroid of tension reinforcement, mm rp ratio of tension reinforcement Ap =bd f 0c compressive strength of concrete, MPa b width of concrete section; mm: This is the same equation based on the ACI method after substituting the pseudo yield strength (fpy) of GFRP rebars for the yield strength of steel (fy) and the area of GFRP reinforcement (Ap) for the area of steel (As). This equation is actually based on tensile failure type in the tension reinforcement. As the tensile failure due to breakage of the GFRP bars is more brittle than that due to crushing of concrete, a compressive failure for GFRP-RC section is preferred and the nominal moment strength can be written as: a 2 Mn Ap fps d 2 2 where Mn is the nominal moment strength, Ap is the GFRPreinforcement area rp bd; r p is the GFRP-reinforcement ratio, b is the beam width, d is the effective depth, fps is the computed stress at the GFRP bars which corresponds to fs of the steel. The maximum value for fps is the usable stress limit of GFRP or the so-called pseudo yield tensile strength, fpy, which corresponds to fy of the steel. The fpy is assumed to be equal to 0.67 fpu, (the factor of safety, f pu =f py 1:5; equals to that usually considered against rupturing steel bars), fpu is the ultimate tensile strength of GFRP and a is the stressblock depth, a b1 c: Knowing that in case of compression failure, as shown in Fig. 1, the strain in the reinforcement, 1 ps, will be less than that of the pseudo yield limit, 1 py, which corresponds to 1 y of the steel. The 1 ps can be expressed in terms of the concrete strain in the extreme compression ®ber, 1 cu, and the distance from that ®ber to the neutral axis, c, as:
1ps 1cu
d 2 c c
3
and fps Ep 1ps
4
From the equilibrium requirements, the compression force C 0:85b1 f 0c bc should be equal to the tension force
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Fig. 1. ACI ¯exural strength for singly reinforced RC section (with GFRP bars).
T rp bd fps : Thus, the distance c can be found as: 2s 3 2 m r m r p p 5d c 4 m rp 1 2 2 2
Ig the moment of inertia of the uncracked transformed section (gross concrete section). 5
where m is a material parameter, equals to Ep ecu = 0:85b1 f 0c ; and Ep is the modulus of elasticity of the GFRP material. 3. Serviceability requirements The de¯ection requirement of the ACI-Code Table 9.5(b) limits the computed de¯ection, D , to a speci®ed maximum permissible value, D a, which depends on the span length of the beam and the type of the member. Therefore, for simply-supported beam of span L loaded by two equal concentrated loads (P=2 each) symmetrically placed about the beam center line as shown in Fig. 2, the maximum de¯ection D computed at the beam center can be written as:
D
Ps 3L2 2 4s2 48Ec Ie
6
where L is the span of the beam, P is the total service concentrated load divided into two concentrated loads P=2 each applied at a distance s from the support, Ec is the modulus of elasticity of concrete, and Ie is the effective moment of inertia of the beam section. According to ACI-Code provisions, the effective moment of inertia, Ie, can be determined as follows: " # Mcr 3 Mcr 3 Ie Ig 7 1Icr 1 2 Ma Ma
Earlier results by the authors [9,10] showed that the current ACI model [7] underestimates the de¯ections in FRP beams and therefore it needs to be revised to account for the properties of FRP materials. There is, however, some research effort to develop new formulae or modify the currently used ones to account for the properties of FRP bars. Some of these formulae have already been suggested and become available in the literature. It is, however, useful to investigate the accuracy of these models before they can be used by practitioners for ®eld applications. Faza and Ganga Rao [11] derived an expression for the effective moment of inertia for FRP-RC beams loaded at the third points. This model is based on the assumption that concrete section between the point loads is fully cracked, while the end sections are partially cracked. Therefore, the cracking moment of inertia, Icr, is used in the middle third section of the beam, and the current ACI-Code equation Ie, is used in the end sections. Thus, the model can be written as: Im
23Icr Ie 8Icr 1 15Ie
8
where Im is the modi®ed moment of inertia valid for two
where, Mcr the cracking moment, Ma the maximum service moment, Icr the moment of inertia of the cracked transformed section,
Fig. 2. The simple beam subjected to two equal concentrated loads symmetrically placed about the beam centerline.
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concentrated point loads applied at the third points on the beam. This means that the smaller the distance between loads, the smaller the portion that is assumed to be fully cracked. Therefore, it is expected that the assumption in this model will produce higher values than the corresponding actual values of the effective moment of inertia when the distance between loads is less than 1/3 of the span. However, comparison between the measured and the corresponding predicted de¯ections using this model showed that the predicted de¯ections correlated well with the measured ones at service load level when the middle third of the span is assumed to be fully cracked regardless of the distance between the two point loads [12]. Another modi®ed expression for the effective moment of inertia for simply supported beams reinforced with FRP bars was proposed by the ACI Committee 440 [13]. It is expressed as follows: Ig Mcr 3 2 aIcr 9 Ie aIcr 1 b Ma in which a and b are reduction factors equal to 0.84 and 7.0, respectively. These factors account for the reduced area of the compression section when the applied moment reaches the cracking moment. When the ®rst term of Branson's expression is divided by b and the second term is multiplied by a , Eq. (9) is obtained. The results of the comparison using this model showed that the predicted de¯ections at service load level were overestimated for some beams [12]. 4. Minimum and maximum reinforcement requirements The ductility requirements of the ACI-Code provisions limit the steel pratio rs As =bd; to a lower and upper limits of rs-min f 0c =4fy (fy is in MPa) and rs-max 0:75rs-bal ; respectively, in which r s-bal is the balanced steel reinforcement ratio. Substituting the material properties of GFRP, the balanced reinforcement ratio expression for GFRP, r p-bal, becomes:
rp2bal
0:003Ep 0:85b1 f 0c fpy 0:003Ep 1 fpy
10
To avoid failure due to concrete rupture, the minimum GFRP reinforcement ratio should be larger than a certain value to assure that the nominal ¯exural strength, f Mn, of the RC beam is greater than the strength of plain concrete beam, Mcr, i.e.
