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Shear strengthening of reinforced concrete beams with PBO-FRCM composites with anchorage
Accepted Manuscript Shear strengthening of reinforced concrete beams with PBO-FRCM composites with anchorage Dorota Marcinczak, Tomasz Trapko, Michał Musiał PII:
S1359-8368(18)31615-9
DOI:
10.1016/j.compositesb.2018.09.061
Reference:
JCOMB 6031
To appear in:
Composites Part B
Received Date: 20 May 2018 Revised Date:
18 August 2018
Accepted Date: 21 September 2018
Please cite this article as: Marcinczak D, Trapko T, Musiał Michał, Shear strengthening of reinforced concrete beams with PBO-FRCM composites with anchorage, Composites Part B (2018), doi: https:// doi.org/10.1016/j.compositesb.2018.09.061. 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 Shear strengthening of reinforced concrete beams with PBO-FRCM composites with anchorage
Dorota Marcinczaka, Tomasz Trapkoa*, Michał Musiała a)
Faculty of Civil Engineering, Wroclaw University of Science and Technology
*) Corresponding author. Tel. +48713203548, fax. +48713221465 e-mail: [email protected] (T. Trapko)
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Pl. Grunwaldzki 11, 50-377 Wroclaw, Poland
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Abstract. In this paper results of tests carried out on beams strengthened in shear with PBO-FRCM composites were presented and compared with theoretical calculations according to the ACI549.4R-13 standard. PBOFRCM (Fibre Reinforced Cementitious Matrix) composites consist of mineral mortar and PBO (p-Phenylene
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Benzobis Oxazole) composite fibres. The mineral mortar makes them a good alternative to the commonly used FRP composites, especially in structures exposed to high temperatures and in historic buildings. FRCM composites mostly fail due to the debonding (without rupture) of the fibres from the mineral mortar. Proper anchorage should be employed to prevent the premature debonding of the composite and to increase the effectiveness of the FRCM reinforcements. As part of this research tests were carried out on 10 RC T-beams
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strengthened in shear with PBO-FRCM composites with different anchorage system. The mechanisms of failure of the beams were analysed and described. A theoretical model based on ACI549.4R-13 (the only existing standard for FRCM composites) was described. Shear capacity was calculated on basis of the characteristics of
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the materials and elements used in the tests. The results of the calculations based on ACI549.4R-13 showed the shear capacity of the T-beams with transverse steel reinforcement and anchored composites to be considerably
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underestimated. The theoretical model needs to be refined and verified on a larger number of elements. The results and the probable causes of the discrepancies between the experimental results and the analytical ones are discussed.
Keywords: beam; shear; PBO-FRCM; strain; stress; anchorage
Nomenclature Ecm
modulus of elasticity of concrete, GPa
Esm
modulus of elasticity of steel, GPa
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ACCEPTED MANUSCRIPT cylindrical compressive strength of concrete, MPa
fc,cube
cubic compressive strength of concrete, MPa
fu
ultimate strength of PBO mesh, MPa
fy
yield stress of steel. MPa
ft
ultimate tensile strength of steel, MPa
bw
beam’s web, m
ffu
ultimate strength of PBO mesh, MPa
Ɛfu
ultimate deformation of composite.
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fc,cyl
1. Introduction
FRCM (Fibre Reinforced Cementitious Matrix) composite reinforcements are a good alternative to the FRP
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(Fibre Reinforced Polymers) system, mainly in historic buildings and structures exposed to high temperatures, owing to the use of mineral-based mortar, instead of epoxy resin, as the matrix bonding the composite with the element being strengthened. In this way epoxy resin’s main drawbacks, i.e. low resistance to high temperatures, toxicity, poor thermal compatibility with concrete and sensitivity to a wet substrate, are eliminated [1, 2]. Elements strengthened using the FRCM system are distinguished by their performance – more plastic than that
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of elements strengthened using the FRP system because of the less perfect bond between the fibres and the matrix than in the case of epoxy resin-based composites. Due to its granulity mortar is unable to thoroughly cover each fibre, which results in nonuniform deformations of the fibres relative to each other in a single bundle.
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Composites of this type usually fail in the mortar/fibres interfacial zone due to the premature debonding of the fibres and their slip. Thus the FRCM system is less effective than the FRP system and the recommendations for
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FRP reinforcement calculations can be inappropriate for FRCM materials. In order to determine the effectiveness of strengthening RC members with the FRCM system it was necessary to carry out tests on members in compression and flexure [3-10]. The tests confirmed the beneficial effect of FRCM reinforcements on the load-bearing capacity of the RC members. Mainly carbon and glass fibres were used in the tests. Tetta et al. [3] compared the effectiveness of shear strengthening RC beams with TRM (Textile Reinforced Mortar) and FRP composites. The effect of the configuration of reinforcement layers and their number was evaluated. Fourteen beams 102×203 mm in cross section and 1077 mm in span were investigated. One of the beams was the reference beam. The other 13 beams were divided into 2 groups. The first group comprised 8
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ACCEPTED MANUSCRIPT beams shear reinforced with TRM composites while the second group comprised 5 beams shear reinforced with FRP composites. In each of the groups three different reinforcement configurations: 1) SB (side bonded), 2) U (U-wrapped around the beam’s bottom and sides) and 3) W (wrapped around the whole cross section) were used. The reinforcement consisted of 1-3 composite layers. Static loading consisted in three-point bending under a load continuously increasing until failure. All the beams reinforced with FRP composites in the SB and U
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configurations failed in shear under a load considerably greater than the reference beam failure load. The load capacity of the beams increased by 103-143%. For beams W the maximum increase in load capacity amounted to 190-195%. The tests showed the TRM system to be less effective than the FRP system, but this depends on
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the number of composite layers and their configuration. The difference in effectiveness between the two systems is most visible when the reinforcement consists of 1 or 2 composite layers. It was also shown that in comparison with a single-layer TRM reinforcements, TRM reinforcements consisting of two composite layers result in a
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large increase in load capacity, owing to the denser mesh and so better interlocking of the composite. Blanksvärd et al. [4] carried out tests on 23 single-span beams loaded with two concentrated forces. All the beams had a 180×500 mm cross section and were 4500 mm long. The flexural reinforcement was made of twelve φ16 bottom bars and two φ16 top bars, whereas the shear reinforcement was varied. All the beams were additionally flexurally strengthened with NSMR (Near Surface Mounted Reinforcement) in order to avoid failure
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in bending. All the beams were reinforced with carbon fibre meshes on mineral mortar. Three carbon fibre meshes, differing in their density (66, 98 and 159 g/m2), were used to make the reinforcements. Various types of mortar, divided into 3 groups differing in their aggregate size, w/c ratio, tensile and compressive strength and
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elastic modulus, were used. Moreover, two of the beams were reinforced with a CFRP mat on epoxy resin. The tests showed that the type of mortar and the aperture size of the mesh have a marked effect on the load-bearing
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capacity of the reinforced members. If a CFRP mesh with densely spaced fibres is used, a greater cracking load is generated and shear strength increases with the number of fibres in the mesh. It was also shown that if a mortar with a low elastic modulus is used, this results in premature cracking in comparison with a mortar characterized by greater stiffness. Thanks to the use of the reinforcement the strains in the stirrups decrease and the principal stresses in the initial stage of loading are reduced, whereby the functional properties improve. In order to improve the effectiveness of FRCM reinforcements, new PBO (p-Phenylene Benzobis Oxazole) fibres, characterized by a higher elastic modulus and greater tensile strength than carbon fibres, were proposed. Tests were carried out on concrete and reinforced concrete members strengthened with the PBO-FRCM system. Flexural members [11-14], compressed members [15-18] and the composite/matrix bond [19-21] were tested. It
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ACCEPTED MANUSCRIPT was shown that thanks to the PBO-FRCM system more plastic behaviour is obtained whereby the internal forces can be redistributed between the structural members. The characteristic feature of PBO-FRCM reinforcements is that slips occurs in the mortar/fibres layer due to the nonuniform covering of the fibres with mortar. So far only few tests of beams reinforced in shear with the PBO-FRCM system have been carried out. Mainly beams rectangular in cross section, reinforced only on their sides and bottom were tested.
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Ombres [11, 13] carried out tests on 3000 mm long rectangular beams 150×25 mm in cross section. Two beam series, differing in their static diagram and shear reinforcement, were tested. In order to avoid flexural failure, the first series beams were additionally flexurally reinforced with two or one layer of PBO mesh glued to their
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bottom. In both series the beams were shear reinforced with one, two or three layers of PBO mesh glued to their bottom and sides in the U (U-wrapped) configuration. In the first series beams the reinforcement had the form of continuous mesh while in the second series beams it had the form of 100 or 150 mm stirrups axially spaced at
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every 260 or 210 mm. The tests showed that the beams shear reinforced with a single layer of PBO mesh were characterized by plastic behaviour, whereas the ones reinforced with a larger number of PBO mesh layers would undergo brittle failure. The highest shear strength was achieved in the case of the beams with the continuous PBO mesh reinforcement. It was also found that in order to ensure the effective transfer of the shearing forces by the reinforcement it is necessary to reduce the spacing and width of the PBO stirrups. The maximum
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deformations in the composite amounted to 0.34% for the beam with discontinuous PBO stirrups in two layers of mesh. Moreover, it was confirmed that the presence of stirrups made of PBO mesh reduces the deformations of the steel stirrups.
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In the course of tests of RC members strengthened with the FRCM composite the latter would often prematurely debond from the member surface. This can be prevented by properly anchoring the composite whereby its
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contribution to the shear strength will increase, as confirmed by the results of tests carried out on beams reinforced with FRP and FRCM composites [22-25], in which different ways of anchoring composite mats were tested. Depending on the way of anchoring the contribution of the composite to the shear strength can be appropriately increased whereby the load-bearing capacity of the whole member will increase. The latest tests [26] were carried out on T-beams strengthened with FRCM materials anchored under the slab. Their aim was to assess the effect of such factors as: the use of anchorage, the degree of the anchorage of U-wrapped meshes, the type of fibres (carbon or glass fibres), the geometry of the mesh and the type of composite system (FRP or TRM) on the shear strength of RC beams. Eleven T-beams 200×450 mm in cross section and with a span length of 3700 mm were tested. The beams had no steel shear reinforcement in the form of stirrups. The shear strength of
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ACCEPTED MANUSCRIPT each of the beams was greater than that of the reference beam and the increase in load capacity ranged from 37 to 191%. The highest degree of strengthening was obtained for the beam with the largest number of anchors. The anchorages would enter into interaction at different load levels, depending on their location along the shear zone length. The increase in anchorage deformation would most quickly appear closest to the point of application of the force, but the highest strain values would occur at 1/3 of the distance of the force to the support. As a result
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of the use of anchorage the strains in the composite increased. For example in the beam with four layers of heavy TRM mesh without anchorage the strains amounted to 2.10‰, whereas in the same beam with anchorage they amounted to 5.21‰. This shows that anchorages markedly improve strengthening effectiveness.
