Failure mechanism of compressed short brick masonry columns confined with FRP strips

Failure mechanism of compressed short brick masonry columns confined with FRP strips

Construction and Building Materials 63 (2014) 180–188 Contents lists available at ScienceDirect Construction and Building Materials journal homepage...

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Construction and Building Materials 63 (2014) 180–188

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Failure mechanism of compressed short brick masonry columns confined with FRP strips Jirˇí Witzany, Tomáš Cˇejka, Radek Zigler ⇑ Department of Building Structures, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, Prague 6 166 29, Czech Republic

h i g h l i g h t s  Experimental research of FRP strengthened brick masonry columns was carried out.  Glass (GFRP) and carbon (CFRP) fabrics were used for strengthening.  The columns were reinforced by wrapping the FRP strips in 4 height levels.  Research has proven effectiveness of masonry columns’ strengthening by FRP wrapping.  Failure mechanism has decisive influence on determination of load-bearing capacity.

a r t i c l e

i n f o

Article history: Received 19 July 2013 Received in revised form 25 March 2014 Accepted 2 April 2014

Keywords: Masonry Brick Reinforcement FRP Wrapping Failure Experiment

a b s t r a c t The article addresses the issues of strengthening and stabilisation of compressed masonry structures by inorganic FRP fabrics. The confinement of a masonry column with fabrics of carbon fibres with a high modulus of elasticity and high tensile strength relieves the transverse tensile stresses in the masonry and increases the ultimate deformation and the ultimate load. The experimental research of brick masonry columns under concentric load performed to-date has pointed out the necessity of adopting a different approach to assessing the load-bearing capacity or residual load-bearing capacity, which takes into account the different failure modes of reinforced and unreinforced brick masonry. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction In the last 15 years, traditional reinforcement and stabilisation methods of building structures have been enriched with FRP-based materials [1]. These involve, in particular, applications in the field of reinforcement of structures in bending, tension and shear, and, to a lesser extent, the increase in their load-bearing capacity in compression by the wrapping of load-bearing elements (mainly columns and pillars [2–4]). FRP-based materials also play a major role in the reinforcement of structures in terms of seismic safety, e.g. [5–8]. FRP-based materials offer numerous benefits in the reinforcement and stabilisation of historic, predominantly masonry structures, thanks to their low weight, high efficiency and potential ⇑ Corresponding author. Tel.: +420 224 357 163; fax: +420 233 339 987. E-mail addresses: [email protected] (J. Witzany), [email protected] (T. Cˇejka), [email protected] (R. Zigler). http://dx.doi.org/10.1016/j.conbuildmat.2014.04.041 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

reversibility, or at least retreatability. The utilisation of FRP-based materials in the area of historic and, in some cases, heritage buildings to-date has primarily concentrated on the stabilisation of vertical load-bearing and vault structures to withstand the effects of horizontal loads due to technical and natural seismicity [9,10]. It is only recently that research into the reinforcement of masonry structures with FRP materials has turned towards enhancing the load-bearing capacity of vertical structures (columns and pillars) by their wrapping around [11,12]. The majority of these research studies focus on brick masonry [13,14], while only a few also address stone masonry [15–17]. The calculation procedures for the identification of the loadbearing capacity of elements wrapped in FRP materials have been developed in great detail for reinforced concrete members and have been incorporated into some standard regulations and national directives [18–21]. These procedures, however, cannot be directly applied to masonry structures. General and universal procedures for the calculation of the load-bearing capacity of