fMn . Mcr
11
The required reinforcement ratio to satisfy the above condition can be derived as follows: For a concrete beam reinforced with steel rebars [8]; p f0 r $ 0:168 c f 0c and fy are in MPa fy For GFRP a factor of safety of 1.5 is assumed against
the possibility of tensile failure of the rebars. Hence, fpy 0:67fpu : Therefore, p0 f rpy $ 0:25 c : 12 fpu Thus, to avoid the possibility of the brittle failure of GFRP rebars and to assure that fMn . Mcr ; the minimum GFRP reinforcement ratio is assumed to be the larger value obtained from Eq. (10) (r p-bal) or Eq. (12). Further, since the failure of GFRP bars is of brittle type, therefore, there is no upper limit for reinforcement ratio. However, the maximum GFRP reinforcement ratio is governed by the practical considerations, e.g. spacing between bars and maximum size of aggregate. It should be noted that composite materials, in general, and GFRP in particular are susceptible to degradation initiated by moisture, temperature, and some loading and environmental conditions. However, such conditions were not accounted for in the aforesaid equations. 5. Test program of ¯exural capacity and serviceability 5.1. Test specimens A series of tests were conducted to study the ¯exural capacity and the serviceability requirements of GFRP-RC beams. A total of ®fteen (15) beams categorized into ®ve groups were tested in this program. Each group was composed of three identical specimens. While group I beams were reinforced with steel bars referred to as control specimens, the other four groups were reinforced with GFRP rebars. Group I beams were reinforced with steel rebars (control specimens), group II beams were reinforced with GFRP rebars considering the same dimensions of the control specimens and designed in accordance with the ACI Code ultimate design theory for compression failureÐ presented earlierÐto have the same capacity of group I beams. The third group (group III) was designed such that the ¯exural strength, serviceability and ductility requirements according to ACI Code are satis®ed. Group IV and V beams were provided with different depths and reinforcements, designed such that the ¯exural strength, serviceability and minimum reinforcement requirements are satis®ed. The serviceability requirement is such that the central de¯ection (computed using ACI Code with 5.5 power in Branson's expression) at service loading is almost the same as that of group I beams. All beams in this series were 2900 mm long, provided with B 8 mm diameter steel stirrups at 100 mm center to center, tested simply supported over a span of 2700 mm, and loaded by two concentrated loads placed at equal distance (100 mm) from the beam centerline as shown in Figs. 2 and 3. The GFRP rebars were of E-glass type (E-glass 76.14%, resin 22.18%, ®ller 1.26%, ultra violet 0.05% and catalysts
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Fig. 3. Test setup. Table 1 Beam details of the ®rst series of test specimens Beam group
Type of reinforcement
Reinforcement details
Reinforcement area, A (mm 2)
Overall depth, h (mm)
Width b (mm)
Effective depth, d (mm)
I II III IV V
STEEL GFRP GFRP GFRP GFRP
3B14 4B19 4B12.7 2B19 4B19
462 1134 507 567 1134
210 210 260 300 250
200 200 200 200 200
160.0 157.5 210.7 247.5 197.5
Table 2 Material properties of the ®rst series of test specimens Group
Bar diameter (mm)
f 0c (MPa) (concrete)
fy (MPa) (Steel)
fu (MPa) (GFRP)
E (MPa)
I II III IV V
14 19 12.7 19 19
31.3 31.3 31.3 40.7 40.7
553 ± ± ± ±
± 700 886 700 700
200000 35630 43370 35630 35630
0.37%) and were manufactured through pultrusion process in which the ®bers are passed through a resin bath and pulled through a die of the bar diameter. Further details of the cross-sections for the beams in this series and the materials properties are summarized in Tables 1 and 2. 5.2. Test results The average measured load±central de¯ection relationships
for the ®ve groups of beams are shown in Fig. 4. The results clearly show the in¯uence of reinforcing bar type and crosssectional dimensions on the overall load±de¯ection relationship. While group I and II beams are almost identical except for the type of reinforcing bars, a noticeable increase in group II beams Es =Ep . 4 de¯ection due to the replacement of steel rebars by relatively lower modulus GFRP rebars. An increase in the cross-sectional depth decreases the de¯ection of the beam. This can be clearly seen in the
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Fig. 4. The average measured load±de¯ection relationships for the ®ve groups of beams of the ®rst series of test specimens.
load±de¯ection relationships of groups III, IV and V beams compared to group II beams as shown in Fig. 4. The predicted loads and central de¯ections at service load (in this paper, the service load is assumed to be about 35% of the ultimate load) using ACI-Code procedure [7] for the ®ve groups of beams are shown in Tables 3 and 4, respectively, along with the corresponding measured results. The results show that groups I and II attained almost the same load capacity. This supports the validity of the procedure used to design the GFRP-RC beams, i.e. the ACI Code ultimate design theory for compression failure. The effect of replacing steel rebars by GFRP rebars on the de¯ection of beams can be clearly seen in the ®gure and in the tables. The increase in de¯ection is actually less than what was expected. For instance, although Es =Ep is larger than 4, the ratio of the central de¯ection of the GFRP-RC group II beams to that of the steel-RC group I beams at service load is 1.96. However, still such increase in de¯ection at service load implies that the de¯ection will control the design of intermediate to long span structural elements reinforced by GFRP bars. The difference between the expected and the measured ratios may be ascribed to the interaction effect of the composite and also to the loading con®guration. The results reported in Table 4 also show the bene®t of increasing the depth and decreasing the reinforcement of group III beams compared to those of group II beams. The increase of the overall depth was 24% (260 mm versus 210 mm for group II). Bene®ts of such increase Table 3 Measured and calculated ultimate load Beam group
I II III IV V
Ultimate load, Pn, (kN) Measured
ACI
56.5 54.7 72.2 94.7 91.2
55.6 51.0 65.9 92.5 84.2
Load ratio (ACI/measured)
0.98 0.93 0.91 0.98 0.92
in depth include reducing the amount of needed GFRP bars by 55% (4B 19 mm versus 4B 12.7 mm), increasing the ¯exural capacity by 32% (54.7 MPa versus 72.2 MPa), reducing the de¯ection at same load (20 kN) by 31% (10.64 versus 7.38). Reducing the amount of GFRP bars implies great reduction in the overall cost of construction. For instance, when the costs of concrete, steel, GFRP and form work are assumed to be US$ 100/m 3, 610/ton, 9150/ton and 2/m 2, respectively, the reduction in cost of the GFRP-RC beams of group III as compared to that of group II is about 40% [14]. Thus, the increase in the overall cost that may result from replacing steel by GFRP bars to reinforce concrete structures can be tremendously reduced by increasing the depth of the cross-section. This, however, may not be the ideal solution for multi-story structures as the reduction in their cross-sectional dimensions is, in most cases, an insisted desired. The results of Fig. 4 also show that groups IV and V attained almost the same load capacity. This again supports the validity of the procedure used to design the GFRP-RC beams for strength. In other words, the ultimate ¯exural capacity of GFRP-RC beams can be reasonably estimated using Whitney's rectangular stress block. Furthermore, these GFRP-RC beams of groups IV and V have almost the same behavior at the service load level. It is interesting to mention that due to the factor of safety used against the possibility of experiencing tensile failure of GFRP rebars fpy 0:67fpu ; all GFRP-RC beams considered in this study showed concrete compressive failures. Typical failure of the test specimens is shown in Fig. 5. While the results show that there is a good agreement between the experimental and theoretical (ACI-Code) results for loads and de¯ections for beams reinforced with steel bars (group I), the results shown in Table 4 for other groups clearly present the fact that the current ACI model prediction for the de¯ection of beams reinforced by GFRP bars is under-estimated. This clearly shows that there is a need to modify the current ACI equation for de¯ection prediction.
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Table 4 Central de¯ection values at service load Beam group
Ultimate load, Pn (kN)
I II III IV V
55.6 51.0 65.9 92.5 84.2
Service load, Ps (kN)
20 20 26 40 33
5.3. De¯ection prediction models As pointed out earlier, there is a need to modify the current ACI equation to predict de¯ections under service loads. To do so, the experimental results obtained in this study were analyzed. The experimental values of the effective moment of inertia Ie were determined using Eq. (6) as follows: Ie exp
1 2
P exp s 3L2 2 4s2 24Ec D exp
13
and from Eq. (7), the power (m) can be written as: ! Ie 2 Icr log Ig 2 Icr m Mcr log Ma
14
Central de¯ection (mm) Measured
ACI
5.44 10.64 11.32 14.23 11.81
5.18 8.14 5.67 5.57 7.73
De¯ection ratio (ACI/measured)
0.95 0.77 0.50 0.39 0.65
The experimental values of the effective moment of inertia determined from Eq. (13) were used in Eq. (14). The regression analysis was performed on the results for service load range. The results suggest that the average value of the power (m) for GFRP-RC beams can be taken approximately as 5.5 rather than 3 as suggested by Branson for steel-RC beams [7]. Thus, the suggested model (Model-A) can be considered as a modi®ed Branson's equation to determine the effective moment of inertia for beams reinforced by GFRP bars. It can be written as: Model A: " # Mcr 5:5 Mcr 5:5 Ie I g 15 1Icr 1 2 Ma Ma Another model (Model B) is suggested based on the analysis of the experimental data of Ie =Icr versus Ma =Mcr
Fig. 5. Typical failure of the test specimens.
