Self-sensing and quantitative assessment of prestressed concrete structures based on distributed long-gauge fiber Bragg grating sensors

Abstract

Quantitative assessment of strengthened concrete structures using self-sensing fiber-reinforced polymer sheets is presented in this article. First, strain distribution along the height of a structure induced by pre-tension force (initiate state) is theoretically estimated. Second, the procedure for parameter estimation of prestressed fiber-reinforced polymer–strengthened structures under external load using measured and pre-tension force–induced strain is established, and nonlinearity caused by random cracks is considered in the method. Both local parameters (neutral axis position, bending stiffness distribution, strain distribution along the cross section, etc.) and global parameter (deflection) of structures can be accurately estimated by measured long-gauge strain responses. Finally, both prestressed fiber–reinforced polymer–strengthened and reinforced concrete beams installed with long-gauge fiber Bragg grating sensors have been experimentally investigated to prove the effectiveness of this method. Experimental results indicate that the estimated neutral axis height and local bending stiffness can reflect initiation of random cracks and deterioration process of structures under increasing external load. Meanwhile, the estimated strain along the beam height and deflection at mid-span agree well with the measured ones, which further verifies the accuracy of the estimated neutral axis position affected by randomly appeared cracks. Hence, the method can be utilized for assessment and maintenance of fiber-reinforced polymer–strengthened structures.

Keywords

Long-gauge fiber Bragg grating sensors prestressed concrete structures quantitative assessment

Introduction

Civil engineering structures play an important role in economic contribution for most countries and have experienced rapid development in the past decades. During their service period, the expected and unexpected factors (material aging, environment effect, operational load, occasional disaster, etc.) will inevitably lead to decrease in bearing capacity of these lifeline structures. Retrofitting and strengthening measures should be taken to ensure safety and service performance when deterioration in these structures reaches a considerable extent.

Fiber-reinforced polymer (FRP) is characterized by high strength, light weight, and corrosion stability, and therefore, it is ideal strengthening material for engineering structures. As there is increase in the number of FRP-strengthened structures, performance assessment of these structures based on different sensing technologies has gained increasing attention. These sensing technologies are generally classified into three types: fiber optic sensors, vibration-based sensors, and carbon fiber–reinforced polymer (CFRP)-based sensors. Wu et al. (2006a) investigated strain monitoring of concrete structures strengthened by prestressed poly-p-phenylene benzobisoxazole (PBO) fiber sheets based on fiber optic sensing (Brillouin Optical Time Domain Reflectometry, BOTDR). Gheorghiu et al. (2005) studied strain measurement of CFRP-strengthened beams under fatigue loading using fiber optic sensors. Zhang et al. (2006) presented heath monitoring of reinforced concrete (RC) beams strengthened by externally post-tensioned FRP tendons based on fiber Bragg grating (FBG) and BOTDR. Monitoring of FRP debonding and epoxy cracking based on global and local fiber optic sensors was studied by Jiang et al. (2010). Many researchers have reported vibration-based damage detection and performance assessment of FRP-strengthened structures. Bonfiglioli et al. (2004) presented modal testing of damaged RC beams repaired with externally bonded CFRP sheets and verified the effectiveness of the strengthening system. Dynamic characteristics (natural frequency and mode shape) can be utilized to evaluate the performance of FRP-strengthened structures (Aref and Alampalli, 2001; Baghiee et al., 2009; Burgueño et al., 2001; Capozucca, 2009, 2013; Lee et al., 2007; Zanardo et al., 2007). Measured modal data can also be used to update the finite model for better understanding of FRP-strengthened structures (Zanardo et al., 2006). CFRP possesses the property of electric resistance and can be regarded as both retrofit and sensing materials (Wu et al., 2006b; Yang et al., 2016b). Yang et al. (2016a) studied the feasibility of resistance change of CFRP for self-monitoring composited structures strengthened with hybrid FRP sheets. Other literatures about performance assessment of FRP-strengthened structures can be found in the studies of Ghosh and Karbhari (2007), Kaiser and Karbhari (2004), Kim et al. (2007), Nassr and El-Dakhakhni (2009), and Saafi and Sayyah (2001). Although many methods have been developed for assessment of FRP-strengthened structures, most of these methods focus on qualitative assessment. This article aims at quantitative assessment of these structures using self-sensing FRP sheets. Deterioration process of such structures caused by randomly appeared cracks can be quantitatively evaluated at both global and local levels.