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FRP-strengthened masonry structures still have to be additionally elaborated. The only known exception are calculation procedures based on several experimental studies carried out on masonry structures reinforced by wrapping with FRP materials, found in an Italian directive [19]. The variability of the physical and mechanical characteristics of masonry requires tailor-made research and, based on it, individual calibration of the used relationships to fit different types of masonry [22]. An essential parameter significantly affecting the resulting efficiency of masonry structure reinforcement with FRP materials is the adhesion of the reinforcing composite layer to the reinforced masonry [23,24]. These issues have been the focus of extensive experimental [25,26] and theoretical research [27,28] recently. Some research studies are oriented towards the effect of binder on the resultant adhesion of the FRP material to underlying masonry [29–31], the effect of FRP buckling due to compressive strains in the vertical direction [32], the formulation of new suitable theoretic models which describe the behaviour of FRP materials in terms of their adhesion to the base material [33], or experimental and theoretical research of the utilisation of new flexible binders for gluing onto external FRP reinforcements [34]. Another area of growing interest in relation to the long-term reliability and durability of FRP-based material reinforcement of structures are the issues of so-called ‘‘secondary creep’’. Experimental research [35,36] has manifested a significant impact of these phenomena on the stress redistribution back into the reinforced elements. Last but not least, besides fire safety issues related to the reliability of reinforcement based on FRP materials (e.g. [37,38]), research on the behaviour of externally bonded FRP systems at elevated operating temperatures, or the effect of freeze–thaw cycles on the performance characteristics of reinforcing layers must be mentioned. Experimental and theoretical research is focused, amongst others, on potential modifications of polymer matrices (e.g. by additions of silica nanoparticles) with the objective of improving their properties [39]. The results of the authors’ research presented in this article address the issues of the efficiency of periodical wrapping of masonry columns with FRP materials (glass and carbon). 2. Experimental research of strengthening masonry columns with FRP based high-strength carbon and glass fibre fabrics The subject of experimental research was the verification of the efficiency, deformation characteristics and the failure mechanism of brickwork columns reinforced by wrapping with FRP based high-strength carbon and glass fibre fabrics.

2.1. Description of test specimens The test specimens had plan dimensions of 290  290 mm, and the height of the pieces was 1020 mm (12 rows of bricks with the bed joint width of 15–20 mm). The test pieces were made of burnt bricks with dimensions of 290  140  65 mm of

the P20 strength grade (the declared compressive strength of bricks being 20 MPa). The binder used was fine-grained lime-cement mortar with a declared compressive strength of 2 MPa. The experimentally determined compressive strengths of individual components of the test pieces (brick strength and mortar strength) and the resulting compressive strength of unreinforced masonry identiˇ SN EN 1996-1-1 [40] are presented in Table 1. fied pursuant to C The columns were reinforced by their wrapping in fabric (one layer) with unidirectionally arranged high-strength carbon fibres (using the TyfoÒ SCH-41 fabric) and unidirectionally arranged high-strength glass fibres (the fabrics used were TyfoÒ SEH-25A and TyfoÒ SEH-51A) glued onto the reinforced columns by means of TyfoÒ S two-component tixotrophic epoxy resin. The material characteristics of these used fabrics are displayed in Table 2. The strips had a width of 75 mm and 150 mm and were placed at 4 levels – at the column’s toe and the column’s head and in the thirds of the column’s height (the axial distance of the strips being 300 mm). The surface of the reinforced columns had been levelled (projecting parts of bricks and mortar were removed, hollows with a maximum depth of 5 mm were filled with epoxy adhesive) and cleaned before the application of reinforcing fabrics, non-cohesive parts of the columns had been removed and columns’ corners had been rounded (the fillet radius was 20 mm). 2.2. Results of experimental loading of masonry columns in concentric compression The test specimens were exposed to an increasing load up to their failure. The load was applied in steps of 60 kN (10% of the presumed ultimate load of unreinforced columns of coursed rubble masonry of rubble sandstone – irregular sandstone blocks). To verify the permanent deformation component, the applied load was removed to the basic loading value of 60 kN after each 3rd loading step. The ultimate load of the column was identified at the collapse of each loaded element. The test specimens were fitted with vertical and horizontal deformation sensors (LVDT) and resistance strain gauges (see Fig. 1). Unlike unreinforced columns, the working diagrams of reinforced masonry columns are characterised by slight ‘‘strengthening‘‘ during the initial loading steps (3–4 loading steps), i.e. by a drop in the growth of vertical deformations dy (by an increase in the stiffness dy/N) as compared to the initial value. The N  dy,t/dy,c relationship is characterised by a steep drop in the values of the respective ratio. The subsequent loading phase brings the stabilization of the dy,t/dy,c ratio in the interval of (0.5; 0.75) up to reaching the ultimate load Nu,m; in unreinforced columns, however, this ratio does not grow under loading levels approaching the ultimate load Nu,m, but, on the contrary, due to the fabric’s ‘‘activation’’ – the growth in springy force (Fig. 4) – a slight decrease in the dy,t/dy,c ratio occurs. The reinforcing effect of a masonry column confined with strips of fabrics of carbon or glass fibres is evident from the comparison of the N  dy time patterns of the reinforced and unreinforced columns presented in Figs. 2–4. The appearance of vertical tensile cracks is accompanied by a gradual marked growth in vertical deformations. Visually observable vertical tensile cracks arose under loading in compression at the value of the vertical deformation dy 2 (0.8 mm; 1.2 mm) where the higher values of vertical deformations dy were reached by the masonry columns with a lower value of the ultimate load Nu,m (see Table 3). The phase preceding the reaching of the ultimate load Nu,m demonstrates a progressive growth in both vertical and horizontal deformations, with this growth being more dramatic in reinforced masonry columns. The ultimate vertical deformations dy,m of the reinforced masonry columns reached values dy,m at reaching the ultimate load Nu,m of 3.98 mm (CFRP) and 2.44 mm (GFRP), i.e. 157% and 256% of the deformations dy,m of the unreinforced columns. The N  dx working diagrams (Figs. 5 and 6) are characterised by a large domain of zero to very small horizontal deformations (dx being smaller than or equal to 0.01 mm) up to the loading level at which structural and hair cracks first arise. Subsequently, a progressive growth in horizontal deformations dx occurs accompanied by visually observable cracks. In the first phase of the action of concentrically compressed masonry, it may be assumed that the horizontal tensile stress +ry exerted by the trend towards greater transverse deformations of the binder in bed joints as compared to masonry units is transferred, due to the lower stiffness (greater duc-