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Fig. 6. The Ie =Icr versus Ma =Mcr for the GFRP-RC beams.
for beams reinforced by GFRP bars. The Ma =Mcr greater than 1.0 are plotted in Fig. 6. sion analysis which was performed on these gests that the effective moment of inertia can follows: Model B: Ie aIcr
for 1:0 ,
Ie Icr
for
Ma , 3:0; Mcr
Ma . 3:0; Mcr
results for The regresresults sugbe taken as
where
a 1:40 2
2 Ma : 15 Mcr
16c
5.4. Model validation 16a
16b
The values of the effective moment of inertia Ie determined using the above-suggested models are plotted versus Ma =Mcr for each group of beams in Figs. 7±10. They are plotted besides the experimental values determined using Eq. (13) and those of the ACI model. The results for those beams reinforced with GFRP bars shown in Figs. 7±10
Fig. 7. The effective moment of inertia versus Ma =Mcr for group II beams.
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563
Fig. 8. The effective moment of inertia versus Ma =Mcr for group III beams.
clearly indicate that there is an abrupt change in the actual effective moment of inertia determined from the experimental results, Eq. (13), once the applied moment exceeds Mcr. The value of Ie(exp) drops to a value slightly above Icr. This is attributed to the effect of the low modular ratio for these beams due to low modulus of elasticity of the GFRP bars. This is another indication that Branson's equation is not recommended for beams reinforced with GFRP rebars. The predicted de¯ections at service load level are computed for models available in the literature as well as for the two suggested models. The results are compared with the corresponding experimental results.
The predicted central de¯ection for each group of beams is calculated using a spreadsheet program. All models considered (®ve models) are summarized in Table 5. The measured and predicted results for GFRP-RC beams, groups II through V, using these models at service load level are summarized in Table 6. The ratio of the predicted with respect to the measured service de¯ection is also shown in Table 6. The error in each model that represents the percentage difference between the predicted and the measured values of short-term service de¯ections for the four groups are presented graphically in Fig. 11. The results show the accuracy of the two models suggested in this study along
Fig. 9. The effective moment of inertia versus Ma =Mcr for group IV beams.
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Table 5 The models used to predict the effective moment of inertia for beams reinforced by GFRP bars Model ACI-318
Expression Ie Ig
Suggested by
Mcr Ma
3
"
1Icr 1 2
Mcr Ma
3 #
23Icr Ie 8Icr 1 15Ie
Faza and Ganga Rao
Im
ACI-440
in which Ie is computed according to ACI-318 " # Ig Mcr 3 Mcr 3 Ie 1aIcr 1 2 b Ma Ma
A
Ie Ig
Mcr Ma
5:5
Faza and Ganga Rao [11]
" 1Icr 1 2
Mcr Ma
5:5 #
2 Ma M Ie 1:40 2 Icr for 1 , a , 3 15 Mcr Mcr
B
Ie Icr for
ACI Committee 318 [7]
ACI Committee 440 [13]
Current study
Current study
Ma .3 Mcr
with that of Faza and Ganga Rao [11]. The results also show that although model B is simple and much easier to use, it is the most accurate one among all other models.
6. Test program of minimum reinforcement condition 6.1. Test specimens As explained earlier, this part of test program was
conducted to investigate the minimum reinforcement requirement for GFRP-RC beams. A total of six (6) beams were tested in this program. They were categorized into two groups. Each group was composed of three identical specimens. Group (MR-1) beams were reinforced with minimum amount of GFRP reinforcement, while group (MR-2) beams were reinforced with reinforcement less than the minimum amount of GFRP rebars. The cross-sections of beam specimens of Groups (MR-1) and (MR-2) were 200 £ 210 mm 2, and 2320 mm long.
Fig. 10. The effective moment of inertia versus Ma =Mcr for group V beams.
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Fig. 11. The error percentage in each model for the four groups of GFRP-RC beams at service load level.
Fig. 12. The average measured load±de¯ection relationships for the two groups of beams of the second series of test specimens. Table 6 Measured and predicted central de¯ections using all models at service load levels Group
P-Service (kN)
D measured (mm)
Model
D predicted (mm)
D predicted/D measured
II
20
10.64
III
26
11.32
IV
40
14.23
V
33
11.81
ACI-318 Faza and Ganga Rao ACI-440 A B ACI-318 Faza and Ganga Rao ACI-440 A B ACI-318 Faza and Ganga Rao ACI-440 A B ACI-318 Faza and Ganga Rao ACI-440 A B
8.14 10.76 12.16 11.35 10.95 5.67 11.14 14.06 10.64 12.18 5.57 12.59 16.19 11.62 14.19 7.73 10.49 11.97 11.13 10.83
0.77 1.01 1.14 1.07 1.03 0.50 0.98 1.24 0.94 1.07 0.39 0.88 1.14 0.82 1.00 0.65 0.89 1.01 0.94 0.92
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Table 7 Beams details and material properties of the second series of test specimens Group
Reinforcement
Ap (mm 2)
fpu (MPa)
EP (MPa)
f 0c (MPa)
b (mm)
h (mm)
d (mm)
MR-1 MR-2
2B12.7 2B9.5
53.4 142.5
886 876
43370 42020
39.6 39.6
200 200
210 210
160.7 162.2
Table 8 The reinforcement ratios of the two groups p Group r p-bal 0:25 f 0c =fpu r min
r used
r /r min
MR-1 MR-2
0.007885 0.004392
1.0083 0.5645
0.00782 0.00778
0.001776 0.001796
0.00782 0.00778
Group (MR-1) was reinforced with 2#4 (B 12.7 mm) GFRP bars (r 1:008rmin ). Group (MR-2) beam specimens was reinforced with 2#3 (B 9.5 mm) GFRP bars (r 0:565rmin ). The two groups were provided with B 8 mm steel stirrup at 100 mm center to center, tested simply supported over a span of 2120 mm, and loaded by two concentrated loads placed at equal distance (100 mm) from the beam center line. Further details of the cross-sections for the beams in this series and the materials properties are summarized in Tables 7 and 8. 6.2. Test results The measured load±de¯ection curves for specimens of the two groups are shown in Fig. 12. The results show that the reinforcement ratio has a signi®cant in¯uence on the behavior of GFRP-RC beams. The ®rst group (MR-1), which was designed such that the reinforcement is minimum, failed in compression (crushing of concrete) as was expected. The second group (MR2), in which the reinforcement is less than the minimum failed in tension due to GFRP rebars tensile failure, rupture of bars. The results shown in Table 9 indicate that MR- 1 beams in which r rmin rbal ; the stress in the GFRP bars reached almost 0.67fpu when the strain in the extreme compression ®ber of concrete reached 0.003. This result was expected since the reinforcement ratio used in beams of this group equals to the balanced reinforcement ratio. This failure is a balanced failure (it is indeed a compression failure since 1cu 0:003 and fpy 0:67fpu ). On the other hand, MR-2 beams in which r , rmin ; the stress in the rebars reached 0.67fpu when the strain in the extreme compression ®ber of concrete was less than
0.003. When the applied loads exceeded that, the stress in rebars exceeded the pseudo yield limit .0:67f pu : When the strain in concrete reached 0.003, the stress in the rebars reached about 800 MPa which is slightly less than the ultimate value of 876 MPa. As the applied load increased, the rebars failed in tension and the beam was cut into two parts. These results support the theoretical derivations that were presented earlier in this paper. 7. Conclusions The validity of using the current ACI-318 code of practice for both strength and serviceability requirements for designing concrete beams reinforced with GFRP rebars was investigated. The results revealed the following remarks: 1. The ¯exural capacity of concrete beams reinforced by GFRP bars can be accurately estimated using the ultimate design theory (when failure occurs due to crushing of concrete in the compression side) which is also applicable to design of concrete beams reinforced by steel bars (over reinforced sections). 2. Due to the low modulus of elasticity of GFRP rebars EGFRP =Esteel < 0:25; de¯ection criterion may control the design of intermediate and long beams reinforced with GFRP rebars. The current ACI equations, developed for steel-reinforced concrete beams, highly underestimates the actual de¯ection of the concrete beams reinforced by GFRP bars. 3. Based on the experimental results, two simple empirical models are suggested to predict the actual service load de¯ection. The accuracy of the models pertains good agreement with measured values. They are simple to use and provide, in most cases, better prediction than those by other models available in the literature. 4. To avoid the possibility of a catastrophic failure due to reinforcing rebars rupture, a model to estimate the minimum required reinforcement ratio is suggested. The model was checked experimentally and pertained good agreement with test results.
