Long-term behavior of fiber-reinforced-polymer-plated concrete beams under sustained loading: Analytical and experimental study

Accepted Manuscript Long-term Behavior of Fiber-reinforced-polymer-plated Concrete Beams under Sustained Loading: Analytical and Experimental Study Sungnam Hong, Sun-Kyu Park PII: DOI: Reference:

S0263-8223(16)30549-9 http://dx.doi.org/10.1016/j.compstruct.2016.05.031 COST 7444

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

26 March 2015 4 April 2016 10 May 2016

Please cite this article as: Hong, S., Park, S-K., Long-term Behavior of Fiber-reinforced-polymer-plated Concrete Beams under Sustained Loading: Analytical and Experimental Study, Composite Structures (2016), doi: http:// dx.doi.org/10.1016/j.compstruct.2016.05.031

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Long-term Behavior of Fiber-reinforced-polymer-plated Concrete Beams under Sustained Loading: Analytical and Experimental Study Sungnam Honga and Sun-Kyu Parkb,* a

Research Professor, College of Engineering, Sungkyunkwan University, 300, Cheongcheong-dong,

Jangan-gu, Suwon, 440-746, Republic of Korea. b

Professor, Department of Civil and Environmental Engineering, Sungkyunkwan University, 300,

Cheongcheong-dong, Jangan-gu, Suwon, 440-746, Republic of Korea. *

Corresponding author; e-mail: [email protected], tel: +82-31-290-7530, fax: +82-31-290-7646

Abstract: Long-term behavior, deformation recovery, and residual strength of fiber-reinforced polymer (FRP)-plated beams were evaluated. Three concrete beams were fabricated: one control, one carbon-FRP (CFRP)-plated, and one glass-FRP (GFRP)-plated. All beams sustained constant loads for 550 days and were then unloaded for 60 subsequent days to evaluate the deformation recovery performances. During this period, the strains of the FRP plates and internal reinforcing steels, cracks, and deflections were recorded for comparison. Several analytical methods predicted the long-term strains and deflections of the FRP-plated beams. The validity and accuracy of the methods were obtained by comparing the analytical and experimental results.

Keywords: Sustained load, Concrete beam, FRP, Analytical method, Long-term

1. Introduction

Fiber-reinforced polymer (FRP) materials have been used for several decades to reinforce concrete structures. Moreover, extensive studies have been conducted on FRP reinforcements. Most studies have focused on the effects of externally bonded (EB) FRP reinforcement on performance improvements in response to flexure and shear of worn concrete members [1-5]. Furthermore, immature debonding failures at the interface between the FRP reinforcement and concrete have been frequently reported [6-8]. Recently, various systems have been tested in attempts to maximize the material performance of FRP reinforcements [9, 10]. Almost all previous studies, however, focused on the immediate behavior of FRPstrengthened concrete members or the characteristics of the structural behavior of FRP-strengthened concrete members under immediate loading. The long-term performance of concrete structures with EB FRPs is recognized; however, research on this subject is insufficient. Over time, the deflections and crack widths within the reinforced structures increase [11]. This negatively affects the usability of these structures. Nevertheless, the research related to long-term behaviors of FRP-plated concrete is limited. Several researchers published experimental results on the long-term behavior of FRP-strengthened members [12-16]. These studies focused on the interfacial bond stress between the concrete and the FRP plates or sheets. Analytical models proposed by Benyouced et al. [17], Diab and Wu [18, 19], Fashi et al. [20], and Hamed and Bradford [21] predict changes in bond stress over time; the accuracy of the models was established by comparing predictions with either experimental or finite-element analysis results. Tan and Saha [22] experimentally and analytically examined the long-term deflection characteristics of concrete beams reinforced with GFRP sheets under sustained loads. The experimental results showed that the long-term deflections decreased as the FRP ratio increased. Furthermore, the study proved that the total deflection of the beam could be more accurately predicted by the adjusted effective modulus method (AEMM) than by the effective modulus method (EMM). Diab et al. [23, 24] published an analytical method for calculating the long-term deflection of FRP-strengthened beams. They concluded that ignoring the creep occurring in the adhesive layer could cause overestimations of the beam’s long-term deflection. This result, however, opposed the discovery made and reported by Masia et al. [25]. Recently, Mari et al. [26] published a theoretical study of the time-dependent behavior of an FRP-strengthened beam subjected to a continuous load. Based on the results of the study, an approximation method for the calculation of long-term deflections was proposed, and the potential of the proposed approximation method was demonstrated with the available experimental results. These studies, however, evaluated the long-term deflection of FRP-reinforced concrete beams in relation to an element test on the timedependent behavior characteristics of the interface model associated with the FRP system, or to an irrational method. Regardless of FRP reinforcement, the long-term behavior of concrete beams is greatly influenced by the creep and drying shrinkage of the component materials. To predict more rational time-dependent deformations, the stress-strain relationship inside the FRP-strengthened beam must be clarified [24]. Furthermore, the total deformation of the beam must be predicted using this stress-strain relationship. Kim et al. [27] provides the only prediction to date of the deformation of FRP-reinforced beams under a sustained load according to this procedure. In their study, the reinforced beams, including the control beam, were subjected to a sustained load for 300 days. For the duration of this period, the beam

deflections and the strains of the concrete, internal reinforcing steel, and FRP plates were recorded. To theoretically predict the long-term behavior, the creep coefficient and shrinkage stress of concrete were calculated using the major design criteria as discussed in [28, 29]. The stress-strain relationships of the concrete, internal reinforcing steel, and FRP plates were theoretically clarified, along with the experimental results. The stress-strain relationships of concrete, internal reinforcing steel, and FRP plating, which change over time, were theoretically clarified and compared with the experimental results. The ACI-318 method using EMM [30], the ACI-318 method using the AEMM [31], Branson’s method [32], and Mayer’s method [33] were used to evaluate and predict the time-dependent deflections of the FRP-plated beams. These methods were also compared with the experimental results. In this study, the long-term behavior of FRP-plated concrete beams subjected to sustained loads is reported. To evaluate the long-term behaviors and deformation recovery performances, reinforced beams and a control beam were subjected to a load for 550 days, followed by an unloaded state for another 60 days. Finally, the beams were tested for bending to determine their residual strength. The deflections, strains, and cracks of the beams were recorded. In addition, the reliability of various analytical methods in predicting the time-dependent strains and deflections was evaluated based on the experimental data recorded for 550 days in this study. For this purpose, the analytical results were compared with the longterm experimental results. 2. Analysis of Long-term Behavior

2.1 Creep and Dry Shrinkage

Regardless of the FRP bonding, the prediction of the long-term deformation of concrete beams requires an accurate estimation of creep, which is a material characteristic of the concrete that composes the most part of the beams. Creep estimation can be achieved through two parameters: the creep coefficient of the concrete and the dry shrinkage strain. These parameters were calculated using the CEBFIP model [28] and the ACI-209 code [29], which have been frequently used in the field of concrete structures. The results were later used to predict the stress, strain, and deflection. In the ACI-209 code and the CEB-FIP model, the creep coefficients are presented as equations (1) and (2), respectively, and the dry shrinkage strains are presented as equations (3) and (4).

0.6 υt= t υ 10 + t 0.6 u

(1)

φ (t , t0 )=φ0 β c (t , t0 )

(2)

ε sh (t )= t ε sh (u ) 35 + t

(3)

ε cs ( t , t0 )=ε cas ( t) + ε cds ( t , t0 )

(4)

2.2 Stress and Strain

The FRP-strengthened beam is a composite beam composed of various materials. In general, the section of a concrete beam strengthened with externally bonded FRP reinforcements consists of concrete, steel reinforcement, and FRP reinforcement, and has one axis of symmetry. To analytically obtain the immediate and long-term strains and stresses, the cross-section of the strengthened beam was assumed to receive flexural moment and axial force, which are caused by the applied load at point O, as shown in Fig. 1. Point O is an artificially selected reference point on the axis of symmetry. The bond between the concrete, the reinforcements (steel reinforcement, and FRP reinforcement), was assumed to be perfect. Furthermore, the plane cross-sections were assumed to remain plane after the deformation.

Fig. 1. Stress and strain distributions in a FRP-strengthened concrete section subjected to moment M and axial force N

The initial value of the strain at t = 0 can be determined from the curvature caused by the immediate load. This is possible because the strain distribution is linear elastic, as shown in Fig. 1. Therefore, the initial strain that occurs after the application of an immediate load can be simply evaluated by adding the strain at the reference point to the numerical value produced when multiplying the curvature caused by the immediate load with the distance from reference point O to a specified point. As shown in equation (5), the strain at reference point O can be calculated using equation (6). If reference point O is selected at the centroid of the transformed section, B = 0 is obtained, and equation (6) can be simplified to the form shown in equation (7).

ε = ε 0 + ψy

(5)

ε 0  I − BN  1  =   2  ψ  Eref ( AI − B ) − B A M 

(6)

ε 0  1 N   =   ψ  Eref  M 

(7)

I in equation (6) is the second moment of inertia of the FRP-bonded concrete section. This value

varies depending on the existence of cracks. The values of I before and after crack occurrence can be calculated using equations (8) and (9), respectively.

