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Analysis of the flexural stiffness of timber beams reinforced with carbon and basalt composite materials
Accepted Manuscript Analysis of the flexural stiffness of timber beams reinforced with carbon and basalt composite materials Pilar de la Rosa García, Alfonso Cobo Escamilla, M.Nieves González García PII:
S1359-8368(15)00596-X
DOI:
10.1016/j.compositesb.2015.10.003
Reference:
JCOMB 3819
To appear in:
Composites Part B
Received Date: 30 June 2015 Accepted Date: 6 October 2015
Please cite this article as: de la Rosa García P, Escamilla AC, González García MN, Analysis of the flexural stiffness of timber beams reinforced with carbon and basalt composite materials, Composites Part B (2015), doi: 10.1016/j.compositesb.2015.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Analysis of the flexural stiffness of timber beams reinforced with carbon and basalt composite materials a,*
b
c
Pilar de la Rosa García ,Alfonso Cobo Escamilla , M. Nieves González García aArchitectural
Construction Department, School of Building Engineering, Polytechnic University of Madrid, Juan de
b.
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Herrera Street, 6, 28040, Madrid. [email protected]. Edification Technology Department, School of Building Engineering, Polytechnic University of Madrid, Juan de
Herrera Street, 6, 28040, Madrid. alfonso.cobo @upm.es cArchitectural
Construction Department, School of Building Engineering, Polytechnic University of Madrid, Juan de
Herrera Street, 6, 28040, Madrid. [email protected] author. Tel. +34687246944
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*Corresponding
Abstract
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In this work, an experimental study on the bending behavior of pine wood beams reinforced with carbon and basalt fiber reinforced plastics, externally glued with epoxy resins has been performed. Different grammage, unidirectional and bi-directional fabrics have been used, and one or three layers applied. The results show good behavior of basalt fiber reinforcements in the stiffness increase of timber beams, achieving similar results to those obtained with carbon fiber.
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Moreover, reinforcements made with bi-directional fabrics produced significant stiffness increases compared to the unidirectional fabrics. Finally, this work includes also the results obtained using the transformed section to predict the stiffness increase that the different types
Keywords:
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of reinforcement analyzed produces.
A. Polymer matrix composites (PMCs)
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A. Wood (pinus sylvestris) B. Mechanical properties D. Mechanical testing 1. Introduction
Historically, wood has been a material used in the field of civil engineering and construction. On many occasions, after some time, the structures need to be reinforced for various reasons: they need to increase the capacity due to a change in use; because of pathological problems which diminish their resistance, or because the excessive deformations are incompatible with the
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ACCEPTED MANUSCRIPT partitions or finishes. The procedures used to reinforce structures have been the focus of numerous studies, due to the fact that the economic volume these types of actions imply is quite considerable. Traditionally, the reinforcement techniques used in timber structures have mainly steel or wood [1]. The use of composite materials and more specifically of fiber reinforced
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polymers (FRP) in the construction industry is relatively recent when compared to the traditional systems.
Wood is a natural material with an excellent relationship between mechanical characteristics
and weigh. This feature is maintained with the use of composite materials as strengthening. In
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terms of the constitutive model, an elastic linear behavior under tensile stress parallel to the fiber up to fracture is admitted, while compression is considered as an initial linear elastic
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behavior followed by a plastic one [2,3].
In sawn timber beams subjected to bending, the predominant failure is due to tensile stress, frequently locating the fracture at the lower beam side. FRP have a linear elastic behavior up to fracture under tensile stress, and they have excellent mechanical properties, with high elasticity module and tensile strength values, in relation to the weight and volume. If a beam is reinforced
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at the bottom side, it increases tensile strength and it is likely to produce an increase in its stiffness. The first relevant application of the use of FRP to reinforce timber structures was carried out in 1995 in the bridge of Sins in Switzerland [4]. In this case, the cross beams of the
of the beams.
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bridge had an excessive deflection, and so the aim to strengthen it was to increase the stiffness
The first studies published on the behavior of timber elements reinforced with FRP correspond
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to the 1960s [5,6]. Research studies have progressively increased in order to expand the knowledge on the matter. Several aspects are analyzed in this type of publications, being stiffness of the elements one of the most important, as well as other issues, such as the load capacity increase, the influence of reinforcement in the fracture mode [7] and the integrity of the bonding surface between wood and the composite material until failure occurs [8,9]. In addition, many studies compare the experimental values obtained in fracture load and stiffness with the analytical values obtained using different calculation models. Usually the models applied are the transformed section, and the ones derived from applying the equilibrium
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ACCEPTED MANUSCRIPT equations to the reinforced section, considering timber behavior model as an elasto-plastic for compression and a linear elastic one under tensile stress. A linear elastic behavior up to the fracture is always considered for composite materials [10]. More recent studies have modeled how strengthening works by applying a finite element method [11,12]. Quanfeng in 2010 [13]
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concludes that this is a reliable method to simulate the behaviour of timber beams reinforced with FRP. The results obtained by different authors concerning the increase in stiffness of
tested beams varies depending on the volume of FRP applied in the section of the beams, the type of fiber that forms the composite material, the type and placement of reinforcements, and
between the timber and the reinforcing material.
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the previous characteristics of the reinforced elements, in addition to the type of bonding
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Some results concerning stiffness increase are presented in the work published by Tingley et al. (2001) [14], where in this case, the beam reinforcement was performed with aramid fiber, resulting in a stiffness increase of about 5% compared to beams without composite reinforcing. Fiorelli et al. (2002) [15] used fiberglass and carbon for the reinforcements, and obtained an increase between 15-30% with a reinforcement volume of 1% and 0.4% of glass fiber FRP
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(GFRP) and carbon FRP (CFRP), respectively. In addition, it was found that increasing the volume of GFRP to 3%, the stiffness increased reached up to 60%. At the same time, the work of Borri A. et al. (2005) [16] compared the behavior of three types of reinforcement -- all of them
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CFRP -- but with different characteristics: the first type consisted on prestressed sheets, the second one, sheets without being prestressed, and finally in the third case, pultruded rods were applied. The difference in the stiffness increase between the three applied types was not
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significant, being the stiffness increase in relation to non-reinforced beams of 22.5-30.3%. More recently, works have been published in which composite materials have been reinforced with sustainable fibers from the environmental point of view, such as basalt [17], hemp and flax [18], analyzing their performance on structural wooden elements. In 2014, Gary M. et al. [19] tested low quality laminated timber beams reinforced with pultrusion rods of basalt fiber-reinforced polymers. In this case, the stiffness increase was 8.4%, with 1.4% reinforcement volume applied to the beams section. Finally, in 2013 Borri A. et al [20] published the findings after
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ACCEPTED MANUSCRIPT testing 45 beams stating that composite materials of different kinds of natural fiber (basalt, flax and hemp) showed a good performance to stiffness increase. Fibers initially used for the manufacture of composite materials in timber beams reinforcement were glass fibers [20-24], and later carbon fibers [25] and aramid fibers [26] were subsequently
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incorporated. The latest trend is focused on the study of the behavior of natural fibers [17-20]. Some authors have analyzed the behavior of reinforced beams to shear stress through sheets arranged transversally and longitudinally to the direction of the wood fiber on the lateral beam sides [27,28]. Another form of shear reinforcement has been carried out with FRP pultruded
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rods embedded in epoxy resin into holes in the lower beam face [29]. This provision of the
reinforcement is intended to diminish the possible early failure to shear effect that the drying
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splits may cause on beams subjected to bending. Integrity of the interphase between composite and wood has also been studied at various times [31], since this is one of the most important aspects influencing the proper functioning of the reinforcements.