Table 9 Theoretical results of beams with different reinforcement ratios of GFRP bars Group
Reinforcement details
fpu (MPa)
Fpy (MPa) ( 0.67 fpu)
fs (MPa) 1c 0:003
e c at fpy
Pn (kN)
MR-1 MR-2
2B 12.7 2B 9.5
886 876
593.6 586.9
590.9 800.2
0.00303 0.001549
46.64 27.2
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5. The engineering characteristics of the GFRP bars considered in this study can be reasonably estimated. However, as the ®eld data are still scarce and the relatively limited number of test specimens, careful attention should be paid to the limits and the capability of the models suggested in this paper. Acknowledgements The authors acknowledge the support of King Abdulaziz City for Science and Technology (KACST), who funded the research project AR-14-35 entitled ªGlass Fiber Reinforced Plastic Rebars: Properties and Applications in Concrete Structures.º References [1] Kakizawa T, Ohno S, Yonezawa T. Flexural behavior and energy absorption of carbon FRP reinforced concrete beams. Fiber-reinforced plastic reinforcement for concrete structures, SP-138, American Concrete Institute, 1993. p. 585±98. [2] Faza SS, Ganga Rao HVS. Theoretical and experimental correlation of behavior of concrete beams reinforced with ®ber reinforced plastic rebars. Fiber-reinforced plastic reinforcement for concrete structures, SP-138, American Concrete Institute, 1993. p. 599±614. [3] Nanni A. Flexural behavior and design of RC members using FRP reinforcement. Journal of the Structural Division, ASCE 1993;119(11):3344±59. [4] Saadatmanesh H, Ehsani M. Fiber composite bar for reinforced concrete construction. Journal of Composite Materials 1991;25(2):188±203. [5] Faza SS, Ganga Rao HVS. Bending and bond behavior of concrete beams reinforced with plastic rebars, Transportation Research
[6]
[7] [8] [9]
[10]
[11]
[12]
[13] [14]
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Record, No. 1290, Vol. 2, Third Bridge Engineering Conference, Transportation Research Board, Washington, DC, 1991. Dolan CW. Kevlar reinforced prestressing for bridge decks, Transportation Research Record, No. 1290, Vol. 1, Third Bridge Engineering Conference, Transportation Research Board, Washington, DC, 1991. ACI Committee 318 Building Code Requirements for Reinforced Concrete and Commentary (ACI 318-92/ACI 318R-92). American Concrete Institute, Detroit, 1992. 353 pp. Wang CK, Salmon CG. Reinforced concrete design, 5. New York: Harper and Row, 1992. 1030 pp. Al-Salloum YA, Alsayed SH, Almusallam TH, Amjad MA. Some design considerations for concrete beams reinforced by FRP bars. Proceedings of The First International Conference on Composites in Infrastructure (ICCI'96), Tucson, Arizona, 1996. p. 318±31. Al-Salloum YA, Alsayed SH, Almusallam TH, Amjad MA. Evaluation of service load de¯ection for beams reinforced by GFRP bars. Proceedings of The Second International Conference on the Use of Advanced Composite Materials in Bridges and Structures, ACMBS II, Montreal, Quebec, Canada, 1996. p. 165±72. Faza SS, Ganga Rao HVS. Pre- and post-cracking de¯ection behavior of concrete beams reinforced with ®bre-reinforced plastic rebars. In: Neale KW, Labossiere P, editors. Proceedings of The First International Conference on the Use of advanced Composite Materials in Bridges and Structures, ACMBS I, Montreal: Canadian Society for Civil Engineering, 1992. p. 151±60. Alsayed SH, Almusallam TH, Al-Salloum YA, Amjad MA. Glass ®ber reinforced plastic rebars: properties and applications for concrete structures, Final Report, Research Project AR-14-35, King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia, 1997. 327 pp. ACI Committee 440, State-of-the-art report on ®ber reinforced plastic FRP reinforcement for concrete structures. American Concrete Institute, 1996. 65 pp. Alsayed SH, Al-Salloum YA. Optimization of ¯exure environment of concrete beams reinforced with ®ber reinforced plastic rebars. Magazine of Concrete Research 1996;47(173):27±36.
www.elsevier.com/locate/compositesb
Performance of glass ®ber reinforced plastic bars as a reinforcing material for concrete structures S.H. Alsayed*, Y.A. Al-Salloum, T.H. Almusallam Department of Civil Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
Abstract The increasing use of ®ber reinforced plastic (FRP) bars to reinforce concrete structures necessitates the need for either developing a new design code or adopt the current one to account for the engineering characteristics of FRP materials. This paper suggests some modi®cations to the currently used ACI model for computing ¯exural strength, service load de¯ection, and the minimum reinforcement needed to avoid rupturing of the tensile reinforcement. Two series of tests were conducted to check the validity of the suggested modi®cations. The ®rst series was used to check the validity of the modi®cations made into the ¯exural and service load de¯ection models. The test results of the ®rst series were also analyzed to develop two simple models for computing the service load de¯ection for beams reinforced with glass FRP (GFRP) bars. The second series was used to check the accuracy of the modi®cation suggested into minimum reinforcement model. Test results of the ®rst series indicate that the ¯exural capacity of the beams reinforced by GFRP bars can be accurately predicted using the ultimate design theory. They also show that the current ACI model for computing the service load de¯ection underestimates the actual de¯ection of these beams. The two suggested models for predicting service load de¯ection accurately estimated the measured de¯ection under service load, and the simpler of the two pertains better predictions than those of the models available in the literature. Test results of the second series reveal that there is an excellent agreement between the predicted and recorded behavior of the test specimens, which suggests the validity of the proposed model for calculating the required minimum reinforcement for beams reinforced by GFRP bars. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Glass ®bers; Reinforced concrete structures
1. Introduction Lately, ®ber reinforced plastic (FRP) materials such as glass ®ber reinforced plastic (GFRP) rebars, as a reinforcing material for concrete structures, have received a great deal of attention among many engineering societies worldwide. Many engineers consider FRP as one of the most innovative material that may overcome the inherited de®ciency of reinforcing concrete structures by steel rebars in harsh environments due to corrosion. In comparison with steel, FRP have higher resistance to corrosion, higher tensile capacity, and lower weight. They are also non-conductive for electricity and non-magnetic. Thus, for structures built in or close to seawater or at similar corrosive environment, where electromagnetic neutrality and/or electric insulation are required, or exposed to deicing salts, FRP may become invaluable. Unfortunately, FRP are not free from hindrances that need to be resolved before they can be prescribed as a * Corresponding author. Tel.: 196614676925; fax: 196614677008. E-mail address: [email protected] (S.H. Alsayed).
