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COMPOSITE SEISMIC RETROFIT AND ADVANCED DISTRIBUTED FIBER OPTIC MONITORING OF AN HISTORICAL BUILDING IN FOLIGNO (ITALY) Dr. F Bastianini, Prof. A di Tommaso University of Architecture of Venice Department of Construction S. Croce 191 Venezia 30135 Italy [email protected], [email protected] Prof. A Borri, Dr. M Corradi University of Perugia Dept of Civil & Environmental Engineering, Via Duranti 93 Perugia 06125 Italy [email protected], [email protected] KEYWORDS: FRP, seismic, retrofit, monitoring, masonry ABSTRACT Fibre reinforced polymers (FRP) are gaining increasing popularity for upgrading, repairing and rehabilitation of existing structures thanks to many interesting advantages against traditional structural materials. Composite applications in civil engineering, that range from embedded non-metallic reinforcements to externally bonded strengthenings, are generally much more recent than other FRP applications, for this reason several questions regarding the assessment of the strengthening effectiveness as well as long term behaviour and durability of the application remain still unsolved. Elmi-Pandolfi building, an historical structure dated 1600 that was seriously damaged in the earthquake of 1997, has been repaired and retrofitted including carbon FRP (CFRP) strengthenings externally bonded to some vaults and walls. Since an innovative strengthening technique intended to lock-out the possible failure mechanisms with CFRP tapes was used for the vaults, its effectiveness has been experimentally proved trough dynamic testing. Furthermore a fibre optic monitorage network based on distributed Brillouin strain sensing was embedded in the CFRP strengthenings in order to evaluate the durability of the application especially in case of further seismic shocks. In this paper the dynamic tests carried out on the biggest of the repaired vaults and preliminary experimental tests characterizing the Brillouin distributed sensing performances are presented. INTRODUCTION Fibre reinforced polymers are obtained saturating carbon, glass or aramid fibers with polymeric matrixes. They are characterized by a variety of advantages, such as lower density, higher stiffness and strength, adjustable mechanical properties, resistance to corrosion, solvents and chemicals, flexible manufacturing and fast application. For these reasons their diffusion in civil engineering is increasing for repairing, upgrading and seismic retrofit of bridges, buildings and other infrastructures (Bakis, 1993). Manufacturing defects such as bubbles, voids, fiber misalignments and improper bonding surface preparation/levelling are quite common in hand lay up applications (Barbero, 1997) and they can have considerable influence on the strength properties. Various non-destructive techniques, such as pull-off, shear-stripping, ultrasonic testing, thermography and acoustic testing have been demonstrated to be effective to assess the quality of application (Bastianini et al., 2000-2002) but in case of particular applications testing procedures aimed to characterize the whole structural behaviour, such as dynamic testing, are to be considered as well. In addition, since CFRP applications in civil engineering are a relatively recent goal, long term monitorage is strongly recommended, considering both the typical CFRP brittle failure behaviour and the critical topic of load transfer from the substrate to the strengthening, a problem often related to stress concentration and manufacturing defects. With simple structural elements such as tie ropes, pre- tensioning or post tensioning rods and cables, few punctual measurements of the strain value can be considered sufficient for monitorage, but in case of seismic retrofit of vaults, arches and masonry panels, where different crack opening patterns can lead to a great variety of possible load distributions, the accuracy of strain measurement becomes less important than an high quantity of measure points capable
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Page 1: COMPOSITE SEISMIC RETROFIT AND ADVANCED DISTRIBUTED … · COMPOSITE SEISMIC RETROFIT AND ADVANCED DISTRIBUTED FIBER OPTIC MONITORING OF AN HISTORICAL BUILDING IN FOLIGNO (ITALY)

COMPOSITE SEISMIC RETROFIT AND ADVANCED DISTRIBUTED FIBER OPTIC MONITORING OF AN HISTORICAL BUILDING IN FOLIGNO (ITALY)

Dr. F Bastianini, Prof. A di Tommaso University of Architecture of Venice

Department of Construction S. Croce 191

Venezia 30135 Italy

[email protected], [email protected]

Prof. A Borri, Dr. M Corradi University of Perugia

Dept of Civil & Environmental Engineering, Via Duranti 93 Perugia 06125

Italy [email protected], [email protected]