This work studies the increase of stiffness experienced on Pine timber sawn beams when reinforced with composite fabrics. Basalt (BRFP) and carbon (CFRP) fabrics with different
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grammage have been applied, placed in "U" shape, wrapping part of the beam section. 2. Materials and testing method
Tests have been performed with 27 timber beams, 9 were tested in flat position and 18 in edge
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position. Timber used has been 78x155mm of section and 1090mm in length Valsain pine. The reinforcement placement has been in "U" shape in all cases, as shown in Figure 1. Tests have been conducted with a universal press, Ibertest Mib, controlling the speed of the displacement
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(0.05 mm/s). The beams were subjected to three-points bending test, applying the load at the center point of the beam (Fig. 2). Bending test for each beam was conducted in two phases. In the first phase, beams were loaded before being reinforced up to a load value producing in the most stressed fibers a tensile stress of approximately 33% of the ultimate fracture strength, so as to obtain the initial load-displacement beam diagram without reinforcement. With this load value, beams did not exceed, in any case, the elastic and linear behavior. Subsequently, they were reinforced with the different types of fabric and number of layers, and were tested to fracture.
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ACCEPTED MANUSCRIPT Reinforcements were performed with CFRP and BFRP, manufacturing the composite material in-situ, at the same time as the reinforcement was being carried out. Nine flat beams studied were reinforced with unidirectional fabrics, 3 of them with basalt fabric of grammage equal to 2
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2
2
2
3
280 g/m (FB280 ), 3 with 600g/m (FB600 ) basalt fiber fabric and 3 with 300 g/m (FC300 )
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carbon fiber fabric. From the 18 edge beams tested, nine were reinforced with unidirectional and nine with bi-directional fabric. The ones reinforced with unidirectional fabrics were divided into three groups, as done with the other flat beams, and were reinforced with FC300, FB600, and FB280 respectively. The nine remaining edge beams were reinforced with bi-directional 2
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carbon fiber fabric, of grammage 210 g/m , placing the reinforcements in three layers (FC210 4
#3 ). Table 1 shows the characteristics of the fabrics used for performing the reinforcements.
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The last row shows the fabric stiffness when under axial stress, obtained as the product of its elasticity module by its thickness. In the case of FC210 #3, the thickness has been considered as the one corresponding to the three layers.
The matrix used for the manufacture of composite materials was epoxy resin, and the same resin has been used as adhesive between the wood and the reinforcement. Prior to the
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application of the first resin coat, the wood surface was cleaned with a brush and a primer coat applied to improve bonding between the composite and wood. After the primer was applied, an 2
initial resin coat, with an approximate yield of 0.5 kg/m was spread. Subsequently, the
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unidirectional fabric reinforcement was placed parallel to the longitudinal direction of the beam, 2
and finally a finishing layer of the same epoxy resin, with an approximate yield of 0.3 kg/m was applied. For the bi-directional fabric reinforcement, (FC210 #3) a similar process was followed,
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although 3 layers of fabric were applied. Figure 3 shows pictures of six of the beams. 3. Test results
The software associated with the testing machine supplied the obtained data, and these corresponded to the applied loads and the vertical displacement experienced by the beams at the load application point. For each beam, two load-displacement graphs were obtained
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unidirectional basalt fibers of 280 g/m2 grammage reinforcement unidirectional basalt fibers of 600 g/m2 grammage reinforcement 3 unidirectional carbon fibers of 300 g/m2 grammage reinforcement 4 bi-directional carbon fiber of 210 g/m2 grammage reinforcement with a triple layer 2
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ACCEPTED MANUSCRIPT corresponding to the beam preload stage before being reinforced, and to the beam test after being reinforced. 3.1. Flat beams reinforced with unidirectional fabrics FB280, FB600, and FC300. Figure 4 presents the results of flat beams reinforced with FB280, FB600, and FC300. Each
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graphic represents the load-displacement diagrams of each beam without reinforcement and after being reinforced. The first column includes three graphics corresponding to the beams
reinforced with FB280, while the second and third columns correspond to the ones reinforced with FB600 and FC300, respectively.
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3.2 Edge beams reinforced with unidirectional fabrics FB280, FB600, and FC300.
Figure 5 shows the results for edge beams, similarly to what is shown in Figure 4 with the flat
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beams. In this case, three beams have also been tested before and after applying the reinforcement with every type of reinforcement.
3.3. Edge beams reinforced with triple-layer fabric FC210 #3
In figure 6, the load-displacement graphs corresponding to the 9 edge beams –with reinforcement of FC210#3 and without it—can be seen.
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4. Analysis of results
4.1. Flat beams reinforced with unidirectional fabrics FC300, FB600, and FB280. The graphs in Figure 4 show a very linear behavior in all cases. In all tested beams, the curves
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of the load-displacement diagrams have higher slope in the case of reinforced beams, which indicates that the increase of stiffness occurs in all cases. Comparing the different fabrics used, it can be observed that the stiffness increase is slightly higher in the case of beams reinforced
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with FB600 and FC300 when compared to the reinforced with FB280. Among the stiffness of beams reinforced with FB600 and FC300, not a clear difference can be observed. Table 2 presents the numeric values of the slope of each of the load-displacement graphic represented in Figure 4. In the second and third columns, the stiffness values of the beams before and after being reinforced, Knr, and Kref respectively, are included. The fourth column indicates the quotient between Kref and Knr (Dexp). All Dexp values are higher than the unit, indicating that the reinforcement has resulted in a stiffness increase in all cases. In the last column, the mean values of the stiffness increase corresponding to each type of reinforcement
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ACCEPTED MANUSCRIPT (Dm) are presented. The analysis of the Dm values suggests that the type of reinforcement resulting in higher increase of stiffness in the tested beams is produced with FB600, followed by the FC300, and finally the FB280. If these results are compared to the axial stiffness of the fabrics used (table 1), it can be seen that there is no relationship between the stiffness of the
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reinforcement placed and the stiffness of the reinforced beam. The FC300 fabric has double the stiffness of FB600 and nevertheless, beams reinforced with FB600 give rise to more stiff solutions than the reinforced with FC300 (table 2).