reinforcing material for concrete structures. The major obstacles are the high initial cost, low modulus of elasticity, lack of ductility and absence of design guidelines. The ®rst of these obstacles is greatly in¯uenced by the manufacturing process. However, different low cost techniques are currently under development by many fabricators. The second and third obstacles (low modulus of elasticity and lack of ductility) are considered the major engineering drawbacks of the FRP materials. This is because when a concrete element is reinforced by FRP rebars, it may undergo larger de¯ection and suffer less margin of safety in comparison to that of its counterpart concrete element reinforced by steel bars. To overcome the fourth obstacle, a bulk of laboratory and ®eld data is needed. It is worth mentioning that the currently available design formulae for designing reinforced concrete (RC) elements as adopted by many design codes were originally developed with regard to that reinforcement is provided by steel. Thus, they may not be equally applicable to design concrete element reinforced by FRP rebars. On account of that, and to bene®t from the advantages of FRP materials, currently utilized design formulae must be reviewed considering the
1359-8368/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 1359-836 8(99)00049-9
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properties of FRP materials. Then, the formulae can be modi®ed, if necessary, to assure adequate safety and serviceability of the FRP concrete structures. The aim of this paper is to present the major results of an extensive research project that was carried out to study the actual behavior of concrete beams reinforced by GFRP bars and subjected to transverse (¯exure) loading. The work checks the suitability of using the existing ACI beam design equations for ¯exure and de¯ection when reinforcement is provided with GFRP bars and suggests the needed modi®cations to the equations in order to account for the engineering properties of GFRP bars. The study also investigates the condition of the required minimum GFRP reinforcement to avoid the catastrophic tensile failure of the beams. Modi®cations to the currently used models are suggested based on the test results of full size beams along with the equivalent data from the literature, whenever available. Further, the predicted service load de¯ections using the suggested models are compared with the measured de¯ections at midspan for these beams and their corresponding predicted values using the ACI model as well as those models available in the literature. It is hoped that the output of this study will help in paving the road for a design code for FRP material, which will help practitioners in designing and constructing concrete structures with FRP material that will ful®ll the strength and serviceability requirements and extend the useful service life of the infrastructure. 2. Flexural strength Before incorporating the GFRP bars into the design codes and standards, extensive research is needed to determine the values and limitations of design parameters. However, to minimize the possibility of having failure due to breakage of the GFRP bars, which is more brittle than failure due to crushing of concrete [1], researchers recommended some reduction factors to be applied to the GFRP ultimate tensile strength, fpu. Faza et al. [2] recommended that the maximum permissible strength, fpy, to be 0.80 of the ultimate strength. Nanni [3] suggested that the strength reduction factor, f , to be taken as 0.70 and the minimum ®ber plastic reinforcement ratio, r pmin, to be the larger of 1.33r pbal (rppbal is the balanced ®ber plastic reinforcement ratio) or 0:24 f 0c =fpu (to assure that fM n . M cr )Ðin general, researchers [2±6] recommended the use of some allowance (reduction factor) ranging from 0.70 to 0.80, that is to account for the possibility of experiencing undesired tensile failure type of GFRP bars. In other words, they have de®ned a pseudo yield point of fpy ranging from 0.70 to 0.80fpu for the FRP reinforcement. The ¯exural strength of a singly-reinforced beam section according to the ACI-Code provisions [7] requires Mu , fMn in which Mu is the required factored moment strength, Mn is the nominal moment strength of
the beam section, and f is the strength reduction factor (f 0:90 for ¯exure). For GFRP-RC beams, the ¯exural strength equation can be written as: fpy 1 Mn Ap fpy d 1 2 0:59rp 0 fc where, Mn nominal moment capacity of a section, N mm Ap area of GFRP rebars in tension region, mm 2 fpy pseudo yield tensile strength of GFRP rebars, MPa d distance from extreme comp. ®ber to centroid of tension reinforcement, mm rp ratio of tension reinforcement Ap =bd f 0c compressive strength of concrete, MPa b width of concrete section; mm: This is the same equation based on the ACI method after substituting the pseudo yield strength (fpy) of GFRP rebars for the yield strength of steel (fy) and the area of GFRP reinforcement (Ap) for the area of steel (As). This equation is actually based on tensile failure type in the tension reinforcement. As the tensile failure due to breakage of the GFRP bars is more brittle than that due to crushing of concrete, a compressive failure for GFRP-RC section is preferred and the nominal moment strength can be written as: a 2 Mn Ap fps d 2 2 where Mn is the nominal moment strength, Ap is the GFRPreinforcement area rp bd; r p is the GFRP-reinforcement ratio, b is the beam width, d is the effective depth, fps is the computed stress at the GFRP bars which corresponds to fs of the steel. The maximum value for fps is the usable stress limit of GFRP or the so-called pseudo yield tensile strength, fpy, which corresponds to fy of the steel. The fpy is assumed to be equal to 0.67 fpu, (the factor of safety, f pu =f py 1:5; equals to that usually considered against rupturing steel bars), fpu is the ultimate tensile strength of GFRP and a is the stressblock depth, a b1 c: Knowing that in case of compression failure, as shown in Fig. 1, the strain in the reinforcement, 1 ps, will be less than that of the pseudo yield limit, 1 py, which corresponds to 1 y of the steel. The 1 ps can be expressed in terms of the concrete strain in the extreme compression ®ber, 1 cu, and the distance from that ®ber to the neutral axis, c, as:
1ps 1cu
d 2 c c
3
and fps Ep 1ps
4
From the equilibrium requirements, the compression force C 0:85b1 f 0c bc should be equal to the tension force
S.H. Alsayed et al. / Composites: Part B 31 (2000) 555±567
557
Fig. 1. ACI ¯exural strength for singly reinforced RC section (with GFRP bars).
T rp bd fps : Thus, the distance c can be found as: 2s 3 2 m r m r p p 5d c 4 m rp 1 2 2 2
Ig the moment of inertia of the uncracked transformed section (gross concrete section). 5
where m is a material parameter, equals to Ep ecu = 0:85b1 f 0c ; and Ep is the modulus of elasticity of the GFRP material. 3. Serviceability requirements The de¯ection requirement of the ACI-Code Table 9.5(b) limits the computed de¯ection, D , to a speci®ed maximum permissible value, D a, which depends on the span length of the beam and the type of the member. Therefore, for simply-supported beam of span L loaded by two equal concentrated loads (P=2 each) symmetrically placed about the beam center line as shown in Fig. 2, the maximum de¯ection D computed at the beam center can be written as:
D
Ps 3L2 2 4s2 48Ec Ie
6
where L is the span of the beam, P is the total service concentrated load divided into two concentrated loads P=2 each applied at a distance s from the support, Ec is the modulus of elasticity of concrete, and Ie is the effective moment of inertia of the beam section. According to ACI-Code provisions, the effective moment of inertia, Ie, can be determined as follows: " # Mcr 3 Mcr 3 Ie Ig 7 1Icr 1 2 Ma Ma
Earlier results by the authors [9,10] showed that the current ACI model [7] underestimates the de¯ections in FRP beams and therefore it needs to be revised to account for the properties of FRP materials. There is, however, some research effort to develop new formulae or modify the currently used ones to account for the properties of FRP bars. Some of these formulae have already been suggested and become available in the literature. It is, however, useful to investigate the accuracy of these models before they can be used by practitioners for ®eld applications. Faza and Ganga Rao [11] derived an expression for the effective moment of inertia for FRP-RC beams loaded at the third points. This model is based on the assumption that concrete section between the point loads is fully cracked, while the end sections are partially cracked. Therefore, the cracking moment of inertia, Icr, is used in the middle third section of the beam, and the current ACI-Code equation Ie, is used in the end sections. Thus, the model can be written as: Im
23Icr Ie 8Icr 1 15Ie
8
where Im is the modi®ed moment of inertia valid for two
where, Mcr the cracking moment, Ma the maximum service moment, Icr the moment of inertia of the cracked transformed section,
Fig. 2. The simple beam subjected to two equal concentrated loads symmetrically placed about the beam centerline.