Table 1 Experimentally determined compressive strengths (MPa) of masonry unit’s components and masonry.

Bricks (fb) Mortar (fm) Masonry (fk)

P01

P02

P11

P12

P21

P25

P26

P27

P28

P32

P33

P34

P35

2.1 19.6 3.67

2.1 19.6 3.67

2.1 19.6 3.67

2.1 19.6 3.67

2.1 19.6 3.67

2.2 18.3 3.44

2.2 18.1 3.43

2.1 22.3 3.96

2.3 22.4 3.97

2.1 20.5 3.74

1.9 19.7 3.66

2.0 19.7 3.67

2.2 22.5 3.98

Note: Material properties were determined by non-destructive drill tests made by special calibrated electric hand drill (2 bricks for each column were tested, 6 test drills were made on each brick, 6 test drills on lime mortar, depth of the drill has been measured and converted to material compressive strength using special calibration formulas) and evaluated according to valid Codes of Standards (EC 6 and others) as follows: fk – characteristic compressive strength of masonry. fk = K  fab  fbm. fb – normalised mean compressive strength of masonry unit (brick). fm – compressive strength of mortar. a, b, K – constants defined by EC6 depending on type of used masonry units and mortar.

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Table 2 Material properties of used FRPs. Material

Product

Composite thickness (mm)

Tensile strengtha (MPa)

Elastic modulusa (MPa)

Tensile strengthb (MPa)

Elastic modulusb (MPa)

Tensile strengthc (MPa)

Elongationa (%)

Carbon Glass Glass

TyfoÒ SCH-41 TyfoÒ SEH-25A TyfoÒ SEH-51A

1.0 0.66 1.3

3790 3240 3240

230 72.7 72.4

986 575 545

95.8 26.1 26.1

509 152 –

1.0 2.2 2.2

Note: Experimental determination of carbon and glass composites’ tensile strength was carried out on test specimens 90–130 mm in length, 30–40 mm in width and 1.5– 2.3 mm in thickness. Loading by tensile force was performed on the LaborTech 4.100SP1 test machine. a Material properties of dry fibres declared by the manufacturer. b Material properties of composites declared by the manufacturer. c Material properties of composites obtained from experimental tensile tests.

Fig. 1. Experimental test specimens, mounting of sensors.

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Fig. 2. Unreinforced columns (a) vertical deformation-to-load pattern dy  N; (b) permanent vertical deformation dy,t to total vertical deformation dy,c pattern in relation to load N.