Ig =

bh 3 h + bh( − x) 2 + (ns − 1) As' ( x − d s' ) 2 + (n s − 1) As (d s − x) 2 + n f A f (d f − x ) 2 12 2

(8)

I cr =

bx 3 + (n s − 1) As' ( x − d s' ) 2 + n s As (d s − x) 2 + n f A f (d f − x ) 2 3

(9)

The curvature, stress, and strain of the FRP-plated beam under an immediate load can be calculated simply by using equations (5)–(7). However, to determine the stress and strain over time, the change in curvature over time must be determined. This change in curvature cannot be determined as easily as the immediate load mentioned above because it is caused by creep and dry shrinkage, which are timedependent characteristics of concrete. In fact, because of the effects of creep and dry shrinkage, the modulus of elasticity of concrete continuously decreases over time. Furthermore, the neutral axis changes

positions to maintain the equilibrium of force between the compressive force in the compression part of the concrete beam and the tensile force in the tension part. The change in the neutral axis causes changes in the geometrical moment of inertia and the geometric characteristics of the cracked section. Considering these complexities, Ghali and Farve [34] proposed equations to determine the changes in the curvature, stress, and strain over time. Equations (10) and (11), which were proposed by Ghali and Farve, can be used to calculate the strain that occurs through creep and dry shrinkage for the period between to and t, as well as the time-dependent changes in the strain and curvature.

∆ε 0 = η[φ (t , t0 )(ε 0 + ψyc ) + ε cs (t , t0 )]

(10)

∆ψ = κ [φ (t , t 0 )(ψ + ε 0 yc / rc2 ) + ε cs (t , t 0 ) y c / rc2 ]

(11)

The time-dependent change in the stress at any fiber of the concrete can be calculated using the following equation:

∆σ c = E c (t )[−φ (t , t 0 )(ε 0 + ψy ) − ε cs (t , t 0 ) + ∆ε 0 + ∆ψ )]

(12)

In equations (10) and (11), η and κ are the axial strain reduction coefficient and the curvature reduction coefficient, respectively, which can be expressed by the following equations:

η = Ac / A

(13)

κ = Ic / I

(14)

The above equations were derived based on the assumption that the reference point is on the neutral axis. Creep and dry shrinkage cause stress redistribution between the various materials comprising the concrete beam. Therefore, to accurately predict the long-term deformation of the strengthened concrete beams, the locational relationship between the reference point and the neutral axis must be clearly defined. Unfortunately, contrary to the above assumption, the neutral axis of the tested beams in this study was located at reference point O, which is the centroid of the transformed section. Therefore, equations (10) and (11) can be rewritten as follows:

∆ε 0' = η [φ (t , t0 )ψyc + ε cs (t , t0 )]

(15)

∆ψ = κ [φ (t , t0 )ψyc ) + ε cs (t , t0 )] / yc

(16)

Parameter ∆ε 0' denotes the changes in the strain caused by the creep and dry shrinkage at the centroid of the compression part. To obtain the strain at reference point O and the changes in this strain, the following two equations can be used:

ε 0=ψ ( yr − x )

(15)

∆ε 0 = yt ∆ψ

(16)

The stress of the concrete immediately after the application of an external load on the beam and after a certain period can be determined by adding the change in the stress to the initial stress value. The concrete strain can also be determined in the same way. The changes in the stress or strain are calculated from the change of curvature. The stress at the top fiber of the concrete and the changes in this stress can be determined using equations (17) and (18). ∆σ c ,top = Ec (t )[φ (t , t0 )ψx + ε cs (t , t0 ) + ∆ψx)]

(17)

σ c ,top = Ec (t0 )ψx

(18)

The total stress and total strain of concrete can be calculated using equations (19) and (20), respectively.

σ

σ c ,total

∆σ

c ,top c ,top 

 











 = Ec (t0 )ψx + Ec (t )[φ (t , t0 )ψx + ε cs (t , t0 ) + ∆ψx )]

ε c ,top



(19)

∆ε

c ,top 











ε c ,total = ψx + [φ (t , t0 )ψx + ε cs (t , t0 ) + ∆ψx )]

(20)

As with concrete, the initial strains, the changes in these strains, and the total strain can be calculated using the following equations:

ε s' = ψ ( x − d s' )

(21)

∆ε s' = ∆ε 0' + ∆ψ ( x − d s' )

(22)

ε s' ,total = ψ ( x − d s' ) + ∆ε 0' + ∆ψ ( x − d s' )

(23)

ε s=ψ (d s − x)

(24)

∆ε s = ∆ε 0 + ∆ψ (d s − yr )

(25)

ε s ,total = ψ (d s − x ) + ∆ε 0 + ∆ψ (d s − yr )

(26)

ε f =ψ (d f − x)

(27)

∆ε f = ∆ε 0 + ∆ψ (d f − yr )

(28)

ε f ,total = ψ (d f − x) + ∆ε 0 + ∆ψ (d f − yr )

(29)

Ghali and Farve [34] stated that it was very troublesome to modify the effective area of the crosssection by repeatedly obtaining the location of the neutral axis over time. Additionally, there was no need to perform repeated calculations since the effective area of the cross-section was characterized by creep or dry shrinkage, which rarely changed. Therefore, the error resulting from not obtaining the new location of the neutral axis was generally small. However, the fact that the neutral axis generally shifted to the bottom of the cross-section due to creep and dry shrinkage was undeniable. Hence, the new location of the neutral axis must be determined over time so as to strictly and accurately determine the deformation of the FRP-strengthened beam.

The balance of forces inside the concrete was maintained even if the stresses changed. In other words, the internal forces for the compression and tension parts for an unknown neutral axis continuously maintained a balanced condition. Additionally, equation (28) can be derived from this condition. In this equation, the strains of the tension steel and the FRP plate are re-expressed as the strain of the compression steel.

εf εs 

 

 σ c ,total 



 d − x 1 d − x     ' f s bx(σ c, top + ∆σ c ,top ) + As' Esε s' = As Es  ε s' + AFRP E f  ε s '  '  2 x − d x − d s  s   

(28)

The internal moment at the section of the FRP-strengthened beam maintains a state of equilibrium together with applied moment Ma. Therefore, the internal momentum can be obtained from the FRP location. Assuming the applied moment is identical to the resisting moment, the strain of the compression steel ε s' can be expressed as equation (29).

1 x  M a − bx(σ c,top + ∆σ c ,top ) d f −  2 3  ε = d −x As' Es (d f − d s' ) − As Es  s ' (d f − d s )  x − ds  ' s

(29)

The location of neutral axis x can be obtained through trial and error based on the method proposed by Tan and Saha [22]. This procedure can be summarized as shown below.

① Distance x to the neutral axis is assumed. ② ε s' is obtained after substituting the assumed x value in equation (29). ③ The calculated ε s' and the assumed x are substituted in equation (28), and then it is checked if the x value satisfies the balance of internal forces.

④ Steps ①-③ are repeated until the x value satisfies the balance of internal forces. Distance x to the neutral axis, which was obtained from the above procedure, is substituted in equations (15)–(29) to obtain the stress and strain over time.

2.3 Deflection

If the deflections are too large, problems in the usability and safety of the beams arise. To minimize these adverse effects, the deflections caused by the bending moment (including both immediate and longterm deflections) must be maintained within the tolerances under the general conditions of the user. For the beam deflections to be controlled, they must be predicted accurately. The immediate deflection of a concrete beam can be obtained through elastic analysis. The maximum immediate deflection of a simply supported beam may vary by loading condition, but it generally takes the form expressed in equations (30). The following equation was derived under the assumption that no crack occurred in the concrete beam:

∆i =

M max l 2 Ec I g

(30)

In the ACI-318 standard, the second effective moment of inertia is used to obtain the immediate deflection under the assumption that a crack occurred. Furthermore, different values of K a are used depending on the loading and support conditions shown in equation (31). When these two values are substituted in equation (30), the above equation can be re-expressed as equation (32). This new equation can be used to calculate the immediate deflection of the cracked beam. Long-term deflection in concrete beams is mainly caused by creep and dry shrinkage. Therefore, the ACI-318 standard introduced deflection factor λ∆ in equation (33) to determine the long-term deflection resulting from creep and dry shrinkage. This factor includes the compression reinforcement ratio ρ ' and time-dependent factor ξ . The compression reinforcement ratio is a section property that reflects the influence of compression reinforcement As' , which decreases the long-term deflection. Additionally, the time-dependent factor is a material property that reflects the combined effects of creep and dry shrinkage. The long-term deflection can be calculated by multiplying the time-dependent factor with the immediate deflection, and can be expressed as equation (34).

2  M M  I e =  cr  I g + 1 −  cr   M a  Ma 

∆i = Ka

λ∆ =

  

2

  I cr ≤ I g 

M max l 2 Ec I e

ξ 1 + 50 ρ '

∆ (cr + sh ) = λ∆ ∆i

(31)

(32)

(33) (34)

In this study, to predict the time-dependent deflections of concrete beams with externally bonded FRP plates, the methods based on ACI-318 [35], EMM [30], and AEMM [31] and the methods proposed by researchers, Branson’s method [32], and Mayer’s method [33], were used. The analysis results were then compared with the experimental results. The effective modulus method (EMM) uses the effective modulus of elasticity to consider the effect on creep. The effective modulus of elasticity of concrete is used in place of Ec when calculating the longterm deflection. In other words, I cr is calculated by substituting the value of equation (35) in equation (9), and I e is obtained by applying the calculated I cr to equation (31). The long-term deflection considering the creep effects can be calculated by applying the obtained I e and the Ee (t ) value evaluated using equation (35) to equation (32).