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concentrated point loads applied at the third points on the beam. This means that the smaller the distance between loads, the smaller the portion that is assumed to be fully cracked. Therefore, it is expected that the assumption in this model will produce higher values than the corresponding actual values of the effective moment of inertia when the distance between loads is less than 1/3 of the span. However, comparison between the measured and the corresponding predicted de¯ections using this model showed that the predicted de¯ections correlated well with the measured ones at service load level when the middle third of the span is assumed to be fully cracked regardless of the distance between the two point loads [12]. Another modi®ed expression for the effective moment of inertia for simply supported beams reinforced with FRP bars was proposed by the ACI Committee 440 [13]. It is expressed as follows: Ig Mcr 3 2 aIcr 9 Ie aIcr 1 b Ma in which a and b are reduction factors equal to 0.84 and 7.0, respectively. These factors account for the reduced area of the compression section when the applied moment reaches the cracking moment. When the ®rst term of Branson's expression is divided by b and the second term is multiplied by a , Eq. (9) is obtained. The results of the comparison using this model showed that the predicted de¯ections at service load level were overestimated for some beams [12]. 4. Minimum and maximum reinforcement requirements The ductility requirements of the ACI-Code provisions limit the steel pratio rs As =bd; to a lower and upper limits of rs-min f 0c =4fy (fy is in MPa) and rs-max 0:75rs-bal ; respectively, in which r s-bal is the balanced steel reinforcement ratio. Substituting the material properties of GFRP, the balanced reinforcement ratio expression for GFRP, r p-bal, becomes:
rp2bal
0:003Ep 0:85b1 f 0c fpy 0:003Ep 1 fpy
10
To avoid failure due to concrete rupture, the minimum GFRP reinforcement ratio should be larger than a certain value to assure that the nominal ¯exural strength, f Mn, of the RC beam is greater than the strength of plain concrete beam, Mcr, i.e.
fMn . Mcr
11
The required reinforcement ratio to satisfy the above condition can be derived as follows: For a concrete beam reinforced with steel rebars [8]; p f0 r $ 0:168 c f 0c and fy are in MPa fy For GFRP a factor of safety of 1.5 is assumed against
the possibility of tensile failure of the rebars. Hence, fpy 0:67fpu : Therefore, p0 f rpy $ 0:25 c : 12 fpu Thus, to avoid the possibility of the brittle failure of GFRP rebars and to assure that fMn . Mcr ; the minimum GFRP reinforcement ratio is assumed to be the larger value obtained from Eq. (10) (r p-bal) or Eq. (12). Further, since the failure of GFRP bars is of brittle type, therefore, there is no upper limit for reinforcement ratio. However, the maximum GFRP reinforcement ratio is governed by the practical considerations, e.g. spacing between bars and maximum size of aggregate. It should be noted that composite materials, in general, and GFRP in particular are susceptible to degradation initiated by moisture, temperature, and some loading and environmental conditions. However, such conditions were not accounted for in the aforesaid equations. 5. Test program of ¯exural capacity and serviceability 5.1. Test specimens A series of tests were conducted to study the ¯exural capacity and the serviceability requirements of GFRP-RC beams. A total of ®fteen (15) beams categorized into ®ve groups were tested in this program. Each group was composed of three identical specimens. While group I beams were reinforced with steel bars referred to as control specimens, the other four groups were reinforced with GFRP rebars. Group I beams were reinforced with steel rebars (control specimens), group II beams were reinforced with GFRP rebars considering the same dimensions of the control specimens and designed in accordance with the ACI Code ultimate design theory for compression failureÐ presented earlierÐto have the same capacity of group I beams. The third group (group III) was designed such that the ¯exural strength, serviceability and ductility requirements according to ACI Code are satis®ed. Group IV and V beams were provided with different depths and reinforcements, designed such that the ¯exural strength, serviceability and minimum reinforcement requirements are satis®ed. The serviceability requirement is such that the central de¯ection (computed using ACI Code with 5.5 power in Branson's expression) at service loading is almost the same as that of group I beams. All beams in this series were 2900 mm long, provided with B 8 mm diameter steel stirrups at 100 mm center to center, tested simply supported over a span of 2700 mm, and loaded by two concentrated loads placed at equal distance (100 mm) from the beam centerline as shown in Figs. 2 and 3. The GFRP rebars were of E-glass type (E-glass 76.14%, resin 22.18%, ®ller 1.26%, ultra violet 0.05% and catalysts
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559
Fig. 3. Test setup. Table 1 Beam details of the ®rst series of test specimens Beam group
Type of reinforcement
Reinforcement details
Reinforcement area, A (mm 2)
Overall depth, h (mm)
Width b (mm)
Effective depth, d (mm)
I II III IV V
STEEL GFRP GFRP GFRP GFRP
3B14 4B19 4B12.7 2B19 4B19
462 1134 507 567 1134
210 210 260 300 250
200 200 200 200 200
160.0 157.5 210.7 247.5 197.5
Table 2 Material properties of the ®rst series of test specimens Group
Bar diameter (mm)
f 0c (MPa) (concrete)
fy (MPa) (Steel)
fu (MPa) (GFRP)
E (MPa)
I II III IV V
14 19 12.7 19 19
31.3 31.3 31.3 40.7 40.7
553 ± ± ± ±
± 700 886 700 700
200000 35630 43370 35630 35630
0.37%) and were manufactured through pultrusion process in which the ®bers are passed through a resin bath and pulled through a die of the bar diameter. Further details of the cross-sections for the beams in this series and the materials properties are summarized in Tables 1 and 2. 5.2. Test results The average measured load±central de¯ection relationships
for the ®ve groups of beams are shown in Fig. 4. The results clearly show the in¯uence of reinforcing bar type and crosssectional dimensions on the overall load±de¯ection relationship. While group I and II beams are almost identical except for the type of reinforcing bars, a noticeable increase in group II beams Es =Ep . 4 de¯ection due to the replacement of steel rebars by relatively lower modulus GFRP rebars. An increase in the cross-sectional depth decreases the de¯ection of the beam. This can be clearly seen in the
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Fig. 4. The average measured load±de¯ection relationships for the ®ve groups of beams of the ®rst series of test specimens.
load±de¯ection relationships of groups III, IV and V beams compared to group II beams as shown in Fig. 4. The predicted loads and central de¯ections at service load (in this paper, the service load is assumed to be about 35% of the ultimate load) using ACI-Code procedure [7] for the ®ve groups of beams are shown in Tables 3 and 4, respectively, along with the corresponding measured results. The results show that groups I and II attained almost the same load capacity. This supports the validity of the procedure used to design the GFRP-RC beams, i.e. the ACI Code ultimate design theory for compression failure. The effect of replacing steel rebars by GFRP rebars on the de¯ection of beams can be clearly seen in the ®gure and in the tables. The increase in de¯ection is actually less than what was expected. For instance, although Es =Ep is larger than 4, the ratio of the central de¯ection of the GFRP-RC group II beams to that of the steel-RC group I beams at service load is 1.96. However, still such increase in de¯ection at service load implies that the de¯ection will control the design of intermediate to long span structural elements reinforced by GFRP bars. The difference between the expected and the measured ratios may be ascribed to the interaction effect of the composite and also to the loading con®guration. The results reported in Table 4 also show the bene®t of increasing the depth and decreasing the reinforcement of group III beams compared to those of group II beams. The increase of the overall depth was 24% (260 mm versus 210 mm for group II). Bene®ts of such increase Table 3 Measured and calculated ultimate load Beam group
I II III IV V
Ultimate load, Pn, (kN) Measured
ACI
56.5 54.7 72.2 94.7 91.2
55.6 51.0 65.9 92.5 84.2
Load ratio (ACI/measured)
0.98 0.93 0.91 0.98 0.92
in depth include reducing the amount of needed GFRP bars by 55% (4B 19 mm versus 4B 12.7 mm), increasing the ¯exural capacity by 32% (54.7 MPa versus 72.2 MPa), reducing the de¯ection at same load (20 kN) by 31% (10.64 versus 7.38). Reducing the amount of GFRP bars implies great reduction in the overall cost of construction. For instance, when the costs of concrete, steel, GFRP and form work are assumed to be US$ 100/m 3, 610/ton, 9150/ton and 2/m 2, respectively, the reduction in cost of the GFRP-RC beams of group III as compared to that of group II is about 40% [14]. Thus, the increase in the overall cost that may result from replacing steel by GFRP bars to reinforce concrete structures can be tremendously reduced by increasing the depth of the cross-section. This, however, may not be the ideal solution for multi-story structures as the reduction in their cross-sectional dimensions is, in most cases, an insisted desired. The results of Fig. 4 also show that groups IV and V attained almost the same load capacity. This again supports the validity of the procedure used to design the GFRP-RC beams for strength. In other words, the ultimate ¯exural capacity of GFRP-RC beams can be reasonably estimated using Whitney's rectangular stress block. Furthermore, these GFRP-RC beams of groups IV and V have almost the same behavior at the service load level. It is interesting to mention that due to the factor of safety used against the possibility of experiencing tensile failure of GFRP rebars fpy 0:67fpu ; all GFRP-RC beams considered in this study showed concrete compressive failures. Typical failure of the test specimens is shown in Fig. 5. While the results show that there is a good agreement between the experimental and theoretical (ACI-Code) results for loads and de¯ections for beams reinforced with steel bars (group I), the results shown in Table 4 for other groups clearly present the fact that the current ACI model prediction for the de¯ection of beams reinforced by GFRP bars is under-estimated. This clearly shows that there is a need to modify the current ACI equation for de¯ection prediction.