Fig. 3. Carbon fibre strips (CFRP) confined columns (a) vertical deformation-to-load pattern dy  N; (b) permanent vertical deformation dy,t to total vertical deformation dy,c pattern in relation to load N.

tility) of the binder in the butt joints, onto the masonry units, or is only limited to them (Fig. 7). This mechanism accounts for a very little transverse deformation (dy ? 0) of the column masonry in the initial loading phase. This fact results in a very weak effect of the reinforcing fabric before the appearance of a vertical tensile crack, the fabric only starts applying more significantly – activating – after the appearance of tensile cracks in the masonry units. The ultimate horizontal deformations dx,m at reaching the ultimate load of reinforced and unreinforced masonry columns reach roughly identical values (dx 2 (0.1; 1.08)). This approximate correspondence of ultimate deformations allows us to formulate a conclusion that the reaching of the ultimate load in unreinforced as well as reinforced masonry columns is accompanied by some ultimate horizontal deformation dx,m; to reach this deformation a greater load in compression is necessary in the case of columns reinforced with strips of fabrics of carbon or glass fibres due to the active action of the wrapping used.

The masonry columns loaded by concentric compressive force, reinforced with strips of fabrics of carbon fibres have a wider domain of elasto-plastic deformations. In the case of experimentally verified columns, this increase in the ultimate deformation of masonry columns reinforced with strips of fabrics of carbon fibres amounted to 192%, and of glass fibres to 44% against the ultimate deformation of an unreinforced masonry column loaded by concentric compressive force. The masonry reinforcement with strips of fabrics of carbon fibres does not have a significant effect on the magnitude of compressive loading under which the first tensile cracks appear. The reinforcement in masonry columns loaded by concentric compressive force starts applying (activating) with the appearance and development of vertical cracks in the masonry. The greater width of the domain of elasto-plastic deformations of reinforced masonry columns loaded by concentric compressive force will positively apply in terms of the action and response of a vertical masonry structure under cyclic – repetitive or dynamic – load (technical, induced and

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Fig. 4. Glass fibre strips (GFRP) confined columns (a) vertical deformation-to-load pattern dy  N; (b) permanent vertical deformation dy,t to total vertical deformation dy,c pattern in relation to load N.

Table 3 Summary of test specimens. Marking

Dimensions Masonry Reinforcement w/d/h (mm) strength fk (MPa)

Ultimate load NExp u,m (kN)

P01_NZ P02_NZ P21_NZ P11_Z_CFRP

290  290  1020

630 660 890 1097

3.67 3.67 3.67 3.67

P12_Z_CFRP P25_Z_GFRP_SEH25A_75

3.67 3.44

P26_Z_GFRP_SEH25A_75 P27_Z_GFRP_SEH25A_150

3.43 3.96

P28_Z_GFRP_SEH25A_150 P32_Z_GFRP_SEH51A_75

3.97 3.74

P33_Z_GFRP_SEH51A_75 P34_Z_GFRP_SEH51A_150

3.66 3.67

P35_Z_GFRP_SEH51A_150

3.98

Unreinforced

Carbon fibres, strips 150 mm Glass fibres, strips 75 mm Glass fibres, strips 150 mm Glass fibres, strips 75 mm Glass fibres, strips 150 mm

1219 1140 1380 1500 930 1500 1100 1260 1022

natural seismicity, cyclic temperature and moisture load). Fig. 8 shows the correspondence of horizontal deformations of masonry and horizontal deformations of the fabric in the crack development phase. The reaching of the ultimate load Nu,m of masonry columns reinforced with strips of fabrics of carbon or glass fibres is characterised by a sudden tear of the fabric in the middle third of the column height usually accompanied by the total disintegration of the column masonry (Fig. 9). Immediately before reaching the ultimate load Nu,m, vertical tensile cracks arise and intensively develop in the middle third of the masonry column height, and the cohesion between the strengthening fabric and the column masonry is partially degraded. Exp The experimentally identified values of the ultimate load Nu,m of masonry columns reinforced with strips of fabrics of carbon or glass fibres in the thirds of the column’s height (Fig. 9) reached average values amounting to 148–174% against the ultimate load values of unreinforced columns. The experimentally identified ultimate load NExp u,m of masonry columns reinforced with strips of fabrics of carbon or glass fibres, as compared to the characteristic loadˇ bearing capacity NTeor u,m of unreinforced columns specified according to the CSN EN 1996-1-1 standard [40], reached 340–540% (GFRP) and 400–440% (CFRP). The experimentally identified ultimate load NExp u,m of unreinforced masonry columns reached 230–320% as compared to the characteristic load-bearing capacity NTeor u,m of unreinˇ SN EN 1996-1-1 standard [40] (Table 4). forced columns specified according to the C

Fig. 5. The horizontal deformation-to-load pattern dx  N in the middle part of unreinforced columns. While analysing the deformation and strain characteristics of masonry columns and their ultimate load, the effect of a potential variability of the properties of individual masonry components and the masonry execution (e.g. scattering of the N  dy relationship of unreinforced columns – Fig. 2a) must be considered. The values of the initial vertical deformations dy (Figs. 2a, 3a, 4a) and the dy,t/dy,c ratio (Figs. 2b, 3b, 4b) of some test columns are affected by inelastic additional pushing of the bed joints (the effect of binder shrinkage in the bed joints of the column masonry, the appearance of horizontal structural cracks, or insufficient initial contact in the bed joint).