KEYWORDS: FRP, seismic, retrofit, monitoring, masonry

ABSTRACT Fibre reinforced polymers (FRP) are gaining increasing popularity for upgrading, repairing and rehabilitation of existing structures thanks to many interesting advantages against traditional structural materials. Composite applications in civil engineering, that range from embedded non-metallic reinforcements to externally bonded strengthenings, are generally much more recent than other FRP applications, for this reason several questions regarding the assessment of the strengthening effectiveness as well as long term behaviour and durability of the application remain still unsolved. Elmi-Pandolfi building, an historical structure dated 1600 that was seriously damaged in the earthquake of 1997, has been repaired and retrofitted including carbon FRP (CFRP) strengthenings externally bonded to some vaults and walls. Since an innovative strengthening technique intended to lock-out the possible failure mechanisms with CFRP tapes was used for the vaults, its effectiveness has been experimentally proved trough dynamic testing. Furthermore a fibre optic monitorage network based on distributed Brillouin strain sensing was embedded in the CFRP strengthenings in order to evaluate the durability of the application especially in case of further seismic shocks. In this paper the dynamic tests carried out on the biggest of the repaired vaults and preliminary experimental tests characterizing the Brillouin distributed sensing performances are presented. INTRODUCTION Fibre reinforced polymers are obtained saturating carbon, glass or aramid fibers with polymeric matrixes. They are characterized by a variety of advantages, such as lower density, higher stiffness and strength, adjustable mechanical properties, resistance to corrosion, solvents and chemicals, flexible manufacturing and fast application. For these reasons their diffusion in civil engineering is increasing for repairing, upgrading and seismic retrofit of bridges, buildings and other infrastructures (Bakis, 1993). Manufacturing defects such as bubbles, voids, fiber misalignments and improper bonding surface preparation/levelling are quite common in hand lay up applications (Barbero, 1997) and they can have considerable influence on the strength properties. Various non-destructive techniques, such as pull-off, shear-stripping, ultrasonic testing, thermography and acoustic testing have been demonstrated to be effective to assess the quality of application (Bastianini et al., 2000-2002) but in case of particular applications testing procedures aimed to characterize the whole structural behaviour, such as dynamic testing, are to be considered as well. In addition, since CFRP applications in civil engineering are a relatively recent goal, long term monitorage is strongly recommended, considering both the typical CFRP brittle failure behaviour and the critical topic of load transfer from the substrate to the strengthening, a problem often related to stress concentration and manufacturing defects. With simple structural elements such as tie ropes, pre-tensioning or post tensioning rods and cables, few punctual measurements of the strain value can be considered sufficient for monitorage, but in case of seismic retrofit of vaults, arches and masonry panels, where different crack opening patterns can lead to a great variety of possible load distributions, the accuracy of strain measurement becomes less important than an high quantity of measure points capable

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to allow to understand the whole static structural behaviour. In these cases distributed sensing system such as the Brillouin scattering analysis in single-mode optical fibres, are to be preferred to multiple discrete gauges, both for economical and reliability considerations. SEISMIC RETROFITTING INTERVENTION Elmi-Pandolfi building (Figure 1) is a clustered complex that takes almost half of a single-standing block in the historical centre of Foligno (Italy). The building, that includes various different structural nuclei affected by changes and modifications during centuries, gained almost stable configuration around the XVII century as a noble house provided with representative halls, residential quarters for the owner’s family and for the housekeepers, and several rooms dedicated to storehouses and commercial activities. The building was seriously damaged by the earthquake of 1997 and may of its structures were repaired including some CFRP strengthenings. The peripheral masonry facing Via Agostini and Via Rutili (respectively left and bottom of figure 1) was strengthened with three horizontal belts of CFRP ribbon placed at different heights. On the side facing Via Agostini some vertical tapes were included too. The vault of the drawing-room was reinforced with CFRP tapes at the extrados intended to lock-out some of the most probable failure mechanisms, and was dynamically tested before and after reinforcement application. Even if various types of failures associated with a vault structure are possible, the most common one is consequence of a mechanism that undergoes the formation of cylindrical hinges. The application of CFRP strengthening tapes at the extrados of the arch is able to prevent cylindrical hinges formation and it can hamper many collapse mechanisms.