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So far no tests on T-beams reinforced with PBO mesh on mineral mortar (PBO-FRCM) have been carried out. Moreover, mainly beams without stirrups have been tested. Therefore the present authors decided to conduct tests on T-beams strengthened with PBO meshes on mineral mortar with anchorage, which have steel shear
of the composite were analysed.
2. Experimental research
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reinforcement in the form of stirrups. The type of anchorage and its effect on shear strength and the mobilisation
Ten T-shaped RC beams strengthened on their side with PBO mesh on mineral mortar (PBO-FRCM) were made
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and tested. One of the beams was the reference beam while the other nine beams were strengthened on their side with PBO-FRCM materials in an identical configuration. The beams were divided into three groups, differing in
2.1. Test specimens
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the way of anchoring the mesh under the slab. All the reinforcements were made of one layer of PBO mesh.
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The tests were carried out on models of T-shaped beams with cross-section of 150x400 mm, simply supported in three-point bending. The total length of T-beams was equal 2300 mm, whereas the effective flexural span was equal to 1600 mm to provide effective anchorage length of the longitudinal reinforcement. The beams were reinforced at the bottom with 5 bars φ20 mm and 2 bars φ20 mm at the top (B500SP, fyk=500 MPa [32]). Stirrups φ8 mm were made of the same type of steel. The selected main tensile reinforcement was supposed to prevent destruction due bending before exhausting the shear strength. The stirrups were spaced by 250 mm (Fig. 1).
Figure 1. Test specimens
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ACCEPTED MANUSCRIPT 2.2. Material properties The beams and specimens for determining the features of concrete were manufactured in a prefabrication plant during a single concreting and vibrating process. In order to determine the strength qualities of concrete the specimens were made as 150x150x150 mm cubes and φ150 mm cylinders with height of 300 mm. Compressive
1) mean cubic compressive strength of concrete fcm,cube=45.95 MPa, 2) mean cylinder compressive strength of the concrete fcm,cyl=44.75 MPa, 3) mean modulus of elasticity of the concrete Ecm=32.13 GPa.
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What is more, strength parameters of reinforcing bars were also defined:
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strength and modulus of elasticity of the concrete were defined prior to commencing the tests:
1) mean yield stress of steel bars fym=526.2 MPa, 2) mean ultimate strength of steel bars ftm=626.3 MPa,
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3) mean modulus of elasticity of bars Esm=206.7 GPa.
The beams were shear reinforced with a mesh made of PBO fibre (p-Phenylene Benzobis Oxazole) Ruredil X Mesh Gold and mineral mortar Ruredil X Mesh M750 [27]. The PBO mesh is a bidirectionally woven sheet with four times more fibres in the main direction as in the lateral direction (Fig. 2). Parameters of the FRCM
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strengthening materials are shown in Table 1. [according 27, 28, 29].
Figure 2. Structure of PBO mesh
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Table 1. Mechanical and geometrical parameters of PBO mesh used for strengthening [27, 28, 29]
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2.3. Beams preparation, test setup and instrumentation 2.3.1. Shear reinforcement
Prior to strengthening the concrete surface was cleaned of laitance, dusted and washed. The corners of each of the beam were rounded in the areas where the reinforcing was applied (Fig. 3). The surfaces of the web were saturated with water for 15 min prior the placing the PBO-FRCM strips. The first mortar layer was applied on the concrete surface by using a smooth metal trowel. The PBO mesh was applied after application of the first mortar layer and then pressed slightly into the mortar. A next laver of mortar was then applied to completely cover the mesh. The same strengthening configuration was used for each of the beams. The width of the PBO mesh strips for
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ACCEPTED MANUSCRIPT each beam was 150 mm and their spacing was 100 mm. The beams were divided into 3 groups, differing in their way of anchoring the reinforcement on the wall (Fig. 4): 1) The beams belonging to group B_P had 20×20 mm cuts made under the slab, which would be half filled with mortar. Then the reinforcement would be made on the wall on the web’s side surfaces and its bottom surface. The PBO strips were 50 mm longer than the web’s height so that they could be wound on a GFRP composite
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bar. The bar, as long as the beam, together with the PBO strips wound on it would be adhesive bonded into the groove under the slab and covered with an outer layer of mortar.
2) The beams belonging to group B_WS had holes 10 mm in diameter made in the web, located 50 mm under
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the slab. The holes were cleaned and a cord made of PBO fibres together with dedicated mineral mortar was inserted into them. Then the reinforcement would be made on the web’s side surfaces and its bottom surface.
glued to the outer surface of the PBO mesh.
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The cord was threaded through the apertures of the PBO mesh and the cord’s end fibres (forming a fan) were
3) The beams belonging to group B_W had an anchorage in the form of a 150 mm wide PBO strip glued under the slab to the beam along its whole length and the direction of the fibres was perpendicular to the shear direction of the mesh strips
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Figure 3. Preparation of beams for PBO-FRCM reinforcement application
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Figure 4. Reinforcement configurations
Strains were measured by strain gauges. On the concrete the strain gauges were located at half the length of the
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beams (in the midsection). They were spaced at every 25 mm in the compression zone on the side surface and in the tension zone on the bottom surface (Fig. 5). On the steel the strain gauges had been glued to the stirrups at their mid height and to the longitudinal bar at the midspan of the beam before concreting. On the outer stirrups made of PBO mesh the strain gauges were placed in the middle of the beam’s web along the direction of the main fibres. Strain gauges were also placed in the anchorage area in order to determine the strains at anchorage failure. Moreover, the deflections of the members were measured. The tests were carried out in a strength testing machine with a range of 0-6000 kN (Fig. 6). A concentrated force was applied via a cylinder equipped with washers. Strains and deflections were registered and crack width was measured at each load level.
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ACCEPTED MANUSCRIPT Figure 5. Arrangement and numbering of strain gauges and inductive sensors (LVDTs) for measuring deflections
Figure 6. Test stand 3. Experimental results and discussions All the members were loaded until they failed. During loading the value of the force and the values of the strains
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in the concrete, the steel and the PBO mesh on side surface and in the anchorage area were registered. Table 2 shows the measured values corresponding to maximum load Pmax. Reference beam B_0 reached an ultimate load of 396.6 kN and failed by shear after the formation of the main diagonal crack in the shear zone (Fig 7). The
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diagonal crack was inclined at an angle of 30° and ran from the support’s edge to the point of application of the concentrated force.. At failure one of the steel stirrups ruptured in the shear zone and the longitudinal steel bars
Table 2. Results of ultimate load tests Figure 7. Failure of reference beam B_0
3.1. Failure mechanism
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yielded.
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All the elements failed in shear, with the main crack running diagonally (Fig. 8). The same failure mechanism, consisting in composite debonding in the fibres/matrix interfacial zone, was observed in all the strengthened beams, whereby the diagonal crack could develop freely. In each beam the matrix/concrete zone was intact,
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which is evidence of good mortar/concrete bonding. Despite the presence of the anchorage no fibres were ruptured in any of the elements. The PBO-FRCM reinforcements would begin to participate in carrying the
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shearing force once the first diagonal cracks appeared, which resulted in increased deformations of the PBO fibres. Deformations in the anchorage would abruptly increase in the final stage of loading. This is evidence of the good performance of the anchorage which allowed the load to further increase until failure. The failure would occur due to the development of a diagonal crack on the slab of the T-section and on the web, under the composite strips. The abrupt development of the diagonal crack on the slab resulted in the loosening of the anchorage, whereby the composite debonded from the surface of the web and the destructive diagonal crack under the stirrups made of PBO mesh could develop freely. This means that after an abrupt cracking of the slab one can expect the web to fail.
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ACCEPTED MANUSCRIPT Figure 8. View of beams after failure and numbering of strain gauges: a) beam B_P, b) beam B_WS, c) beam B_W
In the case of the B_P beams the gain in load bearing capacity relative to the reference beam amounted to 1023%. Under a load of 90-100 kN inclined cracks began to appear between PBO stirrups 13-14 and 11-12 (Fig.
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8a) at the mid height of the beam. In the reference beam inclined cracks began to appear already under the load of 50 kN. This means that the PBO-FRCM reinforcement delayed inclined cracking. Prior to failure an inclined failure initiating crack appeared in the slab under the load of: 225 kN for beam B_P1, 200 kN for beam B_P2
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and 240 kN for beam B_P3. The crack would rapidly propagate and its width would amount to 2-3 mm. The crack would develop from the point of application of the force to the anchorage under the slab and it was inclined at an angle of 30°. Then the crack would run under the slab along the GFRP bar, loosening the
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anchorage whereby the PBO deformed and inclined cracks developed on the web of the beam (Fig. 9a). Once the tensile strength of the cement mortar was exceeded, the PBO stirrups would debond and the inclined cracks would develop under them until the beam failed. In none of the beams the PBO fibres were ruptured or pulled out of the anchorage. As a result of cracking along the anchorage the whole GFRP bar together with the PBO mesh wound around it would debond. The PBO stirrups would debond from the member in the mortar layer
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without damaging the concrete surround (Fig. 9b). Scratches caused by the slippage of the bundles of fibres on the mortar layer were visible on its surface (Fig. 9c). The diagram of the deformations of the steel stirrups indicates that thanks to the strengthening the yielding of the internal shear reinforcement was delayed. In the
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case of the reference beam, the stirrups would yield under the load of 60-110 kN and the maximum strains in the stirrups amounted to 2.3%. Moreover, all the stirrups in the reference beam would yield, whereas in the
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strengthened beams the stirrups located at the midspan would not yield until the instant of member failure.
Figure 9. Detailed view of failure of beams B_P: a) cracking along anchorage, b) debonding of PBO strips from concrete surface, c) visible traces of slippage of PBO fibres on mortar layer
For beams B_WS the gain in bearing capacity relative to the reference beam amounted to 19-21%. Inclined cracks began to develop on the web, between PBO stirrups 13-14 and 11-12 (Fig. 8b) at the mid height of the beam, under the load of 80-90 kN. This indicates that the development of inclined cracks was delayed also in beams B_WS relative to the reference beam. Prior to failure a failure initiating crack would appear in the slab
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ACCEPTED MANUSCRIPT under the load of: 180 kN for beam B_WS1, 200 kN for beam B_WS2 and 210 kN for beam B_WS3. The crack would rapidly propagate and its width would reach 2-3 mm. The crack would develop from the force application point to the anchorage under the slab and it was inclined at an angle of about 30°. As the load was being increased, cracks would propagate towards the web. Cracks would also appear around the anchorage (the PBO fibre fan) under the load of 210-300 kN, i.e. after slab cracking (Fig. 10a). Once the tensile strength of the
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cement mortar was exceeded, the PBO stirrups would debond and the inclined cracks propagated under them until the beam failed. In none of the beams the PBO fibres were ruptured or pulled out of the anchorage. Neither the fan of PBO fibres debonded from the outer stirrups. As a result of cracking along the fan the latter together
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with the PBO mesh would rotate by an angle of about 22° (Fig. 10b). In the B_WS beams the PBO stirrups would debond from the member in the layer of mortar (Fig. 10c) without damaging the concrete surround. The
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diagram of the deformations of the steel stirrups indicates that, similarly as for beams B_P, the yielding of the internal shear reinforcement was delayed thanks to the strengthening. In the reference beam the rebars would yield under the load of 60-110 kN and the maximum strains in the stirrups amounted to 1.84%. In the strengthened beams the stirrups would yield under the load of 100-125 kN and the maximum strains amounted to 2.3%.