4.2 Edge beams reinforced with unidirectional fabrics FC300, FB600, and FB280.
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The behavior of reinforced edge beams (Figure 5) is less linear than that of the flat beams (Figure 4). Again, in all cases, an increase of stiffness is produced in reinforced beams. In
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addition, in the most cases, the stiffness increase of the edge beams is greater than that of the flat beams. Moreover, comparing the fabrics used in reinforcements, it can be seen in this case that the reinforcements FB600 and FC300 present a slightly greater increase than that of the FB280.
Table 3 presents similar information to that of table 2, but in this case the results apply for edge
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beams. Comparing the mean values of Dm, it can be observed that the greatest stiffness increase is experienced by the beams reinforced with fabric FB600, followed by the FC300 and finally the reinforced with FB280, which are those that produce a lower stiffness increase. If
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these results are compared with the results on table 2 of the flat beams, we can see that increases in the case of edge beams are greater, and that in both cases the reinforcements that produce the greatest increase are FB600, and the ones with the smallest stiffness increase are
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FB280. Once again, there is no relationship between the stiffness of the fabric used as reinforcement and stiffness of reinforced beam. In addition, if Dm values of edge beams (table 3) are compared with the flat beams (table 2), it can be confirmed that the stiffness increase in edge beams is greater than that of flat beams. This is because the same fabric produces an increase of the inertia moment, which is greater in an edge beam than in a flat beam. 4.3. Edge beams reinforced with FC210 #3 In the 9 graphs of Figure 6, it can be observed that the stiffness increase of reinforced beams compared to the same non-reinforced ones is significant. It shows a greater stiffness increase
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ACCEPTED MANUSCRIPT regarding the previous cases of unidirectional fabrics. Also, in many cases, the behavior of reinforced beams is not linear throughout the diagram. In table 4 the analytical values of stiffness of beams before and after being reinforced with FC210#3 are indicated. The last column represents the mean value of the stiffness increase Dm
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of the nine tested beams. When this average value is compared with that obtained in the case of unidirectional fabrics, a significant difference can be observed, being the increase in this case, more than double that of the beams reinforced with a unidirectional layer. The axial stiffness of fabric FC210 #3 is nearly identical to the fabric FC300, and nevertheless, the
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increase in stiffness of beams reinforced with FC210 #3 is more than double that of the
reinforced with FC300 (tables 3 and 4). In this case, and given that both fabrics have the same
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modulus of elasticity, the difference in stiffness increases is quite possibly due to the bidirectional nature of FC210 #3 fabric fibers, preventing transversal deformations of the beam in an important part of the section. 5. Analytical study
An analytical study has been carried out calculating the value of the theoretical stiffness (Kth) of
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the beam. This theoretical value has been compared with the experimental value obtained in the tests, in order to study the adjustment between both values.
(1)
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The theoretical stiffness of the beam was obtained from the following equation:
Where Kth is the theoretical stiffness of beam, L is the beam length, Iref is the moment of inertia of the reinforced section and Ew is the modulus of elasticity of wood. The elasticity module of wood has been obtained from the tests performed. For the inertia moment of the reinforced section, the method of the transformed section [31] given below has been used. In Figure 7, on the left, the type section of a reinforced edge beam is represented, while on the right, the transformed section corresponding to this section is reproduced. The transformed
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ACCEPTED MANUSCRIPT section is obtained by multiplying the thickness of the fabric reinforcing the beam, by a coefficient obtained as the quotient between the elasticity module of the reinforcing material and the elasticity module of wood. The dimensions et and bt of the transformed section have been calculated applying the following
EFRP EW
(2)
b t = b FRP ⋅
EFRP EW
(3)
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e t = eFRP ⋅
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equations:
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The value of the elasticity module of the reinforcement (EFRP) is taken from the mechanical properties of the fabric sheets provided by the manufacturer. The value of Ew has been
L3 Ew = mNR ⋅ 48I
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calculated from the experimental values obtained in testing by applying the following equation:
(4)
Once the geometric characteristics of the sections have been determined with equations 2 and
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3, the wood elasticity module values have been calculated using equation 4. Finally, applying equation 1, Kth values were obtained. The values of experimental stiffness (Kexp) and theoretical
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stiffness (Kth) obtained for all tested beams and their comparison are shown in tables 5, 6 and 7. The analysis of tables 5, 6 and 7 suggests that in all cases, the stiffness values obtained using the theoretical values for the inertia moment (Kth) are higher than the stiffness values obtained experimentally in beams tested to bending. However, while for beams strengthened with BFRP, the difference between the experimental and theoretical values is relatively small, with a maximum deviation of 18% in edge beams, for beams reinforced with CFRP, differences are higher, reaching 31% in the edge beams reinforced with FC300 and FC210 #3. The difference in the results obtained with BFRP as opposed to the ones with CFRP, regarding kexp/kth, may be
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ACCEPTED MANUSCRIPT due to the lower E value of the basalt fiber, which "fits" timber better. The enormous difference between the E value of carbon fiber and wood implies that in the interphase between two materials it is necessary to mobilize enormous shear stresses, that might produce some slippage between both materials, decreasing the stiffness of the reinforced beam. It must be
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observed that this occurs for low compression strength values, such as those produced in the range of loads applied in tests. As a strategy to reinforce bending strength, it could be interesting to use materials with a not too high E value. 6. Conclusions
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The knowledge of new reinforcement techniques applied to materials traditionally used such as wood has revealed aspects of great interest. This study has experimentally proven a good
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performance to increase the stiffness of wooden beams, using unidirectional fabrics of both BFRP and CFRP and of bi-directional CFRP fabric systems glued externally with epoxy resins to sawn timber pine beams. The following conclusions can be drawn: -
Beams strengthened with BFRP or CFRP have a higher stiffness than the beams without reinforcement, which implies that this type of reinforcement allows enhancing
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the behavior in limit states of service.
The use of the FB600 fabric produces in flat and edge beams a stiffness increase higher than with the use of fabric FC300. FB280 fabric is the one that shows the lowest
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stiffness increase.
In both beams, flat and edge ones, reinforced with unidirectional fabrics, no relationship between the stiffness of the placed reinforcement and the final stiffness of the
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reinforced beam can be observed. Reinforcements of FC300 have an axial stiffness more than two times higher than the FB600 reinforcements, however, beams reinforced with FB600 are more stiff than the reinforced with FC300.
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The increase in stiffness of edge beams is greater than that of flat beams.
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Bi-directional fabrics FC210#3 give rise to a stiffness increase far greater than other fabrics tested, very possibly because of the bi-directional character of the glued fabric.
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In all cases analyzed, the theoretical stiffness of the beams is lower than the experimental stiffness obtained in tests.
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The difference between the values of theoretical and experimental stiffness in beams strengthened with BFRP is small, not exceeding 18%. Differences with the beams reinforced with CFRP are higher, reaching 31%.
Acknowledgements
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The authors thank the School of Building Engineering of the Technical University of Madrid, for financing this work. Also, the support of Drizoro Construction Products, S.A.U. is gratefully acknowledged. References
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(1) Parvez A. The reinforcement of timber for structural applications and repair. PhD Thesis. University of Bath, UK, 2004.