Compared to “point” strain sensors, long-gauge strain sensors can reflect and identify randomly appeared damages especially for cracked concrete structures (Ansari, 2005; Hong et al., 2012; Li and Wu, 2007, 2010). FBG sensors with the characteristics of measurement with high accuracy, high stability, and dynamic capacity have gained increasing attention for monitoring of engineering structures. However, bare FBG sensor is a typical “point” sensor with the sensing length of about 1 cm, and many kinds of packaged FBG sensors are only used for “point” strain or temperature monitoring. Long-gauge FBG sensors can measure average strain over a certain length of the structures, and any damage occurrence within this region can be identified. Both damage identification of structures in both time domain and frequency domain can be conducted using distributed long-gauge FBG sensors (Hong et al., 2015, 2016; Sigurdardottir and Glisic, 2013). In this article, quantitative assessment of local and global behavior of strengthened concrete structures using self-sensing FRP sheets is presented. Identification of local behavior (crack occurrence, change of neutral axis position, decrease in local bending stiffness, yielding of steel, and strain prediction) and global behavior (deflection prediction) is essential for assessment of FRP-strengthened structures. Theoretical derivation reveals that each long-gauge FBG sensor installed on the surface of the prestressed structure can estimate parameters of local behavior. Distributed deployment of long-gauge sensors can predict parameter of global behavior. Experimental results show that long-gauge strain sensor together with nonlinear analysis is an effective tool for quantitative assessment of nonlinear performance of strengthened RC structures. Therefore, this method is presented.

Theoretical background

Determination of pre-tension force–induced strain

The concrete beam strengthened with prestressed FRP sheets is shown in Figure 1(a). The total height and width of the structures are denoted as h and b, respectively. A total of m long-gauge FBG sensors are supposed to be installed on the strengthened beam. The zone covered by sensor j is denoted as cell j.

Figure 1.

RC beam strengthened by prestressed FRP sheets: (a) FRP-strengthened beam and (b) strain analysis of cell j under external load.

Take cell j for example; total strain is composed of two parts: strain induced by pre-tension force F and strain induced by external load (Figure 1(b)). Strain along the height of the RC beam which is induced by initial pre-tension force F is shown in Figure 1(b). The neutral axis height is denoted as $h_{pj}$ . Therefore, based on plane cross section assumption, strain $ε_{pjz}$ at the point with the distance of z from the bottom surface can be achieved

ε_{pjz} = \frac{- ε_{pj 0} z}{h_{pj}} + ε_{pj 0}

(1)

in which $ε_{pj 0}$ represents pre-tension force–induced strain of the beam bottom. Positive value of equation (1) represents tensile strain, while negative value represents compressive strain.

The stress–strain relationship of compressive concrete proposed by Hognestad is expressed as

σ_{cc} = {\begin{matrix} - f_{c} [\frac{2 ε}{ε_{0}} - {(\frac{ε}{ε_{0}})}^{2}] & if ε_{0} \leq ε < 0 \\ - f_{c} [1 + \frac{0.15 (ε_{0} - ε)}{ε_{u} - ε_{0}}] & if ε_{u} \leq ε < ε_{0} \\ 0 & if ε < ε_{u} \end{matrix}

(2)

in which f_c is compressive concrete strength. $ε_{0}$ is equal to $- 2 \times 10^{- 3}$ and $ε_{u}$ is equal to $- 3.5 \times 10^{- 3}$ . Negative value of equation (2) indicates compressive stress.