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Figure 10. Detailed view of failure of beams B_WS: a) cracking along fan of PBO fibres, b) rotation of fan, c) debonding of PBO mesh from mortar layer
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For beams B_W the gain in bearing capacity relative to the reference beam amounted to 15-27%. In the beams belonging to this series no inclined cracking in the web was observed. Only perpendicular cracks would appear
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between PBO stirrups 13-14 and 11-12 (Fig. 8c), which under the load of 200 kN would reach under the slab and then run parallel to the longitudinal axis of the beam (Fig. 11a). The first inclined crack would appear in the slab under the load of: 400 kN for beam B_W1, 340 kN for beam B_W2 and 300 for beam B_W3. The crack would rapidly develop and its width would amount to 2-3 mm (similarly as in the previous beams). The crack would propagate from the force application point to the anchorage under the slab and was inclined at an angle of 30°. As the load increased, the cracks in the slab would propagate towards the web and inclined cracks would appear on the web. At the same time the width of the perpendicular cracks would reach 2.2.5 mm. Once the tensile strength of the cement mortar was exceeded, the PBO stirrups together with the longitudinal anchorage strip would debond and the inclined cracks would propagate below until the beam failed (Fig. 11b). In none of the
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ACCEPTED MANUSCRIPT beams the PBO fibres ruptured or were pulled out of the anchorage. Behind the supports an inclined crack would propagate towards the end of the PBO strip functioning as anchorage (Fig. 11a). Similarly as in the previous beams, the PBO stirrups would debond from the member in the layer of mortar without damaging the concrete surround. Vertical cracks, which had appeared at the instant when the stirrups debonded, and also scratches indicating the slippage of the fibres, were visible on the longitudinal strips of PBO mesh (Fig. 11c). The ends of
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the longitudinal PBO strip, which were attached beyond the supports, did not become debonded, but the slippage of the fibres was visible on them. This means that the length of anchoring the longitudinal strip beyond the support (350 mm) was sufficient. The diagram of the deflections of the steel stirrups indicates that thanks to the
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strengthening the yielding of the internal shear reinforcement was delayed and its maximum deformations were reduced, which did not happen in the case of beams B_P and B_WS. The stirrups in the strengthened beams would yield under the load of about 60-150 kN and the maximum strains amounted to 1.7%, i.e. to less than in
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the reference beam while the load was greater. This is due to the high axial stiffness of the composite. In beams B_W, besides the perpendicular stirrups also a 150 mm wide (equal to half of the web height) strip of PBO mesh glued to the beam along its longitudinal axis was used.
Figure 11. Detailed view of failure of beams B_W: a) perpendicular cracks changing their direction under
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anchorage, b) debonded PBO stirrups with anchorage, c) scratch indicating slippage of fibres on mortar layer
3.2. Deflection
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One of the analysed parameters was the deflection of the tested members (Fig. 12). The diagram indicates that the beams underwent brittle failure after losing integrity in the anchorage. For all the beams after the loss of
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integrity by the anchorage the deflection is practically linear until failure. The maximum deflections amounted to respectively 14.87 mm for beams B_P, 12.67 mm for beams B_WS and 15.23 mm for beams B_W.
Figure 12. Load deflections of tested beams
3.3. Strains in composites Figure 5 shows the arrangement of strain gauges on the outer PBO stirrups and on the anchorages. Figures 13-15 show the distribution of strains versus load for respectively beams B_P, B_WS and B_P.
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ACCEPTED MANUSCRIPT Figure 13. Diagram of strains in PBO stirrups versus load for beams B_P
Figure 14. Diagram of strains in PBO stirrups versus load for beams B_WS
Figure 15. Diagram of strains in PBO stirrups versus load for beams B_W
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The dashed line marks the moment when the inclined crack appeared, which resulted in a rapid increase in strains in the PBO stirrups located on the beams’ sides where the crack propagated (strain gauges no. 14). This indicates that the PBO stirrups began to take part in carrying tensile stresses in the cracked cross section. The
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stirrups situated closer to the support (strain gauges no. 15) would enter into interaction appropriately later – at the instant when the inclined crack propagated towards the support. For beams B_W the moment when the vertical crack appeared is marked with a dashed line since this crack caused an increase in strains in the PBO
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meshes, whereas the inclined crack appeared only in the final stage of loading. The maximum strain of the composite measured in the middle of the height of the PBO strip for B_P beams (strain gauge number 15) was 8.27‰, which means the use of the total tensile strength of the PBO fibres of around 38% (according to the manufacturer in Table 1), and which represents about 50% of the load capacity of the PBO-FRCM system in the tensile test (Table 1). The maximum strain of the composite measured in the middle of the height of the PBO
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strip for B_WS beams (strain gauge number 14) was 7.85‰, which means the use of the total tensile strength of the PBO fibres of around 37%, and which represents about 45% of the load capacity of the PBO-FRCM system in the tensile test. For beams B_W, the maximum strain of the composite was 6.34‰, which means the use of
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the total tensile strength of PBO fibres of around 30%, and which represents about 36% of the load capacity of the PBO-FRCM system in the tensile test.
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An analysis of the strains in the composite shows that in beams B_P and B_WS the PBO stirrups enter into interaction at a similar load level. In beams B_W, the strains in the stirrups situated closer to the middle of the span due to the appearance of the vertical crack increase quicker while the increase in the strains in the stirrups situated closer to the support occurs towards the end of loading. For most of the test duration no changes in the strain values in the composites were registered. One can also notice that higher values of strains in PBO stirrups were registered in beams B_P and B_WS than in beams B_W, which indicates that in the former case the stirrups were better mobilised. Beams B_W had the most PBO mesh reinforcement, which meant that their axial stuffiness was the highest, whereby lower strains were registered in them. The next diagrams show the distribution of strains in the anchorage areas. Figure 16 shows the strains in the
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ACCEPTED MANUSCRIPT composite in the anchorage zone of beam B_P2 in the case of which the greatest ultimate force was registered. The strain gauges were stuck to the beam directly under the anchorage on both sides of the beam (strain gauges 24-25 on one side and 34-35 on the other side, along the direction of the main fibres of the PBO mesh). The dashed line marks the moment when a crack appeared along the anchorage, causing a rapid increase in strains in the composite under the anchorage. This moment corresponds to the load capacity of the reference beam. It was
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at this moment that the anchorage began to fully interact, until it debonded. The maximum strains in the composite in the anchorage area amounted to 1.00‰ for beam B_P1, 2.91‰ for beam B_P2 and 4.65‰ for beam B_P3. Figure 17 shows the strains in the composite in the anchorage zone of beam B_WS2. The strain
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gauges were glued to the fibre fans on both sides of the beam. The dashed line marks the moment when a crack developed around the anchorage, causing an increment in strains in it. Subsequently the increment has a linear character until the final stage of loading, when it rapidly increases. It is at this moment that the anchorages would
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undergo rotation as a result of the propagation of the inclined crack. The maximum strains in the composite in the anchorage area amounted to 3.24‰ for beam B_WS1, 2.98‰ for beam B_WS2 and 1.58‰ for beam B_WS3. Figure 18 shows the strains in the anchorage zone of beam B_W1. The strain gauges were glued to the longitudinal PBO strip at half of its height in the places where the PBO stirrups were. In the initial stage of loading the strains in the composite are very small. They sharply increase when inclined cracks appear in the
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slab, which in the diagram is marked with the dashed line. This means that the anchorages begin to fully interact at the moment when the slab cracks. The largest strains were registered by strain gauge no. 22 situated closest to the concentrated load, followed by strain gauges 21 and 24 situated at the mid-length of the shear span. The
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maximum strains in the composite in the anchorage area amounted to 2.77‰ for beam B_W1, 4.64‰ for beam B_W2 and 2.78‰ for beam B_W3. A comparison of the results for all the strengthened beams shows that the
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maximum strains in the anchorages reached similar values for the different ways of anchoring and ranged from 1.00 to 4.65‰.
Figure 16. Diagram of strains in anchorages versus load for beams B_P
Figure 17. Diagram of strains in anchorages versus load for beams B_WS
Figure 18. Diagram of strains in anchorages versus load for beams B_W
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ACCEPTED MANUSCRIPT 4. Theoretical model 4.1. ACI549.4R-13 design model [29] Shear strength of beams strengthened with FRCM composite materials. The shear strength of both rectangular and tee beams shear reinforced with FRCM materials is calculated from
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the relation: Vn = φ v (Vc + Vs + V f )
(1)
where Vc, Vs and Vf represent the contribution of respectively: the concrete, the steel and the composite to the shear strength, φv is a strength reducing coefficient which should be assumed as amounting to 0.75 [29]. The
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contributions of the concrete and the steel to the strength should be calculated in accordance with ACI 318 [30] and they amount to respectively:
which acc. to [31] can be simplified to:
V ⋅d ⋅ bw ⋅ d M
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Vc = 0.16 ⋅
f ' c + 17 ρ w ⋅
V c = 0.17 ⋅
(2)
f ' c ⋅ bw ⋅ d
(3)
d s
(4)
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V s = Av ⋅ f yt ⋅
In the above formulas bw stands for the width of the beam’s web. FRCM contribution to shear strength.
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The contribution of the shear FRCM reinforcement is given by (5): V f = n ⋅ A f ⋅ f fv ⋅ d f
(5)
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where n is the number of mesh reinforcement layers and Af is the mesh reinforcement area by unit width effective in shear, df is the effective depth of the shear FRCM reinforcement and for a rectangular cross section it is equal to effective depth d while for a T-shaped cross section it is equal to effective depth d reduced by the height of the slab (Fig. 19).
The design tensile strength of the shear FRCM reinforcement is calculated from Eq. (6): f fv = ε fv ⋅ E f
(6)
The design tensile strain of the shear FRCM reinforcement is calculated from Eq. (7): ε fv = ε fu ≤ 0.004
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(7)
ACCEPTED MANUSCRIPT The ultimate deformations (εfu) of the composite are usually much larger than 4‰. For the considered PBOFRCM system they amount to 17.6‰. The limitation of the deformations to 4‰ is warranted by the fact that in the shear zone the composite is under a complex stress state. For comparison, in the case of flexural FRCM
Figure 19. df values for rectangular and T-shaped cross section
4.3. Boroszański method according to PN-84/B-03264 [33]
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reinforcement calculations the deformations are limited to 12‰, which value is 3 times higher than for shear.