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(2) Buchanan AH. Bending strength of lumber. ASCE J Struct Eng 1990;3:391-397. (3) CNR-DT 201/2005. Guidelines for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Strutures. Timber Structures. Rome, 2007. (4) Motavalli M. FRP Strengthening of wood. Fibre Composites, FS09. EMPA, 2009. (5) Theakston FH. A feasibility study for strengthening timber beams with fibreglass. Can Agric
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ACCEPTED MANUSCRIPT (11) Alam A, Nilson S, Leif E A. Finite Element Delamination Study of a Notched Composite Plate under Flexural Loads. J Mater Sci Eng 2010;4(8). (12) Jenkel C, Kaliske, M. Finite element analysis of timber containing branches. An approach to model the grain course and the influence on the structural behaviour. Eng Struct
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2014;75:237-247. (13) WQLFC. Haojun, HYY.X. Yuye. Experimental study on flexural behaviour of timber beams reinforced with FRP sheets. Ind Constr 2010.
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(18) André A, Johnsson H, Carolin A. Natural fibre composites for strengthening of gluedlaminated timber in tension perpendicular to the grain. In: Proceedings of CICE-3, Miami 2006. p. 13-15.
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ACCEPTED MANUSCRIPT (24) Pavez A, Ansell MP, Smedley D. Mechanical repair of timber beams fractured in flexure using bonded-in reinforcements. J Compos: Part B 2009;40:95-106. (25) Borri A. et al. FRP reinforcement of wood element under bending loads. In: Proceedings of Structural Faults and Repair 2003, Londres.
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Hill International Editions 1999.
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ACCEPTED MANUSCRIPT Figures captions Fig. 1. Placement of the “U” reinforcement for the two types of beams: flat beam and edge beam Fig. 2. Testing pattern
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Figure 3. Reinforced beams during the drying period Figure 4. Load-displacement graphics of the beams without reinforcement and of beams reinforced with FB280, FB600 and FC300.
reinforced with FB280, FB600 and FC300.
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Figure 5. Load-displacement graphics of the edge beams without reinforcement and of beams
Figure 6. Load-displacement graphic of edge beams without reinforcing beams and reinforced
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with FC210#3. Figure 7. Transformed section of the reinforced beams
Tables
Table 1. Geometric and mechanic characerisctics of the fiber fabric.
FB600, and FB280.
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Table 2. Stiffness of the flat beams without reinforcement and beams reinforced with FC300,
Table 3. Stiffness of edge beams without reinforcement, and reinforced with FB280, FB600 and
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FC300.
Table 4. Stiffness of edge beams without reinforcement and reinforced with FC210 #3 Table 5. Values of Kexp and Kth of non-reinforced flat beams and reinforced ones with FB280,
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FB600 and FC300.
Table 6. Values of Kexp and Kth of edge beams without strengthening, and reinforced with FC300, FB600, and FB280. Table 7. Values of Kexp and Kth of the edge beams without strengthening and reinforced with FC210 #3.
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Tables FB280
FB600
FC300
FC210#3
Fiber
Basalt
Basalt
Carbon
Carbon
Unidirectional
Unidirectional
Unidirectional
Bi-directional
Grammage (g/m )
280
600
300
210
Thickness (mm)
0,103
0,222
0,167
0,060
Tensile strtength (MPa)
4.000
4.900
Elasticity module (MPa)
84.000
230.000
Axial stiffness (kN/mm)
8.65
Layout placement of fibers 2
18.65
38.41
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Characteristics
41.40
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Table 1. Geometric and mechanic characerisctics of the fiber fabric.
KNR
KREF
(kN/mm)
(kN/mm)
Dexp
37FB280 58FB280 64FB280 61FB600 68FB600 94FB600 55FC300 62FC300 66FC300
2.98 2.19 2.51 2.06 2.18 2.93 1.50 2.75 2.27
3.45 2.28 2.75 2.71 2.99 3.55 1.79 3.86 2.71
1.16 1.04 1.10 1.32 1.37 1.21 1.19 1.40 1.19
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Beam
Dm 1.10
1.30
1.26
Table 2. Stiffness of the flat beams without reinforcement and beams reinforced with FC300, FB600, and FB280.
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stiffness value of the beams before being reinforced stiffness value of the beams after being reinforced quotient between Kref and Knr value of the stiffness increase corresponding to each type of reinforcement
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Knr Kref Dexp Dm
Beam
KNR
KREF
(kN/mm)
(kN/mm)
Dexp
34FB280 63FB280 65FB280 40FB600 60FB600 73FB600 56FC300 69FC300 72FC300
3.07 3.57 3.72 2.74 3.55 2.61 3.62 2.74 1.68
4.08 4.84 3.93 4.11 5.97 4.36 4.87 3.44 2.18
1.33 1.36 1.06 1.50 1.68 1.67 1.35 1.26 1.30
Dm 1.25
1.62
1.30
Table 3. Stiffness of edge beams without reinforcement, and reinforced with FB280, FB600 and FC300.
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KNR
KREF
(kN/mm)
(kN/mm)
Dexp
Dm
9FC210#3 51FC210#3 67FC210#3 70FC210#3 74FC210#3 76FC210#3 80FC210#3 86FC210#3 96FC210#3
1.68 2.34 2.36 3.55 3.15 4.30 2.46 2.31 3.92
8.84 6.52 7.51 11.52 12.77 5.80 6.91 6.81 6.48
3.78 2.76 2.12 3.66 2.97 2.36 2.99 1.74 2.64
2.78
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Beam
Kth (kN/mm)
Kexp/ Kth
1.16 1.04 1.10 1.32 1.37 1.21 1.19 1.40 1.19
1.21 1.09 1.14 1.46 1.52 1.31 1.55 1.64 1.44
0.96 0.95 0.96 0.90 0.90 0.93 0.77 0.85 0.83
Kexp/ Kth M 0.96
0.91
0.82
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37FB280 58FB280 64FB280 61FB600 68FB600 94FB600 55FC300 62FC300 66FC300
Kexp (kN/mm)
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Beam
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Table 4. Stiffness of edge beams without reinforcement and reinforced with FC210 #3
Table 5. Values of Kexp and Kth of non-reinforced flat beams and reinforced ones with FB280, FB600 and FC300.
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value of experimental stiffness value of theoretical stiffness quotient between Kexp and Kth maen value of Kexp/ Kth corresponding to each type of reinforcement
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Kexp Kth Kexp/ Kth Kexp/ Kth
Kexp
Kth
(kN/mm)
(kN/mm)
Kexp/ Kth
34FB280 63FB280 65FB280 40FB600 60FB600 73FB600 56FC300 69FC300 72FC300
3.07 3.57 3.72 2.74 3.55 2.61 3.62 2.74 1.68
3.38 3.89 4.02 3.37 4.19 3.24 4.85 3.89 2.74
0.91 0.92 0.93 0.81 0.85 0.81 0.75 0.70 0.61
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Beam
Kexp/ Kth M 0.92
0.82
0.69
Table 6. Values of Kexp and Kth of edge beams without strengthening, and reinforced with FC300, FB600, and FB280.