The stress–strain relationship of tensile concrete suggested by Hordijk (1991) is expressed as

σ_{ct} = {\begin{matrix} \begin{matrix} E_{t} ε & if ε_{0} < ε \leq ε_{t} \end{matrix} \\ f_{t} (1 + {(c_{1} \frac{ε - ε_{t}}{ε_{ult} - ε_{t}})}^{3}) \exp (- c_{2} \frac{ε - ε_{t}}{ε_{ult} - ε_{t}}) \\ \begin{matrix} - f_{t} \frac{ε - ε_{t}}{ε_{ult} - ε_{t}} (1 + {c_{1}}^{3}) \exp (- c_{2}) & if ε_{t} < ε \leq ε_{ult} \end{matrix} \\ \begin{matrix} 0 & if ε > ε_{ult} \end{matrix} \end{matrix}

(3)

in which $ε_{ult} = ε_{t} + 5.136 G_{f}^{I} / h f_{t}$ , and h means crack bandwidth; $G_{f}^{I}$ is tensile fracture energy and equal to $100 N / m$ ; $ε_{t} = f_{t} / E_{t}$ ; c₁ and c₂ are equal to 3 and 6.93, respectively. E_t is Young’s modulus of tensile concrete. f_t is tensile concrete strength. Positive value of equation (3) indicates tensile stress.

The stress–strain relationship of steel bars is expressed as

σ_{s} = {\begin{matrix} E_{s} ε & if 0 \leq ε < ε_{y} or ε_{y} < ε < 0 \\ f_{y} & if ε \geq ε_{y} \\ - f_{y} & if ε \leq - ε_{y} \end{matrix}

(4)

in which E_s is elastic modulus, and f_y is yield strength; yield strain $ε_{y} = f_{y} / E_{s}$ . Positive value of equation (4) represents tensile stress, while negative value represents compressive stress.

For FRP material, the stress–strain relationship of elastic model is expressed as

σ_{f} = E_{f} ε

(5)

in which E_f represents elastic modulus of FRP material.

According to equation (1), strain along the height of the beam can be obtained if $ε_{pj 0}$ and $h_{pj}$ are assumed. Therefore, stress along the height of the beam can be obtained based on equations (2) to (4).

Then, axial force balance equation of the RC beam under initial pre-tension force F can be expressed as

\sum σ_{i} A_{i} + F = \int_{0}^{h} σ_{c} (ε_{pjz}) b d z + σ_{s 1} A_{s 1} + σ_{s 2} A_{s 2} + F = 0

(6)

Meanwhile, moment balance equation can be expressed as

M_{1} + M_{2} = \int_{0}^{h} σ_{c} (ε_{p j z}) b z d z + σ_{s 1} A_{s 1} a_{s 1} + σ_{s 2} A_{s 2} (h - a_{s 2}) = 0

(7)

in which M₁ and M₂ represent clockwise moment (positive value) and anticlockwise moment (negative value), respectively. $σ_{s 1}$ and $σ_{s 2}$ represent stress of steel bars near the bottom and top of the beam, respectively. $σ_{c} (ε_{pjz})$ represents concrete stress at the coordinate of z. $A_{s 1}$ and $A_{s 2}$ represent area of steel bars near the bottom and top of the beam, respectively. $a_{s 1}$ and $a_{s 2}$ are shown in Figure 1(b). Based on equations (6) and (7), $ε_{pj 0}$ and $h_{pj}$ can be solved and therefore pre-tension force–induced strain $ε_{pjz}$ can be determined using equation (1). The process to solve equations (6) and (7) is shown in Figure 2. First, $ε_{pj 0}$ and $h_{pj}$ are assumed to lie within a certain range. Second, pre-tension force–induced strain along the height can be obtained using equation (1). Third, stress along the height can be achieved according to material properties. Finally, $ε_{pj 0}$ and $h_{pj}$ can be estimated by minimizing errors of axial force and moment. Parameter r₁ in Figure 2 represents the error between the total estimated axial force (calculated by assumed $ε_{pj 0}$ and $h_{pj}$ ) and pre-tension force F. Parameter r₂ in Figure 2 represents the error between the clockwise moment M₁ and anticlockwise moment M₂ (calculated by assumed $ε_{pj 0}$ and $h_{pj}$ ). Parameter r in Figure 2 is defined to reflect the degree of approximation between the assumed parameters ( $ε_{pj 0}$ and $h_{pj}$ ) and actual ones. Minimum value among all the elements in matrix r (calculated by all assumed $ε_{pj 0}$ and $h_{pj}$ ) indicates that the corresponding assumed $ε_{pj 0}$ and $h_{pj}$ are the optimum solutions of equations (6) and (7).