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The model for calculating the shear strength of a reinforced concrete beam according to standard ACI 318 [30] is a safe model yielding an underestimated strength value. In order to obtain a beam shear strength value closer to
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the experimental one the model included in standard PN-84/B-03264 [33] can be used. This model is based on the kinematically allowable solution which yields the maximum possible strength estimate (top-bottom estimation). The load-bearing capacity of diagonal cross sections in members of constant height is checked using the general condition:
where: ∑
+
+
(8)
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≤
is the sum of the forces in the stirrups perpendicular to the member’s axis, cut through by a
diagonal crack; ∑
is the sum of the forces in the bent bars cut through by the diagonal crack; and
is the component of the force transmitted by the compression zone of a diagonal cross section, perpendicular to
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the member’s axis, amounting to:
=
ℎ
(9)
Coefficient ßs depends on the member’s load and support conditions. For a direct support and load, standard [33] recommends assuming βs=0.15. In the above formulas b is the web’s width, h0 is the beam’s effective depth and cs is the length of the oblique projection onto the member’s longitudinal axis in accordance with the formula: ℎ
= where:
(10)
is the transverse force per unit length, transmitted by stirrups with constant spacing s, calculated from
the formula:
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(11)
Therefore the load-bearing capacity of members reinforced with solely stirrups should be checked using the condition: =2
ℎ
−
(12)
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≤
Rb is the compressive strength of the concrete, Ras – is the design strength of the steel in the stirrups and Fs – the cross-sectional area of the stirrup arm.
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4.3. Comparison of results
The experimental results and the results of the calculations acc. to ACI549.4R-13 are compared in Table 3, which also shows analytical/experimental strength ratios. The mean value of maximum shearing force VmaxLAB
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and the mean value of maximum experimental composite deformation εmaxLAB were experimentally determined. The experimental beam data: beam web width bw = 0.15 m and effective depth d=0.242 m were used in the analytical calculations.
The tables shows two theoretical strength values. VnACI is the strength calculated assuming the composite deformation of 4‰ and strength reducing coefficient φv = 0.75. Since the theoretical model does not take into
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account the anchorage of the composite the above deformation and strength constraints are very severe and result in a large strength underestimation. Therefore strength Vn2ACI, in the case of which composite deformations
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consistent with the experimental results and no strength reduction (φv=1) were assumed, was introduced.
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Table 3. Comparison of analytical and experimental results
In the case of the experimentally investigated beams, the ACI549.4R-13 standard leads to an over twofold underestimation of the shear strength. The main reason can be the way of calculating the strength of the RC Tbeam without reinforcement. The analytical calculations yielded the value of 93.26 kN, whereas the reference beam underwent shear failure under the shearing force of 198 kN. This is due to the ultimate bearing capacity theory assumptions. The ACI formulas are based on statically allowable fields of internal forces, which enable the bottom-up estimation of strength (its lowest possible value). In order to obtain a value closer to the experimental strength one can use the Boroszański method adopted for calculations in accordance with Polish standard PN-84/B-03264 [33], based on the kinematically allowable solution which yields the maximum
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ACCEPTED MANUSCRIPT possible strength estimate (top-bottom estimation). For the experimentally investigated beam the theoretical strength determined acc. to PN-84/B-03264 amounts to 170.48 kN, which value is much closer to the experimental one. Another reason for the shear strength underestimation is the fact that the theoretical model does not take into account the anchorage of the composite. Despite the assumption of deformations larger than 4‰, the shear
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strength (Vf ) of the composite amounts to 8.5 kN, i.e. it is about four times lower than the experimental one. The effective height (df) of the mesh assumes that the composite’s end under the slab is free, whereas it is actually
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anchored in or under the latter. A more reliable result would be obtained if height df was increased.
5. Conclusions
The above tests and analyses have demonstrated that PBO mesh can be used to effectively shear reinforce
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beams. However, the PBO-FRCM technology is still new and new findings continue to be reported. From the present research one can draw the following conclusions:
1. Thanks to the use of the PBO-FRCM system the shear strength of members loaded in shear increases. In the tests the shear strength was found to increase by 10-27% in comparison with the unstrengthened reference beam. In the case of high compressive strength concrete, the increase in load capacity is relatively small. For concrete
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with lower compressive strength, the contribution of the composite to the shear capacity is larger. 2. Since slippage occurs between the fibres and matrix of the PBO-FRCM reinforcement it is necessary to properly anchor the composite to prevent the premature debonding of the mesh.
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3. The same failure mechanism was observed in each of the strengthened beams. The mechanism consisted in the development of an inclined crack in the web and in the slab and in the propagation of a crack along/around the
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anchorage, resulting in the debonding of the latter and the outer stirrups from the surface of the member, in the layer between the fibres and the matrix. 4. The proposed way of anchoring the outer stirrups improves the utilization of the tensile strength of the PBO mesh. No PBO fibres ruptured in any of the beams. 5. Thanks to the use of anchorage the strength properties of the PBO mesh can be better utilized. In the tests the maximum strains in the composite reached 8.23‰, which amounts to 47% of the ultimate tensile strain. In the tested beams strengthened with the PBO-FRCM system without anchorage the maximum strains in the composite reached 3.5‰ [10], which proves the effectiveness of the strengthening. 6. For B_W beams, the largest shear capacity increase of 27% was obtained. This is related to the highest axial
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ACCEPTED MANUSCRIPT stiffness of the composite, because the anchorage included a PBO mesh strip along the entire length of the beam. In these beams, the smallest use of the composite was obtained, i.e. the smallest strain of the PBO mesh, which is also connected with highest axial stiffness. 7. The presence of reinforcement did not change the slope of the diagonal features. The major diagonal crack was inclined at an angle approximately 45˚ for both the control beam and the reinforced beams.
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8. Diagonal cracks in the strengthened beams with strip anchorage (B_W) appeared under almost twice the load, than in the reference beam without strengthening. This phenomenon was not observed for B_P and B_WS beams.
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9. Currently, ACI549.4R-13 is the only standard wholly dedicated to FRCM composite reinforcements, which includes calculation recommendations. The tests and the analyses have shown that one can safely estimate the shear strength of T-beams acc. to standard ACI549.4R-13, but the obtained strength values are underestimated.
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In the case of the beams with the composite anchored the experimentally determined strength is by about 70% higher than the one yielded by the analytical calculations.
As part of further research other ways of anchoring PBO-FRCM materials should be proposed and a way of preventing the slippage and debonding of the PBO mesh from the member’s surface should be found. Additionally, the computational model for FRCM shear strengthening needs to be refined and experimentally
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verified on a larger number of elements, especially T-beams with the composite anchored. As a result, a better insight into how the reinforcement mechanism works will be gained, providing the basis for developing more
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precise guidelines for designing such reinforcements without significantly underrating their strength
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Trapko T. The influence of temperature on the durability and effectiveness of strengthening of concrete with CFRP composites. Engineering and Building. 2010;10:561-64 (in Polish).
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Z.C. Tetta, L.N. Koutas, D.A. Bournas. Textile-reinforced mortar (TRM) versus fiber-reinforced polymers (FRP) in shear strengthening of concrete beams, Composites: Part B. 2015;77:338-348.
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Blanksvärd T, Täljsten B, Carolin A. Shear strengthening of concrete structures with the use of mineralbased composites. ASCE Journal of Composites for Construction. 2009;13:25-34.
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T.C. Triantafillou, C.G. Papanicolaou. Shear strengthening of reinforced concrete members with textile
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ACCEPTED MANUSCRIPT reinforced mortar (TRM) jackets. Materials and Structures. 2006;39:93–103. 6.
Y.A. Al.-Salloum, H.M. Elsanadedy, S.H. Alsayed, R.A. Iqbal. Experimental and numerical study for the shear strengthening of reinforced concrete beams using Textile-Reinforced Mortar. ASCE Journal of Composites for Construction. 2012;6(1):74-90.
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10. E. Tzoura, T.C. Triantafillou. Shear strengthening of reinforced concrete T-beams under cyclic loading with TRM or FRP jackets. Materials and Structures. 2016;49(1-2):17-28.
11. Ombres L. Shear capacity of concrete beams strengthened with cement based composite materials. In: Proceedings of the 6th International Conference on FRP Composites in Civil Engineering. (CICE 2012). Roma, Italy; 2012, Paper No. 01-281.
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12. Ombres L. Flexural analysis of reinforced concrete beams strengthened with a cement based high strength composite material. Composite Structures. 2011;94:143–55. 13. Ombres L. The structural performances of PBO-FRCM strengthened RC beams. Structures and Buildings.
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Proceedings of the Institution of Civil Engineers Structures and Buildings. 2011;164(SB4):265–272. 14. G. Loreto, S. Babaeidaarabad, L. Leardini, A. Nanni. RC beams shear-strengthened with fabric-reinforced-
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cementitious-matrix (FRCM) composite. International Journal of Advanced Structural Engineering. 2015;7(4):341-352.
15. Trapko T. Fibre Reinforced Cementitious Matrix confined concrete elements. Materials and Design. 2013;44:382-391.
16. Trapko T. Behaviour of Fibre Reinforced Cementitious Matrix strengthened concrete columns under eccentric compression loading. Materials and Design. 2014;54:947-957. 17. Trapko T. Effect of eccentric compression loading on the strains of FRCM confined concrete columns. Construction and Building Materials. 2014;61:97-105. 18. Trapko T. Confined concrete elements with PBO-FRCM composites. Construction & Building Materials.
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ACCEPTED MANUSCRIPT 2014;73:332-338. 19. T. D'Antino, C. Carloni, L.H. Sneed, C. Pellegrino. Matrix-fiber bond behavior in PBO FRCM composites: A fracture mechanics approach. Engineering Fracture Mechanics. 2014(117):94–111. 20. D’Ambrisi A, Feo L, Focacci F. Experimental analysis on bond between PBO-FRCM strengthening materials and concrete. Composites: Part B. 2013;44(1):524-34.
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21. Ombres L. Analysis of the bond between Fabric Reinforced Cementitious Mortar (FRCM) strengthening systems and concrete. Composites: Part B. 2014;69:418-26.
22. Modifi A, Chaallal O, Benmokrane B, Neale K. Performance of end-anchorage systems for RC beams
2012;16(3):322-31.
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strengthened in a shear with epoxy-bonded FRP. ASCE Journal of Composites for Construction.
23. D. Baggio, K. Soudki, M. Noel. Strengthening of shear critical RC beams with various FRP systems.
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Construction and Building Materials. 2014;66:634-644.
24. Trapko T., Urbańska D., Kamiński M. Shear strengthening of reinforced concrete beams with PBO-FRCM composites. Composites: Part B. 2015;80:63-72.
25. Trapko T., Musiał M. PBO mesh mobilization via different ways of anchoring PBO-FRCM reinforcements. Composites. Part B: Engineering. 2017;118:67-74.