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561
Table 4 Central de¯ection values at service load Beam group
Ultimate load, Pn (kN)
I II III IV V
55.6 51.0 65.9 92.5 84.2
Service load, Ps (kN)
20 20 26 40 33
5.3. De¯ection prediction models As pointed out earlier, there is a need to modify the current ACI equation to predict de¯ections under service loads. To do so, the experimental results obtained in this study were analyzed. The experimental values of the effective moment of inertia Ie were determined using Eq. (6) as follows: Ie exp
1 2
P exp s 3L2 2 4s2 24Ec D exp
13
and from Eq. (7), the power (m) can be written as: ! Ie 2 Icr log Ig 2 Icr m Mcr log Ma
14
Central de¯ection (mm) Measured
ACI
5.44 10.64 11.32 14.23 11.81
5.18 8.14 5.67 5.57 7.73
De¯ection ratio (ACI/measured)
0.95 0.77 0.50 0.39 0.65
The experimental values of the effective moment of inertia determined from Eq. (13) were used in Eq. (14). The regression analysis was performed on the results for service load range. The results suggest that the average value of the power (m) for GFRP-RC beams can be taken approximately as 5.5 rather than 3 as suggested by Branson for steel-RC beams [7]. Thus, the suggested model (Model-A) can be considered as a modi®ed Branson's equation to determine the effective moment of inertia for beams reinforced by GFRP bars. It can be written as: Model A: " # Mcr 5:5 Mcr 5:5 Ie I g 15 1Icr 1 2 Ma Ma Another model (Model B) is suggested based on the analysis of the experimental data of Ie =Icr versus Ma =Mcr
Fig. 5. Typical failure of the test specimens.
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Fig. 6. The Ie =Icr versus Ma =Mcr for the GFRP-RC beams.
for beams reinforced by GFRP bars. The Ma =Mcr greater than 1.0 are plotted in Fig. 6. sion analysis which was performed on these gests that the effective moment of inertia can follows: Model B: Ie aIcr
for 1:0 ,
Ie Icr
for
Ma , 3:0; Mcr
Ma . 3:0; Mcr
results for The regresresults sugbe taken as
where
a 1:40 2
2 Ma : 15 Mcr
16c
5.4. Model validation 16a
16b
The values of the effective moment of inertia Ie determined using the above-suggested models are plotted versus Ma =Mcr for each group of beams in Figs. 7±10. They are plotted besides the experimental values determined using Eq. (13) and those of the ACI model. The results for those beams reinforced with GFRP bars shown in Figs. 7±10
Fig. 7. The effective moment of inertia versus Ma =Mcr for group II beams.
S.H. Alsayed et al. / Composites: Part B 31 (2000) 555±567
563
Fig. 8. The effective moment of inertia versus Ma =Mcr for group III beams.
clearly indicate that there is an abrupt change in the actual effective moment of inertia determined from the experimental results, Eq. (13), once the applied moment exceeds Mcr. The value of Ie(exp) drops to a value slightly above Icr. This is attributed to the effect of the low modular ratio for these beams due to low modulus of elasticity of the GFRP bars. This is another indication that Branson's equation is not recommended for beams reinforced with GFRP rebars. The predicted de¯ections at service load level are computed for models available in the literature as well as for the two suggested models. The results are compared with the corresponding experimental results.
The predicted central de¯ection for each group of beams is calculated using a spreadsheet program. All models considered (®ve models) are summarized in Table 5. The measured and predicted results for GFRP-RC beams, groups II through V, using these models at service load level are summarized in Table 6. The ratio of the predicted with respect to the measured service de¯ection is also shown in Table 6. The error in each model that represents the percentage difference between the predicted and the measured values of short-term service de¯ections for the four groups are presented graphically in Fig. 11. The results show the accuracy of the two models suggested in this study along
Fig. 9. The effective moment of inertia versus Ma =Mcr for group IV beams.
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S.H. Alsayed et al. / Composites: Part B 31 (2000) 555±567
Table 5 The models used to predict the effective moment of inertia for beams reinforced by GFRP bars Model ACI-318
Expression Ie Ig
Suggested by
Mcr Ma
3
"
1Icr 1 2
Mcr Ma
3 #
23Icr Ie 8Icr 1 15Ie
Faza and Ganga Rao
Im
ACI-440
in which Ie is computed according to ACI-318 " # Ig Mcr 3 Mcr 3 Ie 1aIcr 1 2 b Ma Ma
A
Ie Ig
Mcr Ma
5:5
Faza and Ganga Rao [11]
" 1Icr 1 2
Mcr Ma
5:5 #
2 Ma M Ie 1:40 2 Icr for 1 , a , 3 15 Mcr Mcr
B
Ie Icr for
ACI Committee 318 [7]
ACI Committee 440 [13]
Current study
Current study
Ma .3 Mcr
with that of Faza and Ganga Rao [11]. The results also show that although model B is simple and much easier to use, it is the most accurate one among all other models.
6. Test program of minimum reinforcement condition 6.1. Test specimens As explained earlier, this part of test program was
conducted to investigate the minimum reinforcement requirement for GFRP-RC beams. A total of six (6) beams were tested in this program. They were categorized into two groups. Each group was composed of three identical specimens. Group (MR-1) beams were reinforced with minimum amount of GFRP reinforcement, while group (MR-2) beams were reinforced with reinforcement less than the minimum amount of GFRP rebars. The cross-sections of beam specimens of Groups (MR-1) and (MR-2) were 200 £ 210 mm 2, and 2320 mm long.
Fig. 10. The effective moment of inertia versus Ma =Mcr for group V beams.
S.H. Alsayed et al. / Composites: Part B 31 (2000) 555±567
565
Fig. 11. The error percentage in each model for the four groups of GFRP-RC beams at service load level.