E e (t ) =

E c (t 0 ) [1 + φ (t, t0 )]

(35)

The adjusted effective modulus method (AEMM) uses the effective modulus of elasticity where the reduction coefficient has been applied to the creep coefficient and the adjusted effective modulus of elasticity in equation (36). Reduction coefficient χ (t , t0 ) for normal-strength concrete can be taken as 0.8 [36, 37]. Furthermore, to calculate the long-term deflection, the adjusted effective modulus of elasticity is used in place of Ec , and the application procedure is identical to that of EMM.

Eea (t ) =

Ec (t0 ) [1 + χ (t , t0 )φ (t , t0 )]

(36)

Branson’s method separately evaluates the deflection caused by creep and the deflection caused by dry shrinkage. The sum of these two deflections is the long-term deflection. Reduction factor Kφ is considered when predicting the long-term deflection caused by creep. This factor has a form similar to that of deflection factor λ∆ in the ACI-318 standard. Factor λ∆ is dependent on both the compression reinforcement ratio and the time-dependent coefficient. However, the reduction coefficient Kφ is affected only by the compression reinforcement ratio, as shown in equation (37). The long-term deflection caused by creep can be calculated by multiplying the reduction factor and the creep coefficient with the immediate deflection calculated using equation (30), and can be expressed as equation (38). The deflection caused by dry shrinkage, on the other hand, can be calculated based on curvature ψ sh resulting from the dry shrinkage of concrete. This curvature can be determined using the fictitious tensile force method [32], and can be expressed as equation (39). The long-term deflection caused by dry shrinkage can be calculated using equation (40).

Kφ =

0.85 1 + 50 ρ '

(37)

∆ cr = Kφφ (t , t0 )∆i

(38)

Te Ec I cr ,t

(39)

ψ sh = ∆ sh =

ψ sh l 2 8

(40)

Mayer’s method is almost identical to Branson’s method, but Mayer’s method modifies the reduction factor Kφ , as shown in equation (41). The modified reduction factor is dependent on the tension reinforcement ratio as well as on the compression reinforcement ratio.

Kφ =

1 1 100 ρn 2 1+ ρ ' / ρ

For more detailed information on the aforementioned analytical methods, see Kim et al. [27].

3. Experimental Program

(41)

3.1 Specimen Parameters and Dimensions

Three concrete beams were fabricated with equal dimensions (as shown in Fig. 2) with widths of 200 mm, heights of 300 mm, and concrete covers of 30 mm. Furthermore, the beams had lengths of 2,700 mm and net span lengths of 2,400 mm. Concrete beams are traditionally doubly reinforced, with larger areas of tension steel than of compression steel to induce ductile failure. Thus, different sizes of reinforcing bars (rebar) were used to fabricate doubly reinforced beams in this study. Three D10 rebars (total area of 214 mm2) were used as tension steel, and three D13 rebars (total area of 380 mm2) were used as compression steel. To prevent the occurrence of shear failure before flexural failure, D10 stirrups were placed at 100mm intervals along the lengths of the beams. The main variable considered in the experiment was the type of the FRP plate employed. One beam was used as a control beam with no FRP plate, while carbon-FRP (CFRP) and glass-FRP (GFRP) plates were bonded externally to the other two beams, respectively. These FRP plates were bonded over lengths of 2,160 mm, corresponding to 90% of the net spans of the beams. The variables used in the long-term experiment are listed in Table 1 below.

Table 1. Summary of test beams.

Fig. 2. Beam details.

3.2 Material Properties

To produce the beams, ready-mixed concrete with a specified concrete strength of 24 MPa was used. Three cylinders were used for the compression test, all with diameters of 100 mm and heights of 200 mm. The measured average compressive strength was 25.7 MPa. The following rebar types were used: for the tension steel, three D10 deformed rebars with equal yield strengths of 457.2 MPa; for the compression steel, three D13 deformed rebars with equal yield strengths of 466.2 MPa; and for the shear rebars (i.e., the stirrup steel), D10 deformed rebars. The mechanical properties of the concrete and steel rebars are listed in Table 2.

Table 2. Concrete and steel rebar properties.

CFRP and GFRP plates were used as the EB FRP reinforcements. To determine the mechanical properties of these plates, three specimens with widths of 50 mm and lengths of 700 mm for each FRP system were produced and subjected to tension tests. For the tension test, a universal testing machine (UTM) with a capacity of 500 kN was employed, and a loading velocity of 1.5 mm/min was applied. The average mechanical properties of the FRP plates are summarized in Table 3, which also lists the manufacturerprovided mechanical properties of the epoxy resin used to bond the FRP plates to the concrete.

Table 3. Properties of FRP plates and epoxy resin.

3.3 Test Procedure

To evaluate the long-term behavior of the FRP-strengthened beams (as shown in Fig. 3), each beam sustained a load of 25 kN for 550 days. To measure the strain of the rebars, two strain gauges were respectively bonded to the tension and compression steel. The strain of the FRP plates was measured with several strain gauges bonded to the surface of the FRP plates along the beam. To measure the deflection, a dial gauge was installed at the bottom midspan point of the beam. The presence of cracks was determined by visual inspection. Data were acquired daily from several gauges using a data logger (TC31K, Tokyo Sokki), and then organized using a personal computer. After 550 days, the 25-kN sustained load was removed from the beams. The deflection and strain at the midspan points were then recorded periodically for 60 days to investigate the deformation recovery capacity of the beams. Thereafter, to evaluate the residual strength of the beams, four-point load flexural tests were conducted up to failure, at a loading velocity of 1 mm/min. The strain was measured at the same points used during the long-term test, and the deflection at the midspan was measured using a linear variable differential transformer (LVDT) instead of a dial gauge. Data were acquired using a data logger (EDX-1500A, Kyowa).

Fig. 3. Experimental setup.

3.4 Temperature and Humidity Variation

Experiments were conducted in the Bridge Laboratory at Sungkyunkwan University, in Suwon, South Korea. Suwon is located approximately 30 km from Seoul, the capital of South Korea, at the eastern end of the Asian continent, and has an annual average temperature of 12.2 °C. The average temperatures in August and January are 25.4 °C and -2.5 °C, respectively (based on normal year values). During the experiment period, the average relative humidity was 71%, with the lowest monthly humidity (56%) in February and the highest monthly humidity (82%) in July on average. The relative humidity is about 79% in summer, which is very humid, and about 64% in spring and winter, which is relatively dry. Suwon has four distinct seasons (spring, summer, autumn, and winter). Figs. 4(a) and (b) show the temperatures and relative humidity measured over the 610 days of the experiment, displaying that the temperature and humidity varies as expected with the change of seasons. As shown in Fig. 3, the strengthened beams and the control beam were all exposed outdoors to these conditions, including the seasonal changes in temperature and humidity.

Fig. 4. Ambient outdoor air temperature and relative humidity over 610 consecutive days.

4. Results and discussion: Long-term test

4.1 Test results

4.1.1 Time-strain relationship

The immediate and long-term strains that appeared in the tension and compression steels, as well as in the FRP plates, from the sustained load of 25 kN for 550 days were recorded. The immediate strain is defined as the strain that occurs immediately when a load is applied to a beam, whereas the long-term strain is defined as the strain that occurs in a beam under a sustained load for a long period of time. The total strain is the sum of the maximum strain, immediate strain, and long-term strain during the loading period. For the immediate strain of tension steel, LCS and LGS beams, which were the CFRP- and GFRPstrengthened beams, had strains 63% and 14% smaller, respectively, than the immediate strain for the SNF control beam. The strain of the LGS beam was 128% larger than that of the LCS beam. The longterm strain of the LCS beam was 5% smaller than that of the SNF beam, and 2% larger than that of the SNF beam. The total strains of LCS and LGS beams were 33% and 6% smaller, respectively, than that of the SNF beam. Meanwhile, the total strain of LGS beam was 42% larger than that of the LCS beam. These strains are listed in the table inset in Fig. 5. Among the tested beams, the LCS beam reinforced using a CFRP plate showed the smallest strain throughout the loading period. Thus, indicating better reinforcing effects in terms of the strain for the tension steel. The total strains of the tension steel for each beam are shown as a function of time in Fig. 5. Fig. 5. Total strain of tension steels. The immediate strain, long-term strain, and total strain of the compression steels are listed in the table inset in Fig. 6. The immediate strains of the LCS and LGS beams were 22% and 32% smaller, respectively than that of SNF beam. The LCS beam had a 17% larger immediate strain than the LGS beam. The long-term strains of the LCS and LGS beams were 19% and 24% larger, respectively, than that of the SNF beam. However, the long-term strain of LGS beam was 7% larger than that of the LCS beam. The total strains of the LCS and LGS beams were higher by 12% and 15% than that of SNF beam. The total strain of the LCS beam was 4% smaller than that of the LGS beam. The total strains of the compression steels as a function of time are shown in Fig. 6. Fig. 6. Total strain of compression steels. Throughout the loading period, the LGS beam showed larger FRP strains than that for the LCS beam. Regarding the immediate strain of the FRP plates, the LGS beam logged values 102% larger than those of the LCS beam. Regarding the long-term strain and total strain, the LGS beam showed 5% and 24% larger values than the LCS beam. The changes in the FRP strains in the FRP-strengthened beams as a function of time are shown in Fig. 7. Fig. 7. Total strain of CFRP and GFRP plates The experimental results revealed the SNF control beam and the GFRP-reinforced LGS beam indicated similar long-term strains. This may result from the smaller modulus of elasticity of the GFRP compared to the CFRP; thus, the GFRP plate could not maintain a sufficient tensile force. The strains of the tension steels and FRP plates did not increase continuously over time, as shown in Figs. 5 and 7. This indicates that a factor other than the sustained load influenced the expression of the strains of the tension steels and FRP plates. Additionally, it can be intuited that this factor was ambient

temperature, not relative humidity. This is because, during the test period of 550 days, the changes of the strain in the tension steels and FRP plates coincided significantly with the changes in temperature [see Fig. 4(a)] but not with the relative humidity [see Fig. 4(b)]. This phenomenon must result from the tension steels and FRP plates, which are tension reinforcements, being attached to the inside and surface of the tensile part of the beam, so that they are directly exposed to the outside temperature. If the ambient temperature continuously increases or decreases, the strains of the tension steels and FRP plates will also continuously increase or decrease.