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26. Z.C. Tetta, L.N. Koutas, D.A. Bournas. Shear strengthening of full-scale RC T-beams using textilereinforced mortar and textile-based anchors. Composites: Part B. 2016;95:225-239 Ruredil, X Mesh Gold Data Sheet, Ruredil SPA, Milan, Italy, 2009.
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Technical approval The Road and Bridge Research Institute, Poland. No AT/2011-02-2701/1.
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29. ACI Committee 549, Guide to Design and Construction of Externally Bonded Fabric-Reinforced
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Cementitious Matrix (FRCM) Systems for Repair and Strengthening Concrete and Masonry Structures, ACI549.4R-13, Farmington, Hills, MI, U.S.A., 2013. 30. ACI Committee: Building Code Requirements for Structural Concrete (ACI 318-11) American Concrete Institute, Farmington Hills, MI. 31. Wu Wei Kuo, T.T.C. Hsu, Shyh Jiann Hwang. 2014. Shear Strength of Reinforced Concrete Beams, ACI Structural Journal, 2014;111(4):809-818. 32. PN-EN 1992:2008. Eurocode 2. Design of concrete structures – Part 1-1: General rules and rules for buildings. 33. PN-84/B-03264 Concrete, reinforced concrete and prestressed structures - Static calculations and design.
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ACCEPTED MANUSCRIPT Acknowledgments The authors greatly acknowledge the VISBUD-Projekt Sp. z o.o. (http://www.visbud-projekt.pl) for providing
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the strengthening material used in the experimental investigations.
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Table 1. Mechanical and geometrical parameters of PBO mesh used for strengthening [27, 28, 29] Ultimate tensile Tensile strength Young modulus Thickness of strain ffz [MPa] Ef [GPa] composite [mm] ɛ [%] PBO fibres 5800 270 2.15 PBO-FRCM system 1664 137 1.76 0.0455
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396.60 432.37 485.92 464.01 472.87 479.52 472.24 505.58 474.72 458.03
[‰] 6.96 7.77 6.09 5.79 7.60 6.65 5.18 6.34 3.68
Deflection at ultimate load [mm]
Shear strengthening effectiveness [-]
11.77 14.87 11.40 12.67 11.24 10.39 14.75 15.23 -
1.10 1.23 1.17 1.19 1.21 1.19 1.27 1.20 1.15
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B_0 B_P1 B_P2 B_P3 B_WS1 B_WS2 B_WS3 B_W1 B_W2 B_W3
Composite strain at ultimate load
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Beam
Ultimate load Pmax [kN]
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VnACI2 [kN] 101.76
VmaxLAB/VnACI2 [-] 0.44 0.43 0.42
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Table 3. Comparison of analytical and experimental results VmaxLAB ƐmaxLAB VnACI Beams [kN] [‰] [kN] B_P 230.36 7.4 B_WS 237.44 7.0 73.13 B_W 239.72 6.0
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S1359-8368(18)31615-9
DOI:
10.1016/j.compositesb.2018.09.061
Reference:
JCOMB 6031
To appear in:
Composites Part B
Received Date: 20 May 2018 Revised Date:
18 August 2018
Accepted Date: 21 September 2018
Please cite this article as: Marcinczak D, Trapko T, Musiał Michał, Shear strengthening of reinforced concrete beams with PBO-FRCM composites with anchorage, Composites Part B (2018), doi: https:// doi.org/10.1016/j.compositesb.2018.09.061. 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 Shear strengthening of reinforced concrete beams with PBO-FRCM composites with anchorage
Dorota Marcinczaka, Tomasz Trapkoa*, Michał Musiała a)
Faculty of Civil Engineering, Wroclaw University of Science and Technology
*) Corresponding author. Tel. +48713203548, fax. +48713221465 e-mail: [email protected] (T. Trapko)
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Pl. Grunwaldzki 11, 50-377 Wroclaw, Poland
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Abstract. In this paper results of tests carried out on beams strengthened in shear with PBO-FRCM composites were presented and compared with theoretical calculations according to the ACI549.4R-13 standard. PBOFRCM (Fibre Reinforced Cementitious Matrix) composites consist of mineral mortar and PBO (p-Phenylene
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Benzobis Oxazole) composite fibres. The mineral mortar makes them a good alternative to the commonly used FRP composites, especially in structures exposed to high temperatures and in historic buildings. FRCM composites mostly fail due to the debonding (without rupture) of the fibres from the mineral mortar. Proper anchorage should be employed to prevent the premature debonding of the composite and to increase the effectiveness of the FRCM reinforcements. As part of this research tests were carried out on 10 RC T-beams
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strengthened in shear with PBO-FRCM composites with different anchorage system. The mechanisms of failure of the beams were analysed and described. A theoretical model based on ACI549.4R-13 (the only existing standard for FRCM composites) was described. Shear capacity was calculated on basis of the characteristics of
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the materials and elements used in the tests. The results of the calculations based on ACI549.4R-13 showed the shear capacity of the T-beams with transverse steel reinforcement and anchored composites to be considerably
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underestimated. The theoretical model needs to be refined and verified on a larger number of elements. The results and the probable causes of the discrepancies between the experimental results and the analytical ones are discussed.
Keywords: beam; shear; PBO-FRCM; strain; stress; anchorage
Nomenclature Ecm
modulus of elasticity of concrete, GPa
Esm
modulus of elasticity of steel, GPa
-1-
ACCEPTED MANUSCRIPT cylindrical compressive strength of concrete, MPa
fc,cube
cubic compressive strength of concrete, MPa
fu
ultimate strength of PBO mesh, MPa
fy
yield stress of steel. MPa
ft
ultimate tensile strength of steel, MPa
bw
beam’s web, m
ffu
ultimate strength of PBO mesh, MPa
Ɛfu
ultimate deformation of composite.
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fc,cyl
1. Introduction
FRCM (Fibre Reinforced Cementitious Matrix) composite reinforcements are a good alternative to the FRP
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(Fibre Reinforced Polymers) system, mainly in historic buildings and structures exposed to high temperatures, owing to the use of mineral-based mortar, instead of epoxy resin, as the matrix bonding the composite with the element being strengthened. In this way epoxy resin’s main drawbacks, i.e. low resistance to high temperatures, toxicity, poor thermal compatibility with concrete and sensitivity to a wet substrate, are eliminated [1, 2]. Elements strengthened using the FRCM system are distinguished by their performance – more plastic than that
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of elements strengthened using the FRP system because of the less perfect bond between the fibres and the matrix than in the case of epoxy resin-based composites. Due to its granulity mortar is unable to thoroughly cover each fibre, which results in nonuniform deformations of the fibres relative to each other in a single bundle.
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Composites of this type usually fail in the mortar/fibres interfacial zone due to the premature debonding of the fibres and their slip. Thus the FRCM system is less effective than the FRP system and the recommendations for
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FRP reinforcement calculations can be inappropriate for FRCM materials. In order to determine the effectiveness of strengthening RC members with the FRCM system it was necessary to carry out tests on members in compression and flexure [3-10]. The tests confirmed the beneficial effect of FRCM reinforcements on the load-bearing capacity of the RC members. Mainly carbon and glass fibres were used in the tests. Tetta et al. [3] compared the effectiveness of shear strengthening RC beams with TRM (Textile Reinforced Mortar) and FRP composites. The effect of the configuration of reinforcement layers and their number was evaluated. Fourteen beams 102×203 mm in cross section and 1077 mm in span were investigated. One of the beams was the reference beam. The other 13 beams were divided into 2 groups. The first group comprised 8
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ACCEPTED MANUSCRIPT beams shear reinforced with TRM composites while the second group comprised 5 beams shear reinforced with FRP composites. In each of the groups three different reinforcement configurations: 1) SB (side bonded), 2) U (U-wrapped around the beam’s bottom and sides) and 3) W (wrapped around the whole cross section) were used. The reinforcement consisted of 1-3 composite layers. Static loading consisted in three-point bending under a load continuously increasing until failure. All the beams reinforced with FRP composites in the SB and U
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configurations failed in shear under a load considerably greater than the reference beam failure load. The load capacity of the beams increased by 103-143%. For beams W the maximum increase in load capacity amounted to 190-195%. The tests showed the TRM system to be less effective than the FRP system, but this depends on
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the number of composite layers and their configuration. The difference in effectiveness between the two systems is most visible when the reinforcement consists of 1 or 2 composite layers. It was also shown that in comparison with a single-layer TRM reinforcements, TRM reinforcements consisting of two composite layers result in a
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large increase in load capacity, owing to the denser mesh and so better interlocking of the composite. Blanksvärd et al. [4] carried out tests on 23 single-span beams loaded with two concentrated forces. All the beams had a 180×500 mm cross section and were 4500 mm long. The flexural reinforcement was made of twelve φ16 bottom bars and two φ16 top bars, whereas the shear reinforcement was varied. All the beams were additionally flexurally strengthened with NSMR (Near Surface Mounted Reinforcement) in order to avoid failure
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in bending. All the beams were reinforced with carbon fibre meshes on mineral mortar. Three carbon fibre meshes, differing in their density (66, 98 and 159 g/m2), were used to make the reinforcements. Various types of mortar, divided into 3 groups differing in their aggregate size, w/c ratio, tensile and compressive strength and
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elastic modulus, were used. Moreover, two of the beams were reinforced with a CFRP mat on epoxy resin. The tests showed that the type of mortar and the aperture size of the mesh have a marked effect on the load-bearing
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capacity of the reinforced members. If a CFRP mesh with densely spaced fibres is used, a greater cracking load is generated and shear strength increases with the number of fibres in the mesh. It was also shown that if a mortar with a low elastic modulus is used, this results in premature cracking in comparison with a mortar characterized by greater stiffness. Thanks to the use of the reinforcement the strains in the stirrups decrease and the principal stresses in the initial stage of loading are reduced, whereby the functional properties improve. In order to improve the effectiveness of FRCM reinforcements, new PBO (p-Phenylene Benzobis Oxazole) fibres, characterized by a higher elastic modulus and greater tensile strength than carbon fibres, were proposed. Tests were carried out on concrete and reinforced concrete members strengthened with the PBO-FRCM system. Flexural members [11-14], compressed members [15-18] and the composite/matrix bond [19-21] were tested. It
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ACCEPTED MANUSCRIPT was shown that thanks to the PBO-FRCM system more plastic behaviour is obtained whereby the internal forces can be redistributed between the structural members. The characteristic feature of PBO-FRCM reinforcements is that slips occurs in the mortar/fibres layer due to the nonuniform covering of the fibres with mortar. So far only few tests of beams reinforced in shear with the PBO-FRCM system have been carried out. Mainly beams rectangular in cross section, reinforced only on their sides and bottom were tested.
