Rectangular high-strength concrete columns confined with carbon fiber-reinforced polymer (CFRP) under eccentric compression loading

Construction and Building Materials 193 (2018) 604–622

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Rectangular high-strength concrete columns confined with carbon fiber-reinforced polymer (CFRP) under eccentric compression loading Junlong Yang, Jizhong Wang ⇑, Ziru Wang State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China

h i g h l i g h t s
Eccentric behavior of FRP wrapped high-strength concrete columns were investigated.
Effects of CFRP layout, layers and pre-damaged condition were considered.
A new model was proposed for the FRP confined concrete based on a large database.

a r t i c l e

i n f o

Article history: Received 9 April 2018 Received in revised form 17 September 2018 Accepted 30 October 2018

Keywords: CFRP strengthening columns High strength concrete Eccentric compression loading Confined concrete Ductility

a b s t r a c t A total of 16 rectangular high-strength columns were constructed and 14 of them were strengthened with carbon fiber reinforced polymer (CFRP) strips externally along the column. All these columns were tested under eccentric compression loading with the eccentricity range from 50 mm to 100 mm. The main variables in this study included CFRP layout, the number of CFRP sheets and pre-damaged condition. The failure modes, axial load-midspan deflection curves, ductility factors and the strain distribution of CFRP were analyzed. The test results show that the ductility and ultimate capacity of columns were obviously increased by wrapping CFRP sheets around the columns. Specifically, for the eccentricity equal to 50 mm, the horizontal fully wrapped CFRP exhibited the most extraordinary mechanical performance than other strengthened specimens. When the eccentricity increased to 100 mm, the ductility and energy absorption ability were enhanced significantly on the specimens strengthened with longitudinal CFRP and wrapped with horizontal CFRP strips simultaneously. However, as for the specimens which were pre-damaged before retrofitting, the strengthened effect was largely weakened regardless of the value of eccentricity. Finally, a new stress-strain model was proposed for the FRP confined concrete according to a large database, which can be either applied to the normal strength concrete or high strength concrete. Based on the proposed model, the axial ultimate capacity of all the strengthened columns in the present study and other researches were calculated and compared to the test data. It is evident from the results that satisfactory accuracy and good agreement can be found between the theoretical predictions and test observations. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction With more large-span and high-rise buildings emerging extensively in the past three decades, high-strength concrete has been widely used for compression members (i.e., columns, shear walls etc.) in the building construction. In bridge engineering, high strength concrete is used for the construction of large-span bridges, piers and so on. Furthermore, many docks, breakwaters and oil platforms in ocean engineering are made up of highstrength concrete. However, with the improvement of the concrete ⇑ Corresponding author. E-mail address: [email protected] (J. Wang). https://doi.org/10.1016/j.conbuildmat.2018.10.226 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

strength, the brittleness increases and deformation capacity reduces as a result, which is a major drawback of high-strength concrete and severely limits the further use of it to some extent. Extensive studies [1–8] have shown that the dilation and deformation of core concrete can be effectively constrained by the external confinement (e.g., spiral reinforced bar, steel jacket, fiber reinforced polymer), which can be achieved by increasing the confining stress around the columns. Among the different external reinforcements, FRP has become a relatively popular reinforcement material for civil engineering structures due to its extraordinary properties of high strength-weight ratio, corrosion resistance, high fatigue resistance and ease of construction [9–11]. Therefore, by wrapping the FRP around high-strength concrete members, it can effectively

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

restrain deformation of the core concrete and improve ductility of the members [12,13]. It can be reasonably speculated that the combination of FRP and high strength concrete may have great engineering significance for practical design. Several investigations have been conducted on the FRP strengthened normal-strength and high-strength concrete members [14–21], especially for columns, and results show that the mechanical performance (i.e., ultimate capacity, ductility etc.) of retrofitted columns are more superior to the reference columns. A total of 112 small-scale FRP strengthened columns with concrete strength up to 112 MPa were tested by Cui and Sheikh [22] under concentric loading. It was found that the brittleness of highstrength concrete was apparently alleviated because of the external confinement provided by FRP. Moreover, the energy absorption capacity and ductility factor were increased with the number of FRP layers and decreased with the concrete strength. Vincent and Ozbakkaloglu [23] argued that (ultra) high strength concrete columns wrapped with FRP circumferentially can exhibit superb ductile behavior under uniaxial compression loading only when sufficiently constrained. Nevertheless, if the FRP confinement was inadequate, strain reduction factor may still degrade significantly, which manifested FRP made little contribution to the enhancement of ductility. Although many studies have been undertaken on FRP strengthened high-strength concrete columns by a few researchers, most of them paid much attention to the compressive performance of columns under uniaxial loads. However, in real construction process, the purely concentric compression loading cannot be emerged due to construction error and inaccuracy, especially for the columns at the sides and corners of the buildings. Moreover, bending moment may easily occur in the earthquakes because of horizontal acceleration. Therefore, it is more reasonable to investigate the mechanical performance of FRP retrofitted columns under eccentric loading rather than traditional concentric loads. A few studies about high-strength concrete columns confined with FRP under eccentric loads have been conducted by Hadi’s group in the past ten years [24–26]. It can be concluded from these investigations that the improvement of ultimate capacity of FRP strengthened high-strength concrete was considerably decreased with the eccentricity, however, the ductility factors still outperformed the unwrapped columns. Moreover, when compared with unconfined reinforced high-strength concrete columns, FRP strengthened plain concrete columns exhibited better mechanical behavior. In addition, the strengthened high-strength concrete columns were superior to the retrofitted normal-strength specimens when concerning the maximum axial capacity under eccentric loading according to the test results conducted by Hadi [27]. Nevertheless, in these studies tested by Hadi’s group, the shapes of cross section are all circle rather than square or rectangle. Considering that square or rectangular columns are more common during construction and the distribution of confinement stress in the FRP strips of different shape of cross section exist significant difference [28], there is a need to investigate the mechanical behavior of rectangular FRP strengthened high-strength concrete columns under eccentric loads. Columns tested by Song et al. [29], verified that the effectiveness of FRP confinement of rectangular columns was degraded with eccentricity increasing. However, the parametric analysis suggested that the relative strength of axial capacity decreased exponentially with the increased grade of concrete strength, which was contradictory with the conclusion proposed by Hadi [27]. More importantly, in all the above-mentioned studies, the FRP sheets were applied to the columns along the full height, which is normally unnecessary for the traditional columns during strengthening process. Besides, several researchers [30,31] have found that vertical FRP sheets bonded in the tensile zone of normal-strength columns can attain better ultimate capacity when

605

the eccentricity was relatively large, whereas few studies presented investigations on the strengthening effect of vertical FRP wrapped high-strength concrete columns under eccentric loading. Hence there is an urgent need to conduct further researches on the FRP retrofitted rectangular high-strength concrete columns eccentrically with different FRP strengthening schemes. Against the above background, a total of sixteen large-scale rectangular columns cast by high-strength concrete were tested under eccentric loading. Fourteen of them were strengthened with externally wrapped CFRP strips along the columns and two test columns were set as control columns. The main variables in this study included eccentricity (i.e., 50 mm and 100 mm), CFRP layout, the number of CFRP sheets and pre-damaged condition. For the eccentricity equal to 50 mm, the CFRP strengthening schemes included horizontal strip reinforcement and fully wrapped reinforcement along the height of the columns, while the vertical CFRP sheets were mainly used when the eccentricity reached 100 mm. Moreover, two of the strengthening columns were pre-damaged before the test to simulate the mechanical performance of the slightly-damaged columns after retrofitting. The failure modes, ductility and strain analysis were conducted systematically, and a new stress-strain model was proposed for FRP confined concrete with concrete strength range from low to ultra-high according to a large database. It showed a good agreement between the theoretical predictions provided by the calculated formulae based on the new proposed model and test data from present study and other researches. Moreover, they can provide a valuable guideline for engineering design of high-strength concrete columns strengthened by CFRP under eccentric load.