Fig. 1: geometric survey of Elmi-Pandolfi building. CFRP strengthenings have been used for the drawing-room vault (upper left) and of

the external bearing masonry (left, bottom and right periphery) (courtesy Servizi di Ingegneria Ldt.). The length of the solid-brick masonry vault is 10.3 m, width is 7.4 m, while its average thickness is 12 cm. The vault rehabilitation started with removal of the filling material up to the haunches, where the solid clay bricks of the arched lintel are inserted into the outer wall. At the vault extrados six reinforcement solid-brick arches have been found during filling material removal (figure 2). After surface cleaning by sanding and water based solvents (figure 3) and then levelling the surface of the outer vault area, bedding bands were created using suitable epoxy putty. Before putty application, surface was prepared with a suitable epoxy primer. A first layer of CFRP was laid with epoxy-resin over the bedding bands. An accurate surface preparation was necessary considering that CFRP sheet is very sensitive to local effects connected with the irregularity of the laying surface. It should be noted that, despite careful preparation, areas with abrupt variations in curvature may occur. In these cases experimental tests showed high degree of weakness of thin CFRP sheets. After the CFRP sheets have been laid, a small amount of

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putty was cast over each lintel, onto which a steel plate fitted with a steel wedge were placed. The latter was designed to house anchoring rods, inserted diagonally, long enough to reach the height of the springer. Tapes of mono-directional carbon fabric, 200 mm wide, bonded at the vaults extrados where used for all strengthenings. The fabric was impregnated by an appropriate epoxy resin furnished by the fiber producer (producer: Mapei, product denomination: Mapewrap C UNI-AX 300/20).

Figure 2: geometric survey of vault extrados before reinforcement (left) and schematic representation of CFRP and hollow-brick walls position (right).

Figure 3: the masonry vault of the drawing-room dated 1600 during

surface preparation for CFRP application. Figure 4: Hollow-brick walls under construction.

The work was completed traditionally with the construction of hollow-brick walls (figure 4), arranged at a distance apart equivalent to that of the overlaying hollow floor slab (approx 80-150 cm). The hollow brick walls were constructed over CFRP sheets at vault extrados. The substitution of filling material with hollow brick walls has positive effects thanks to the dead load decrease. When the connection between masonry vault and hollow brick walls is effective, their construction also prevents the formation of cylindrical hinges at vault extrados and it causes high increases of inducing mechanism activation loads. A further CFRP reinforcement was applied over the hollow-brick walls (figures 5-7).

Figure 5: a possible collapse mechanism for a masonry vault: the filling material over the vault only stabilises the structure.

Figure 6: the substitution of the filling material with hollow brick walls produces a benefit in terms of dead load and of vault strength.

Figure 7: the application of CFRP materials and hollow brick walls can prevent the formation of some collapse mechanisms.

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DYNAMIC TESTING Dynamic tests have now been recognised as a efficient method to obtain a reliable estimate of key properties for masonry structures, such as resonance frequencies, modal damping and mode shapes. Some researchers have studied and installed permanent monitoring networks and forced-vibration testing projects have been carried out on large masonry buildings. Forced-vibration tests, in particular, lead to well-defined frequency response curves for the structure. A Welsh cloister vault in Elmi-Pandolfi Building was dynamically tested before and after CFRP reinforcement application. The main objective of this research program was to obtain an experimental database of the same masonry vault in both configurations (un-reinforced and reinforced) to be used in the development of 2D and 3D finite element models of the vaulted structure. These models are currently being implemented in the state-of-the-art programs for seismic analysis of masonry buildings. The first series of forced-vibration tests were carried out in July, 2002. The same experimental procedures were used again in September, 2002 after vault reinforcement. The masonry vault was tested imposing a horizontal dynamic load located at vault abutment. The tests allowed to study the dynamic behaviour under different configurations: un-strengthened vault, CFRP strengthened vault, CFRP and hollow-brick wall strengthened vault. A vibrodyne or shaker was used for harmonic load application, sweeping frequency up to 7.50Hz in 0.42Hz increments, and sweeping the load force as well according to equation (1), where Fmax is maximum load induced by the vibrodyne and ω is the angular frequency.