Fig. 12. The average measured load±de¯ection relationships for the two groups of beams of the second series of test specimens. Table 6 Measured and predicted central de¯ections using all models at service load levels Group
P-Service (kN)
D measured (mm)
Model
D predicted (mm)
D predicted/D measured
II
20
10.64
III
26
11.32
IV
40
14.23
V
33
11.81
ACI-318 Faza and Ganga Rao ACI-440 A B ACI-318 Faza and Ganga Rao ACI-440 A B ACI-318 Faza and Ganga Rao ACI-440 A B ACI-318 Faza and Ganga Rao ACI-440 A B
8.14 10.76 12.16 11.35 10.95 5.67 11.14 14.06 10.64 12.18 5.57 12.59 16.19 11.62 14.19 7.73 10.49 11.97 11.13 10.83
0.77 1.01 1.14 1.07 1.03 0.50 0.98 1.24 0.94 1.07 0.39 0.88 1.14 0.82 1.00 0.65 0.89 1.01 0.94 0.92
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Table 7 Beams details and material properties of the second series of test specimens Group
Reinforcement
Ap (mm 2)
fpu (MPa)
EP (MPa)
f 0c (MPa)
b (mm)
h (mm)
d (mm)
MR-1 MR-2
2B12.7 2B9.5
53.4 142.5
886 876
43370 42020
39.6 39.6
200 200
210 210
160.7 162.2
Table 8 The reinforcement ratios of the two groups p Group r p-bal 0:25 f 0c =fpu r min
r used
r /r min
MR-1 MR-2
0.007885 0.004392
1.0083 0.5645
0.00782 0.00778
0.001776 0.001796
0.00782 0.00778
Group (MR-1) was reinforced with 2#4 (B 12.7 mm) GFRP bars (r 1:008rmin ). Group (MR-2) beam specimens was reinforced with 2#3 (B 9.5 mm) GFRP bars (r 0:565rmin ). The two groups were provided with B 8 mm steel stirrup at 100 mm center to center, tested simply supported over a span of 2120 mm, and loaded by two concentrated loads placed at equal distance (100 mm) from the beam center line. Further details of the cross-sections for the beams in this series and the materials properties are summarized in Tables 7 and 8. 6.2. Test results The measured load±de¯ection curves for specimens of the two groups are shown in Fig. 12. The results show that the reinforcement ratio has a signi®cant in¯uence on the behavior of GFRP-RC beams. The ®rst group (MR-1), which was designed such that the reinforcement is minimum, failed in compression (crushing of concrete) as was expected. The second group (MR2), in which the reinforcement is less than the minimum failed in tension due to GFRP rebars tensile failure, rupture of bars. The results shown in Table 9 indicate that MR- 1 beams in which r rmin rbal ; the stress in the GFRP bars reached almost 0.67fpu when the strain in the extreme compression ®ber of concrete reached 0.003. This result was expected since the reinforcement ratio used in beams of this group equals to the balanced reinforcement ratio. This failure is a balanced failure (it is indeed a compression failure since 1cu 0:003 and fpy 0:67fpu ). On the other hand, MR-2 beams in which r , rmin ; the stress in the rebars reached 0.67fpu when the strain in the extreme compression ®ber of concrete was less than
0.003. When the applied loads exceeded that, the stress in rebars exceeded the pseudo yield limit .0:67f pu : When the strain in concrete reached 0.003, the stress in the rebars reached about 800 MPa which is slightly less than the ultimate value of 876 MPa. As the applied load increased, the rebars failed in tension and the beam was cut into two parts. These results support the theoretical derivations that were presented earlier in this paper. 7. Conclusions The validity of using the current ACI-318 code of practice for both strength and serviceability requirements for designing concrete beams reinforced with GFRP rebars was investigated. The results revealed the following remarks: 1. The ¯exural capacity of concrete beams reinforced by GFRP bars can be accurately estimated using the ultimate design theory (when failure occurs due to crushing of concrete in the compression side) which is also applicable to design of concrete beams reinforced by steel bars (over reinforced sections). 2. Due to the low modulus of elasticity of GFRP rebars EGFRP =Esteel < 0:25; de¯ection criterion may control the design of intermediate and long beams reinforced with GFRP rebars. The current ACI equations, developed for steel-reinforced concrete beams, highly underestimates the actual de¯ection of the concrete beams reinforced by GFRP bars. 3. Based on the experimental results, two simple empirical models are suggested to predict the actual service load de¯ection. The accuracy of the models pertains good agreement with measured values. They are simple to use and provide, in most cases, better prediction than those by other models available in the literature. 4. To avoid the possibility of a catastrophic failure due to reinforcing rebars rupture, a model to estimate the minimum required reinforcement ratio is suggested. The model was checked experimentally and pertained good agreement with test results.
Table 9 Theoretical results of beams with different reinforcement ratios of GFRP bars Group
Reinforcement details
fpu (MPa)
Fpy (MPa) ( 0.67 fpu)
fs (MPa) 1c 0:003
e c at fpy
Pn (kN)
MR-1 MR-2
2B 12.7 2B 9.5
886 876
593.6 586.9
590.9 800.2
0.00303 0.001549
46.64 27.2
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5. The engineering characteristics of the GFRP bars considered in this study can be reasonably estimated. However, as the ®eld data are still scarce and the relatively limited number of test specimens, careful attention should be paid to the limits and the capability of the models suggested in this paper. Acknowledgements The authors acknowledge the support of King Abdulaziz City for Science and Technology (KACST), who funded the research project AR-14-35 entitled ªGlass Fiber Reinforced Plastic Rebars: Properties and Applications in Concrete Structures.º References [1] Kakizawa T, Ohno S, Yonezawa T. Flexural behavior and energy absorption of carbon FRP reinforced concrete beams. Fiber-reinforced plastic reinforcement for concrete structures, SP-138, American Concrete Institute, 1993. p. 585±98. [2] Faza SS, Ganga Rao HVS. Theoretical and experimental correlation of behavior of concrete beams reinforced with ®ber reinforced plastic rebars. Fiber-reinforced plastic reinforcement for concrete structures, SP-138, American Concrete Institute, 1993. p. 599±614. [3] Nanni A. Flexural behavior and design of RC members using FRP reinforcement. Journal of the Structural Division, ASCE 1993;119(11):3344±59. [4] Saadatmanesh H, Ehsani M. Fiber composite bar for reinforced concrete construction. Journal of Composite Materials 1991;25(2):188±203. [5] Faza SS, Ganga Rao HVS. Bending and bond behavior of concrete beams reinforced with plastic rebars, Transportation Research
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Record, No. 1290, Vol. 2, Third Bridge Engineering Conference, Transportation Research Board, Washington, DC, 1991. Dolan CW. Kevlar reinforced prestressing for bridge decks, Transportation Research Record, No. 1290, Vol. 1, Third Bridge Engineering Conference, Transportation Research Board, Washington, DC, 1991. ACI Committee 318 Building Code Requirements for Reinforced Concrete and Commentary (ACI 318-92/ACI 318R-92). American Concrete Institute, Detroit, 1992. 353 pp. Wang CK, Salmon CG. Reinforced concrete design, 5. New York: Harper and Row, 1992. 1030 pp. Al-Salloum YA, Alsayed SH, Almusallam TH, Amjad MA. Some design considerations for concrete beams reinforced by FRP bars. Proceedings of The First International Conference on Composites in Infrastructure (ICCI'96), Tucson, Arizona, 1996. p. 318±31. Al-Salloum YA, Alsayed SH, Almusallam TH, Amjad MA. Evaluation of service load de¯ection for beams reinforced by GFRP bars. Proceedings of The Second International Conference on the Use of Advanced Composite Materials in Bridges and Structures, ACMBS II, Montreal, Quebec, Canada, 1996. p. 165±72. Faza SS, Ganga Rao HVS. Pre- and post-cracking de¯ection behavior of concrete beams reinforced with ®bre-reinforced plastic rebars. In: Neale KW, Labossiere P, editors. Proceedings of The First International Conference on the Use of advanced Composite Materials in Bridges and Structures, ACMBS I, Montreal: Canadian Society for Civil Engineering, 1992. p. 151±60. Alsayed SH, Almusallam TH, Al-Salloum YA, Amjad MA. Glass ®ber reinforced plastic rebars: properties and applications for concrete structures, Final Report, Research Project AR-14-35, King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia, 1997. 327 pp. ACI Committee 440, State-of-the-art report on ®ber reinforced plastic FRP reinforcement for concrete structures. American Concrete Institute, 1996. 65 pp. Alsayed SH, Al-Salloum YA. Optimization of ¯exure environment of concrete beams reinforced with ®ber reinforced plastic rebars. Magazine of Concrete Research 1996;47(173):27±36.