Figure 2.

Flowchart of global and local behavior assessment of prestressed FRP-strengthened structures.

Parameter estimation of prestressed FRP-strengthened beams under external load

External load–induced strain $ε_{ejz}$ along the height of the strengthened beam is shown in Figure 1(b). The neutral axis height under external load is denoted as $h_{ej}$ . Therefore, strain at the point with the distance of z from the bottom surface can be expressed as

ε_{ejz} = \frac{- ε_{ej 0} z}{h_{ej}} + ε_{ej 0}

(8)

Hence, total strain $ε_{tjz}$ at the point with the distance of z from the bottom surface can be achieved

ε_{tjz} = ε_{pjz} + ε_{ejz}

(9)

In particular, total strain $ε_{tj 0}$ at the bottom of the beam can be expressed as

ε_{tj 0} = ε_{pj 0} + ε_{ej 0}

(10)

in which $ε_{ej 0}$ represents measured average strain over a certain gauge length covered by sensor j.

If $h_{ej}$ is assumed, strain along the height of the beam $ε_{ejz}$ can be obtained using equation (8), and therefore, total strain $ε_{tjz}$ can be achieved. Total stress of concrete and steel bars can be obtained based on equations (2) to (4), and external load–induced stress of FRP $σ_{f}$ is equal to $ε_{ej 0} E_{f}$ .

Axial force balance equation of prestressed structure under external load can be expressed as

\sum σ_{i} A_{i} + F = \int_{0}^{h} σ_{c} (ε_{t j z}) b d z + σ_{s 1} A_{s 1} + σ_{s 2} A_{s 2} + ε_{e j 0} E_{f} A_{f} + F = 0

(11)

in which $σ_{c} (ε_{tjz})$ represents total stress of concrete at the coordinate of z. $σ_{s 1}$ and $σ_{s 2}$ represent total stress of steel bars near the bottom and top of the beam, respectively. $A_{f}$ represents area of FRP.

Based on equation (11), $h_{ej}$ can be solved, and therefore, external load–induced strain $ε_{ejz}$ can be determined using equation (8). The process of solving equation (11) is demonstrated in Figure 2. First, $h_{ej}$ is assumed to lie within a certain range. Second, external load–induced strain along the height can be obtained using equation (8), and total strain can be obtained using equation (9). Third, total stress along the height can be achieved according to material properties. Finally, actual $h_{ej}$ can be estimated by minimizing error of axial force. $δ$ represents error of axial force, and minimum $δ$ indicates that the assumed $h_{ej}$ is the optimum solution of equation (11).

Curvature $ϕ_{j}$ induced by external load can be achieved

ϕ_{j} = \frac{ε_{ej 0}}{h_{ej}}

(12)

Local bending stiffness $E I_{j}$ of element covered by sensor j can be obtained

E I_{j} = \frac{M_{j}}{ϕ_{j}}

(13)

in which $M_{j}$ represents average moment of the element covered by sensor j, and it can be calculated by external load or stress distribution along the height of the beam.