)sin()( max tFtF ω= (1) Acceleration data were recorded using piezoelectric accelerometers both along tangential and normal directions with respect to the vault surface. Displacements were measured using a laser vibrometer pointing at different target positions at vault abutment, haunch and crown. The selected position of the vibrodyne is illustrated by a bold arrow in Figure 8. Force amplitudes Fmax, proportional to the square of the rotation frequency, varied from 0 to 2.06kN during the three series of tests which were carried out with frequency sweeps between 0 and 7.50Hz. The response of the vault was recorded with a Catman-Spider8 data acquisition system. Data were sampled at 500Hz for 8 seconds. Typical time-histories recorded during the forced-vibration tests are shown in Figure 9. The data shown in Figure 9 was obtained for an operation frequency of 7.50Hz.

1

432

0,0 0,2 0,4 0,6 0,8 1,0

-1,0x10-5

-5,0x10-6

0,0

5,0x10-6

1,0x10-5

Dis

plac

emen

t (m

)

Time (sec)

Figure 8: survey of vault intrados with vibrodyne position (1)

anchored to the external wall, and LASER vibrometer target points (2,3,4).

Figure 9: Example of recorded data for an operation frequency of 7.5Hz.

The analysis has to be done considering the maximum displacement measured at the target points, as a function of the load frequency. In figures 9, 10 and 11, positive displacements are plotted comparing un-strengthened and strengthened vault, while negative displacements showed the same structural behaviour and therefore have been omitted. Tests carried out on the un-reinforced vault were executed after removing the filling material from vault extrados. Then CFRP was applied to vault extrados and the

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displacement peak amplitude decreased compared to the ones measured for unstrengthened vault, while their resonance frequency remained almost constant. After the construction of low hollow-brick walls over the CFRP strengthened vault a further strengthening effect was detected in terms of a very high decrease of displacement peak amplitude.

0,0E+00

5,0E-06

1,0E-05

1,5E-05

2,0E-05

2,5E-05

3,0E-05

1 2 3 4 5 6 7 8Frequency (Hz)

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plac

emen

ts (m

)

Un-reinforced vaultCFRP reinf.CFRP+walls

0,0E+00

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2,0E-05

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3,0E-05

1 2 3 4 5 6 7 8Frequency (Hz)

Dis

plac

emen

ts (m

)

Un-reinforced vaultCFRP reinf.CFRP+walls

Figure 9: displacements vs. frequency recorded at target point 4.

Figure 10: displacements vs. frequency recorded at target point 3.

0,E+00

1,E-05

2,E-05

3,E-05

4,E-05

5,E-05

6,E-05

7,E-05

8,E-05

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1,E-04

1 2 3 4 5 6 7 8Frequency (Hz)

Dis

plac

emen

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)

Un-reinforced vault

CFRP reinf.

CFRP+walls

Figure 11: displacements vs. frequency recorded at target point 2. DISCRETE FIBRE OPTIC SENSORS AND DISTRIBUTED BRILLOUIN SYSTEM Fibre optic sensors (FOS) are often preferred for embedding in FRP materials due to a variety of advantages that include longer durability in harsh environments, no electro-magnetic interference (EMI), higher material compatibility, and smaller dimension. Fabry-Perot cavities (Lawrence, 1997), Bragg gratings (Morey, 1989), fiber interferometers (Inaudi, 1995) and other FOS technologies have been used for strain and temperature sensing of composite members both in laboratory tests and in monitorage applications. The most part of the mentioned FOS, with the exception of fibre interferometers, are characterized by small sensitive areas (usually limited to some mm) and requires complex wiring or multiplexing systems for multiple point sensitivity. Fibre-optic interferometers have gage lengths that can range up to some tenths of meters, but they are capable to give only an integral displacement information over the whole length, and cannot therefore be considered as distributed systems. Brillouin distributed strain sensing is substantially different from other FOS technologies being based on an optical effect that spontaneously arises during light propagation in common telecom optical fibres. Brillouin scattering is a non-linear process that affects a fraction of the incident “monochromatic” photons that are travelling along the fibre, frequency shifting them trough anelastic collisions in which the photon energy difference is spent in the production/annihilation of phonons of acoustic vibration. Since the phonon energy is influenced by the mechanical strain and by the medium density, which varies with temperature, the relation between Brillouin shift and fiber strain (or temperature) can be used for sensing purposes (Horiguchi, 1989). Brillouin optical time-domain reflectometers (BOTDR) can provide distributed sensing combining time domain analysis of light pulse propagation with spectrum analysis of Brillouin scattered photons. BOTDR have been experimentally applied for large structure temperature