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Kexp
Kth
(kN/mm)
(kN/mm)
Kexp/ Kth
Kexp/ Kth M
9FC210#3 51FC210#3 67FC210#3 70FC210#3 74FC210#3 76FC210#3 80FC210#3 86FC210#3 96FC210#3
1.68 2.34 2.36 3.55 3.15 4.30 2.46 2.31 3.92
2.79 3.53 3.56 4.83 4.41 5.63 3.66 3.51 5.25
0.60 0.66 0.66 0.73 0.71 0.76 0.67 0.66 0.75
0.69
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Table 7. Values of Kexp and Kth of the edge beams without strengthening and reinforced with FC210 #3.
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S1359-8368(15)00596-X
DOI:
10.1016/j.compositesb.2015.10.003
Reference:
JCOMB 3819
To appear in:
Composites Part B
Received Date: 30 June 2015 Accepted Date: 6 October 2015
Please cite this article as: de la Rosa García P, Escamilla AC, González García MN, Analysis of the flexural stiffness of timber beams reinforced with carbon and basalt composite materials, Composites Part B (2015), doi: 10.1016/j.compositesb.2015.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Analysis of the flexural stiffness of timber beams reinforced with carbon and basalt composite materials a,*
b
c
Pilar de la Rosa García ,Alfonso Cobo Escamilla , M. Nieves González García aArchitectural
Construction Department, School of Building Engineering, Polytechnic University of Madrid, Juan de
b.
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Herrera Street, 6, 28040, Madrid. [email protected]. Edification Technology Department, School of Building Engineering, Polytechnic University of Madrid, Juan de
Herrera Street, 6, 28040, Madrid. alfonso.cobo @upm.es cArchitectural
Construction Department, School of Building Engineering, Polytechnic University of Madrid, Juan de
Herrera Street, 6, 28040, Madrid. [email protected] author. Tel. +34687246944
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*Corresponding
Abstract
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In this work, an experimental study on the bending behavior of pine wood beams reinforced with carbon and basalt fiber reinforced plastics, externally glued with epoxy resins has been performed. Different grammage, unidirectional and bi-directional fabrics have been used, and one or three layers applied. The results show good behavior of basalt fiber reinforcements in the stiffness increase of timber beams, achieving similar results to those obtained with carbon fiber.
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Moreover, reinforcements made with bi-directional fabrics produced significant stiffness increases compared to the unidirectional fabrics. Finally, this work includes also the results obtained using the transformed section to predict the stiffness increase that the different types
Keywords:
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of reinforcement analyzed produces.
A. Polymer matrix composites (PMCs)
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A. Wood (pinus sylvestris) B. Mechanical properties D. Mechanical testing 1. Introduction
Historically, wood has been a material used in the field of civil engineering and construction. On many occasions, after some time, the structures need to be reinforced for various reasons: they need to increase the capacity due to a change in use; because of pathological problems which diminish their resistance, or because the excessive deformations are incompatible with the
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ACCEPTED MANUSCRIPT partitions or finishes. The procedures used to reinforce structures have been the focus of numerous studies, due to the fact that the economic volume these types of actions imply is quite considerable. Traditionally, the reinforcement techniques used in timber structures have mainly steel or wood [1]. The use of composite materials and more specifically of fiber reinforced
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polymers (FRP) in the construction industry is relatively recent when compared to the traditional systems.
Wood is a natural material with an excellent relationship between mechanical characteristics
and weigh. This feature is maintained with the use of composite materials as strengthening. In
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terms of the constitutive model, an elastic linear behavior under tensile stress parallel to the fiber up to fracture is admitted, while compression is considered as an initial linear elastic
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behavior followed by a plastic one [2,3].
In sawn timber beams subjected to bending, the predominant failure is due to tensile stress, frequently locating the fracture at the lower beam side. FRP have a linear elastic behavior up to fracture under tensile stress, and they have excellent mechanical properties, with high elasticity module and tensile strength values, in relation to the weight and volume. If a beam is reinforced
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at the bottom side, it increases tensile strength and it is likely to produce an increase in its stiffness. The first relevant application of the use of FRP to reinforce timber structures was carried out in 1995 in the bridge of Sins in Switzerland [4]. In this case, the cross beams of the
of the beams.
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bridge had an excessive deflection, and so the aim to strengthen it was to increase the stiffness
The first studies published on the behavior of timber elements reinforced with FRP correspond
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to the 1960s [5,6]. Research studies have progressively increased in order to expand the knowledge on the matter. Several aspects are analyzed in this type of publications, being stiffness of the elements one of the most important, as well as other issues, such as the load capacity increase, the influence of reinforcement in the fracture mode [7] and the integrity of the bonding surface between wood and the composite material until failure occurs [8,9]. In addition, many studies compare the experimental values obtained in fracture load and stiffness with the analytical values obtained using different calculation models. Usually the models applied are the transformed section, and the ones derived from applying the equilibrium
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ACCEPTED MANUSCRIPT equations to the reinforced section, considering timber behavior model as an elasto-plastic for compression and a linear elastic one under tensile stress. A linear elastic behavior up to the fracture is always considered for composite materials [10]. More recent studies have modeled how strengthening works by applying a finite element method [11,12]. Quanfeng in 2010 [13]
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concludes that this is a reliable method to simulate the behaviour of timber beams reinforced with FRP. The results obtained by different authors concerning the increase in stiffness of
tested beams varies depending on the volume of FRP applied in the section of the beams, the type of fiber that forms the composite material, the type and placement of reinforcements, and
between the timber and the reinforcing material.