3. Discussion of results  The experimental research completed to-date has revealed that the efficiency of masonry reinforcement by its wrapping in ‘‘non-prestressed’’ FRP based on high-strength

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Fig. 6. (a) The horizontal deformation-to-load pattern dx  N in the middle part of columns confined with carbon fibre strips (CFRP); (b) the horizontal deformation-to-load pattern dx  N in the middle part of columns confined with glass fibre strips (GFRP).

Fig. 7. The brick–mortar interaction mechanism.

carbon and glass fibre fabrics is not only the function of the FRP’s mechanical properties and amounts, but it also significantly relies on the mechanism applied during the masonry failure process as well as on the deformation (strain) properties of the masonry. In the case of masonry in which primarily the application the compressive failure mechanism – where masonry integrity is gradually degraded by the crushing of its components until the phase of complete masonry failure at reaching the ultimate deformation and the ultimate masonry loading in compression – may be assumed, the tensile ‘‘capacity’’ of the FRP is not fully exploited. The achieved value of ultimate load of confined masonry in compression, in this case, as compared to the ultimate load in compression at which the FRP’s tensile strength is efficiently exploited, is lower and does not principally differ from the ultimate load-bearing capacity of unconfined masonry. The failure occurs by reaching the ultimate masonry deformation in compression dym simultaneously with relatively low horizontal deformations dxm. This fact must be considered in the calculation procedure

of the load-bearing capacity of masonry strengthened by FRP where the above described failure mechanism under compressive loading may objectively be assumed.  In the case of masonry loaded by compression in which the application the failure mechanism characterised by the appearance and development of tensile cracks passing in the direction of compressive trajectories and accompanied by a gradual growth in horizontal deformations dx and a prominent redistribution of compressive stresses along the masonry cross section may be assumed, the fabric’s (composite’s) tensile strength is efficiently applied and exploited. By its tensile strength, the FRP based on high-strength carbon and glass fibre fabrics prevents the development and propagation of vertical tensile cracks (horizontal deformations dx) thus contributes to the increased load-bearing capacity of the masonry in compression. The FRP is activated due to induced strain caused by transverse/horizontal deformations of the compressed masonry. Unlike the previous case, this failure mechanism and the mutual ‘‘masonry – fabric (composite)’’ interaction usually allows for the full exploitation of the capacity of the masonry and its individual components in compression. The ultimate load of masonry in compression significantly grows in such cases due to the effect of the masonry’s confinement in FRP applied in the form of non-prestressed wrapping strips, as compared to the ultimate load of masonry unconfined with fabrics.  The failure along the masonry cross section at the point of its wrapping in a composite has a characteristic arrangement of tensile cracks in the bed joint corresponding to the concentration of transverse (horizontal) compressive forces causing ‘‘masonry-composite’’ interaction on the edges of the masonry wrapped in FRP composite (Fig. 10). After the failure of the adhesion between the masonry and the composite in the area (on the surface) between the edges of the wrapped column, horizontal compressive forces due to the mutual ‘‘masonry-composite’’ interaction are ‘‘concentrated’’ into the area of the masonry edges. A multiaxial stress state arises in the central part of the horizontal cross section around the masonry column’s

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Fig. 8. Horizontal deformations of masonry and horizontal deformations of the fabric in the crack development phase.

Fig. 9. Failure of a masonry column confined with glass fibre strips upon reaching the ultimate load.