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Ombres [11, 13] carried out tests on 3000 mm long rectangular beams 150×25 mm in cross section. Two beam series, differing in their static diagram and shear reinforcement, were tested. In order to avoid flexural failure, the first series beams were additionally flexurally reinforced with two or one layer of PBO mesh glued to their
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bottom. In both series the beams were shear reinforced with one, two or three layers of PBO mesh glued to their bottom and sides in the U (U-wrapped) configuration. In the first series beams the reinforcement had the form of continuous mesh while in the second series beams it had the form of 100 or 150 mm stirrups axially spaced at
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every 260 or 210 mm. The tests showed that the beams shear reinforced with a single layer of PBO mesh were characterized by plastic behaviour, whereas the ones reinforced with a larger number of PBO mesh layers would undergo brittle failure. The highest shear strength was achieved in the case of the beams with the continuous PBO mesh reinforcement. It was also found that in order to ensure the effective transfer of the shearing forces by the reinforcement it is necessary to reduce the spacing and width of the PBO stirrups. The maximum
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deformations in the composite amounted to 0.34% for the beam with discontinuous PBO stirrups in two layers of mesh. Moreover, it was confirmed that the presence of stirrups made of PBO mesh reduces the deformations of the steel stirrups.
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In the course of tests of RC members strengthened with the FRCM composite the latter would often prematurely debond from the member surface. This can be prevented by properly anchoring the composite whereby its
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contribution to the shear strength will increase, as confirmed by the results of tests carried out on beams reinforced with FRP and FRCM composites [22-25], in which different ways of anchoring composite mats were tested. Depending on the way of anchoring the contribution of the composite to the shear strength can be appropriately increased whereby the load-bearing capacity of the whole member will increase. The latest tests [26] were carried out on T-beams strengthened with FRCM materials anchored under the slab. Their aim was to assess the effect of such factors as: the use of anchorage, the degree of the anchorage of U-wrapped meshes, the type of fibres (carbon or glass fibres), the geometry of the mesh and the type of composite system (FRP or TRM) on the shear strength of RC beams. Eleven T-beams 200×450 mm in cross section and with a span length of 3700 mm were tested. The beams had no steel shear reinforcement in the form of stirrups. The shear strength of
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ACCEPTED MANUSCRIPT each of the beams was greater than that of the reference beam and the increase in load capacity ranged from 37 to 191%. The highest degree of strengthening was obtained for the beam with the largest number of anchors. The anchorages would enter into interaction at different load levels, depending on their location along the shear zone length. The increase in anchorage deformation would most quickly appear closest to the point of application of the force, but the highest strain values would occur at 1/3 of the distance of the force to the support. As a result
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of the use of anchorage the strains in the composite increased. For example in the beam with four layers of heavy TRM mesh without anchorage the strains amounted to 2.10‰, whereas in the same beam with anchorage they amounted to 5.21‰. This shows that anchorages markedly improve strengthening effectiveness.
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So far no tests on T-beams reinforced with PBO mesh on mineral mortar (PBO-FRCM) have been carried out. Moreover, mainly beams without stirrups have been tested. Therefore the present authors decided to conduct tests on T-beams strengthened with PBO meshes on mineral mortar with anchorage, which have steel shear
of the composite were analysed.
2. Experimental research
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reinforcement in the form of stirrups. The type of anchorage and its effect on shear strength and the mobilisation
Ten T-shaped RC beams strengthened on their side with PBO mesh on mineral mortar (PBO-FRCM) were made
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and tested. One of the beams was the reference beam while the other nine beams were strengthened on their side with PBO-FRCM materials in an identical configuration. The beams were divided into three groups, differing in
2.1. Test specimens
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the way of anchoring the mesh under the slab. All the reinforcements were made of one layer of PBO mesh.
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The tests were carried out on models of T-shaped beams with cross-section of 150x400 mm, simply supported in three-point bending. The total length of T-beams was equal 2300 mm, whereas the effective flexural span was equal to 1600 mm to provide effective anchorage length of the longitudinal reinforcement. The beams were reinforced at the bottom with 5 bars φ20 mm and 2 bars φ20 mm at the top (B500SP, fyk=500 MPa [32]). Stirrups φ8 mm were made of the same type of steel. The selected main tensile reinforcement was supposed to prevent destruction due bending before exhausting the shear strength. The stirrups were spaced by 250 mm (Fig. 1).
Figure 1. Test specimens
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ACCEPTED MANUSCRIPT 2.2. Material properties The beams and specimens for determining the features of concrete were manufactured in a prefabrication plant during a single concreting and vibrating process. In order to determine the strength qualities of concrete the specimens were made as 150x150x150 mm cubes and φ150 mm cylinders with height of 300 mm. Compressive
1) mean cubic compressive strength of concrete fcm,cube=45.95 MPa, 2) mean cylinder compressive strength of the concrete fcm,cyl=44.75 MPa, 3) mean modulus of elasticity of the concrete Ecm=32.13 GPa.
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What is more, strength parameters of reinforcing bars were also defined:
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strength and modulus of elasticity of the concrete were defined prior to commencing the tests:
1) mean yield stress of steel bars fym=526.2 MPa, 2) mean ultimate strength of steel bars ftm=626.3 MPa,
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3) mean modulus of elasticity of bars Esm=206.7 GPa.
The beams were shear reinforced with a mesh made of PBO fibre (p-Phenylene Benzobis Oxazole) Ruredil X Mesh Gold and mineral mortar Ruredil X Mesh M750 [27]. The PBO mesh is a bidirectionally woven sheet with four times more fibres in the main direction as in the lateral direction (Fig. 2). Parameters of the FRCM
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strengthening materials are shown in Table 1. [according 27, 28, 29].
Figure 2. Structure of PBO mesh
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Table 1. Mechanical and geometrical parameters of PBO mesh used for strengthening [27, 28, 29]
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2.3. Beams preparation, test setup and instrumentation 2.3.1. Shear reinforcement
Prior to strengthening the concrete surface was cleaned of laitance, dusted and washed. The corners of each of the beam were rounded in the areas where the reinforcing was applied (Fig. 3). The surfaces of the web were saturated with water for 15 min prior the placing the PBO-FRCM strips. The first mortar layer was applied on the concrete surface by using a smooth metal trowel. The PBO mesh was applied after application of the first mortar layer and then pressed slightly into the mortar. A next laver of mortar was then applied to completely cover the mesh. The same strengthening configuration was used for each of the beams. The width of the PBO mesh strips for
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ACCEPTED MANUSCRIPT each beam was 150 mm and their spacing was 100 mm. The beams were divided into 3 groups, differing in their way of anchoring the reinforcement on the wall (Fig. 4): 1) The beams belonging to group B_P had 20×20 mm cuts made under the slab, which would be half filled with mortar. Then the reinforcement would be made on the wall on the web’s side surfaces and its bottom surface. The PBO strips were 50 mm longer than the web’s height so that they could be wound on a GFRP composite
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bar. The bar, as long as the beam, together with the PBO strips wound on it would be adhesive bonded into the groove under the slab and covered with an outer layer of mortar.
2) The beams belonging to group B_WS had holes 10 mm in diameter made in the web, located 50 mm under
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the slab. The holes were cleaned and a cord made of PBO fibres together with dedicated mineral mortar was inserted into them. Then the reinforcement would be made on the web’s side surfaces and its bottom surface.
glued to the outer surface of the PBO mesh.
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The cord was threaded through the apertures of the PBO mesh and the cord’s end fibres (forming a fan) were
3) The beams belonging to group B_W had an anchorage in the form of a 150 mm wide PBO strip glued under the slab to the beam along its whole length and the direction of the fibres was perpendicular to the shear direction of the mesh strips
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Figure 3. Preparation of beams for PBO-FRCM reinforcement application
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Figure 4. Reinforcement configurations
Strains were measured by strain gauges. On the concrete the strain gauges were located at half the length of the
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beams (in the midsection). They were spaced at every 25 mm in the compression zone on the side surface and in the tension zone on the bottom surface (Fig. 5). On the steel the strain gauges had been glued to the stirrups at their mid height and to the longitudinal bar at the midspan of the beam before concreting. On the outer stirrups made of PBO mesh the strain gauges were placed in the middle of the beam’s web along the direction of the main fibres. Strain gauges were also placed in the anchorage area in order to determine the strains at anchorage failure. Moreover, the deflections of the members were measured. The tests were carried out in a strength testing machine with a range of 0-6000 kN (Fig. 6). A concentrated force was applied via a cylinder equipped with washers. Strains and deflections were registered and crack width was measured at each load level.
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ACCEPTED MANUSCRIPT Figure 5. Arrangement and numbering of strain gauges and inductive sensors (LVDTs) for measuring deflections
Figure 6. Test stand 3. Experimental results and discussions All the members were loaded until they failed. During loading the value of the force and the values of the strains
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in the concrete, the steel and the PBO mesh on side surface and in the anchorage area were registered. Table 2 shows the measured values corresponding to maximum load Pmax. Reference beam B_0 reached an ultimate load of 396.6 kN and failed by shear after the formation of the main diagonal crack in the shear zone (Fig 7). The
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diagonal crack was inclined at an angle of 30° and ran from the support’s edge to the point of application of the concentrated force.. At failure one of the steel stirrups ruptured in the shear zone and the longitudinal steel bars
Table 2. Results of ultimate load tests Figure 7. Failure of reference beam B_0
3.1. Failure mechanism
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yielded.
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All the elements failed in shear, with the main crack running diagonally (Fig. 8). The same failure mechanism, consisting in composite debonding in the fibres/matrix interfacial zone, was observed in all the strengthened beams, whereby the diagonal crack could develop freely. In each beam the matrix/concrete zone was intact,
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which is evidence of good mortar/concrete bonding. Despite the presence of the anchorage no fibres were ruptured in any of the elements. The PBO-FRCM reinforcements would begin to participate in carrying the
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shearing force once the first diagonal cracks appeared, which resulted in increased deformations of the PBO fibres. Deformations in the anchorage would abruptly increase in the final stage of loading. This is evidence of the good performance of the anchorage which allowed the load to further increase until failure. The failure would occur due to the development of a diagonal crack on the slab of the T-section and on the web, under the composite strips. The abrupt development of the diagonal crack on the slab resulted in the loosening of the anchorage, whereby the composite debonded from the surface of the web and the destructive diagonal crack under the stirrups made of PBO mesh could develop freely. This means that after an abrupt cracking of the slab one can expect the web to fail.
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ACCEPTED MANUSCRIPT Figure 8. View of beams after failure and numbering of strain gauges: a) beam B_P, b) beam B_WS, c) beam B_W
In the case of the B_P beams the gain in load bearing capacity relative to the reference beam amounted to 1023%. Under a load of 90-100 kN inclined cracks began to appear between PBO stirrups 13-14 and 11-12 (Fig.