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the previous characteristics of the reinforced elements, in addition to the type of bonding
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Some results concerning stiffness increase are presented in the work published by Tingley et al. (2001) [14], where in this case, the beam reinforcement was performed with aramid fiber, resulting in a stiffness increase of about 5% compared to beams without composite reinforcing. Fiorelli et al. (2002) [15] used fiberglass and carbon for the reinforcements, and obtained an increase between 15-30% with a reinforcement volume of 1% and 0.4% of glass fiber FRP
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(GFRP) and carbon FRP (CFRP), respectively. In addition, it was found that increasing the volume of GFRP to 3%, the stiffness increased reached up to 60%. At the same time, the work of Borri A. et al. (2005) [16] compared the behavior of three types of reinforcement -- all of them
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CFRP -- but with different characteristics: the first type consisted on prestressed sheets, the second one, sheets without being prestressed, and finally in the third case, pultruded rods were applied. The difference in the stiffness increase between the three applied types was not
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significant, being the stiffness increase in relation to non-reinforced beams of 22.5-30.3%. More recently, works have been published in which composite materials have been reinforced with sustainable fibers from the environmental point of view, such as basalt [17], hemp and flax [18], analyzing their performance on structural wooden elements. In 2014, Gary M. et al. [19] tested low quality laminated timber beams reinforced with pultrusion rods of basalt fiber-reinforced polymers. In this case, the stiffness increase was 8.4%, with 1.4% reinforcement volume applied to the beams section. Finally, in 2013 Borri A. et al [20] published the findings after
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ACCEPTED MANUSCRIPT testing 45 beams stating that composite materials of different kinds of natural fiber (basalt, flax and hemp) showed a good performance to stiffness increase. Fibers initially used for the manufacture of composite materials in timber beams reinforcement were glass fibers [20-24], and later carbon fibers [25] and aramid fibers [26] were subsequently
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incorporated. The latest trend is focused on the study of the behavior of natural fibers [17-20]. Some authors have analyzed the behavior of reinforced beams to shear stress through sheets arranged transversally and longitudinally to the direction of the wood fiber on the lateral beam sides [27,28]. Another form of shear reinforcement has been carried out with FRP pultruded
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rods embedded in epoxy resin into holes in the lower beam face [29]. This provision of the
reinforcement is intended to diminish the possible early failure to shear effect that the drying
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splits may cause on beams subjected to bending. Integrity of the interphase between composite and wood has also been studied at various times [31], since this is one of the most important aspects influencing the proper functioning of the reinforcements.
This work studies the increase of stiffness experienced on Pine timber sawn beams when reinforced with composite fabrics. Basalt (BRFP) and carbon (CFRP) fabrics with different
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grammage have been applied, placed in "U" shape, wrapping part of the beam section. 2. Materials and testing method
Tests have been performed with 27 timber beams, 9 were tested in flat position and 18 in edge
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position. Timber used has been 78x155mm of section and 1090mm in length Valsain pine. The reinforcement placement has been in "U" shape in all cases, as shown in Figure 1. Tests have been conducted with a universal press, Ibertest Mib, controlling the speed of the displacement
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(0.05 mm/s). The beams were subjected to three-points bending test, applying the load at the center point of the beam (Fig. 2). Bending test for each beam was conducted in two phases. In the first phase, beams were loaded before being reinforced up to a load value producing in the most stressed fibers a tensile stress of approximately 33% of the ultimate fracture strength, so as to obtain the initial load-displacement beam diagram without reinforcement. With this load value, beams did not exceed, in any case, the elastic and linear behavior. Subsequently, they were reinforced with the different types of fabric and number of layers, and were tested to fracture.
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ACCEPTED MANUSCRIPT Reinforcements were performed with CFRP and BFRP, manufacturing the composite material in-situ, at the same time as the reinforcement was being carried out. Nine flat beams studied were reinforced with unidirectional fabrics, 3 of them with basalt fabric of grammage equal to 2
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2
2
2
3
280 g/m (FB280 ), 3 with 600g/m (FB600 ) basalt fiber fabric and 3 with 300 g/m (FC300 )
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carbon fiber fabric. From the 18 edge beams tested, nine were reinforced with unidirectional and nine with bi-directional fabric. The ones reinforced with unidirectional fabrics were divided into three groups, as done with the other flat beams, and were reinforced with FC300, FB600, and FB280 respectively. The nine remaining edge beams were reinforced with bi-directional 2
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carbon fiber fabric, of grammage 210 g/m , placing the reinforcements in three layers (FC210 4
#3 ). Table 1 shows the characteristics of the fabrics used for performing the reinforcements.
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The last row shows the fabric stiffness when under axial stress, obtained as the product of its elasticity module by its thickness. In the case of FC210 #3, the thickness has been considered as the one corresponding to the three layers.
The matrix used for the manufacture of composite materials was epoxy resin, and the same resin has been used as adhesive between the wood and the reinforcement. Prior to the
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application of the first resin coat, the wood surface was cleaned with a brush and a primer coat applied to improve bonding between the composite and wood. After the primer was applied, an 2
initial resin coat, with an approximate yield of 0.5 kg/m was spread. Subsequently, the
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unidirectional fabric reinforcement was placed parallel to the longitudinal direction of the beam, 2
and finally a finishing layer of the same epoxy resin, with an approximate yield of 0.3 kg/m was applied. For the bi-directional fabric reinforcement, (FC210 #3) a similar process was followed,
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although 3 layers of fabric were applied. Figure 3 shows pictures of six of the beams. 3. Test results
The software associated with the testing machine supplied the obtained data, and these corresponded to the applied loads and the vertical displacement experienced by the beams at the load application point. For each beam, two load-displacement graphs were obtained
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unidirectional basalt fibers of 280 g/m2 grammage reinforcement unidirectional basalt fibers of 600 g/m2 grammage reinforcement 3 unidirectional carbon fibers of 300 g/m2 grammage reinforcement 4 bi-directional carbon fiber of 210 g/m2 grammage reinforcement with a triple layer 2
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ACCEPTED MANUSCRIPT corresponding to the beam preload stage before being reinforced, and to the beam test after being reinforced. 3.1. Flat beams reinforced with unidirectional fabrics FB280, FB600, and FC300. Figure 4 presents the results of flat beams reinforced with FB280, FB600, and FC300. Each
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graphic represents the load-displacement diagrams of each beam without reinforcement and after being reinforced. The first column includes three graphics corresponding to the beams
reinforced with FB280, while the second and third columns correspond to the ones reinforced with FB600 and FC300, respectively.
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3.2 Edge beams reinforced with unidirectional fabrics FB280, FB600, and FC300.
Figure 5 shows the results for edge beams, similarly to what is shown in Figure 4 with the flat
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beams. In this case, three beams have also been tested before and after applying the reinforcement with every type of reinforcement.
3.3. Edge beams reinforced with triple-layer fabric FC210 #3
In figure 6, the load-displacement graphs corresponding to the 9 edge beams –with reinforcement of FC210#3 and without it—can be seen.
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4. Analysis of results
4.1. Flat beams reinforced with unidirectional fabrics FC300, FB600, and FB280. The graphs in Figure 4 show a very linear behavior in all cases. In all tested beams, the curves
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of the load-displacement diagrams have higher slope in the case of reinforced beams, which indicates that the increase of stiffness occurs in all cases. Comparing the different fabrics used, it can be observed that the stiffness increase is slightly higher in the case of beams reinforced
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with FB600 and FC300 when compared to the reinforced with FB280. Among the stiffness of beams reinforced with FB600 and FC300, not a clear difference can be observed. Table 2 presents the numeric values of the slope of each of the load-displacement graphic represented in Figure 4. In the second and third columns, the stiffness values of the beams before and after being reinforced, Knr, and Kref respectively, are included. The fourth column indicates the quotient between Kref and Knr (Dexp). All Dexp values are higher than the unit, indicating that the reinforcement has resulted in a stiffness increase in all cases. In the last column, the mean values of the stiffness increase corresponding to each type of reinforcement
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ACCEPTED MANUSCRIPT (Dm) are presented. The analysis of the Dm values suggests that the type of reinforcement resulting in higher increase of stiffness in the tested beams is produced with FB600, followed by the FC300, and finally the FB280. If these results are compared to the axial stiffness of the fabrics used (table 1), it can be seen that there is no relationship between the stiffness of the
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reinforcement placed and the stiffness of the reinforced beam. The FC300 fabric has double the stiffness of FB600 and nevertheless, beams reinforced with FB600 give rise to more stiff solutions than the reinforced with FC300 (table 2).