2. Experimental program 2.1. Specimen design A total of sixteen specimens were designed and tested in this study including two control specimens. All columns were comprised of a test zone in the center of specimens with a rectangular cross section of 150 mm  200 mm and a corbel end at each end of the columns, with a total height of 1200 mm. According to the Chinese code [GB50011-2010] [32], the balanced state between the tensile failure and compressive failure can be approximately estimated by the relationship of the real eccentricity and 0.3 h (h, the width of section), about 60 mm in this study. Therefore, in order to apply the eccentric loads under different eccentricity and prevent premature failure, two kinds of dimensions of corbel have been designed. It can be seen from Fig. 1 that the two corbels were 150 mm  300 mm and 150 mm  400 mm for the eccentricity equal to 50 mm and 100 mm respectively, which may lead to tensile failures and compressive failures as expected. Thus, axial load applied concentrically on the corbel ends will create a load with a desirable eccentricity in the test region. Each specimen has four 14 mm diameter deformed rebars uniformly distributed around the column core section with longitudinal geometric reinforcement ratio equivalent to the minimum value as [GB500112010] [32] stated to simulate the retrofitting process of deficient columns in real construction. The transverse reinforcement was made of 6 mm diameter ties with spacing equal to 200 mm in the test zone, and a reduced spacing, equal to 50 mm, was adopted in the corbel end to avoid localized damage. All longitudinal rebars were anchored into the corbel ends with a sufficient anchorage length. The reinforcement details of specimens and mechanical properties of steel reinforcement can be seen in Fig. 1 and Table 1, respectively. In addition, to make ease for the following description, the four sides of the cross section was named as side A, B, C, D and the eccentric loads was applied near the side B.

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(a) Eccentricity = 50mm

(b) Eccentricity = 100mm

(c) Cross section

Fig. 1. Section dimension and reinforcement details of specimens.

Table 1 Mechanical properties of steel reinforcement. Material

Diameter (mm)

Young’s modulus (GPa)

Yield strength (MPa)

Ultimate strength (MPa)

Longitudinal steel reinforcement Transverse steel reinforcement

14 6

200 200

403.7 365.3

561.2 497.2

with strip spacing of 100 mm around the column. In order to reflect the difference of various transverse reinforcement, the other two reinforcement schemes (i.e., ‘‘HF” reinforcement and ‘‘HN” reinforcement) were set up with the same volume ratio of CFRP to confined concrete (Zhao et al. 2000) [34]. The parameter l is the theoretical volume ratio of CFRP laminates and core concrete, which can be calculated by Eq. (1). The ‘‘HF” means horizontal fully reinforcement, while the ‘‘HN” stands for horizontal strip reinforcement with strip spacing equal to 50 mm. The ‘‘V” reinforcement represents longitudinal CFRP sheets wrapped in the tensile zone. In this test, the H series strengthened schemes (i.e., ‘‘HS”, ‘‘HF” and ‘‘HN”) were mainly used under 50 mm eccentricity and ‘‘V” reinforcement only applied to the large eccentricity equal to 100 mm, as seen in Fig. 2.

The designed grade of high-strength concrete in this test was C60, and the columns were prepared using a traditional mix proportion design specification according to the Chinese code [JGJ55-2011] [33]. The mix comprised of 52.5 grade cement, crushed gravel with a maximum size of 20 mm and fine aggregate. In order to enhance the performance and quality of high-strength concrete mix, fly ash and slag were added at 10% and 5% of the cementing content by weight respectively and polycarboxylic superplasticizer was also used. The final mix proportion is listed in Table 2. All the specimens were cast with the same batch of mix proportions and the average cube compressive strength during the test was 56.2 MPa. The CFRP unidirectional plain weave used in this study was supplied by a local manufacturer with the nominal thickness and weight equal to 0.167 mm and 300 g/m2 respectively. The mechanical properties of CFRP provided by the manufacturers and obtained by conducting CFRP coupon tests are both listed in Table 3, along with the properties of the epoxy resin. Before wrapping CFRP around the square high-strength RC columns, the four corners in columns were treated as fillet with 15 mm (i.e., b/10, with b, the width of section) radius to prevent local failure of the composite sheets at the corner. After 28-day cured in standard condition, the surface of all the columns were then thoroughly coated with epoxy to improve the concrete-CFRP bond and the impregnated CFRP strips was then hand-wrapped on the surface of columns. A 100 mm overlap was added at the end of the revolution for bonding integrity. There are four CFRP strengthening layouts in this study, called ‘‘HS” reinforcement, ‘‘HF” reinforcement, ‘‘HN” reinforcement and ‘‘V” reinforcement respectively. The ‘‘HS” represents horizontal strip reinforcement

l ¼

V CFRP 2nts ðb þ hÞ ¼ bh ðs þ s0 Þ V concrete

ð1Þ

where, l is the volume ratio of CFRP to confined concrete; VCFRP = the volume of CFRP laminates; Vconcrete = the volume of core concrete; n = number of CFRP layer; s = width of CFRP strips; s0 = spacing of CFRP strips, as for ‘‘HF” reinforcement; t = thickness of CFRP sheets. The specimen details of all tested columns are shown in Table 4. These columns can be divided into two groups according to the eccentricity and each group consisted of 8 specimens. The label of the specimens in this test was comprised of letters and numbers. The first letters S and L means the eccentricity value: 50 mm and 100 mm, respectively. The second letter indicates the CFRP layout, R, F, S, N and V represent control specimen, ‘‘HF” reinforcement,

Table 2 Concrete mix proportion. Strength grade

Cement (kg)

Sand (kg)

Gravel (kg)

Water (kg)

Fly ash (kg)

Slag (kg)

Water-reducing Agent (kg)

C60

446

702

1054

168

54

26

6.214

607

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622 Table 3 Mechanical properties of CFRP and resin. Material

CFRP Resin

Provided by manufacturers

Obtained from coupon tests

Young’s modulus (GPa)

Ultimate tensile strength (MPa)

Strain at rupture

Young’s modulus (GPa)

Ultimate tensile strength (MPa)

Strain at rupture

237 3.08

4300 40.1

0.0183 0.0257

240 /

4250 /

0.0177 /

Nominal thickness (mm/ply)

0.167 /

Fig. 2. Strengthening schemes of specimens.

Table 4 Test matrix of specimens. Specimen ID

fcm/MPa

Eccentricity/mm

CFRP layout

SR SS2 SN2 SF1 SS3 SS4 SF2 SS2-P LR LS2 LV1 LV2 LS2V1 LS2V2 LS2V3 LS2V1-P

56.2

50 50 50 50 50 50 50 50 100 100 100 100 100 100 100 100

/ HS2 HS2 HF1 HS3 HS4 HF2 HS2 / HS2 V1 V2 HS2-V1 HS2-V2 HS2-V3 HS2-V1

a

Details Control Strip width and spacing @ 100 mm Strip width and spacing @ 50 mm / Strip width and spacing @ 100 mm Strip width and spacing @ 100 mm / Pre-damage to cracking Control Strip width and spacing @ 100 mm CFRP anchorage on both ends CFRP anchorage on both ends Strip width and spacing @100 mm Strip width and spacing @ 100 mm Strip width and spacing @ 100 mm Pre-damage to cracking

Note: (a) ‘‘HF” means horizontal full reinforcement (around column), ‘‘HS” stands for horizontal strip reinforcement with strip spacing equal to 100 mm, ‘‘HN” refers to horizontal strip reinforcement with strip spacing equal to 50 mm, ‘‘V” refers to vertical strip reinforcement and the following number represents the layers of CFRP sheets.

‘‘HS” reinforcement, ‘‘HN” reinforcement and ‘‘V” reinforcement respectively. The following number (if any) means the layer of CFRP reinforcement; the last letter P (if any) illustrates the test column is pre-damaged before CFRP strengthening. For example, specimen LS2V1 had two layers horizontal CFRP strips with width and spacing both equal to 100 mm and one layer of vertical CFRP sheet in tensile zone of the column under a 100 mm eccentricity. 2.2. Test setup and instrumentation The test setup is shown in Fig. 3. All the columns were tested under eccentric loading in structural engineering laboratory of Dalian University of Technology. The 5000 kN compression test

machine was utilized to test all the columns until failure. The axial force on the loading end was directly measured by a load cell on the test machine. In order to facilitate the eccentric loads, two steel hinges were applied at the end of the specimen to permit in-plane rotation and transmit load generated by the machine to the surface of column during the test. The center axis of the steel hinge was aligned with the center of corbel surface. Thus, the predefined eccentricity can be achieved accurately. The lateral deflection along the height of the column was monitored by three LVDTs installed on the left profile steel. The LVDT at the mid-height of the column measured the midspan deflection. Several strain gauges were placed on the rebars and CFRP sheets horizontally and vertically to obtain the strain distribution

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J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

Load cell

Steel hinge e

LVDT

Loading frame Specimen

Profile steel Steel hinge

Steel base (a) Schematic

Fig. 4. Locations of strain gauges on steel reinforcement.

performance of the slightly-damaged columns after retrofitting. The pre-damaged strategy is stated as below. The axial load was applied on the top of the specimens with the loading rate of 10 kN/min, until the axial load reached 85% of the predesigned capacity for the specimens with eccentricity of 50 mm and the maximum width of crack on the A, C side both reached 0.5 mm for the columns under larger eccentricity. 3. Results and analysis 3.1. Failure modes