4.1.2 Time-deflection relationship

The immediate deflections, long-term deflections, and total deflections of all beams in this study are listed in the table inset in Fig. 8. Immediate deflection is defined as the deflection that occurs immediately after a load is applied to a beam, and long-term deflection is defined as the deflection that occurs in a beam under a sustained load for a long period of time. The total deflection is the sum of the maximum, immediate, and long-term deflections during the loading period. Overall, the FRP-strengthened beams had smaller deflection values than the unreinforced control beam. The immediate deflections of the LCS and LGS beams were 38% and 35% smaller, respectively, than those of the SNF beam. The long-term deflection values of the LCS beam were 3% smaller than those of the SNF beam. On the other hand, the long-term deflections of the LGS beam were 10% larger than those of the SNF beam. The total deflection of the LCS beam was 14% smaller than that of the SNF beam, whereas the total deflection of the LGS beam was 4% smaller than that of the SNF beam. The total deflection of the LCS beam was 10% smaller than that of the LGS beam. The experimental results revealed that the attachment of an FRP plate to the tensile surface of a beam could decrease the immediate deflection, possibly improving the usability of the beam. Furthermore, among all the tested beams, the LCS beam reinforced with CFRP plates showed the smallest long-term deflection, which was smaller than those of the SNF control beam and the GFRP-strengthened LGS beam. Furthermore, as shown in Fig. 8, the deflections of the SNF beam started to converge over time after 200 days, whereas the deflections of the FRP-strengthened LCS and LGS beams increased continuously over time. In addition, the LGS and SNF beams showed no significant differences in deflection. This may result from the modulus of elasticity of the GFRP plate being smaller than that of the rebar. Furthermore, part of the tensile force in the GRFP-strengthened beam was shared by the GFRP plate; however, the main tensile force was borne by the rebar. In conclusion, for immediate and long-term deflections, the beam reinforced with CFRP plates showed the best resistance effects, as shown in Fig. 8. Fig. 8. Total deflection of the tested beams

4.1.3 Cracking pattern

It was observed that as soon as the 25 kN sustained load was applied, four or five cracks appeared in each beam. Fig. 9 indicates the distribution of the cracks where the sections marked with “30” indicate the cracks that occurred on the 30th day after the sustained load was applied. The cracks without numbers indicate that they were reported after the 550-day loading period. Between 13 and 14 cracks of varying

lengths were observed in the beams on the last day of the experiment. Furthermore, the control, CFRP-, and GFRP-strengthened beams had maximum crack lengths of 210 mm, 180 mm, and 230 mm, respectively. The GFRP-strengthened beam had a greater crack length than the control beam, probably because the modulus of elasticity of the GFRP plate was smaller than that of steel. Since the GFRP plate could not resist a significant portion of the tensile force, the full crack behavior was dominated by the characteristics of the tension steel. Furthermore, the strengthened beams showed a smaller-than-average crack space than was seen in the control beam. Table 4 lists the numbers of cracks and the maximum and average crack spaces measured in each beam.

Fig. 9. Cracking patterns

Table 4 Measured crack characteristics

4.2. Analytical results

4.2.1. Comparison of strain

To predict the strains of the steel rebars and FRP plates, the equations in Fig. 1(b) were used. In particular, to consider the reduction of the modulus of elasticity of concrete over time under a sustained load, the EMM and AEMM were applied to calculate the strains. The creep and dry-shrinkage strains were evaluated with the ACI-209 standard and the equations of the CEB-FIP model. The results obtained from the analysis indicated a 20% maximum error between the two standards. The results obtained for the SNF and LGS beams based on EMM showed trends very similar to those of the experimental values; however, at around day 300, maximum errors of 28% and 82% occurred in the tension steel of the SNF beam and the compression steel of LGS beam, respectively. When the analytical values of the LCS beam obtained through EMM were compared with the experimental values, maximum differences of 107% and 93% were found in the tension and compression steels, respectively. Unlike the internal reinforcing steels, the predicted strains of the FRP plates were very different from the experimental values. This is probably because the effect of the temperature was not appropriately reflected in the prediction of the strain. Moreover, the strains of the FRP plates after being loaded for 450 days rapidly increased beyond the values predicted with EMM. The rapid increase of the strain in the FRP plate seems to have been caused by a problem in the measurement performance of the strain gauges, resulting from extended exposure to open air. The strains predicted by EMM for each beam and the experimental values are compared in Fig. 10.

Fig. 10. Comparison of the strain data with EMM prediction

The differences between the strains predicted with the AEMM and those predicted with the EMM were very small. The values predicted with the AEMM were larger by about 2% compared to those predicted with EMM for all beams. This indicates that the analytical results using the EMM and AEMM did not differ significantly. This seems to be caused by the small effect of the age coefficient χ (t , t0 ) (0.8). The

strains predicted with the AEMM and the experimental values are compared in Fig. 11.

Fig. 11. Comparison of the strain data with AEMM prediction

As shown in Figs. 10 and 11, predictions using the EMM and AEMM showed good agreement with the strains of the tension steels for each beam; however, the strains of the compression steels were somewhat underestimated. The CFRP-strengthened LCS beam showed the largest difference between the predicted and experimental values, whereas the SNF beam showed the smallest difference. In general, when concrete undergoes long-term plastic deformation due to self-loading and a sustained external load, the stresses in the compressed section are transmitted from the concrete to the compression steel. The concrete stresses decreased because the plastic deformation of the concrete was limited by dry shrinkage. Furthermore, these stresses were transmitted to the compression steels. These phenomena were observed in this study as well as in that conducted by Kim et al. [27]. The increasing patterns of stress and deformation of the compression steels caused by creep under a sustained load were more conspicuous in the FRP-strengthened concrete beams than in the control beams. As a result, the predicted values for the strain of the compression steels of LGS and LCS beams were much smaller than the experimental values. The FRP plates together with the tension steel resist tensile forces; hence, the reinforced beams have greater resistance to deformation. Thus, the FRP-strengthened beams can resist greater increases of the stresses and strains than the unreinforced control beam can. Therefore, to more accurately predict the long-term strain of the compression steels of concrete beams with EB FRP plates, other factors related to the long-term strain used for general concrete beams must be appropriately evaluated and adjusted. To evaluate the effects of temperature changes on the creep coefficient and strain, the equations in Figs. 1(a) and (b) were used. The creep coefficient showed significant differences based on the changes in the temperature; however, the strains showed a difference of less than 2% when the temperature change was considered when compared to the case where the temperature change was disregarded. Therefore, an effective method for considering temperature changes for the prediction of the long-term strain for FRP-strengthened beams is required.

4.2.2. Comparison of deflection To predict the long-term deflection of FRP-strengthened beams, the ACI-318 methods using the EMM and AEMM, Branson's method, and Mayer's method were used [see Fig. 1(d)]. To determine the creep and dry-shrinkage strains, the ACI-209 standard and the equations of the CEB-FIP model were used. The long-term deflection was evaluated by incorporating these equations in the deflection formula. In each beam and method, the deflections predicted with the CEB-FIP model were somewhat larger than the deflections predicted using the ACI-209 standard. The maximum difference between the standards was 26%. This resulted from the calculated differences in the creep coefficient, which was greater for the CEB-FIP model than that for the ACI-209 standard. When the deflections were predicted with the EMM and AEMM, based on the equations of ACI-318, the difference in the results between the two methods did not exceed 2.4%. This was attributed to the small effect of the age coefficient (0.8), as with the prediction of the strain. Furthermore, when the deflection values acquired by the EMM and AEMM were compared, the deflection values obtained using the

AEMM were found to be more similar to the experimental values than those obtained using EMM. Regarding the deflections calculated by EMM, the values acquired from the CEB-FIP model showed a 22.9% error for the SNF beam, a 17.8% error for the LCS beam, and a 17.1% error for the LGS beam based on the loading period of 550 days. Furthermore, the values obtained using ACI-219 showed errors of 13.1%, 6.9%, and 6.2% for the SNF, LCS, and LGS beams, respectively. The values predicted with EMM and the experimental values are shown in Fig. 12. Fig. 12. Comparison of the deflection data with EMM prediction For the creep coefficients and dry-shrinkage strains acquired using the methodology of ACI-209, the deflections errors acquired using the AEMM for 550 days of loading were 10.7%, 5.2%, and 4.7% for the SNF, LCS, and LGS beams, respectively. The values predicted using the AEMM and the experimental values are shown in Fig. 13. The results of the EMM and AEMM analyses using the ACI-209 and CEBFIP models tended to start converging after approximately 100 days. Additionally, the analytical longterm deflection results, excluding the immediate deflection, were similar to the experimental results. However, the analytical results for total deflections, including the immediate deflection, were somewhat larger than the experimental results.