Based on local bending stiffness or curvature distribution, the deflection of the structure under external load can be calculated using structural mechanics.

Experimental verification

Description of self-sensing FRP sheets

A total of two procedures for manufacturing self-sensing FRP sheets are required in the experiment. First, bare FBG sensors within several plastic tubes are packaged by basalt fibers (Figure 3(a)). The distance between adjacent fixation ends indicates the sensing length of packaged sensors. The plastic tube is designed to make sure that bare FBG sensor can freely move, and therefore, average strain over the sensing length is measured. Both measurement accuracy and dynamic measurement capacity have been verified in Hong et al. (2012), and detailed information about this kind of packaged FBG sensor can be found in this reference. For newly strengthened structures with FRP, the packaged FBG sensors can be embedded in the FRP sheets (Figure 3(b)). For existing strengthened structures with FRP, the packaged FBG sensors can be installed with epoxy resin on the surface of the FRP sheets (Figure 3(c)). The characteristics of small diameter and fiber packaging materials for the packaged sensors can make sure sensors and FRP be bonded with high reliability. In this experiment, type 2 of self-sensing FRP sheet has been utilized for monitoring and retrofit of concrete structures.

Figure 3.

Self-sensing FRP sheets: (a) basalt fiber–packaged long-gauge FBG sensors, (b) Type 1 of self-sensing FRP sheet, and (c) Type 2 of self-sensing FRP sheet.

Experiment setup

Experiment of a concrete beam strengthened with self-sensing FRP was conducted to verify the effectiveness of the method (Figure 4(a)). Meanwhile, a RC beam was also designed for comparison (Figure 4(b)). The specimens have the total length of 3100 mm, the span of 2800 mm, the width of 150 mm, and the height of 300 mm. Longitudinal steel bars near the bottom and top have the diameter of 20 and 14 mm, respectively. The cubic compressive strength of concrete f_cu is 41 MPa, and the side length of the cube is 150 mm. Hence, axial compressive strength of concrete f_c is about 32.8 MPa which is determined by f_cu multiplied by a factor of 0.8, and the tensile strength of concrete f_t is about 3 MPa which is determined by $0.3 {f_{c}}^{2 / 3}$ (CEB-FIP Model Code 1990, 1993). The Young’s modulus of tensile concrete is ×3.3310⁴ MPa. The yield strength and elastic modulus of steel bars are 375 MPa and 2.06 × 10⁵ MPa, respectively. The same strengthened beam has originally been applied in the study of Yang et al. (2016a) for the purpose of verifying the effectiveness of CFRP electrical behavior for self-sensing, and in this article, the strengthened beam is used for verification of the above-mentioned quantitative assessment method with additionally installed long-gauge FBG sensors. Hybrid FRP with two layers of basalt fiber–reinforced polymer (BFRP) and one layer of CFRP sheets is applied. The width and thickness of BFRP are 150 and 0.153 mm, respectively. CFRP has the width of 70 mm and thickness of 0.111 mm. According to the standard test method of FRP (American Concrete Institute (ACI) Committee, 2004), the elastic modulus for BFRP is about ×0.8210⁵ MPa, and the elastic modulus for CFRP is about ×2.310⁵ MPa. The pre-tension force F is 13.37 kN. Detailed information about the strengthening procedure can be found in Yang et al. (2016a). Seven FBG sensors (denoted as T1 to T7) were installed on the bottom of FRP for the strengthened beam, and one FBG sensor (namely, C1) was placed on the compression zone of mid-span for comparison with strain estimated by sensor T4. Nine FBG sensors (denoted as S0 to S8) were installed on the bottom of the RC beam. All FBG sensors have the gauge length of 30 cm. One linear variable displacement transducer (LVDT) displacement transducer was also placed at mid-span. The test beams are divided into seven cells (denoted as cell 1 to cell 7), and each cell corresponds to each sensor. The type of FBG interrogator is SM 130 from the company of Micron Optics. In addition, the strain data were measured with the sampling frequency of 10 Hz when the load reaches the expected one for each load step.