(b) Photograph Fig. 3. Test setup.

throughout the test procedure. The specific locations of strain gauges on steel reinforcement and CFRP are depicted in Figs. 4 and 5, respectively. For the reason that there were many strain gauges at the mid-height cross section of the columns, it is reasonable to use three letters to label the gauges as follows: the first letter F, S and L represents that the strain gauge was installed on CFRP, stirrups and longitudinal rebars, the second letter stands for the column side where gauge was pasted, the last letter means the direction (i.e., transverse or longitudinal) of the strain gauge. For example, F-D-t represents that there is a transverse strain gauge installed on CFRP in side D of the specimen. Due to the eccentric load along the line BD, there is no big difference between the transverse strain of CFRP on the side A and side C. Therefore, only one set of transverse gauges were placed on the side of A or C economically for convenience. 2.3. Test methods According to the test methods of Chinese standard [35], the load was applied by force gradually until specimen failure. The loading rate was 20 kN/min until it reached 90% of calculated ultimate load and then was kept at 5 kN/min. The test was terminated when the failure of specimens occurred. In this test, two columns were predamaged before wrapping CFRP strips to simulate the mechanical

All the columns were tested to failure. As for the control specimens, the failure pattern was correlated to the eccentricity and was generally governed by a sudden crushing of the concrete in compression zone. The typical failure modes of control specimens are depicted in Fig. 6. When the eccentricity equal to 50 mm, there was little change of the specimen before peak load and the midspan deflection was developed slowly. However, after the load reached the maximum value, the concrete in compressive zone at the mid-height of the column was crushing and severely spalling in a short time. Moreover, the deflection and deformation of the column increased extensively accompanied with the emerging of many vertical and diagonal cracks on sides A and C. The buckling of longitudinal rebar in the compressive zone was also observed in the following procedure. For the specimen LR, several horizontal cracks were emerged firstly when the axial load was approaching to 80% of peak load at the top of the column and the width of these cracks range from 1 mm to 5 mm. As the load increasing, concrete at the opposite side of the developing cracks crushed, which led to the final failure of the specimen. Due to the use of high-strength concrete, the failure process was extremely brittle both for specimen SR and LR, especially for the column SR. Besides, the failure modes of control specimen were in accordance with the traditional failure pattern of small and large eccentric compression columns, which reflected the correctness of the predesigned value of eccentricity. After strengthening with CFRP, the damage of retrofitted columns was much less severe and the ductility increased significantly compared with control specimens. The failure modes of the specimens wrapped with CFRP under 50 mm eccentricity are shown in Fig. 7. It can be detected that the damage patterns are influenced by CFRP layouts and the number of CFRP layers to some extent. For specimen SS2, the CFRP strips in compression region at

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

609

Fig. 5. Locations of strain gauges on CFRP.

Fig. 6. Failure mode of unwrapped columns.

the midspan of the columns slightly bulged with sporadic popping sounds when the load was approaching to the peak load, which indicated that the CFRP strips started to take effect gradually. Several horizontal cracks were found on the concrete tensile side between CFRP strips and the deflection of the column increased extensively at the same time. Finally, large-area crushing of concrete in the compression zone was happened at the top of the column. As shown in Fig. 7(b), (c), the damage degree of crushing concrete at the end of loading successively alleviated with the increasing of CFRP layers. Therefore, the confinement effect provided by CFRP strips exhibited obviously positive correlation with the CFRP volumetric ratio. Besides, with the same volumetric ratio of CFRP and core concrete, specimen SN2 was wrapped with narrow width and spacing CFRP strips and SF1 was retrofitted by CFRP sheets fully wrapped around the column. It can be detected from Fig. 7(d) that there was no large area of concrete spalling during the loading and the CFRP strips were still intact after test, which reflected better confinement and ductility compared with SS2. As for column SF1, the cracks and deformation of the core concrete cannot be detected directly due to the exterior wrapped CFRP sheets, whereas sporadic noises could be heard during the test. When axial load reached the maximum value, the CFRP sheets

were gradually rupture by fiber at the bottom of the column and the crushed concrete was spalling slowly. After that, the specimen can still carry the axial load and bending moment simultaneously until the deformation was too large to resist the loading. While there is only one layer of CFRP wrapped around specimen SF1, it can achieve satisfactory strengthening effect compared with SS2 and SN2. Moreover, the rupture of CFRP sheets will not happen as for specimen SF2 and the ductility performance is extremely superior to the column SS4 at the same volumetric ratio of CFRP. Therefore, the mechanical performance of fully wrapped CFRP sheets is the most superb strengthening scheme with respect to the other FRP layouts. Compared with specimen SS2, the failure process of SS2-P was much more rapidly, which illustrated the pre-damage before test may have great impact on the ductility of specimens. The typical damage patterns of the specimens with eccentricity of 100 mm are presented in Fig. 8. For specimen LS2, the failure procedure was similar to LR, but the number of transverse cracks was less and concrete crushing area was smaller compared to LR. Furthermore, the ductility was apparently enhanced in the light of larger midspan deflection and deformation at the end of the test. As shown in Fig. 8(c), the horizontal cracks emerged uniformly and

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J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

Fig. 7. Failure mode of wrapped columns for 50 mm eccentricity.

developed slowly with the axial load increasing accompanied with ‘‘cracking” noises. When the load reached peak capacity, the rupture of CFRP sheets on the side D was observed and the corresponding concrete in compression zone was also crushing and spalling at the same time. However, there was almost no large transverse crack on the side A and C of specimen LV2 during the loading and the vertical composite sheets were intact after test due to the increasing number of CFRP layers, which exhibited the splendid effect of vertical strengthening. The final failure of the column occurred with the concrete crushing at the mid-height of the specimen. The debonding of vertical CFRP sheets was detected at the end of the columns strengthened with ‘‘HS” and ‘‘V” reinforcement simultaneously because of the pronounced curvature of deformation in the test procedure. Considering that the specimen LS2V1-P was pre-damaged before test and the longitudinal CFRP sheet was not enough to carry the bending moment produced by the large eccentricity, the rupture of vertical CFRP was observed near the middle of the column. The phenomenon demonstrated that the ultimate axial capacity may degrade for the predamaged specimen. As for the specimens LS2V1, LS2V2, LS2V3, the mechanical behavior, especially for ductility, was considerably increased with the number of vertical CFRP sheet layers.

3.2. Load-displacement curves The experimental axial load-midspan deflection curves of all the specimens are shown in Fig. 9. The subfigure caption was comprised of a letter and a word. The first letters S and L represents the eccentricity: 50 mm and 100 mm, respectively. The following word stands for the main test parameter in this study. It is evident that the shape of the curves was influenced by the CFRP strengthening schemes and pre-damaged condition. In addition, the curves of CFRP retrofitted columns generally exhibited better mechanical behavior compared with control specimen. In order to analyze the performance of CFRP strengthening columns quantificationally, the midspan deflection and the corresponding load at the peak (i.e., Dm and Pm), and ultimate (i.e., Du and Pu) point were listed in Table 5. In this test, the Du is defined as the displacement corresponding to 85% of the post-peak load. The improvement of peak load caused by the additional CFRP sheets was up to 37.19% with the eccentricity equal to 50 mm. According to the Fig. 9(a), the peak load of specimen SS2, SN2, SF1 were found to be 8.35, 10.93 and 17.80% larger than the reference specimen SR at the same volumetric ratio of CFRP. The deflections corresponding to the peak load of the above-mentioned

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

611

Fig. 8. Failure mode of wrapped columns for 100 mm eccentricity.