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8a) at the mid height of the beam. In the reference beam inclined cracks began to appear already under the load of 50 kN. This means that the PBO-FRCM reinforcement delayed inclined cracking. Prior to failure an inclined failure initiating crack appeared in the slab under the load of: 225 kN for beam B_P1, 200 kN for beam B_P2
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and 240 kN for beam B_P3. The crack would rapidly propagate and its width would amount to 2-3 mm. The crack would develop from the point of application of the force to the anchorage under the slab and it was inclined at an angle of 30°. Then the crack would run under the slab along the GFRP bar, loosening the
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anchorage whereby the PBO deformed and inclined cracks developed on the web of the beam (Fig. 9a). Once the tensile strength of the cement mortar was exceeded, the PBO stirrups would debond and the inclined cracks would develop under them until the beam failed. In none of the beams the PBO fibres were ruptured or pulled out of the anchorage. As a result of cracking along the anchorage the whole GFRP bar together with the PBO mesh wound around it would debond. The PBO stirrups would debond from the member in the mortar layer
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without damaging the concrete surround (Fig. 9b). Scratches caused by the slippage of the bundles of fibres on the mortar layer were visible on its surface (Fig. 9c). The diagram of the deformations of the steel stirrups indicates that thanks to the strengthening the yielding of the internal shear reinforcement was delayed. In the
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case of the reference beam, the stirrups would yield under the load of 60-110 kN and the maximum strains in the stirrups amounted to 2.3%. Moreover, all the stirrups in the reference beam would yield, whereas in the
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strengthened beams the stirrups located at the midspan would not yield until the instant of member failure.
Figure 9. Detailed view of failure of beams B_P: a) cracking along anchorage, b) debonding of PBO strips from concrete surface, c) visible traces of slippage of PBO fibres on mortar layer
For beams B_WS the gain in bearing capacity relative to the reference beam amounted to 19-21%. Inclined cracks began to develop on the web, between PBO stirrups 13-14 and 11-12 (Fig. 8b) at the mid height of the beam, under the load of 80-90 kN. This indicates that the development of inclined cracks was delayed also in beams B_WS relative to the reference beam. Prior to failure a failure initiating crack would appear in the slab
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ACCEPTED MANUSCRIPT under the load of: 180 kN for beam B_WS1, 200 kN for beam B_WS2 and 210 kN for beam B_WS3. The crack would rapidly propagate and its width would reach 2-3 mm. The crack would develop from the force application point to the anchorage under the slab and it was inclined at an angle of about 30°. As the load was being increased, cracks would propagate towards the web. Cracks would also appear around the anchorage (the PBO fibre fan) under the load of 210-300 kN, i.e. after slab cracking (Fig. 10a). Once the tensile strength of the
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cement mortar was exceeded, the PBO stirrups would debond and the inclined cracks propagated under them until the beam failed. In none of the beams the PBO fibres were ruptured or pulled out of the anchorage. Neither the fan of PBO fibres debonded from the outer stirrups. As a result of cracking along the fan the latter together
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with the PBO mesh would rotate by an angle of about 22° (Fig. 10b). In the B_WS beams the PBO stirrups would debond from the member in the layer of mortar (Fig. 10c) without damaging the concrete surround. The
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diagram of the deformations of the steel stirrups indicates that, similarly as for beams B_P, the yielding of the internal shear reinforcement was delayed thanks to the strengthening. In the reference beam the rebars would yield under the load of 60-110 kN and the maximum strains in the stirrups amounted to 1.84%. In the strengthened beams the stirrups would yield under the load of 100-125 kN and the maximum strains amounted to 2.3%.
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Figure 10. Detailed view of failure of beams B_WS: a) cracking along fan of PBO fibres, b) rotation of fan, c) debonding of PBO mesh from mortar layer
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For beams B_W the gain in bearing capacity relative to the reference beam amounted to 15-27%. In the beams belonging to this series no inclined cracking in the web was observed. Only perpendicular cracks would appear
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between PBO stirrups 13-14 and 11-12 (Fig. 8c), which under the load of 200 kN would reach under the slab and then run parallel to the longitudinal axis of the beam (Fig. 11a). The first inclined crack would appear in the slab under the load of: 400 kN for beam B_W1, 340 kN for beam B_W2 and 300 for beam B_W3. The crack would rapidly develop and its width would amount to 2-3 mm (similarly as in the previous beams). The crack would propagate from the force application point to the anchorage under the slab and was inclined at an angle of 30°. As the load increased, the cracks in the slab would propagate towards the web and inclined cracks would appear on the web. At the same time the width of the perpendicular cracks would reach 2.2.5 mm. Once the tensile strength of the cement mortar was exceeded, the PBO stirrups together with the longitudinal anchorage strip would debond and the inclined cracks would propagate below until the beam failed (Fig. 11b). In none of the
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ACCEPTED MANUSCRIPT beams the PBO fibres ruptured or were pulled out of the anchorage. Behind the supports an inclined crack would propagate towards the end of the PBO strip functioning as anchorage (Fig. 11a). Similarly as in the previous beams, the PBO stirrups would debond from the member in the layer of mortar without damaging the concrete surround. Vertical cracks, which had appeared at the instant when the stirrups debonded, and also scratches indicating the slippage of the fibres, were visible on the longitudinal strips of PBO mesh (Fig. 11c). The ends of
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the longitudinal PBO strip, which were attached beyond the supports, did not become debonded, but the slippage of the fibres was visible on them. This means that the length of anchoring the longitudinal strip beyond the support (350 mm) was sufficient. The diagram of the deflections of the steel stirrups indicates that thanks to the
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strengthening the yielding of the internal shear reinforcement was delayed and its maximum deformations were reduced, which did not happen in the case of beams B_P and B_WS. The stirrups in the strengthened beams would yield under the load of about 60-150 kN and the maximum strains amounted to 1.7%, i.e. to less than in
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the reference beam while the load was greater. This is due to the high axial stiffness of the composite. In beams B_W, besides the perpendicular stirrups also a 150 mm wide (equal to half of the web height) strip of PBO mesh glued to the beam along its longitudinal axis was used.
Figure 11. Detailed view of failure of beams B_W: a) perpendicular cracks changing their direction under
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anchorage, b) debonded PBO stirrups with anchorage, c) scratch indicating slippage of fibres on mortar layer
3.2. Deflection
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One of the analysed parameters was the deflection of the tested members (Fig. 12). The diagram indicates that the beams underwent brittle failure after losing integrity in the anchorage. For all the beams after the loss of
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integrity by the anchorage the deflection is practically linear until failure. The maximum deflections amounted to respectively 14.87 mm for beams B_P, 12.67 mm for beams B_WS and 15.23 mm for beams B_W.
Figure 12. Load deflections of tested beams
3.3. Strains in composites Figure 5 shows the arrangement of strain gauges on the outer PBO stirrups and on the anchorages. Figures 13-15 show the distribution of strains versus load for respectively beams B_P, B_WS and B_P.
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ACCEPTED MANUSCRIPT Figure 13. Diagram of strains in PBO stirrups versus load for beams B_P
Figure 14. Diagram of strains in PBO stirrups versus load for beams B_WS
Figure 15. Diagram of strains in PBO stirrups versus load for beams B_W
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The dashed line marks the moment when the inclined crack appeared, which resulted in a rapid increase in strains in the PBO stirrups located on the beams’ sides where the crack propagated (strain gauges no. 14). This indicates that the PBO stirrups began to take part in carrying tensile stresses in the cracked cross section. The
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stirrups situated closer to the support (strain gauges no. 15) would enter into interaction appropriately later – at the instant when the inclined crack propagated towards the support. For beams B_W the moment when the vertical crack appeared is marked with a dashed line since this crack caused an increase in strains in the PBO
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meshes, whereas the inclined crack appeared only in the final stage of loading. The maximum strain of the composite measured in the middle of the height of the PBO strip for B_P beams (strain gauge number 15) was 8.27‰, which means the use of the total tensile strength of the PBO fibres of around 38% (according to the manufacturer in Table 1), and which represents about 50% of the load capacity of the PBO-FRCM system in the tensile test (Table 1). The maximum strain of the composite measured in the middle of the height of the PBO
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strip for B_WS beams (strain gauge number 14) was 7.85‰, which means the use of the total tensile strength of the PBO fibres of around 37%, and which represents about 45% of the load capacity of the PBO-FRCM system in the tensile test. For beams B_W, the maximum strain of the composite was 6.34‰, which means the use of
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the total tensile strength of PBO fibres of around 30%, and which represents about 36% of the load capacity of the PBO-FRCM system in the tensile test.
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An analysis of the strains in the composite shows that in beams B_P and B_WS the PBO stirrups enter into interaction at a similar load level. In beams B_W, the strains in the stirrups situated closer to the middle of the span due to the appearance of the vertical crack increase quicker while the increase in the strains in the stirrups situated closer to the support occurs towards the end of loading. For most of the test duration no changes in the strain values in the composites were registered. One can also notice that higher values of strains in PBO stirrups were registered in beams B_P and B_WS than in beams B_W, which indicates that in the former case the stirrups were better mobilised. Beams B_W had the most PBO mesh reinforcement, which meant that their axial stuffiness was the highest, whereby lower strains were registered in them. The next diagrams show the distribution of strains in the anchorage areas. Figure 16 shows the strains in the
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ACCEPTED MANUSCRIPT composite in the anchorage zone of beam B_P2 in the case of which the greatest ultimate force was registered. The strain gauges were stuck to the beam directly under the anchorage on both sides of the beam (strain gauges 24-25 on one side and 34-35 on the other side, along the direction of the main fibres of the PBO mesh). The dashed line marks the moment when a crack appeared along the anchorage, causing a rapid increase in strains in the composite under the anchorage. This moment corresponds to the load capacity of the reference beam. It was
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at this moment that the anchorage began to fully interact, until it debonded. The maximum strains in the composite in the anchorage area amounted to 1.00‰ for beam B_P1, 2.91‰ for beam B_P2 and 4.65‰ for beam B_P3. Figure 17 shows the strains in the composite in the anchorage zone of beam B_WS2. The strain
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gauges were glued to the fibre fans on both sides of the beam. The dashed line marks the moment when a crack developed around the anchorage, causing an increment in strains in it. Subsequently the increment has a linear character until the final stage of loading, when it rapidly increases. It is at this moment that the anchorages would
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undergo rotation as a result of the propagation of the inclined crack. The maximum strains in the composite in the anchorage area amounted to 3.24‰ for beam B_WS1, 2.98‰ for beam B_WS2 and 1.58‰ for beam B_WS3. Figure 18 shows the strains in the anchorage zone of beam B_W1. The strain gauges were glued to the longitudinal PBO strip at half of its height in the places where the PBO stirrups were. In the initial stage of loading the strains in the composite are very small. They sharply increase when inclined cracks appear in the
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slab, which in the diagram is marked with the dashed line. This means that the anchorages begin to fully interact at the moment when the slab cracks. The largest strains were registered by strain gauge no. 22 situated closest to the concentrated load, followed by strain gauges 21 and 24 situated at the mid-length of the shear span. The
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maximum strains in the composite in the anchorage area amounted to 2.77‰ for beam B_W1, 4.64‰ for beam B_W2 and 2.78‰ for beam B_W3. A comparison of the results for all the strengthened beams shows that the
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maximum strains in the anchorages reached similar values for the different ways of anchoring and ranged from 1.00 to 4.65‰.