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monitorage (Thévenaz, 1999), tunnel damage sensing, ground landslides monitoring and underground water level sensing (Komatsu, 2002), and other similar applications. In comparison with other FOS technologies, Brillouin technique seem characterized by lower sensitivity, repeatability and accuracy, but the advantage of a real distributed sensing can easily overcome these defects when a huge amount of measurement points can help to understand the whole structure behaviour much better than a limited number of high precision data, or when long sensing networks allow the detection of local phenomena whose location is impossible to be predicted “a priori”. Since Brillouin technique requires only a common low-cost single-mode telecom fiber as a sensing element and can work with fiber lengths up to several tenths of km, also economical considerations make Brillouin much more attractive than other FOS when very wide sensing networks or disposable gauges are required. EVALUATION OF THE BRILLOUIN FIBER-OPTIC MONITORAGE NETWORK Single mode optical fiber suitable for Brillouin sensing has been applied on most of vault and masonry strengthenings. On external walls, the fiber circuit has been arranged in order to have a strain sensing section bonded to the CFRP (figure 12) and a temperature sensing section loosely placed in a raceway located nearby the bonded fiber (figure 13). This arrangement has been designed in order to provide distributed thermal compensation data and to assess that the glass phase transition temperature of the polymeric matrix is never reached, being the wall surface directly exposed to sunlight heating. Distributed thermal compensation has instead not been included in the vault monitoring system, since great thermal unhomogeneities are not expected in the closed environment. Preliminary Brillouin testing have been conducted on the vault using 32m of a “smart” CFRP ribbon (figure 14) that was bonded on the strengthening using epoxy resin. The smart CFRP was manufactured with a proprietary technique weaving a 900µm, a 125µm, and a 600µm fiber into a 10cm wide carbon/glass tape, respectively positioned at 1, 5 and 9 cm from tape side edge. After the application, the three embedded optical fibers were connected in series by fusion splices, obtaining a total sensing circuit length of 96m.

Fig. 12: optical fiber for Brillouin sensing embedded into CFRP strengthenings on the

external masonry.

Fig. 13: detail of an inspection box of the cable raceway where is placed temperature sensing fiber

and of the strain sensing fiber bonded to CFRP.

Fig. 14: smart CFRP tape placed on vault.

Preliminary tests were performed on the masonry vault in order to evaluate Brillouin technique sensitivity to moderate deformations. Since the strain levels obtained with the highest load considered safe for such structure, taking into account its age and the damages caused by 1997 earthquake, was of the same order of magnitude of the noise floor level of the test equipment, a patent pending data processing was developed, capable to enhance the signal-noise ratio trough numerical correlation of strain data detected at close physical locations by different sensing fibers. Using all the three fibers data a numerical correlation was developed in order to enhance sensitivity trough a signal-noise ratio improvement. Tri-dimensional strain distribution plots with good correspondence to the expected patterns have been obtained (figure 15, 16), and considering optical fiber layout, strain data provided by Brillouin system have been used for vault deformation reconstruction (figure 17, 18).

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Figure 15: strain distributions on CFRP strengthened masonry vault

loaded with 7 kN at haunch location. Figure 16: strain distributions on CFRP strengthened masonry vault

loaded with 10 kN at haunch location.

Figure 17: schematic representation of the strengthened vault where

the optical sensing fiber is evidenced. Figure 18: example of reconstruction of the vault deformation

according to Brillouin strain data. Further testing has been conducted using a second sensing circuit placed on the external masonry facing Via Rutili. The loop was made connecting in series three separate single-mode fibers that have been previously embedded into a “smart” carbon fiber mono-directional ribbon analogous to the one used for the vault. The “active” length of the sensing circuit, that is the length actually bonded to the masonry (Figure 22), is of 14 meter for each fiber, while some loose segments for thermal compensation have been left at the input point of the loop and at the connections points between different fibers (Figure 19).

Fig. 19: detailed schematic for the test circuit on the external masonry.

A flat jack has been then inserted into a transversal masonry panel (figure 20) realizing a configuration capable to produce a local out-of-plane deformation of the external bearing masonry wall, with a consequent tensile strain at its external surface. Door opening of the transversal panel was properly shored with steel proppings (figure 21) and the flat jack was placed at the same quota of the sensing fibers in order to ensure the maximum sensitivity of the system.