columns were also enhanced successively, which indicated that the confinement of CFRP strips took effect much earlier with the width and spacing decreasing. Therefore, the constraint effect of fully wrapped strengthening scheme was the most superior layout with the volume ratio of CFRP and core concrete unchanged. Moreover, it was found that the increment of peak load of specimen SS4 and SF2 was 21.60 and 37.19% respectively, hence the superiority of ‘‘HF” reinforcement was again verified. It is evident from Fig. 9(b) that the increasing strengthening ratio (i.e., the number of CFRP layers) was propitious to exert the confinement of CFRP, which was consistent with the failure modes of corresponding specimens. While there was a little difference of the peak load in load-midspan deflection curve between specimen SS2-P and SS2, the specimen SS2-P exhibited more rapid post-peak load degradation and the ultimate capacity decreased significantly compared with SS2. The peak load and ultimate load decreased and the corresponding deflection increased when the eccentricity changed from 50 mm to 100 mm. As shown in Fig. 9(d), (e), the vertical CFRP sheet in tensile zone can exhibit better mechanical performance than the transverse CFRP strips, and the columns strengthened with ‘‘HS” and ‘‘V” reinforcement (i.e., mixed strengthening scheme) can achieve the highest axial capacity and the best ductility. The enhancement of peak load for specimens LS2V1, LS2V2, LS2V3 was 20.45, 29.61 and 39.52%. Therefore, it is suggested that the mixed strengthening scheme is more suitable for the specimen under large eccentricity. As the circumstance stated before, the load-midspan deflection curve of the pre-damaged column LS2V1-P was also inferior to the other normally strengthening col-

umn, but the mechanical response was still better than the control specimen. Hence it can be speculated that more layers of FRP are needed for the strengthening process of pre-damaged columns. 3.3. Ductility For the reason that the ductility can directly reflect the plastic deformation capacity of the specimens, in this study, the ductility factor was introduced by two methods. The displacement ductility factor lD, i.e., the ratio of ultimate displacement Du and yield displacement Dy, was calculated by Eq. (2) in the first method. The Du is defined as the displacement corresponding to 85% of the postpeak load as mentioned before, and the Dy is obtained according to the ‘‘general yield moment method” as illustrated by Zhu [36]. The displacement at yielding is assumed as the abscissa of the intersection point between the line OB and the horizontal at the peak load in Fig. 10. The point B on the load versus midspan deflection curve has the same abscissa of point A that is the intersection point between the tangent line of the curve at origin and the horizontal line of peak load. In the second method, the area under the entire load-midspan deflection curve (i.e., the total energy absorption capacity) was calculated by numerical integration to predict the ductility of the specimen according to the research by Hadi [27,37]. The results of displacement ductility factor and energy absorption are shown in Table 5 and Fig. 11. The definition of figure caption in Fig. 11 was the same as Fig. 9.

lD ¼ Du =Dy

ð2Þ

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

1100

1100

900

900

700

700

Load (kN)

Load (kN)

612

500 SR SS2 SN2 SF1 SS4 SF2

300

100 0

3

6

9

12

15

18

500

300

SR SS2 SS3 SS4

100 0

21

3

6

Midspan deflection (mm)

9

(a) S-layout

15

18

21

(b) S-layer

1100

600

900

500 400

700

Load (kN)

Load (kN)

12

Midspan deflection (mm)

500

300 200

300 SR SS2 SS2-P

100 0

3

6

9

12

15

18

LR LS2 LV1 LV2

100

21

0

3

6

9

(c) S-preload

15

18

21

24

27

(d) L-layout

600

600

500

500

400

400

Load (kN)

Load (kN)

12

Midspan deflection (mm)

Midspan deflection (mm)

300 200

300 200

LR LS2V1 LS2V2 LS2V3

100

0

3

6

9

12

15

18

21

24

LR LS2V1 LS2V1-P

100

27

Midspan deflection (mm)

(e) L-layer

0

3

6

9

12

15

18

21

24

27

Midspan deflection (mm)

(f) L- preload

Fig. 9. Load and midspan deflection relationship of test specimens (eccentricity – test parameter).

As shown in Fig. 11, the displacement ductility factor and energy absorption of the specimens were both increased with the volumetric ratio of CFRP under the eccentricity of 50 mm except pre-damaged column. Moreover, the fully wrapped specimen exhibited the most extraordinary ductility compared to the other strengthening columns, which verified the superiority of ‘‘HF” reinforcement again. Specifically, the increasement of displacement ductility factor for specimens SF1 and SF2 was 55.41 and 95.14% larger than SR respectively and the energy absorption of SF1 was almost equivalent to the column SS4. However, when the specimen

was pre-damaged before strengthening, the energy absorption was degraded severely as well as displacement ductility factor. It is evident that the value of Earea for column SS2-P was approximately 33.6% smaller than the reference specimen SR. For the eccentricity equal to 100 mm, there was little difference of the enhancement of ductility between the specimen LV1 and LS2. Hence the vertical strengthening scheme was indeed effective when the eccentricity was relatively high. Besides, the mixed CFRP layout (i.e., LS2V1  LS2V3) can achieve the best confinement effect and the increasement of displacement ductility factor was increased with

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J. Yang et al. / Construction and Building Materials 193 (2018) 604–622 Table 5 Main test results of each specimen. Specimen

CFRP layout

Dy (mm)

Py (kN)

Dm (mm)

Pm (kN)

dPm (%)

Du (mm)

Pu (kN)

lD

dlD (%)

Earea (kNmm)

SR SS2 SN2 SF1 SS3 SS4 SF2 SS2-P LR LS2 LV1 LV2 LS2V1 LS2V2 LS2V3 LS2V1-P

/ HS2 HN2 HF1 HS3 HS4 HF2 HS2 / HS2 V1 V2 HS2-V1 HS2-V2 HS2-V3 HS2-V1

2.14 1.91 2.28 3.04 2.00 3.26 3.09 1.68 3.56 6.89 4.47 5.76 5.02 4.12 4.20 3.32

717.98 757.20 668.96 669.57 655.19 815.47 881.81 612.99 343.68 399.88 397.11 393.59 375.25 369.84 376.24 344.98

2.70 2.95 4.30 6.95 4.50 6.10 5.40 2.80 6.10 10.1 8.60 12.3 12.2 11.2 11.3 6.95

732.47 793.66 812.54 863.50 880.55 890.70 1004.9 760.92 401.46 435.84 462.37 502.77 483.57 520.33 560.12 441.23

/ 8.350 10.93 17.89 20.22 21.60 37.19 3.880 / 8.560 15.17 25.24 20.45 29.61 39.52 9.910

4.80 5.80 7.40 10.6 7.30 12.9 13.5 4.75 9.70 21.7 14.6 22.5 17.8 17.2 18.1 11.5

622.54 673.92 690.95 734.83 747.72 757.18 854.26 644.58 340.87 370.43 393.12 427.42 411.65 441.74 475.76 375.20

2.24 3.03 3.24 3.48 3.65 3.95 4.37 2.83 2.72 3.14 3.27 3.91 3.55 4.16 4.30 3.45

/ 35.28 44.63 55.41 62.89 76.18 95.14 26.16 / 15.55 20.09 43.62 30.33 52.96 58.00 26.70

5125.59 8399.26 9292.44 13460.7 9920.24 13626.3 17174.0 3402.76 5013.93 8273.59 7805.28 9823.31 7576.12 8994.71 10178.6 4841.03

Note: (a) d Pm represents the improvement of peak load and dlD represents the improvement of displacement ductility factor.

P A

Pm Py

C

M

Y B

O

Δy

Δm

Δ

Fig. 10. General yield moment method diagram.

the longitudinal CFRP layers. It should be noticed that the energy absorption of specimen purely retrofitted with ‘‘V” reinforcement was slightly larger than the corresponding mixed strengthening columns, which may result from the vertical CFRP debonding at the end of the column. In addition, it is still suggested that high strengthening ratio is needed for the pre-damaged specimens due to the poor mechanical performance of SS2-P and LS2V1-P. 3.4. Strain analysis The strain of steel reinforcement and CFRP sheets can directly reflect the magnitude of confinement on the core concrete provided by the external constraint. Detailed analysis of the strain on reinforcement bars (i.e., longitudinal rebars and transverse hoops) and CFRP sheets were conducted, and part of the results are shown in Fig. 12 due to the limited space. All the strain in Fig. 12 was measured by the strain gauges located at the midheight of the column and average value was calculated by the two CFRP strips near the middle of the column for the specimens under small eccentricity. As illustrated in Fig. 12(a), (b), the longitudinal rebar in the compressive zone was yielding at the end of the loading, while the strain of transverse hoops and tensile steel reinforcement were still relatively low for specimen SR. Moreover, the strain of longitudinal tensile reinforcement was developed rapidly until yielding after the load reached the ultimate capacity Pu as shown in Fig. 12(b). However, the increasement in the strain of compressive

rebars for specimen LR was minor, which indicated that the yielding of tensile reinforcement occurred before the concrete crushing. Therefore, the results of strain analysis of specimen SR and LR was correspondence with the traditional failure pattern of small and large eccentricity columns. In addition, the peak load was also apparently decreased with the increased eccentricity. It is evident from Fig. 12(c), (d) that the deformation of core concrete can be effectively constrained in the light of the low strain value of stirrups throughout the test. Nevertheless, the effectiveness of confinement was decreased considerably with the eccentricity increasing because of the decreasing confined concrete area. As shown in Fig. 12(e)–(g), the confinement effect was increased with the CFRP layers under the small eccentricity of 50 mm, whereas the effectiveness was gradually decreased. The ultimate transverse CFRP strain of SS3 was almost the same as the specimen SS4. Besides, the confinement can be consistently improved as the width and spacing of CFRP strips reducing when the volumetric ratio of FRP remained constant. However, the different strengthening performance was found as the eccentricity increasing to 100 mm. The longitudinal ultimate strain of vertical CFRP sheet in tensile zone was almost linearly increasing with the increment of CFRP layers. As for specimen LS2V3, the maximum value of longitudinal strain was up to 12,000 le, which demonstrated that it was reasonable to use vertical CFRP sheets under larger eccentric loading. Accordingly, the number of CFRP layers should be selected according to the real eccentricity and strengthening schemes. As depicted in Fig. 12(h), the ultimate strain of pre-damaged columns was correspondingly degraded. Moreover, by comparing the strain distribution under different eccentricity, it can be predicted that the vertical CFRP sheets contributed more to weaken the influence of pre-damage.