Fig. 13. Comparison of the deflection data with AEMM prediction

The deflections were predicted using Branson’s method, based on the dry-shrinkage strain and the creep coefficient when using ACI-209 methodology. The results indicated that the experimental values were somewhat overestimated for the prediction of the total deflection. When only the long-term deflections were compared, however, they closely approached the experimental values at around day 550. It was noted the overall trend of the deflection-time curve of the beams was more similar when the CEB-FIP model was used than when the ACI-209 standard was used. However, the long-term deflection predicted using Branson’s method showed considerable errors when compared with the experimental value. For the total deflections calculated using Branson's method, the values acquired from the CEB-FIP model showed a 63.9% error for the SNF beam, a 46.3% error for the LCS beam, and a 48.4% error for the LGS beam based on 550 loading days. Furthermore, the values acquired using the ACI-219 methodology showed 21.2%, 7.8%, and 11.7% errors for the SNF, LCS, and LGS beams, respectively. The experimental values as well as those predicted using Branson’s method are shown in Fig. 14. The use of Branson’s method resulted in larger deflection values than when the CEB-FIP model was used. This seems to result from the creep coefficients of the CEB-FIP model being larger than those calculated when using the ACI-209 standard. Additionally, the creep coefficient was not directly multiplied when the deflection was calculated based on Branson’s method. The creep coefficient values of the concrete based on the ACI-209 standard converged towards 0.95, which is smaller than 1, whereas the creep coefficient values of the CEB-FIP model tended to continuously increase from 0 to 1.4. Compared to the long-term deflections predicted with Branson’s method, as shown in Fig. 14, an error of less than 5% was acquired for each beam based on the data collected on day 550. Furthermore, the long-term deflections acquired when using the ACI-209 standard began to converge at day 100, while those acquired using the CEB-FIP model continuously increased until beginning to converge after 400 days.

Fig. 14. Comparison of the deflection data with Branson's method of prediction The results predicted when using Mayer’s method showed trends similar to those of the experimental results of each beam. For the total deflection of the beams, the values calculated using the ACI-209 standard started to converge from day 100; however, the values calculated using the CEB-FIP model tended to increase continuously over time. In particular, when the CEB-FIP model was applied, the values calculated for the LGS beam and the experimental values showed good agreement; however, they showed a 12.5% error for the SNF beam. Furthermore, when the ACI-209 standard was used, the predicted values were somewhat underestimated compared to the experimental values for the LCS and LGS beams, with errors of 19.5% and 14.9%, respectively. The deflection results predicted using Mayer’s method are shown in Fig. 15. The predicted results for the long-term deflection, excluding the immediate deflection from the total deflection, were similar to or somewhat smaller than the experimental results for the deflection behavior after 550 days. When the ACI-209 standard was used, the deflections started to converge at day 100, but when the CEB-FIP model was used no convergence occurred. Additionally, the long-term deflections continuously increased over time. Among the many methods used to predict long-term deflections, Mayer's method produced the most accurate predictions. This is because, unlike the other methods, Mayer’s method considers the trend of decreasing long-term deflection according to the increasing amount of compression steels, through the coefficient of reduction according to the compression steel ratio K φ . Furthermore, the concrete beams used in the experiment in this study were over-reinforced, with the amount of compression steel exceeding that of tension steel. Fig. 15. Comparison of the deflection data with the Mayer's method of prediction

The results of this study were obtained from experiments based on a very limited beam numbers, sizes, and reinforcement ratios. Therefore, different results may be obtained for beams with different reinforcement ratios and sizes. To draw more general conclusions, long-term experiments considering various important factors that can influence the long-term behavior of FRP-strengthened beams are required.

5. Deformation Recovery

To evaluate the deformation recovery performance of the tested beams, the 25 kN sustained load was removed on the 550th day. The strains in the tension and compression steels and the strains of the FRP plates were measured periodically for the following 60 days. The measured values are shown in Figs. 5-8. In general, when a sustained load is removed from a beam, a certain amount of strain is instantaneously restored in a phenomenon called the “instantaneous recovery of deformation,” which is generally smaller than the instantaneous deformation that occurs immediately after loading. Table 5 shows the deflections, strains in the tension and compression steel and strains of the FRP plate due to the instantaneous deformations after loading of 25 kN. Additionally, the instantaneous recovery of the deformation after the removal of the 25 kN load on day 550 is also shown in Table 5.

Table 5 Comparison of instantaneous deformation with instantaneous recovery of deformation

If the ratio of the instantaneous deformation to the instantaneous recovery of deformation is greater than 1, this implies that the instantaneous deformation is greater than the instantaneous recovery of the deformation. In the case of the control beam, this ratio is greater than (or very close to) 1. However, in the FRP-strengthened beams, the ratio is less than 1, implying that the instantaneous recovery of deformation is greater than the instantaneous deformation in these beams. Therefore, these results may relate to the bonding of the FRP plates to the bottom of the beams. The net deformation recovery is the total deformation recovery minus the instantaneous deformation obtained by removing the sustained load from the beam. Among the tested beams, the SNF control beam experienced the greatest long-term deformation and showed the greatest long-term deformation recovery. In contrast, the CFRP-strengthened LCS beam showed the smallest long-term deformation recovery among the strengthened beams. In conclusion, the long-term deformation recovery is proportional to the long-term deformation.

6. Results and discussion: Residual strength test

6.1 Failure mode

To evaluate the residual strength, all beams were subjected to flexural tests until failure after a period of 60 days for deformation recovery observations had passed. The SNF control beam showed a sharp increase in its crack spacing after cracking loads and concrete crushing occurred at the top of the beam at midspan following the yield of the tension steel. This failure is typical of flexural failure in concrete beams and relates to the tension and compression steels being below the maximum steel ratio necessary to induce ductile failure. The final failure modes of the FRP-strengthened beams are shown in Fig. 16. Before each tension steel yielded, the crack patterns seen in the SNF beam appeared similar to those of the strengthened beams. However, the tensile forces in the concrete due to the flexure cracks at the midspan were transferred to the FRP plates after the tension steel yielded. As a result, local stress concentrations occurred between the FRP plates and the concrete. As the applied loads increased, the interfacial stresses at the boundary of the concrete and the FRP plates continuously increased. At the time when the interfacial stresses exceeded a certain value, bond failure occurred and was seen to progress toward the beam end which was accompanied by a loud noise. Consequently, as shown in Fig. 16, the beams strengthened with FRP plates failed by intermediate flexural and crack induced interfacial debonding. Fig. 16. Failure modes of the strengthened beams

However, some aspects of the debonding failures of the two strengthened beams differed. Debonding on the CFRP-strengthened beam started at the midspan point and quickly spread to one end of the CFRP plate; whereas debonding on the GFRP-strengthened beam also started at the midspan, but propagated slowly to one end of the GFRP plate.

6.2 Load-FRP strain relationship To observe the variation in strain of the FRP plates according to the increasing load in the strengthened beams, strain gauges were bonded to the surface of the FRP plates (as previously shown in Fig. 2). Figure 17 shows the measured load-FRP strain curves. At the point of the debonding failure of the FRPstrengthened beams, the strains of the CFRP plate and the GFRP plate were 3,743 µ and 6,236 µ (mm/mm × 10-6), respectively. These strains corresponded to about 19% and 25% of the ultimate strain applied to each FRP plate, respectively. Therefore, the FRP reinforcements experienced bonding failure without fully exhibiting their material capacity. Moreover, in terms of the efficient use of the FRP reinforcements, the strain of the GFRP plate at the point of the debonding failure was approximately 1.7 times greater than that of the CFRP plate, which indicates that GFRP is more efficient than CFRP. The FRP-strengthened beams failed by intermediate flexural and crack induced interfacial debonding. This debonding failure occurs when a flexural member, such as the beam, is strengthened with a sufficiently long and thin reinforcement such as the FRP plate. The bond length of the FRP plate used in the strengthening of an actual structure is typically determined by the workable length of the span. Therefore, this mode of failure is highly likely in real-world situations. Hence, it is critical to discover the threshold strains of the FRP plates at the debonding failure points in the FRP-strengthened beams since the contribution of the FRP plates to the flexural resistance must be accurately assessed to determine the flexural strength of the strengthened beams. As mentioned, the strains on the CFRP and GFRP plates were 19% and 25%, respectively, of the ultimate strain at the time of the debonding failure. However, these values are very small compared to those reported in recent studies. For example, according to Hong [4] the ratio of effective strain (the strain at debonding of the FRP plate for very large beams that failed by intermediate flexural and crack induced interfacial debonding) to the ultimate strain was about 45%. From this difference, it can be concluded that a sustained load on an FRP-strengthened beam can reduce the bond strength between the FRP plate and the concrete.