Table 4 Teor Ultimate loads NExp u,m and theoretical load bearing capacities Nu,m of unreinforced and reinforced columns. Marking

Ultimate load NExp u,m (kN)

Theoretical load bearing capacity NTeor u,m (kN) Fibres str.a

Fibres str.b

P01_NZ P02_NZ P21_NZ P11_Z_CFRP P12_Z_CFRP P25_Z_GFRP_SEH25A_75 P26_Z_GFRP_SEH25A_75 P27_Z_GFRP_SEH25A_150 P28_Z_GFRP_SEH25A_150 P32_Z_GFRP_SEH51A_75 P33_Z_GFRP_SEH51A_75 P34_Z_GFRP_SEH51A_150 P35_Z_GFRP_SEH51A_150

630 660 890 1097 1219 1140 1380 1500 930 1500 1100 1260 1022

277 277 277 625 625 384 382 460 461 471 462 507 530

– – – 457 457 303 302 353 353 – – – –

Teor NExp u,m/Nu,m

2.27 2.38 3.21 1.76a 1.95a 2.97a 3.61a 3.26a 2.02a 3.18 2.38 2.49 1.93

(2.40)b (2.67)b (3.76)b (4.57)b (4.25)b (2.63)b

ˇ Nteor u,m of unreinforced columns (labelled NZ) was calculated pursuant to CSN EN 1996-1-1. Nteor u,m of confined columns (labelled Z) was calculated as follows

: NTeor u;m ¼Ui;m 



cm  fk;m þ d 

2:5  l ft;CFRP  1 þ 2:5  l 100



 Am



where Am – masonry cross section area, U – decreasing factor, Ui in the head, or Um in the middle of structure’s height, fk,m – characteristic value of masonry compressive 4e strength, cm – factor of masonry degradation level, d  d ¼ 1  hi;mk , ei (emk) – compressive force eccentricity (in the head or in the middle of structure’s height), l – transverse reinforcement percentage, ft,CFRP – CFRP tensile strength. Teor Note: It is evident, from the NExp u,m/Nu,m ratio, that the formula used for load-bearing capacity determination of confined columns needs some refinement. a Composite strength declared by the manufacturer (989 MPa). b Composite strength obtained from experimental tensile tests (carbon – 509 MPa, glass SEH25A – 152 MPa).

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Fig. 10. Masonry failure along the cross section.

wrapping, passing gradually into a predominantly uniaxial stress state in the extreme parts of the column masonry. In this phase, it is primarily the central part of the column in which triaxial stresses act that resists the compressive load acting on the column, unlike the gradually separating extreme parts of the masonry. 4. Summary The stabilising and reinforcing effect of FRP based on highstrength carbon and glass fibre fabrics is manifested in masonry structures (columns, walls) loaded by compression in which the tensile and shear failure mechanism is primarily applied during the appearance of defects (compressive failure, tensile failure, shear failure) and their successive failure. In the case of masonry structures susceptible to predominantly compressive failures – crushing, delamination, crack branching – depending on the fabric’s application method, the masonry reinforcement effect fails to apply to the necessary extent corresponding to the FRP’s tensile strength. This serious fact must be considered while determining the admissible load-bearing capacity of masonry confined with FRP. These are, above all, the cases of brick (regular) coursed masonry of walls and columns with a regular bond and thin bed joints (615 mm) with high compressive-strength mortar (corresponding to the strength of bricks). Acknowledgements The article was written with support from the NAKI DF12P01OVV037 project ‘‘Progressive non-invasive methods of the stabilisation, conservation and reinforcement of historic structures and their parts with composite materials based on fibres and nanofibres’’ funded by the Ministry of Culture of the Czech Republic. References [1] Saadatmanesh H. Extending service life of concrete and masonry structures with fiber composites. Constr Build Mater 1997;11(5–6):327–35. [2] Avramidou N, Drdácky´ MF, Procházka PP. Strengthening against damage of brick walls by yarn composites. In: Proceedings of the 6th international conference on inspection, appraisal, repair & maintenance of buildings & structures, 15–17 December 1999, Melbourne. Singapore: CI-Premier Pte. Ltd.; 1999. p. 51–8. [3] Doran B, Koksal HO, Turgay T. Nonlinear finite element modeling of rectangular/square concrete columns confined with FRP. Mater Des 2009; 30:3066–75. [4] Wu YF, Jiang Ch. Effect of load eccentricity on the stress–strain relationship of FRP-confined concrete columns. Compos Struct 2012;98:228–41. [5] Corradi M, Borri A, Vignoli A. Strengthening techniques tested on masonry structures struck by the Umbrian-Marche earthquake of 1997–1998. Constr Build Mater 2002;16(4):229–39.

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