4. Ultimate load capacity analysis 4.1. Reinforced mechanism The final failure modes of the retrofitted columns were closely related to the CFRP strengthening schemes and CFRP layers. For the reason that the reinforced mechanism of vertical CFRP sheets and transverse CFRP reinforcement were essentially different, they were separately treated when calculating the ultimate load capacity in this study. The compressive strength of the core concrete can be significantly improved by externally wrapping lateral CFRP around the

614

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

5.0

18000

5.0

18000

16000

16000

10000 3.5 8000 3.0

6000 4000

4.0

12000 10000

3.5 8000 3.0

6000 4000

2.5

2.5

2000 0

2000 SR

SS2

SN2

SF1

SS4

SF2

2.0

0

SR

Specimen

SS2

SS3

SS4

2.0

Specimen

(a) S-layout

(b) S-layer

18000

5.0

5.0

10000

16000

4.5 Displacement ductility factor Energy (kN·mm)

4.5 14000 Energy (kN·mm)

Displacement ductility factor

4.0

12000

4.5 14000

12000

4.0

10000 3.5 8000 6000

3.0

4000

8000 4.0 6000

3.5

4000

2.5

2000

2.0

0

3.0

Displacement ductility factor

Energy (kN·mm)

14000

Displacement ductility factor Energy (kN·mm)

4.5

2.5

2000 SR

SS2

SS2-P

LR

LS2

LV1

LV2

Specimen

Specimen

(c) S-preload

(d) L-layout 5.0

5.0

10000

10000

Energy (kN·mm)

8000 4.0 6000

3.5

4000

3.0

2000

LR

LS2V1

LS2V2

LS2V3

4.5 Displacement ductility factor Energy (kN·mm)

4.5

0

2.0

8000 4.0 6000

4000

2.5

2000

2.0

0

Specimen

(e) L-layer

3.5 3.0

Displacement ductility factor

0

2.5

LR

LS2V1

LS2V1-P

2.0

Specimen

(f) L- preload

Fig. 11. Energy absorption and ductility factor of the specimens (eccentricity – test parameter).

high-strength concrete columns, and the axial capacity and ductility can also be enhanced. Therefore, the stress as well as strain of core concrete is definitely influenced by the horizontal confine-

ment. According to the literature [38,39], the stress-strain relationship is usually comprised of a straight-line portion and a parabolic portion. Thus, in this paper, the new relationship between stress

615

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622 800

450

Pm=732.47 kN

600

350

Pu=622.54 kN

Pu=340.87 kN

300

500

Load (kN)

Load (kN)

Pm=401.46 kN

400

700

400 300

250 200 150

200

100

L-B-l L-D-l S-A-t

100 0

-2000

-1500

L-B-l L-D-l S-A-t

50 -1000

-500

0

0 -1500-1000 -500

500

0

(a) SR

(b)LR 500

800 Pm=793.66 kN

350 Load (kN)

Load (kN)

400

Pu=673.92 kN

600

Pm=435.84 kN

450

700

500 400 300

100 0 -1000

0

Pu=340.87 kN

300 250 200 150

S-A-t F-A-t F-B-t F-D-t

200

S-A-t F-A-t F-B-t F-D-t

100 50 0 -500

1000 2000 3000 4000 5000 6000 7000

0

500

Strain (με)

(c) SS2

1500

2000

2500

1000 900

800

Pu

Pu

800

700

700 Load (kN)

600 Load (kN)

1000 Strain (με)

(d) LS2

900

500 400 300

600 500 400 300

200

200

SS2 SN2 SF1

100 0

SS2 SS3 SS4

100

1000 2000 3000 4000 5000 6000 7000 8000 9000 Strain (με)

0

1000

2000

(e) F-B-t

3000 4000 Strain (με)

5000

6000

7000

(f) F-B-t

600

800 700

500 Pu

600 Load (kN)

400 Load (kN)

500 1000 1500 2000 2500 3000 3500 Strain (με)

Strain (με)

300

Pu

500 400 300

200

SS2 SS2-P LS2V1 LS2V1-P

200 LS2V1 LS2V2 LS2V3

100

0

1500 3000 4500 6000 7500 9000 10500 12000 Strain (με)

100 0

1000

2000

(g) F-D-l Fig. 12. Strain distribution of the specimens.

3000 4000 Strain (με)

(h) F-B-t

5000

6000

7000

616

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

and strain was introduced by the Eq. (3) proposed by Cao et al. [40] as shown in Fig. 13

rc ¼

8 > < f co > :



2 eecoc f co þ

f cc f co ecc eco






ec eco

ðec  eco Þ

2 

ð3Þ

eco 6 ec 6 ecc

σc f cc 1

ð4Þ

where, ffrp is the ultimate tensile strength of the FRP strips.

0 6 ec 6 eco

where, r c = stress of the confined concrete; ec = strain of the confined concrete; fco and fcc are axial compressive strength of the unconfined concrete, equal to fc, and ultimate compressive strength of the confined concrete respectively. The strain at the axial compressive strength of the unconfined concrete eco and ultimate strain of the confined concrete ecc are defined. As shown in Fig. 13, the position of points (fco, eco) and (fcc, ecc) were the most important information when the shape of stressstrain relationship was fixed. The calculation of the latter one was relatively more crucial because extensive researches have been conducted on the axial compressive strength and strain of unconfined concrete. Several representative calculated models [29,34,38,41–43] have been established to solve the confining stress and corresponding strain of FRP strengthening rectangular concrete columns to date. A summary of the key parameters considered by these 6 models is listed in Table 6. The influence factors of ultimate strength of rectangular confined concrete can be seen in Table 6 as follows: (a) the confining stress provided by FRP, fl, which can be calculated by Eq. (4); (b) the corner radius rc. According to the literature [28], this parameter has great impact on the rectangular FRP strengthened columns. Therefore, the default value of the rc is taken as b/10; (c) the shape factor ks. This is a unique coefficient only possessed by rectangular cross section and it is calculated by Eq. (5) from the description by Campione and Miraglia [44]; (d) the effective strain of FRP, eeff,FRP. The value should be observed from strain gauge (if any) or taken as 0.6eult by Lam and Teng [38]; (e) the volumetric ratio of FRP, l, which is defined before in Eq. (1).

f co

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 f l ¼ 2f frp t= h þ b

2

ks ¼

2

ð5Þ

Among the above-mentioned 6 models, there was no model taking all the influence factors into consideration in the meantime, which reflected the insufficient comprehensiveness for these models when calculated the stress-strain relationship of confined concrete. Therefore, the drawbacks of existing proposals necessitate the development of a new constitutive model. A total of 77 specimens from 6 literature were listed in Table 7. The parameter ranges of these specimens are as follows: the concrete cubic compressive strength fco = 22.8–105.5 MPa (including high-strength concrete), b = 100–152 mm, h = 100–225 mm, t = 0.121–2 mm, rc = 5–38 mm. The relationship of dimensionless confined concrete strength fcc/fco and nominal confining stress ksl (ffrp/fco) is shown graphically in Fig. 14. According to the Chinese code [49], the cubic compressive strength of high-strength concrete is above 60 MPa, while the rest is defined as normalstrength concrete. It is evident from Fig. 14 that the value of fcc/ fco of normal-strength concrete was extensively larger than highstrength concrete with the nominal confining stress increasing, which indicated that the confinement of CFRP was more effective for normal-strength concrete. More importantly, the confined concrete strength of high-strength concrete exhibited slow growth during the whole period, which can be attributable to the significant brittleness of high-strength concrete. Therefore, two best-fit models are obtained for normal-strength concrete and highstrength concrete respectively as depicted in Eq. (6). According to the Fig. 14, the fitting result was satisfactory in this study due to the large test database from different literature. It should be noticed that the fcc/fco may be below 1.0 when the nominal confining stress of FRP exceeds a certain lower value. Thus, the lower limit of the dimensionless confined concrete strength was set to 1.0 for Eq. (6).

f cc f co

E2

½bh  4ðr 2c  14 pr 2c Þ  13 ðb  2r c Þ  13 ðh  2r c Þ bh  4ðr2c  14 pr 2c Þ

8
 f > < 0:7664 þ 1:917ks l ffrp for normal - strength concrete co
 ¼ > : 0:9427 þ 0:2297ks l fffrp for high - strength concrete co ð6Þ

As seen in Fig. 15, the relationship between the dimensionless strain of confined concrete, ecc/eco, and ksl (ffrp/fco) was little different with the concrete strength increasing. For the reason that the test data from the listed researches are all small specimens, the size effect should be taken into consideration and smaller ultimate strain values may occur for large specimens as stated by Campione and Miraglia [44]. Therefore, it was relatively conservative to take the base line (shown in Eq. (7)) of the lower limit in Fig. 15 to assess the confined strain.