Fig. 17. Load-FRP strain curves

6.3 Load-deflection relationship

Table 6 summarizes the cracking, yield, and ultimate (or debonding) loads at the midspans of the beams including the deflections corresponding to these loads. A close examination shows that the EB FRP plates at the bottoms of the concrete beams increased the cracking, yield, and ultimate loads.

Table 6 Test results

The load-deflection curves for all tested beams are shown in Fig. 18. The load-deflection curves can be classified according to the cracks in the concrete, the yield of the tension steel, and the debonding of the FRP plate. Close examination of the load-deflection curves in Fig. 11 reveals that the strengthened beams showed similar behavior between the cracking and yield loads regardless of the FRP plates applied in the section. This phenomenon must occur because the strengthened beams have the same tensile strength as concrete, and the ratio of the area of the FRP plate is very small compared to the sectional area of the

beam. The effects of each type of FRP plate for the behavior after the yield are clear since the CFRP plate had much better mechanical properties than the GFRP plate. By strengthening the beams with the FRP plates, the cracking load was increased by up to 9%, and deflections corresponding to the cracking load were decreased by up to 11%. This indicates that the application of the FRP plates to the bottoms of the beams improved the usability. Furthermore, the strengthened beams had greater yield and ultimate loads than the control beam. The ultimate loads of the CFRP-plated LCS beam and the GFRP-plated LGS beam were 26% and 7% higher, respectively, than that of the SNF beam. Furthermore, when the strengthened beams were compared, the ultimate load of the LCS beam was approximately 18% greater than that of the LGS beam. As shown in Fig. 11, the beam strengthened with the CFRP plate (with a greater modulus of elasticity and tensile strength than the GFRP plate) showed the greatest load-carry capacity among the tested beams; however, its behavior at failure was very brittle. Nevertheless, the GFRP plate in the LGS beam underwent gradual debonding based on a certain load after its yield point, thus providing much greater ductility than the LCS beam. The bonding failure of the strengthened beams would have been delayed had the sustained load not decreased the bonding strength of the FRP plate to the concrete, as shown in Fig. 18. Additionally, their load-carrying capacities would have been even greater. Fig. 18. Load-deflection curves

7. Conclusions

In this study, experimental and analytical research was conducted to evaluate the long-term behavior of concrete beams with EB FRP plates under sustained loads. The following conclusions were drawn from the experimental and analytical results:

1) The LCS beam reinforced with a CFRP plate had immediate deflections that were 35% and 5% smaller than those of the unreinforced SNF control beam and the LGS beam reinforced with a GFRP plate, respectively. Furthermore, when comparing the deflections measured on day 550, i.e., the last measurement day of the long-term deflection, the FRP-strengthened LCS and LGS beams showed 4% and 14% smaller deflections than the control beam, respectively. These results arise from the modulus of elasticity of the GFRP plate being smaller than that of the CFRP plate. In the final analysis, the experiment proved that the presence of EB FRP plates was very useful for controlling the deflection of beams under immediate and sustained loads. 2) The predictions of strain based on important design standards (CEP-FIP and ACI), EMM, and AEMM showed very good following properties, although they were slightly different from the experimental values of the tension and compression steel. On the other hand, the predicted strain results for the FRP plates were very different. The reason for this appears to be the temperature change effects were not appropriately reflected in the strain predictions for the FRP plates. Therefore, an effective method for considering temperature changes over time is required for a more accurate prediction of the long-term deformations of beams using EB FRP plates.

3) The methods used in this study provided relatively accurate predictions of the long-term deflections of the FRP-strengthened concrete beams. In particular, Mayer’s method provided the most accurate analytical results among the different deflection prediction methods. This was due to Mayer’s method considering the compression steel ratio, which is an important factor for predicting the long-term deflection, as the ratio between the compression steel and the tension steel. This trend was more conspicuous since the beams used in the long-term experiment were over-reinforced. 4) The instantaneous deformation of the SNF control beam was greater than the instantaneous recovery of the deformation. However, the results of the FRP-strengthened beams opposed those of the SNF beam. The instantaneous recovery of the deformation was proportional to the instantaneous deformation. 5) To evaluate the residual strength of the beams, the FRP-strengthened beams were subjected to loading that ultimately caused failure by FRP debonding. This debonding started at the midspan and progressed to one end of the FRP plate. Furthermore, the effective strain ratio of the strengthened beams (or the ratio of the strain at the debonding point to the ultimate strain) was between 19% and 25%, which is about half the value of effective strain ratios reported in other studies. This strongly suggests that the combination of the environmental loads and the sustained loads on the FRP-strengthened beams weakened the bonds between the FRP plates and the concrete beams. Finally, it was evident from these various tests that the CFRP-plated beam had the greatest residual strength.

Notation

A , B and I transformed cross-section area and its first and second moment about a horizontal axis through reference point O area of compression part Ac

Af

total area of FRP plate

As

total area of tension steel

As'

total area of compression steel

A

area of a transformed section composed of Ac plus ns ( As' + As ) + n f A f

Ec

modulus of elasticity of concrete

E c (t )

modulus of elasticity of concrete at age t

Ec (t0 ) modulus of elasticity of concrete at age t 0

Ee (t )

effective modulus of elasticity of concrete at age t

Eea (t )

adjusted effective modulus of elasticity of concrete at age t

Ef

modulus of elasticity of FRP plate

Eref

an arbitrarily chosen value of a reference modulus of elasticity = Ec

Es

modulus of elasticity of steel

Ic

moment of inertia of compression zone about an axis through reference point O

I cr

moment of inertia of a cracked section

I cr ,t

moment of inertia of a cracked section at time t

Ie

effective moment of inertia

Ig

moment of inertia of a gross section

I

Ka

moment of inertia about an axis through O of an age-adjusted transformed section composed of Ac plus ns As + n f A f deflection coefficient depending on support conditions

Kφ

combined reduction factor considering compressive reinforcement ratio

M

moment

Ma

applied moment

M cr

cracking moment

M max

maximum moment

N

axial force

T

fictitious compressive force caused by shrinkage

b

beam width

bf

width of FRP plate

ds

distance from the top compressive fiber to the centroid of tension steel

d s'

distance from the top compressive fiber to the centroid of compression steel

df

distance from the top compressive fiber to the centroid of FRP plate

e

eccentricity of the steel reinforcement and FRP plate

h

beam height

l

beam length

n

modular ratio

nf

modular ratio of FRP plate to concrete = E f / Ec

ns

modular ratio of steel to concrete = Es / Ec

rc2

radius of gyration of the concrete area

t

age of concrete

t0

age of concrete when drying starts at end of moist curing

tf

thickness of FRP plate

x

distance to the neutral axis from the top fiber of concrete for cracked section

y

distance from the reference point to the fiber considered

yc

distance to the center of compression part from the neutral axis

yr

distance to the reference point from the top fiber of concrete

yt

distance to the reference point from the neutral axis

β c (t , t0 ) correction term for effect of time on creep coefficient (CEB-FIP model)

ε

strain at any fiber

ε0

immediate strain at reference point O

ε 0'

immediate strain at the center of compression part

εc

modulus of elasticity of concrete

ε c,top

immediate strain at the top fiber of concrete

ε c,total

total strain at the top fiber of concrete

ε cs (t , t0 ) shrinkage strain (CEB-FIP model) ε cas (t ) autogenous shrinkage strain at concrete age t (CEB-FIP model) ε cds (t , t0 ) drying shrinkage strain at concrete age t since the start of drying at age t0 (CEB-FIP model)

εf

immediate strain at FRP plate

ε f ,total

total strain at FRP plate

εs

immediate strain at tension steel

ε s,total

total strain at tension steel

ε sh (t )

shrinkage strain (ACI 209 model)

ε sh (u )

ultimate shrinkage strain (ACI 209 model)

ε s'

immediate strain at compression steel

ε s' ,total

total strain at compression steel

η

axial strain reduction coefficient

κ

curvature reduction coefficient

λ∆ ξ

long-term deflection factor time-dependent factor for sustained loads (5 years or more = 2.0, 12 months = 1.4, 6 months = 1.2, 3 months = 1.0)

ρ

tension reinforcement ratio

ρ'

compression reinforcement ratio

σ0

immediate stress at reference point O

σ 0'

immediate stress at the center of compression part

σ c,top

immediate stress caused by moment and axial force at the top fiber of concrete

σ c,total

total stress at the top fiber of concrete

σf

immediate stress at FRP plate

σs

immediate stress at tension steel

σ s'

immediate stress at compression steel

νt

creep coefficient (ACI 209 model)

νu

ultimate creep coefficient (ACI 209 model)

φ0

notional creep coefficient (CEB-FIP model)

φ (t , t0 ) creep coefficient (CEB-FIP model) χ (t, t0 ) reduction factor on the creep coefficient

ψ

curvature caused by moment and axial force

ψ sh

curvature caused by shrinkage

∆ cr

deflection caused by creep

∆ (cr + sh) long-term deflection considering creep and shrinkage effects ∆i

immediate deflection

∆ sh

deflection caused by shrinkage

∆ε 0

change in strain caused by creep and shrinkage at reference point O

∆ε 0'

change in strain caused by creep and shrinkage at the center of compression part

∆ε c,top

change in stress caused by creep and shrinkage at the top fiber of concrete

∆ε f

change in strain caused by creep and shrinkage at FRP plate

∆ε s

change in strain caused by creep and shrinkage at tension steel

∆ε s'

change in strain caused by creep and shrinkage at compression steel

∆σ 0

change in stress caused by creep and shrinkage at reference point O

∆σ 0'

change in stress caused by creep and shrinkage at the center of compression part

∆σ c

change in stress at any fiber in concrete

∆σ c ,top change in stress caused by creep and shrinkage at the top fiber of concrete ∆σ f

change in stress in FRP plate

∆σ s

change in stress in tension steel

∆σ s'

change in stress in compression steel

∆ψ

change in curvature caused by creep and shrinkage

Acknowledgement This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) and funded by the Ministry of Education (2013R1A1A2059122).