Figure 4.

Experimental setup and sensor placement: (a) FRP-strengthened beam and (b) RC beam.

Result analysis

Before initiation of cracks, the test beams were gradually loaded under load control. After initiation of cracks, the specimens are loaded under displacement control mode. The measured load–deflection and load–strain curves are shown in Figure 5. The cracking load, yielding load, and ultimate load are about 26, 147, and 173 kN, respectively, for FRP-strengthened beam. At the ultimate stage, obvious debonding of FRP sheets occurs within the area covered by cells 4 and 5. The cracking load, yielding load, and ultimate load are about 18, 117, and 127 kN, respectively, for RC beam. Compared to RC beam, the cracking load, bearing capacity, and ultimate strain have been improved obviously for prestressed FRP-strengthened beam (Figure 5).

Figure 5.

(a) Measured load–deflection curve and (b) measured load–strain curve.

Based on pre-tension force F, pre-tension force–induced strain $ε_{pj 0}$ and neutral axis height $h_{pj}$ can be estimated according to the process shown in Figure 2. First, $ε_{pj 0}$ is assumed to lie within the range from −40 µε to −20 µε. $h_{pj}$ is assumed to lie within the range from 150 to 260 mm. Under the condition of certain assumed $ε_{pj 0}$ , different pre-tension force–induced strain distribution $ε_{pjz}$ along the height of the structure can be obtained with gradual increase in $h_{pj}$ from 150 to 260 mm. Second, stress distribution can be achieved by material properties. Then, comprehensive error r can be obtained based on equations (6) and (7) (Figure 2). Consequently, $h_{pj}$ corresponding to certain assumed $ε_{pj 0}$ and minimum r can be extracted (Figure 6). For example, minimum r is equal to 0.243 under the condition of $ε_{pj 0} = - 40 μ ε$ , and the corresponding $h_{pj}$ is equal to 190 mm. Similarly, all the minimum r and corresponding $h_{pj}$ can be achieved. Finally, $ε_{pj 0}$ can be determined corresponding to minimum value of all the minimum r (Figure 6). $ε_{pj 0}$ and $h_{pj}$ are identified as −28.8 µε and 203 mm, respectively, and corresponding comprehensive error r is equal to 0.006. Submitting the identified $ε_{pj 0}$ and $h_{pj}$ into equation (1), pre-tension force–induced strain distribution along the beam height (initial state) can be calculated (Figure 7).

Figure 6.

Determination of pre-tension force–induced strain.

Figure 7.

Typical pre-tension force–induced and external load–induced strain.

Based on the measured strain $ε_{ej 0}$ and the above-mentioned identified pre-tension force–induced strain $ε_{pjz}$ , neutral axis height $h_{ej}$ of structure under external load can be identified according to the process shown in Figure 2. First, $h_{ej}$ is assumed to lie within the range from 100 to 250 mm. Different external load–induced strain distribution $ε_{ejz}$ along the height of the structure can be obtained with gradual increase in $h_{ej}$ from 100 to 250 mm. Accordingly, total strain $ε_{tjz}$ can be obtained using equation (9). Second, stress distribution can be achieved by material properties. Then, error of axial force δ can be obtained based on equation (11) (Figure 2). Finally, $h_{ej}$ corresponding to minimum δ can be determined (Figure 8). Take cell 4 for example; minimum errors of δ are equal to 0.078, 0.086, and 0.333 kN when the external loads are 20, 30.15, and 40 kN, respectively. The corresponding $h_{e 4}$ is equal to 145, 165, and 182 mm, respectively. Submitting the identified $h_{ej}$ into equation (8), external load–induced strain distribution can be calculated (Figure 7), and total strain distribution is shown in Figure 9.

Figure 8.