4.2 Edge beams reinforced with unidirectional fabrics FC300, FB600, and FB280.
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The behavior of reinforced edge beams (Figure 5) is less linear than that of the flat beams (Figure 4). Again, in all cases, an increase of stiffness is produced in reinforced beams. In
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addition, in the most cases, the stiffness increase of the edge beams is greater than that of the flat beams. Moreover, comparing the fabrics used in reinforcements, it can be seen in this case that the reinforcements FB600 and FC300 present a slightly greater increase than that of the FB280.
Table 3 presents similar information to that of table 2, but in this case the results apply for edge
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beams. Comparing the mean values of Dm, it can be observed that the greatest stiffness increase is experienced by the beams reinforced with fabric FB600, followed by the FC300 and finally the reinforced with FB280, which are those that produce a lower stiffness increase. If
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these results are compared with the results on table 2 of the flat beams, we can see that increases in the case of edge beams are greater, and that in both cases the reinforcements that produce the greatest increase are FB600, and the ones with the smallest stiffness increase are
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FB280. Once again, there is no relationship between the stiffness of the fabric used as reinforcement and stiffness of reinforced beam. In addition, if Dm values of edge beams (table 3) are compared with the flat beams (table 2), it can be confirmed that the stiffness increase in edge beams is greater than that of flat beams. This is because the same fabric produces an increase of the inertia moment, which is greater in an edge beam than in a flat beam. 4.3. Edge beams reinforced with FC210 #3 In the 9 graphs of Figure 6, it can be observed that the stiffness increase of reinforced beams compared to the same non-reinforced ones is significant. It shows a greater stiffness increase
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ACCEPTED MANUSCRIPT regarding the previous cases of unidirectional fabrics. Also, in many cases, the behavior of reinforced beams is not linear throughout the diagram. In table 4 the analytical values of stiffness of beams before and after being reinforced with FC210#3 are indicated. The last column represents the mean value of the stiffness increase Dm
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of the nine tested beams. When this average value is compared with that obtained in the case of unidirectional fabrics, a significant difference can be observed, being the increase in this case, more than double that of the beams reinforced with a unidirectional layer. The axial stiffness of fabric FC210 #3 is nearly identical to the fabric FC300, and nevertheless, the
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increase in stiffness of beams reinforced with FC210 #3 is more than double that of the
reinforced with FC300 (tables 3 and 4). In this case, and given that both fabrics have the same
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modulus of elasticity, the difference in stiffness increases is quite possibly due to the bidirectional nature of FC210 #3 fabric fibers, preventing transversal deformations of the beam in an important part of the section. 5. Analytical study
An analytical study has been carried out calculating the value of the theoretical stiffness (Kth) of
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the beam. This theoretical value has been compared with the experimental value obtained in the tests, in order to study the adjustment between both values.
(1)
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The theoretical stiffness of the beam was obtained from the following equation:
Where Kth is the theoretical stiffness of beam, L is the beam length, Iref is the moment of inertia of the reinforced section and Ew is the modulus of elasticity of wood. The elasticity module of wood has been obtained from the tests performed. For the inertia moment of the reinforced section, the method of the transformed section [31] given below has been used. In Figure 7, on the left, the type section of a reinforced edge beam is represented, while on the right, the transformed section corresponding to this section is reproduced. The transformed
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ACCEPTED MANUSCRIPT section is obtained by multiplying the thickness of the fabric reinforcing the beam, by a coefficient obtained as the quotient between the elasticity module of the reinforcing material and the elasticity module of wood. The dimensions et and bt of the transformed section have been calculated applying the following
EFRP EW
(2)
b t = b FRP ⋅
EFRP EW
(3)
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e t = eFRP ⋅
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equations:
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The value of the elasticity module of the reinforcement (EFRP) is taken from the mechanical properties of the fabric sheets provided by the manufacturer. The value of Ew has been
L3 Ew = mNR ⋅ 48I
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calculated from the experimental values obtained in testing by applying the following equation:
(4)
Once the geometric characteristics of the sections have been determined with equations 2 and
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3, the wood elasticity module values have been calculated using equation 4. Finally, applying equation 1, Kth values were obtained. The values of experimental stiffness (Kexp) and theoretical
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stiffness (Kth) obtained for all tested beams and their comparison are shown in tables 5, 6 and 7. The analysis of tables 5, 6 and 7 suggests that in all cases, the stiffness values obtained using the theoretical values for the inertia moment (Kth) are higher than the stiffness values obtained experimentally in beams tested to bending. However, while for beams strengthened with BFRP, the difference between the experimental and theoretical values is relatively small, with a maximum deviation of 18% in edge beams, for beams reinforced with CFRP, differences are higher, reaching 31% in the edge beams reinforced with FC300 and FC210 #3. The difference in the results obtained with BFRP as opposed to the ones with CFRP, regarding kexp/kth, may be
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ACCEPTED MANUSCRIPT due to the lower E value of the basalt fiber, which "fits" timber better. The enormous difference between the E value of carbon fiber and wood implies that in the interphase between two materials it is necessary to mobilize enormous shear stresses, that might produce some slippage between both materials, decreasing the stiffness of the reinforced beam. It must be
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observed that this occurs for low compression strength values, such as those produced in the range of loads applied in tests. As a strategy to reinforce bending strength, it could be interesting to use materials with a not too high E value. 6. Conclusions
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The knowledge of new reinforcement techniques applied to materials traditionally used such as wood has revealed aspects of great interest. This study has experimentally proven a good
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performance to increase the stiffness of wooden beams, using unidirectional fabrics of both BFRP and CFRP and of bi-directional CFRP fabric systems glued externally with epoxy resins to sawn timber pine beams. The following conclusions can be drawn: -
Beams strengthened with BFRP or CFRP have a higher stiffness than the beams without reinforcement, which implies that this type of reinforcement allows enhancing
-
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the behavior in limit states of service.
The use of the FB600 fabric produces in flat and edge beams a stiffness increase higher than with the use of fabric FC300. FB280 fabric is the one that shows the lowest
-
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stiffness increase.
In both beams, flat and edge ones, reinforced with unidirectional fabrics, no relationship between the stiffness of the placed reinforcement and the final stiffness of the
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reinforced beam can be observed. Reinforcements of FC300 have an axial stiffness more than two times higher than the FB600 reinforcements, however, beams reinforced with FB600 are more stiff than the reinforced with FC300.