Figure 16. Diagram of strains in anchorages versus load for beams B_P
Figure 17. Diagram of strains in anchorages versus load for beams B_WS
Figure 18. Diagram of strains in anchorages versus load for beams B_W
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ACCEPTED MANUSCRIPT 4. Theoretical model 4.1. ACI549.4R-13 design model [29] Shear strength of beams strengthened with FRCM composite materials. The shear strength of both rectangular and tee beams shear reinforced with FRCM materials is calculated from
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the relation: Vn = φ v (Vc + Vs + V f )
(1)
where Vc, Vs and Vf represent the contribution of respectively: the concrete, the steel and the composite to the shear strength, φv is a strength reducing coefficient which should be assumed as amounting to 0.75 [29]. The
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contributions of the concrete and the steel to the strength should be calculated in accordance with ACI 318 [30] and they amount to respectively:
which acc. to [31] can be simplified to:
V ⋅d ⋅ bw ⋅ d M
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Vc = 0.16 ⋅
f ' c + 17 ρ w ⋅
V c = 0.17 ⋅
(2)
f ' c ⋅ bw ⋅ d
(3)
d s
(4)
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V s = Av ⋅ f yt ⋅
In the above formulas bw stands for the width of the beam’s web. FRCM contribution to shear strength.
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The contribution of the shear FRCM reinforcement is given by (5): V f = n ⋅ A f ⋅ f fv ⋅ d f
(5)
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where n is the number of mesh reinforcement layers and Af is the mesh reinforcement area by unit width effective in shear, df is the effective depth of the shear FRCM reinforcement and for a rectangular cross section it is equal to effective depth d while for a T-shaped cross section it is equal to effective depth d reduced by the height of the slab (Fig. 19).
The design tensile strength of the shear FRCM reinforcement is calculated from Eq. (6): f fv = ε fv ⋅ E f
(6)
The design tensile strain of the shear FRCM reinforcement is calculated from Eq. (7): ε fv = ε fu ≤ 0.004
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(7)
ACCEPTED MANUSCRIPT The ultimate deformations (εfu) of the composite are usually much larger than 4‰. For the considered PBOFRCM system they amount to 17.6‰. The limitation of the deformations to 4‰ is warranted by the fact that in the shear zone the composite is under a complex stress state. For comparison, in the case of flexural FRCM
Figure 19. df values for rectangular and T-shaped cross section
4.3. Boroszański method according to PN-84/B-03264 [33]
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reinforcement calculations the deformations are limited to 12‰, which value is 3 times higher than for shear.
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The model for calculating the shear strength of a reinforced concrete beam according to standard ACI 318 [30] is a safe model yielding an underestimated strength value. In order to obtain a beam shear strength value closer to
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the experimental one the model included in standard PN-84/B-03264 [33] can be used. This model is based on the kinematically allowable solution which yields the maximum possible strength estimate (top-bottom estimation). The load-bearing capacity of diagonal cross sections in members of constant height is checked using the general condition:
where: ∑
+
+
(8)
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≤
is the sum of the forces in the stirrups perpendicular to the member’s axis, cut through by a
diagonal crack; ∑
is the sum of the forces in the bent bars cut through by the diagonal crack; and
is the component of the force transmitted by the compression zone of a diagonal cross section, perpendicular to
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the member’s axis, amounting to:
=
ℎ
(9)
Coefficient ßs depends on the member’s load and support conditions. For a direct support and load, standard [33] recommends assuming βs=0.15. In the above formulas b is the web’s width, h0 is the beam’s effective depth and cs is the length of the oblique projection onto the member’s longitudinal axis in accordance with the formula: ℎ
= where:
(10)
is the transverse force per unit length, transmitted by stirrups with constant spacing s, calculated from
the formula:
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(11)
Therefore the load-bearing capacity of members reinforced with solely stirrups should be checked using the condition: =2
ℎ
−
(12)
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≤
Rb is the compressive strength of the concrete, Ras – is the design strength of the steel in the stirrups and Fs – the cross-sectional area of the stirrup arm.
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4.3. Comparison of results
The experimental results and the results of the calculations acc. to ACI549.4R-13 are compared in Table 3, which also shows analytical/experimental strength ratios. The mean value of maximum shearing force VmaxLAB
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and the mean value of maximum experimental composite deformation εmaxLAB were experimentally determined. The experimental beam data: beam web width bw = 0.15 m and effective depth d=0.242 m were used in the analytical calculations.
The tables shows two theoretical strength values. VnACI is the strength calculated assuming the composite deformation of 4‰ and strength reducing coefficient φv = 0.75. Since the theoretical model does not take into
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account the anchorage of the composite the above deformation and strength constraints are very severe and result in a large strength underestimation. Therefore strength Vn2ACI, in the case of which composite deformations
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consistent with the experimental results and no strength reduction (φv=1) were assumed, was introduced.
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Table 3. Comparison of analytical and experimental results
In the case of the experimentally investigated beams, the ACI549.4R-13 standard leads to an over twofold underestimation of the shear strength. The main reason can be the way of calculating the strength of the RC Tbeam without reinforcement. The analytical calculations yielded the value of 93.26 kN, whereas the reference beam underwent shear failure under the shearing force of 198 kN. This is due to the ultimate bearing capacity theory assumptions. The ACI formulas are based on statically allowable fields of internal forces, which enable the bottom-up estimation of strength (its lowest possible value). In order to obtain a value closer to the experimental strength one can use the Boroszański method adopted for calculations in accordance with Polish standard PN-84/B-03264 [33], based on the kinematically allowable solution which yields the maximum
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ACCEPTED MANUSCRIPT possible strength estimate (top-bottom estimation). For the experimentally investigated beam the theoretical strength determined acc. to PN-84/B-03264 amounts to 170.48 kN, which value is much closer to the experimental one. Another reason for the shear strength underestimation is the fact that the theoretical model does not take into account the anchorage of the composite. Despite the assumption of deformations larger than 4‰, the shear
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strength (Vf ) of the composite amounts to 8.5 kN, i.e. it is about four times lower than the experimental one. The effective height (df) of the mesh assumes that the composite’s end under the slab is free, whereas it is actually
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anchored in or under the latter. A more reliable result would be obtained if height df was increased.
5. Conclusions
The above tests and analyses have demonstrated that PBO mesh can be used to effectively shear reinforce
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beams. However, the PBO-FRCM technology is still new and new findings continue to be reported. From the present research one can draw the following conclusions:
1. Thanks to the use of the PBO-FRCM system the shear strength of members loaded in shear increases. In the tests the shear strength was found to increase by 10-27% in comparison with the unstrengthened reference beam. In the case of high compressive strength concrete, the increase in load capacity is relatively small. For concrete
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with lower compressive strength, the contribution of the composite to the shear capacity is larger. 2. Since slippage occurs between the fibres and matrix of the PBO-FRCM reinforcement it is necessary to properly anchor the composite to prevent the premature debonding of the mesh.
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3. The same failure mechanism was observed in each of the strengthened beams. The mechanism consisted in the development of an inclined crack in the web and in the slab and in the propagation of a crack along/around the
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anchorage, resulting in the debonding of the latter and the outer stirrups from the surface of the member, in the layer between the fibres and the matrix. 4. The proposed way of anchoring the outer stirrups improves the utilization of the tensile strength of the PBO mesh. No PBO fibres ruptured in any of the beams. 5. Thanks to the use of anchorage the strength properties of the PBO mesh can be better utilized. In the tests the maximum strains in the composite reached 8.23‰, which amounts to 47% of the ultimate tensile strain. In the tested beams strengthened with the PBO-FRCM system without anchorage the maximum strains in the composite reached 3.5‰ [10], which proves the effectiveness of the strengthening. 6. For B_W beams, the largest shear capacity increase of 27% was obtained. This is related to the highest axial
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ACCEPTED MANUSCRIPT stiffness of the composite, because the anchorage included a PBO mesh strip along the entire length of the beam. In these beams, the smallest use of the composite was obtained, i.e. the smallest strain of the PBO mesh, which is also connected with highest axial stiffness. 7. The presence of reinforcement did not change the slope of the diagonal features. The major diagonal crack was inclined at an angle approximately 45˚ for both the control beam and the reinforced beams.
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8. Diagonal cracks in the strengthened beams with strip anchorage (B_W) appeared under almost twice the load, than in the reference beam without strengthening. This phenomenon was not observed for B_P and B_WS beams.
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9. Currently, ACI549.4R-13 is the only standard wholly dedicated to FRCM composite reinforcements, which includes calculation recommendations. The tests and the analyses have shown that one can safely estimate the shear strength of T-beams acc. to standard ACI549.4R-13, but the obtained strength values are underestimated.
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In the case of the beams with the composite anchored the experimentally determined strength is by about 70% higher than the one yielded by the analytical calculations.
As part of further research other ways of anchoring PBO-FRCM materials should be proposed and a way of preventing the slippage and debonding of the PBO mesh from the member’s surface should be found. Additionally, the computational model for FRCM shear strengthening needs to be refined and experimentally
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verified on a larger number of elements, especially T-beams with the composite anchored. As a result, a better insight into how the reinforcement mechanism works will be gained, providing the basis for developing more
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ACCEPTED MANUSCRIPT Acknowledgments The authors greatly acknowledge the VISBUD-Projekt Sp. z o.o. (http://www.visbud-projekt.pl) for providing
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the strengthening material used in the experimental investigations.
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Table 1. Mechanical and geometrical parameters of PBO mesh used for strengthening [27, 28, 29] Ultimate tensile Tensile strength Young modulus Thickness of strain ffz [MPa] Ef [GPa] composite [mm] ɛ [%] PBO fibres 5800 270 2.15 PBO-FRCM system 1664 137 1.76 0.0455
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396.60 432.37 485.92 464.01 472.87 479.52 472.24 505.58 474.72 458.03
[‰] 6.96 7.77 6.09 5.79 7.60 6.65 5.18 6.34 3.68
Deflection at ultimate load [mm]
Shear strengthening effectiveness [-]
11.77 14.87 11.40 12.67 11.24 10.39 14.75 15.23 -
1.10 1.23 1.17 1.19 1.21 1.19 1.27 1.20 1.15
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B_0 B_P1 B_P2 B_P3 B_WS1 B_WS2 B_WS3 B_W1 B_W2 B_W3
Composite strain at ultimate load
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Beam
Ultimate load Pmax [kN]
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VnACI2 [kN] 101.76
VmaxLAB/VnACI2 [-] 0.44 0.43 0.42
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Table 3. Comparison of analytical and experimental results VmaxLAB ƐmaxLAB VnACI Beams [kN] [‰] [kN] B_P 230.36 7.4 B_WS 237.44 7.0 73.13 B_W 239.72 6.0
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