E1 1

ε cc

ε co

O

εc

Fig. 13. Stress-strain relationship of confined concrete.

Table 6 Influence factors of ultimate strength and strain formula of rectangular confined concrete. No.

1 2 3 4 5 6 7

Source

Mirmiran et al. [41] Zhao [34] ACI 440 [42] Lam and Teng [38] Youssef et al. [43] Song [29] Proposed Model

Influence factor Confining stress

Shape factor

Corner radius

FRP effective strain

FRP volume ratio

Yes Yes Yes Yes Yes Yes Yes

No No Yes Yes Yes No Yes

Yes No Yes Yes Yes No Yes

No Yes No Yes No Yes Yes

No Yes No No Yes No Yes

Table 7 Test data of FRP strengthening square (rectangular) concrete columns. Specimen

Width of section, b (mm)

Depth of section, h (mm)

Corner radius, rc (mm)

Fiber typeb

Young’s Modulus, Efrp (GPa)

Effective tensile strain, eeff,frp

FRP thickness c, t (mm)

FRP layers, n

Width of FRP, s (mm)

Spacing of FRP, s0 (mm)

Unconfined Concrete strength d, fco (Mpa)

Concrete strength ratio, fcc/fco

Strain ratio, ecc/eco

Shape factor, ks

FRP volume ratio, l

FRP strength ratio, ffrp/fco

R [45]

S5-C3 S25-C3(1) S25-C3(2) S38-C3(1) S5-C5 S25-C4(1) S25-C4(2) S25-C5 S38-C4 S38-C5 S5-A9 S25-A3 S25-A6 S25-A9 S25-A12 S38-A9

152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0

152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0 152.0

5.0 25 25 38 5.0 25 25 25 38 38 5.0 25 25 25 25 38

C C C C C C C C C C A A A A A A

82.7 82.7 82.7 82.7 82.7 82.7 82.7 82.7 82.7 82.7 13.6 13.6 13.6 13.6 13.6 13.6

0.0023 0.0056 0.0063 0.0071 0.0044 0.0059 0.0070 0.0065 0.0089 0.0086 0.0148 0.0112 0.0127 0.0094 0.0104 0.0097

0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.420 0.420 0.420 0.420 0.420 0.420

3 3 3 3 5 4 4 5 4 5 9 3 6 9 12 9

500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

40.000 40.000 40.000 40.000 41.810 41.810 34.100 34.100 34.100 34.100 40.950 40.950 40.950 40.950 40.950 40.950

0.94 0.99 1.03 1.13 1.00 1.16 1.46 1.61 1.66 1.92 1.25 1.19 1.19 1.24 1.28 1.23

1.25 4.70 4.45 5.40 5.10 6.75 10.2 10.6 9.60 12.0 1.25 1.30 1.30 1.30 1.30 1.25

0.42 0.69 0.69 0.82 0.42 0.69 0.69 0.69 0.82 0.82 0.42 0.69 0.69 0.69 0.69 0.82

0.0237 0.0237 0.0237 0.0237 0.0395 0.0316 0.0316 0.0395 0.0316 0.0395 0.0995 0.0332 0.0663 0.0995 0.1326 0.0995

4.760 11.58 13.03 14.68 8.700 11.67 16.98 15.76 21.58 20.86 4.920 3.720 4.220 3.120 3.450 3.220

Z [34]

NC1-2 NC1-3 NC1-4 NC1-5 NC1-6 NC1-7 NC2-5

100.0 100.0 100.0 100.0 100.0 100.0 100.0

100.0 100.0 100.0 100.0 100.0 100.0 100.0

10 10 10 10 10 10 10

C C C C C C C

220 220 220 220 220 220 220

0.0097 0.0097 0.0097 0.0097 0.0097 0.0097 0.0097

0.121 0.121 0.121 0.121 0.121 0.121 0.121

1 1 1 2 2 2 2

300 300 300 300 300 300 50

0 0 0 0 0 0 100

25.460 25.460 25.460 25.460 25.460 25.460 22.800

1.27 1.34 1.32 1.38 1.49 1.38 0.83

2.08 2.26 2.32 3.36 3.67 3.55 2.38

0.57 0.57 0.57 0.57 0.57 0.57 0.57

0.0048 0.0048 0.0048 0.0097 0.0097 0.0097 0.0032

83.95 83.95 83.95 83.95 83.95 83.95 93.74

P [46]

1 2

152.0 152.0

152.0 152.0

38 38

C C

38.1 38.1

0.0083 0.0090

1.000 2.000

1 1

610 610

0 0

25.140 25.140

1.57 2.09

7.70 9.70

0.82 0.82

0.0263 0.0526

12.58 13.64

L [38]

S1R15 S1R25 S2R15 S3R25

150.0 150.0 150.0 150.0

150.0 150.0 150.0 150.0

15 25 15 25

C C C C

257 257 257 257

0.0103 0.0105 0.0097 0.0116

0.165 0.165 0.165 0.165

1 1 2 3

600 600 600 600

0 0 0 0

32.100 32.100 32.100 22.860

1.24 1.41 1.79 3.29

2.26 4.64 4.35 7.62

0.57 0.70 0.57 0.70

0.0044 0.0044 0.0088 0.0132

82.46 84.07 77.66 130.4

Oz-1[47]

A10R15L3-1 A10R15L3-2 A10R30L3-1 A10R30L3-2 A10R15L5-1 A10R15L5-2 A10R30L5-1 A10R30L5-2 A15R15L3-1 A15R15L3-2 A15R30L3-1 A15R30L3-2 A15R15L5-1 A15R15L5-2 A15R30L5-1 A15R30L5-2 A20R15L3-1 A20R15L3-2 A20R30L3-1 A20R30L3-2

150.0 150.0 150.0 150.0 150.0 150.0 150.0 150.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 112.5 112.5 112.5 112.5

150.0 150.0 150.0 150.0 150.0 150.0 150.0 150.0 187.5 187.5 187.5 187.5 187.5 187.5 187.5 187.5 225.0 225.0 225.0 225.0

15 15 30 30 15 15 30 30 15 15 30 30 15 15 30 30 15 15 30 30

C C C C C C C C C C C C C C C C C C C C

240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240

0.0080 0.0095 0.0078 0.0080 0.0067 0.0076 0.0096 0.0072 0.0077 0.0063 0.0076 0.0052 0.0056 0.0090 0.0068 0.0084 0.0061 0.0075 0.0077 0.0080

0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234

3 3 3 3 5 5 5 5 3 3 3 3 5 5 5 5 3 3 3 3

300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

72.380 72.380 72.380 72.380 72.380 72.380 73.520 73.520 73.520 73.520 73.520 73.520 75.810 75.810 75.810 75.810 75.810 75.810 74.480 74.480

1.02 1.01 1.13 1.10 1.04 1.05 1.23 1.12 1.05 1.02 1.11 0.97 1.07 1.06 1.16 1.13 0.96 0.99 0.95 1.05

7.80 6.88 5.39 4.98 11.4 9.97 7.20 6.72 5.07 5.00 4.49 3.95 6.51 8.47 4.92 5.85 6.11 5.42 5.13 4.83

0.57 0.57 0.75 0.75 0.57 0.57 0.75 0.75 0.51 0.51 0.70 0.70 0.51 0.51 0.70 0.70 0.41 0.41 0.59 0.59

0.0187 0.0187 0.0187 0.0187 0.0312 0.0312 0.0312 0.0312 0.0187 0.0187 0.0187 0.0187 0.0312 0.0312 0.0312 0.0312 0.0187 0.0187 0.0187 0.0187