References

1. Chen JF, Teng JG. Shear capacity of FRP strengthened RC beams: FRP debonding. Constr Build Mater 2003;17(1):27-41. 2. Carolin A, Taljsten B. Theoretical study of strengthening for increased shear bearing capacity. J Compos Constr 2005;9(6):497-506. 3. Ibell T, Darby A, Denton S. Research issues related to the appropriate use of FRP in concrete structures. Constr Build Mater 2009;23(4):1521-1528. 4. Hong S. Effect of intermediate crack debonding on the flexural strength of CFRP-strengthened RC beams. Mech Compos Mater 2014;50(4):521-534. 5. Hong S. Effects of the amount and shape of carbon-fiber-reinforced polymer strengthening elements on the ductile behavior of reinforced concrete beams. Mech Compos Mater 2014;50(4):603-614. 6. Cho DY, Park SK, Hong S. Bond-slip behavior of CFRP plate-concrete interface. Mech Compos Mater 2011;47(5):529-538. 7. Yao J, Teng JG. Plate end debonding in FRP-plated RC beams - I: experiments. Eng Struct 2007;29(10):2457-2471.

8. 7. Yao J, Teng JG. Plate end debonding in FRP-plated RC beams - II: strength model. Eng Struct 2007;29(10):2472-2486. 9. Yang DS, Park SK, Neale WK. Flexural behaviour of reinforced concrete beams strengthened with prestressed carbon composites. Compos Struct 2009;88(4):497-508. 10. Hong S. Evaluation of the bond and flexural behavior in RC beams strengthened with prestressed NSM CFRP reinforcements. PhD Thesis, Seoul: Sungkyunkwan University, 2010. 11. Saha M K, Tan KH. Long-term deflections of FRP-strengthened beams under sustained loads. In: Proceedings of the 2nd International Conference on FRP Composites in Civil Engineering (CICE/2), Adelaide, 8-10 December 2004. p. 261-266. 12. Mazzotti C, Savoia M. Long-term behaviour of FRP-strengthened beams. In: Proceedings of the 8th International Symposium on Fiber Reinforced Polymer Reinforcement for Concrete Structures (FRPRCS/8), Patras, 16-18 July 2007. p. 1-10. 13. Sobuz HR, Ahmed E, Sutan NM, Hasan NMS, Uddin MA, Uddin MJ. Bending and time-dependent responses of RC beams with bonded carbon fiber composite laminates. Constr Build Mater 2012;29:597-611. 14. Plevris N, Triantafillou TC. Time-dependent behavior of RC members strengthened with FRP laminates, J Struct Eng 1994;120(3):1016-1042. 15. Al Chami G, Thériault M, Neale KW. Creep behavior of CFRP-strengthened reinforced concrete beams. Constr Build Mater 2009;23:1640-1652. 16. Muller M, Toussaint E, Destrebecq JF, Grédiac M. Investigation into the time dependent behavior of reinforced concrete specimens strengthened with externally bonded CFRP-plates. Compos Part BEng 2007;38(4):417-428. 17. Benyoucef S, Tounsi A, Benrahou KH, Adda Bedia EA. Time-dependent behavior of RC beams strengthened with externally bonded FRP plates: interfacial stresses analysis. Mech Time-Depend Mater 2007;11:231-248. 18. Diab H, Wu Z. A linear viscoelastic model for interfacial long-term behaviour of FRP-concrete interface. Compos B Eng 2008;39:730-772. 19. Diab H, Wu Z. Nonlinear constitutive model for the time-dependent behaviour of FRP-concrete interface. Compos Sci Technol 2007;2007(67):2323-2333. 20. Fashi B, Benrahou KH, Krour B, Tounsi A, Benyoucef S, Adda Bedia EA. Analytical analysis of interfacial stresses in FRP-RC hybrid beams with time dependent deformations of RC beam. Acta Mech Solida Sin 2011;24(6):519-526. 21. Hamed E, Bradford MA. Creep in concrete beams strengthened with composite materials. Eur J Mech A/Solids 2010;29:951-965. 22. Tan KH, Saha MK. Long-term deflections of reinforced concrete beams externally bonded with FRP system. J Compos Construct 2006;10(6):474-82. 23. Diab HM, Wu ZS, Ahmed E. Analytical study on long-term deflections of beams strengthened by prestressed FRP sheets. In: Proceedings of the 6th International Symposium on Innovation and Sustainability of Structures in Civil Engineering (ISISS/6), Beijing, 26-27 July 2015. p. 1886-1899. 24. Diab HM, Wu ZS, Ahmed E. Long-term deflections of beams strengthened by prestressed and nonprestressed FRP sheets. Int J Eng Innov Tec 2013;3(2):108-114.

25. Reda Taha MM, Masia MJ, Choi KK, Shrive PL, Shrive, NG. Creep effects in plain and fibrereinforced polymer strengthened reinforced concrete beams. ACI Struct J 2010;107(6):627-635. 26. Antonio RM, Eva O, Jesús M, Bairán ND. Simplified method for the calculation of long-term deflections in FRP-strengthened reinforced concrete beams, Compos Part B-Eng 2013;45(1):1368-1376. 27. Kim SH, Han KB, Kim KS, Park SK. Stress-strain and deflection relationships of RC beam bonded with FRPs under sustained load. Compos Part B-Eng 2009;40(4):292-304. 28. CEB bulletin 213/214. CEB-FIP Model Code 1990. London, England; Thomas Telford house, 1993. 29. ACI Committee 209. Prediction of creep, shrinkage, and temperature effects in concrete structures. Farmington Hills, MI: American Concrete Institute, 1992. 30. Neville AM, Dilger WH, Brooks JJ. Creep of plain and structural concrete. London and New York: Construction Press, 1983. 31. Bazant ZP. Prediction of concrete creep effects using age-adjusted effective modulus method. ACI J 1972;69(4):212-217. 32. Branson DE. Deformation of concrete structures. New York: McGraw-Hill, 1977. 33. Mayer H. Dei Berechnung der Durchbiegung von Stahl-beton-Bauteilen. Deutscher Ausschuss Für Stahlbeton, 1976. 34. Ghali A, Farve R. Concrete structures: stresses and deformations. London: Chapman and Hall, 1986. 35. ACI Committee 318. Building Code Requirements for Reinforced Concrete and Commentary. Farmington Hills, MI: American Concrete Institute, 2002. 36. Ezeldin AS, Shiah TW. Analytical immediate and long-term deflections of fiber-reinforced concrete beams. J Struct Eng 1995;121(4):727-738. 37. Gilbert RI. Deflection calculation for reinforced concrete structures - Why we sometimes get it wrong. ACI Struct J 1999;96(6):1027-1032.

b ds'

∆ε c,top ε c,top

As'

∆ε 0

O

M df h

ε

'

'

yr

yc

∆σ c ,top σ c ,top

ε c,total

ε s'

∆ε s'

∆ψ

∆σ s'

' 0

x

ψ

σ c ,total

σ s'

∆σ

' 0

σ

' 0

O'

ds

N.A.

yt

O

σ 0 ∆σ 0

ε 0 ∆ε 0

As

εs

σs

∆ε s

O

∆σ s

Af

tf

εf

σ f ∆σ f

∆ε f

bf

Fig. 1. Stress and strain distributions in a FRP-strengthened concrete section subjected to moment M and axial force N

Sustained load 12.5 kN12.5 kN 150

1100

200

1100

CS1, CS2

FP5

FP4

180

FP3

3-D10

FP2

FP1

TS1, TS2

3-D13

150 D10@100

FRP plate

300 @ 3 = 900

(Unit: mm) 2160

300

2700 A's: 3-D13 Stirrup: D10 @ 125 As: 3-D10 Epoxy FRP Plate

CS: Compression steel gauges TS: Tension steel gauges

Cover: 30 mm

Dial gauge

FP: FRP plate gauge

200

Fig. 2. Beam details.

Fig. 3. Experimental setup.

Spring

Temperature [oC]

40

Summer

Fall

Winter

Spring

Summer

Fall

Highest temperature : 37 C

30

20

10 Lowest temperature : − 4 C

0

-10 0

100

200

300

400

500

600

700

Time [days]

(a) Air temperature 120 Spring

Summer

Fall

Winter

Spring

Summer

Fall

Relative h umidity [%]

100 80 60 40

Average : 71%

20 0 0

100

200

300

400

500

600

700

Time [days]

(b) Relative humidity Fig. 4. Ambient outdoor air temperature and relative humidity over 610 consecutive days.