Determination of neutral axis position of the beam under external load.

Figure 9.

Typical total strain distribution.

Neutral axis height of the FRP-strengthened beam under different load level is shown in Figure 10(a). Before initiation of cracks, the neutral axis height remains constant, while the neutral axis height will increase after initiation and propagation of cracks. Meanwhile, neutral axis height of the RC beam under different load level (shown in Figure 10(b)) can also be determined by treating pre-tension force F as zero in the process of Figure 2. By comparison of neutral axis height between strengthened beam and RC beam, prestressed FRP can improve cracking load and delay the speed of crack propagation (Figure 10(c)).

Figure 10.

Identified neutral axis height of beams under external load: (a) FRP-strengthened beam, (b) RC beam, and (c) comparison of neutral axis height.

Based on the identified neutral axis height, strain at any coordinate of the beam height can be estimated by the long-gauge sensors on the bottom of the beam (equation (8)). Take cell 4 for example; strain at the coordinate of 290 mm of the beam height is estimated by long-gauge sensor T4 (Figure 11). Meanwhile, strain at the same point is also measured by long-gauge sensor C1 (Figure 11). The estimated strain agrees well with the measured one, which further proves the precision of the estimated neutral axis height. Compared to the directly measured results, strain can be estimated with the relative error of about 5% except when the load reaches 170 kN and obvious debonding of FRP sheets initiates. Based on equation (12), average curvature along the length of the strengthened beam can be achieved (Figure 12).

Figure 11.

Strain prediction of strengthened beam.

Figure 12.

Curvature estimation of strengthened beam.

Average moment $M_{j}$ of the zone covered by sensor j can be obtained using external load. Submitting the estimated curvature $ϕ_{j}$ and calculated $M_{j}$ into equation (13), local bending stiffness can be achieved for FRP-strengthened beam (Figure 13(a)) and RC beam (Figure 13(b)). The results obviously reflect the deterioration process of structures under external load. Meanwhile, the identified bending stiffness can be used for quantitative assessment of damage extent of structures. By comparison of local bending stiffness between strengthened beam and RC beam, prestressed FRP can improve local bending stiffness of structures after concrete cracking (Figure 13(c)).

Figure 13.

Identified local bending stiffness of beams under external load: (a) FRP-strengthened beam, (b) RC beam, and (c) comparison of local bending stiffness.

The above-mentioned analysis focuses on local behavior assessment of structures. The distributed deployment of long-gauge sensors enables the ability of global assessment of structures. Based on the curvature and bending stiffness distribution along the structure, deflection of the structure can be calculated using structural mechanics (Figure 14). The estimated deflection at mid-span agrees well with the measured one by displacement transducer. Compared to the directly measured results, strain can be estimated with the relative error of about 5% except when the load reaches 170 kN and obvious debonding of FRP sheets initiates.

Figure 14.

Deflection estimation of FRP-strengthened beam (at mid-span).

Conclusion

The method of quantitative assessment of strengthened structures using self-sensing FRP sheets is developed in this article, and some conclusions are listed as follows:

Theoretical derivation reveals that long-gauge strain sensor together with nonlinear analysis is an effective tool for local and global behavior assessment of FRP-strengthened structures.

Experiment results indicate that the estimated neutral axis position and local bending stiffness can reflect deterioration process of the structure under increasing external load and therefore can be used as quantitative indicators of damage extent.

Experimental results demonstrate that structural responses (strain along the height and deflection) can be estimated with the relative error of about 5%, which also proves the accuracy of the estimated neutral axis position affected by randomly appeared cracks.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The paper was supported by grants from National Natural Science Foundation of China (grant no. 51508269), Natural Science Foundation of Jiangsu Province (grant no. BK20150957), and University Science Research Project of Jiangsu Province (grant no. 15KJB580007). The support from China Scholarship Council (CSC) is also appreciated.

ORCID iD

Wan Hong

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