25.85 30.89 22.67 23.89 21.26 23.76 25.57 21.00 24.04 20.07 22.40 17.50 16.51 26.78 18.49 23.49 20.15 24.05 26.08 24.47

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

Sourcea

(continued on next page) 617

618

Table 7 (continued) Sourcea

Oz-2[48]

Width of section, b (mm)

Depth of section, h (mm)

Corner radius, rc (mm)

Fiber typeb

Young’s Modulus, Efrp (GPa)

Effective tensile strain, eeff,frp

FRP thickness c, t (mm)

FRP layers, n

Width of FRP, s (mm)

Spacing of FRP, s0 (mm)

Unconfined Concrete strength d, fco (Mpa)

Concrete strength ratio, fcc/fco

Strain ratio, ecc/eco

Shape factor, ks

FRP volume ratio, l

FRP strength ratio, ffrp/fco

A20R15L5-1 A20R15L5-2 A20R30L5-1 A20R30L5-2

112.5 112.5 112.5 112.5

225.0 225.0 225.0 225.0

15 15 30 30

C C C C

240 240 240 240

0.0074 0.0059 0.0086 0.0070

0.234 0.234 0.234 0.234

5 5 5 5

300 300 300 300

0 0 0 0

74.480 74.480 74.480 74.480

0.99 1.09 1.10 1.01

7.15 5.37 6.68 5.27

0.41 0.41 0.59 0.59

0.0312 0.0312 0.0312 0.0312

24.06 17.51 25.29 22.33

A10R15L5-1 A10R15L5-2 A10R30L5-1 A10R30L5-2 A10R15L8-1 A10R15L8-2 A10R30L8-1 A10R30L8-2 A15R15L5-1 A15R15L5-2 A15R30L5-1 A15R30L5-2 A15R15L8-1 A15R15L8-2 A15R30L8-1 A15R30L8-2 A20R15L5-1 A20R15L5-2 A20R30L5-1 A20R30L5-2 A20R15L8-1 A20R15L8-2 A20R30L8-1 A20R30L8-2

150.0 150.0 150.0 150.0 150.0 150.0 150.0 150.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 112.5 112.5 112.5 112.5 112.5 112.5 112.5 112.5

150.0 150.0 150.0 150.0 150.0 150.0 150.0 150.0 187.5 187.5 187.5 187.5 187.5 187.5 187.5 187.5 225.0 225.0 225.0 225.0 225.0 225.0 225.0 225.0

15 15 30 30 15 15 30 30 15 15 30 30 15 15 30 30 15 15 30 30 15 15 30 30

C C C C C C C C C C C C C C C C C C C C C C C C

240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240

0.0075 0.0069 0.0082 0.0082 0.0071 0.0061 0.0063 0.0069 0.0068 0.0062 0.0082 0.0078 0.0059 0.0055 0.0085 0.0055 0.0064 0.0068 0.0075 0.0069 0.0069 0.0070 0.0064 0.0069

0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234 0.234

5 5 5 5 8 8 8 8 5 5 5 5 8 8 8 8 5 5 5 5 8 8 8 8

300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

100.19 100.19 102.19 102.19 105.24 105.24 105.52 105.52 100.19 100.19 102.19 102.19 105.24 105.24 105.52 105.52 100.19 100.19 102.19 102.19 105.24 105.24 105.52 105.52

0.94 0.99 1.03 0.97 1.00 0.94 1.07 0.99 0.94 0.97 0.97 1.00 0.99 0.95 1.08 1.02 0.96 0.97 1.02 1.01 0.96 0.95 1.04 1.01

5.26 5.95 4.30 4.10 11.1 4.92 4.58 5.56 5.55 4.22 4.30 4.21 6.21 8.47 4.94 4.60 5.06 4.31 4.18 4.15 7.80 8.22 4.63 4.38

0.57 0.57 0.75 0.75 0.57 0.57 0.75 0.75 0.51 0.51 0.70 0.70 0.51 0.51 0.70 0.70 0.41 0.41 0.59 0.59 0.41 0.41 0.59 0.59

0.0312 0.0312 0.0312 0.0312 0.0499 0.0499 0.0499 0.0499 0.0312 0.0312 0.0312 0.0312 0.0499 0.0499 0.0499 0.0499 0.0312 0.0312 0.0312 0.0312 0.0499 0.0499 0.0499 0.0499

17.97 16.53 19.26 19.26 16.19 13.91 14.33 15.69 16.29 14.85 19.26 18.32 13.46 12.54 19.33 12.51 15.33 16.29 17.61 16.21 15.74 15.96 14.56 15.69

Note: (a) R = Rochette and Labossiere (2000); Z = Zhao et al. (2000); P = Pessiki et al. (2001); L = Lam and Teng (2003); Oz-1 = Ozbakkaloglu (2013a); Oz-2 = Ozbakkaloglu (2013b); (b) A = AFRP, C = CFRP, G = GFRP; (c) The thickness is nominal thickness provided by the local supplier; (d) If the cylinder compressive strength of concrete is not available in the above-mentioned references, the equations, f0co = 0.8fcm and f0co = 1.05 fco, will be used to calculate this specific value.

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

Specimen

619

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

1.5

However, the vertical FRP reinforcement can achieve higher tensile strength under large eccentricity. Due to the plane-section hypothesis and the higher tensile strength of FRP than reinforcing bar, it is not effective to utilize longitudinal FRP sheets for small eccentricity columns. In addition, the ‘‘V” and ‘‘HS” reinforcement can be used simultaneously to strengthen the concrete columns, whereas their strengthening effect should be taken into consideration respectively. As mentioned above, the mixed reinforcement has little effect on the strengthening of the small eccentricity columns and hence was not be discussed further in this paper.

1.0

4.2. Calculation of ultimate load capacity

4.0 3.5 3.0

fcc / fco

2.5

Rochette and Labossiere (2000) Zhao et al. (2000) Pessiki et al. (2001) Lam and Teng (2003) Ozbakkaloglu (2013a) Ozbakkaloglu (2013b) Best-fit for normal-strength concrete Best-fit for high-strength concrete

Proposed model: fcc / fco=0.7664+1.917ksμ ffrp / fco

2.0

Proposed model:

0.5 0.0

It is necessary to clarify that the balanced-relative height of compression zone must be figured out before the following calculations. As a result of the application of vertical FRP reinforcement, there are two balanced states. In the first condition, reinforcing bar yields as concrete reaches ultimate compressive strength simultaneously, the other circumstance is that the concrete in compression zone is crushed when the longitudinal FRP reaches its ultimate tensile strain immediately. Therefore, two balancedrelative height of compression zone should be introduced by the Eqs. (8) and (9) as follows.

fcc / fco=0.9427+0.2297ksμ ffrp / fco

0.2

0.4

0.6

0.8

1.0

1.2

ksμ ffrp / fco Fig. 14. Determination of confined strength of FRP confined concrete.

12 10

nb ¼

εcc / εco

8

Rochette and Labossiere (2000) Zhao et al. (2000) Pessiki et al. (2001) Lam and Teng (2003) Ozbakkaloglu (2013a) Ozbakkaloglu (2013b)

2

0.0

0.2

0.4

0.6

0.8

1.0

b1 1 þ f y =ðEs ecc Þ

ð9Þ

R ecc

1.2

b1 ¼ 2

ksμ ffrp / fco

rc ðec Þec dec 1  R ecc rc ðec Þdec  ecc 0

!

0

ð10Þ

For large eccentricity columns (ncfb 6 n 6 nb ), the ultimate axial load capacity can be calculated by the Eqs. (11)–(14) at below.

Fig. 15. Determination of ultimate strain of FRP confined concrete.

f frp ecc ¼ 1 þ 5:5ks lð Þ eco f co

ð8Þ

where, ncfb, nb = balanced-relative height of the concrete compression zone controlled by FRP and reinforcement bar respectively; b1= the height coefficient of the equivalent rectangular concrete stress distribution, as shown in Fig. 16, should be recalculated as Eq. (10) according to literature [32]; ecfu = the calculated ultimate strain of longitudinal FRP sheet, the value is taken as min{0.01, 0.67eult} in this paper; fy = yield strength of tensile reinforcement bar; Es = modulus of the reinforcement bar.

6 4

b1 ecc ecc þ ecfu

ncfb ¼

Base line: εcc / εco=1+5.5ksμ ffrp / fco

0

ð7Þ

0

N ¼ a1 f cc bx þ f y As  f y As  Efrp ecf Acf

Fig. 16. Equivalent rectangular stress diagram.