0 Beams

Tension steel strain [µ]

250

SNF LCS LGS

Immediate: (a) 710 269 614

Strain (µ) Long-term: (b) 720 682 732

Total: (a)+(b) 13414303 951 1436

500 750 1000 SNF LCS LGS

1250 1500 Unloading

Unloading

1750 0

100

200

300

400

500

Time [days]

Fig. 5. Total strain of tension steels.

600

700

0

Compression steel strain [µ]

Beams SNF LCS LGS

-250

Strain (µ) Long-term: (b) -514 -631 -674

Immediate: (a) -160 -125 -104

SNF LCS LGS

Total: (a)+(b) -674 -756 -778

-500

-750

Unloading

Unloading

-1000 0

100

200

300

400

500

600

700

Time [days]

Fig. 6. Total strain of compression steels. 0 Beams LCS LGS

FRP plate strain [µ]

500

Strain (µ) Long-term: (b) 1255 1323

Immediate: (a) 305 617

Total: (a)+(b) 1560 1940

LCS LGS

1000

1500

2000 Unloading

2500

0

100

200

Unloading

300

400

500

600

700

Time [days]

Fig. 7. Total strain of CFRP and GFRP plates 0 Beams SNF LCS LGS

Deflection [mm]

2

Immediate: (a) 1.64 1.02 1.07

Deflection (mm) Long-term: (b) 3.87 3.75 4.24

SNF LCS LGS

Total: (a)+(b) 5.51 4.77 5.31

4

6

Unloading

Unloading

8 0

100

200

300

400

500

Time [days]

Fig. 8. Total deflection of the tested beams

600

700

SNF

30

30

30 30

30

30

LCS 30

30

30

30

30

30 30

LGS 30 30

30 30

30 30

30

Fig. 9. Cracking patterns

2000

SNF (EMM)

Total strain [µ]

1500

1000 Experiment CEB-FIP ACI-209

500

Tension 0

Compression -500

-1000 0

100

200

300

400

500

Time after Loading [day] (a) Steel strain of the SNF Beam 2000

LCS (EMM)

Total strain [µ]

1500

1000 Experiment CEB-FIP ACI-209

500

Tension 0

Compression -500

-1000 0

100

200

300

400

Time after Loading [day] (b) Steel strain of the LCS Beam

500

2000

LGS (EMM)

Total strain [µ]

1500

1000 Experiment CEB-FIP ACI-209

500

Tension 0

Compression -500

-1000 0

100

200

300

400

500

Time after Loading [day] (c) Steel strain of the LGS Beam 2000

LCS (EMM)

Total strain [µ]

1500

1000

500 Experiment CEB-FIP ACI-209

Tension 0

0

100

200

300

400

500

Time after Loading [day] (d) CFRP strain of the LCS Beam 2000

LGS (EMM)

Total strain [µ]

1500

1000

500 Experiment CEB-FIP ACI-209

Tension 0

0

100

200

300

400

500

Time after Loading [day] (e) GFRP strain of the LGS Beam Fig. 10. Comparison of the strain data with EMM prediction

2000

SNF (AEMM)

Total strain [µ]

1500

1000 Experiment CEB-FIP ACI-209

500

Tension 0

Compression -500

-1000 0

100

200

300

400

500

Time after Loading [day] (a) Steel strain of the SNF Beam 2000

LCS (AEMM)

Total strain [µ]

1500

1000 Experiment CEB-FIP ACI-209

500

Tension 0

Compression -500

-1000 0

100

200

300

400

500

Time after Loading [day] (b) Steel strain of the LCS Beam 2000

LGS (AEMM)

Total strain [µ]

1500

1000 Experiment CEB-FIP ACI-209

500

Tension 0

Compression -500

-1000 0

100

200

300

400

Time after Loading [day] (c) Steel strain of the LGS Beam

500

2000

LCS (AEMM)

Total strain [µ]

1500

1000

500 Experiment CEB-FIP ACI-209

Tension 0

0

100

200

300

400

500

Time after Loading [day] (d) CFRP strain of the LCS Beam 2000

LGS (AEMM)

Total strain [µ]

1500

1000

500 Experiment CEB-FIP ACI-209

Tension 0

0

100

200

300

400

500

Time after Loading [day] (e) GFRP strain of the LGS Beam Fig. 11. Comparison of the strain data with AEMM prediction

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

SNF (EMM)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

Time after Loading [day] (a) SNF Beam

500

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LCS (EMM)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (b) LCS Beam Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LGS (EMM)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (c) LGS Beam Fig. 12. Comparison of the deflection data with EMM prediction

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

SNF (AEMM)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

Time after Loading [day] (a) SNF Beam

500

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LCS (AEMM)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (b) LCS Beam Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LGS (AEMM)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (c) LGS Beam Fig. 13. Comparison of the deflection data with AEMM prediction

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

SNF (Branson)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

Time after Loading [day] (a) SNF Beam

500

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LCS (Branson)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (b) LCS Beam Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LGS (Branson)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (c) LGS Beam Fig. 14. Comparison of the deflection data with Branson's method of prediction

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

SNF (Mayer)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

Time after Loading [day] (a) SNF Beam

500

Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LCS (Mayer)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (b) LCS Beam Experiment (Total) CEB-FIP (Total) ACI-209 (Total)

Deflection [mm]

8

LGS (Mayer)

6

4

2 Experiment (Long-term) CEB-FIP (Long-term) ACI-209 (Long-term)

0

0

100

200

300

400

500

Time after Loading [day] (c) LGS Beam Fig. 15. Comparison of the deflection data with the Mayer's method of prediction

(a) LCS beam

(b) LGS beam

Fig. 16. Failure modes of the strengthened beams

80 LCS LGS

Load [kN]

60

40

20

0

0

1000

2000

3000

4000

5000

6000

FRP plate strain [µ]

Fig. 17. Load-FRP strain curves

100 Intermidiate flexural crack induced interfacial debonding

S NF LC S LG S

Sudden debonding of CFRP plate

80

Load [kN]

17.8% 26.1%

60

7.1%

Concrete crushing

40 Progressive debonding of GFRP plate

20

0 0

10

20

30

Deflection [mm]

Fig. 18. Load-deflection curves

40

50

Table 1. Summary of test beams. FRP plate Beam

Layer

Remarks

-

-

No strengthening

50

2160

1 Ply

CFRP-strengthened

50

2160

1 Ply

GFRP-strengthened

Type

Bond width

Bond length

[-]

[mm]

[mm]

SNF

-

-

LCS

CFRP

LGS

GFRP

Table 2. Concrete and steel rebar properties.

Concrete

Specified concrete strength [MPa]

Measured compressive strength [MPa]

24

Steel rebar

Modulus of elasticity

Slump

[MPa]

[mm]

25.7

2.16 × 10

4

140

Type

Diameter

Yield strength

Tensile strength

Modulus of elasticity

[-]

[mm]

[MPa]

[MPa]

[MPa]

D10

10

457.2

766.3

2.01 × 105

D13

13

466.2

679.3

2.11 × 105

Table 3. Properties of FRP plates and epoxy resin.

FRP plate

Epoxy resin

Type

Width

Thickness

Tensile strength

Modulus of elasticity

[-]

[mm]

[mm]

[MPa]

[MPa]

CFRP

50

1.2

3000

1.65 × 105

GFRP

50

1.2

1000

4.0 × 104

Tensile strength

Bond strength

Modulus of elasticity

Working time limit

[MPa]

[MPa]

[MPa]

[min]

35

2

2,000 to 3,000

26

Table 4 Measured crack characteristics Number of cracks

Maximum crack spacing

Average crack spacing

(-)

(mm)

(mm)

SNF

14

55.4

13.02

LCS

13

20

12.71

LGS

13

22.3

12.05

Beams

Table 5 Comparison of instantaneous deformation with instantaneous recovery of deformation Beams

Measured at midspan

Deflection (mm)

Strain of tension steel (×10-6)

Strain of compression steel (×10-6)

Strain of FRP plate (×10-6)

SNF

LCS

LGS

Immediate: (a)

1.642

1.020

1.070

Recovery: (b)

1.445

1.124

1.226

(a)/(b)

1.136

0.907

0.873

Immediate: (a)

710

269

614

Recovery: (b)

815

431

774

(a)/(b)

0.971

0.624

0.793

Immediate: (a)

-160

-125

-104

Recovery: (b)

-95

-142

-140

(a)/(b)

1.684

0.880

0.743

Immediate: (a)

-

305

617

Recovery: (b)

-

533

813

(a)/(b)

-

0.572

0.759

Table 6 Test results Cracking Beams

Pcr

Pcr /Pstr

(kN) SNF

δcr

Yield

δcr/δstr

(mm)

Py

Py /Pstr

(kN)

Ultimate

δy

δy/δstr

(mm)

Pu

Pu /Pstr

(kN)

δu

δu/δstr

(mm)

1

2.24

1

46.69

1

4.4

1

57.58

1

21.52

1

LCS

32.18

1.09

1.99

0.89

61.4

1.32

5.22

1.19

72.62

1.26

8.83

0.41

LGS

31.44

1.06

2.02

0.90

54.86

1.17

5.44

1.24

61.65

1.07

13.03

0.61