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Fig. 20: detailed view of the flat jack embedded into the

transversal masonry panel. Fig. 21: out-of-plane load applications to the external bearing masonry with a flat jack. Door opening was shored with steel

propping to enhance bucking stiffness. Brillouin distributed spectra were collected along the sensing fiber at different load steps, and the deformation of the external face of the bearing masonry was evaluated through a difference plot between the absolute strain profile at each load step and the reference one taken with no applied load. Residual strains were recorded after load had been removed completely. In figure 23 the various areas of the sensing circuit are identified and coupled to the respective strains profile distributions; it has to be noticed that the strain distribution is well detected by all three fibers in correspondence of the flat jack position.

Figure 22: “smart” CFRP with Brillouin sensing fibers placed on the external surface of the bearing masonry.

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Fig. 23: identification of the different sensing areas on the analyzer display and on the structure.

A direct comparison between the different fibers embedded in the smart-CFRP tape (Figure 23) shows how the higher sensitivity was obtained with the 125µm bare fiber, while the smoother response was given from the 900 µm fiber. The 600 µm fiber seems the best compromise between sensitivity and easier handling and has therefore to be preferred for future applications.

Fig. 24: comparative plot of the strain data measured by the three different fibers.

CONCLUSIONS Strengthening technique based on the application of CFRP tapes to vault’s extrados in order to lock-out the most probable failure mechanisms has been demonstrated to be effective through dynamic testing, and it was noticed that it produces notable reductions on the displacement peak values but not on the resonance frequencies. A carbon fiber “smart” composite capable to introduce acceptable optical losses have been developed and successfully tested in a real historical heritage monitorage application. Trough the use of multiple sensing fibers and thanks to a correlation data processing technique the signal-noise ratio of Brillouin strain

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analysis has been improved and detection of small (∼50µε) strain levels has been successfully performed. As a conclusion Brillouin strain sensing with embedded optical fibers in composite materials has been demonstrated to be effective and economically advantageous for quality control purposes and structural FRP strengthening monitorage. ACKNOWLEDGEMENTS The financial support of ISRIM the Italian Ministry of University and Scientific Research (MURST) – Cofin 2002, and of the industrial partner Federal Trade S.p.A. are gratefully acknowledged. Special thanks are due to Dr. A. Giannantoni, Dr. A. Annunziata (ISRIM) , Mr. R. Toigo, Mr. M. Toffanin (Federal Trade SpA) Mr. R. Ali (Ando Europe Ltd.) , Mr. M. Parente, Mr. P. Grati and Mr. W. Toscano (SEAL SpA) for their friendly cooperation. REFERENCES 1. Bakis C.E., “Fiber-Reinforced-Plastic (FRP) Reinforcement For Concrete Structures: properties And

Applications”, Dev. in Civil Eng., 42, 13-27, 1993. 2. Barbero E.J.: Introduction to Composite Materials Design, Taylor & Francis, USA, 21-25, 1997. 3. Bastianini F., Di Tommaso A., and Pascale G., “Ultrasonic non-destructive assessment of bonding

defects in composite structural strengthenings”, Composite Struct., 53 (4), pp. 463-467, 2001. 4. Bastianini F., and Di Tommaso A., “Non-destructive techniques for bonding evaluation in external

FRP structural strengthenings”, Proc. of 8th ECNDT, Barcelona, Spain, 2002. 5. Bastianini F., Di Tommaso A., “Ultrasonic And Thermographic Non-Destructive Techniques For

Bonding Evaluation In External FRP Structural Strengthenings”, Proc. of ACMBS III, Ottawa, Canada, pp.37-44, 2000.

1. Horiguchi T., Kurashima T. and Tateda M., “Tensile Strain Dependence of Brillouin Frequency Shift in Silica Optical Fibers”, IEEE Photonics Tech. Lett., 1 (5), 107-108, 1989.

6. Inaudi D., Elamari A., Pflug L., Gisin N., Breguet J. and Vurpillot S., Low-coherence deformation sensors for the monitoring of civil-engineering structures", Sensor and Actuators A, 44 , 125-130, 1995.

2. Lawrence, C., Nelson D., Bennet T. and Spingarn J., "Determination of process-induced residual stress in composite materials using embedded fiber optic sensors", SPIE, 3042, 154-165, 1997.

7. Morey W., Meltz G. and Glenn W.H., “Fiber optic Bragg grating sensors”, SPIE, 1169, 98-107, 1989.


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