ð11Þ

620

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

Table 8 Comparison of experimental and calculated results. Source

Specimen ID

Cubic compressive strength fcm (MPa)

Eccentricity (mm)

CFRP layout

Pexp (kN)

Pcal (kN)

Pcal/Pexp

Hadi and Widiarsa [50]

1HC25 1V2HC25 3HC25 1HC50 1V2HC50 3HC50

79.5 79.5 79.5 79.5 79.5 79.5

25 25 25 50 50 50

HS1 HS2-V1 HS3 HS1 HS2-V1 HS3

2076 2296 2269 1433 1533 1534

1833.5 1871.6 1891.7 1442.5 1477.5 1497.4

0.88 0.82 0.83 1.01 0.96 0.98

Xian et al. [51]

C-02 C-03 C-05 C-06 C-07 C-08 C-09 C-10 C-12 C-13 C-14 C-15

30.3 29.0 26.2 24.4 29.8 22.4 22.8 26.0 45.8 41.2 45.5 41.8

175 175 175 175 175 175 175 175 175 175 175 175

V1 HS1 V1 V1 HS1 V2 V2 HS1-V1 V1 HS1 V2 HS1-V1

900.0 875.0 580.0 678.0 750.0 645.0 640.0 745.0 895.0 815.0 957.0 872.0

876.83 851.08 678.75 653.38 699.99 637.07 643.19 649.57 919.14 808.65 968.44 876.95

0.97 0.97 1.17 0.96 0.93 0.99 1.00 0.87 1.03 0.99 1.01 1.01

Zhou and Huang [52]

ES1 ES2 ES3 ES4 ES5

41.0 41.0 41.0 41.0 41.0

50 50 50 50 50

HS2 HS3 HS4 HF3 HS3

645.6 697.3 770.7 878.0 661.2

609.85 644.21 682.41 764.68 664.21

0.94 0.92 0.89 0.87 1.00

Present study

SS2 SN2 SF1 SS3 SS4 SF2 SS2-P LS2 LV1 LV2 LS2V1 LS2V2 LS2V3 LS2V1-P

56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2 56.2

50 50 50 50 50 50 50 100 100 100 100 100 100 100

HS2 HN2 HF1 HS3 HS4 HF2 HS2P HS2 V1 V2 HS2-V1 HS2-V2 HS2-V3 HS2-V1P

793.7 812.5 863.5 880.6 890.7 1005 760.9 435.8 462.4 502.8 483.6 520.3 560.1 441.2

820.91 820.91 820.91 863.58 909.69 909.69 820.91 418.43 437.45 458.03 457.70 481.26 591.00 457.70

1.03 1.01 0.95 0.98 1.02 0.91 1.08 0.96 0.95 0.91 0.95 0.92 1.06 1.04

Average of Pcal/Pexp Standard derivation of Pcal/Pexp Coefficient of variation

0.967 0.070 0.072

0

0

Ne ¼ a1 f cc b x ðh0  x=2Þ þ f y As ðh0  a0s Þ þ Efrp e¼

1þ

!  2 1 l0 h n1 n2  ei þ  as 1400ei =h0 h 2

ecf ¼ ecc ðb1 h  xÞ=x

ecf Acf as

ð12Þ

ð13Þ ð14Þ

where, N = axial compressive capacity; e = distance between the action point of axial force and the action point of resultant force of tension reinforcement bar; ei = the distance between the action point of axial force and the vertical axis of the column section; l0 = the calculated height of column;n1 ¼ 0:5f cc A=N 6 1:0; n2 ¼ 1:15  0:01l0 =h 6 1:0; a1 = the strength coefficient of the equivalent rectangular concrete stress distribution, should be calculated as Eq. (15); x = the height of concrete compression zone; f0y = yield strength of compressive reinforcement bar; A0s = cross section area of all longitudinal compressive reinforcement bar; As = cross section area of all longitudinal tensile reinforcement bar; h0 = effective height of cross section; a0s = distance between the action point of resultant force of compressive reinforcement and the edge of concrete columns; Ecf = modulus of the CFRP sheet; ecf = the calculated strain of longitudinal CFRP sheet; Acf = cross section area of all longitudinal CFRP sheets. The fcc should be equivalent to fco when the columns have no horizontal CFRP reinforcement. For the circumstance of n < ncfb and n < 2a0s =h0 , the

relative height of compression zone should meet the equations n ¼ ncfb and n ¼ 2a0s =h0 respectively.

R ecc

a1 ¼

0

rc ðec Þ dec b1 f cc ecc

ð15Þ

For small eccentricity columns (n > nb ), the ultimate load capacity can be calculated by the Eqs. (16)–(20) as following. 0

0

N ¼ a1 f cc bx þ f y As  rs As  Ecf ecf Acf 0

0

Ne ¼ a1 f cc bx ðh0  x=2Þ þ f y As ðh0  a0s Þ þ Ecf ecf Acf as

e¼

1þ

1 1400ei =h0

!  2 l0 h n1 n2  ei þ  as 2 h

ð16Þ ð17Þ

ð18Þ

ecf ¼ ecc ð b1 h  x Þ=x

ð19Þ

rs ¼ ½ ðn  b1 Þ=ðnb  b1 Þ   f y

ð20Þ

where, rs is the stress of the longitudinal reinforcement, if n > 2b1  nb , then rs ¼ f y .

J. Yang et al. / Construction and Building Materials 193 (2018) 604–622

2400 Present study Hadi and Widiarsa (2012) Zhou and Huang (2004) Xian et al. (2004)

2100

Calculated (kN)

1800 1500

+20%

1200

-20%

900 600 300

0

300

600

900

1200

1500

1800

2100

2400

Test (kN) Fig. 17. Theoretical predictions versus test observations.

4.3. Comparison of tested and calculated ultimate load capacity According to the ultimate axial capacity formulae of FRP strengthened columns under eccentricity above, the calculated results of ultimate capacity in this study and other relevant literature are listed in Table 8 and Fig. 17 graphically. The cubic compressive concrete strength of the 37 specimens listed in Table 8 ranges from 22.4 to 79.5 MPa, which indicated that the formulae can be used both for the normal-strength and high-strength concrete simultaneously and verified the correctness of the new proposed model for stress-strain relationship of FRP confined concrete. It is evident from Table 8 that the calculated results fit well with the test data. The ratio of the calculated value to experimental data ranges from 0.82 to 1.17 with the average of 0.967 and variation coefficient equal to 0.07 for all the specimens. The test results are within a ±20% margin of error, which can be speculated that the proposed equations can be used to calculate ultimate axial load capacity of the FRP strengthened columns reasonably and provide reference for the engineering design. 5. Conclusions Based on the tests conducted on the mechanical performance of CFRP strengthened rectangular high-strength concrete columns under eccentric loading in this study, the main conclusions that can be drawn from this study are as follows: (1) The control specimens exhibited significant brittleness both under the eccentricity of 50 mm and 100 mm, which corresponded with the traditional failure modes of small and large eccentricity columns respectively. However, the ductility factor and energy absorption of the CFRP strengthened columns were improved extensively compared with the reference specimens. Moreover, the enhancement was increased with the number of CFRP layers. (2) According to the load-midspan curves of all specimens, the columns wrapped with CFRP exhibited more splendid behavior of load versus deflection curve than control columns except the pre-damaged columns regardless of the value of the eccentricity. However, it can be supposed from the performance of all pre-damaged columns that predamage may have great impact both on the ductility and axial capacity of the specimens.

621

(3) In light of the results of ductility analysis, it is suggested that the ‘‘HF” reinforcement scheme is the first choice as stated before under the eccentricity of 50 mm. Under the larger eccentricity, the displacement ductility factor was gradually increased for the specimens LS2V1, LS2V2 and LS2V3, which were all larger than the columns only strengthened with vertical CFRP sheets or horizontal CFRP strips as expected. (4) The transverse strain of CFRP strips at the mid-height of the column was gradually decreased with the increment of eccentricity. This may be attributable to the relatively smaller area of the effective confined core concrete. Therefore, it is reasonable to choose suitable strengthening scheme and CFRP layers based on the eccentricity. More importantly, the ultimate strain of CFRP may have extensive degradation due to pre-damage before the CFRP strengthening process. Thus, more layers are needed for the pre-damaged specimens. (5) The best-fit equations of the relationship between dimensionless strength of confined concrete as well as strain and nominal confining stress were proposed. It should be noted that the confinement provided by CFRP was more effective when applied to normal strength concrete. Furthermore, the ultimate axial capacity formulae were also proposed based on the above-mentioned models, which can provide a good agreement when compared with a large amount of independent test data.

Conflict of interest None.

Acknowledgments This work was supported by the National Natural Science Foundation of China [grant numbers 51178078, 51208077].

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