-
The increase in stiffness of edge beams is greater than that of flat beams.
-
Bi-directional fabrics FC210#3 give rise to a stiffness increase far greater than other fabrics tested, very possibly because of the bi-directional character of the glued fabric.
-
In all cases analyzed, the theoretical stiffness of the beams is lower than the experimental stiffness obtained in tests.
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The difference between the values of theoretical and experimental stiffness in beams strengthened with BFRP is small, not exceeding 18%. Differences with the beams reinforced with CFRP are higher, reaching 31%.
Acknowledgements
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The authors thank the School of Building Engineering of the Technical University of Madrid, for financing this work. Also, the support of Drizoro Construction Products, S.A.U. is gratefully acknowledged. References
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Hill International Editions 1999.
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ACCEPTED MANUSCRIPT Figures captions Fig. 1. Placement of the “U” reinforcement for the two types of beams: flat beam and edge beam Fig. 2. Testing pattern
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Figure 3. Reinforced beams during the drying period Figure 4. Load-displacement graphics of the beams without reinforcement and of beams reinforced with FB280, FB600 and FC300.
reinforced with FB280, FB600 and FC300.
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Figure 5. Load-displacement graphics of the edge beams without reinforcement and of beams
Figure 6. Load-displacement graphic of edge beams without reinforcing beams and reinforced
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with FC210#3. Figure 7. Transformed section of the reinforced beams
Tables
Table 1. Geometric and mechanic characerisctics of the fiber fabric.
FB600, and FB280.
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Table 2. Stiffness of the flat beams without reinforcement and beams reinforced with FC300,
Table 3. Stiffness of edge beams without reinforcement, and reinforced with FB280, FB600 and
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FC300.
Table 4. Stiffness of edge beams without reinforcement and reinforced with FC210 #3 Table 5. Values of Kexp and Kth of non-reinforced flat beams and reinforced ones with FB280,
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FB600 and FC300.
Table 6. Values of Kexp and Kth of edge beams without strengthening, and reinforced with FC300, FB600, and FB280. Table 7. Values of Kexp and Kth of the edge beams without strengthening and reinforced with FC210 #3.
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Tables FB280
FB600
FC300
FC210#3
Fiber
Basalt
Basalt
Carbon
Carbon
Unidirectional
Unidirectional
Unidirectional
Bi-directional
Grammage (g/m )
280
600
300
210
Thickness (mm)
0,103
0,222
0,167
0,060
Tensile strtength (MPa)
4.000
4.900
Elasticity module (MPa)
84.000
230.000
Axial stiffness (kN/mm)
8.65
Layout placement of fibers 2
18.65
38.41
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Characteristics
41.40
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Table 1. Geometric and mechanic characerisctics of the fiber fabric.
KNR
KREF
(kN/mm)
(kN/mm)
Dexp
37FB280 58FB280 64FB280 61FB600 68FB600 94FB600 55FC300 62FC300 66FC300
2.98 2.19 2.51 2.06 2.18 2.93 1.50 2.75 2.27
3.45 2.28 2.75 2.71 2.99 3.55 1.79 3.86 2.71
1.16 1.04 1.10 1.32 1.37 1.21 1.19 1.40 1.19
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Beam
Dm 1.10
1.30
1.26
Table 2. Stiffness of the flat beams without reinforcement and beams reinforced with FC300, FB600, and FB280.
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stiffness value of the beams before being reinforced stiffness value of the beams after being reinforced quotient between Kref and Knr value of the stiffness increase corresponding to each type of reinforcement
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Knr Kref Dexp Dm
Beam
KNR
KREF
(kN/mm)
(kN/mm)
Dexp
34FB280 63FB280 65FB280 40FB600 60FB600 73FB600 56FC300 69FC300 72FC300
3.07 3.57 3.72 2.74 3.55 2.61 3.62 2.74 1.68
4.08 4.84 3.93 4.11 5.97 4.36 4.87 3.44 2.18
1.33 1.36 1.06 1.50 1.68 1.67 1.35 1.26 1.30
Dm 1.25
1.62
1.30
Table 3. Stiffness of edge beams without reinforcement, and reinforced with FB280, FB600 and FC300.
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KNR
KREF
(kN/mm)
(kN/mm)
Dexp
Dm
9FC210#3 51FC210#3 67FC210#3 70FC210#3 74FC210#3 76FC210#3 80FC210#3 86FC210#3 96FC210#3
1.68 2.34 2.36 3.55 3.15 4.30 2.46 2.31 3.92
8.84 6.52 7.51 11.52 12.77 5.80 6.91 6.81 6.48
3.78 2.76 2.12 3.66 2.97 2.36 2.99 1.74 2.64
2.78
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Beam
Kth (kN/mm)
Kexp/ Kth
1.16 1.04 1.10 1.32 1.37 1.21 1.19 1.40 1.19
1.21 1.09 1.14 1.46 1.52 1.31 1.55 1.64 1.44
0.96 0.95 0.96 0.90 0.90 0.93 0.77 0.85 0.83
Kexp/ Kth M 0.96
0.91
0.82
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37FB280 58FB280 64FB280 61FB600 68FB600 94FB600 55FC300 62FC300 66FC300
Kexp (kN/mm)
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Table 4. Stiffness of edge beams without reinforcement and reinforced with FC210 #3
Table 5. Values of Kexp and Kth of non-reinforced flat beams and reinforced ones with FB280, FB600 and FC300.
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value of experimental stiffness value of theoretical stiffness quotient between Kexp and Kth maen value of Kexp/ Kth corresponding to each type of reinforcement
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Kexp Kth Kexp/ Kth Kexp/ Kth
Kexp
Kth
(kN/mm)
(kN/mm)
Kexp/ Kth
34FB280 63FB280 65FB280 40FB600 60FB600 73FB600 56FC300 69FC300 72FC300
3.07 3.57 3.72 2.74 3.55 2.61 3.62 2.74 1.68
3.38 3.89 4.02 3.37 4.19 3.24 4.85 3.89 2.74
0.91 0.92 0.93 0.81 0.85 0.81 0.75 0.70 0.61
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Beam
Kexp/ Kth M 0.92
0.82
0.69
Table 6. Values of Kexp and Kth of edge beams without strengthening, and reinforced with FC300, FB600, and FB280.
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Kexp
Kth
(kN/mm)
(kN/mm)
Kexp/ Kth
Kexp/ Kth M
9FC210#3 51FC210#3 67FC210#3 70FC210#3 74FC210#3 76FC210#3 80FC210#3 86FC210#3 96FC210#3
1.68 2.34 2.36 3.55 3.15 4.30 2.46 2.31 3.92
2.79 3.53 3.56 4.83 4.41 5.63 3.66 3.51 5.25
0.60 0.66 0.66 0.73 0.71 0.76 0.67 0.66 0.75
0.69
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Table 7. Values of Kexp and Kth of the edge beams without strengthening and reinforced with FC210 #3.
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