Experimental investigation on the compressive behaviour of FRP-confined rectangular concrete columns

This paper presents a comprehensive experimental study on the behaviour of FRP-confined concrete in square and rectangular columns and focuses on some issues that might be addressed with a view to improving the predictive models. For this purpose, 31 prismatic concrete specimens with a height of 600 mm and low- and medium-strength concrete (20–35 MPa) were tested under centred compression. The parameters studied were the aspect ratio between the sides of the section (1, 1.5 and 2), the radius of curvature of the corners (20, 25 and 30 mm) and the number of carbon FRP layers applied. The experimental results included stress–strain curves of specimens and detailed information about the confined concrete strength and the axial and lateral strain achieved on the FRP jacket during the tests. The stress–strain response and ultimate condition are analysed, showing that FRP jacketing is an efficient technique for increasing the strength and strain capacity, but that confinement efficiency decreases as the aspect ratio of the section increases. In spite of such decrease, significant strength improvement was achieved for low-strength concrete in rectangular sections with aspect ratios of 1.5 (strength gain up to 81%), and even 2 (up to 36%). The axial strength of the tests was compared with the design criteria of four international guidelines, resulting in predictions that did not properly fit for rectangular sections. A predictive equation is proposed to assess the axial compressive strength of the FRP-confined concrete, which includes a better adjustment for the strain efficiency factor and the shape factor for rectangular columns.


Introduction
The strengthening of concrete structures is the field of construction where composite materials made of FRPs (fibrereinforced polymers) are being introduced most quickly and with the greatest success [1,2], mainly due to their corrosion resistance, good mechanical properties and lightness that translates into ease and savings in the execution of works. Typical FRP applications include flexural strengthening [3], shear strengthening [4] or strengthening of beam-column joints suffering from both flexural and shear deficiencies [5].
One of the most widespread use of these materials is the confinement of reinforced concrete columns in existing structures such as bridges or buildings. Numerous experimental studies have been carried out on the behaviour of FRP-confined concrete, most of them on small circular section specimens. Berthet et al. [6] investigated different parameters such as the confinement level, the mechanical properties of the FRP jackets and the compressive strength of the concrete core. They concluded that the stress-strain response depends on the jacket stiffness and that the efficiency of the confinement lightly decreases with the concrete core strength. Cui and Sheikh [7] tested cylindrical specimens with concrete strength between 45 and 112 MPa and showed that with an increase of the unconfined concrete strength, the confinement efficiency of the FRP jackets decreased remarkably. Similar findings were reported by Li [8] and Vincent and Ozbakkaloglu [9]. A database with test results of cylindrical specimens published in the literature can be consulted in Ozbakkaloglu and Lim [10] and De Lorenzis and Tepfers [11].
Although to a lesser extent, tests have also been carried out on non-circular section specimens, where confinement is less efficient. Harries and Carey [12] tested standard cylinders and similarly sized square specimens showing that square samples exhibited lower confinement levels than circular ones having the same jacket. Other authors have also tested square [13][14][15] and rectangular sections [16] and studied the influence of the rounding radius of the corners [17][18][19]. The experimental results showed that increasing the radius of the corners significantly improves the compressive concrete strength and this has been corroborated by various numerical analyses [16,20].
In recent years, different theoretical models, both analysis-oriented (e.g. [21][22][23]), and design-oriented models have been proposed. The design recommendations that have been published in some countries [24][25][26][27] usually adopt designoriented models, providing simple empirical formulations to calculate the increase in strength and strain of concrete. They are generally empirical models based on available experimental results. Many of these models have been developed for columns with circular section (e.g. [28][29][30]), but others are also valid for square [31,32] or rectangular [33] sections.
Several authors have reported an assessment of the existing predictive models. Nisticò et al. [31] collected a database, including circular and square concrete columns noting that the experimental results for rectangular sections are limited. The study of Fanaradelli et al. [34] focuses on non-circular columns and revealed that most of the models are applied to columns with ascending second branches, but in fact, the behaviour of rectangular columns may present descending second branches so the existing models cannot satisfactorily describe their behaviour.
Further investigation is required to improve the predictive performance of the models and there are two key parameters, which have crucial influence on their adequacy: the effect of confinement in non-circular sections and the effective strain at break of the FRP. The proposals of the existing models adopted by design guides differ on these two key issues noted.

Effect of confinement in non-circular sections
It is known that the confinement of non-circular columns is less efficient than the confinement of circular columns. In a circular cross section, the jacket exerts a uniform confining pressure over the entire perimeter. In the case of a rectangular cross section, the confining action is mostly concentrated at the corners rather than around the entire perimeter and the confining stress field is not uniform. The theoretical models are mostly based on approaches created for columns with circular cross sections, which are then modified by a "shape factor" [35][36][37]. This "shape factor" concept was originally proposed for rectangular RC columns with transverse steel confinement [38] and it is usually defined as the ratio between the effective confinement area and the gross area of the column cross section (A e /A c ). The fib bulletin 90 [24] and the Italian design guide [27] consider the generally accepted approach of an effectively confined area defined by four second-degree parabolas with initial angles starting at 45° to the face of the column. This assumption is not valid for rectangular sections with a high aspect ratio, since the parabolas would overlap and a negative value might be obtained for A e /A c . To avoid this, the ACI guideline [26] adopts the model proposed by Lam and Teng [33] in which the cross-sectional area of effectively confined concrete is defined by parabolas whose initial slopes are diagonal lines between the column corners. The latest revision of the Technical Report TR55, by the Concrete Society [25], assumes conservative values for average confining stress, rather than explicitly defining an effectively confined area, and indicates that confinement is of little benefit when the aspect ratio is greater than 1.5. Other design guidelines indicate that for rectangular sections with an aspect ratio greater than 2, the formulations should be used with caution [24] or are not recommended unless testing demonstrates their effectiveness [26,27].
Other authors have made different proposals for calculating the shape factor, which lead to smaller values and are more influenced by the radius of curvature with which the section corners are rounded. Thus, Karam and Tabara [39] proposed a shape factor for rectangular sections given by

Effective strain at break of the FRP
The ultimate strength of the confined concrete is closely related with the failure strain of the reinforcement in the confined element, which is called effective ultimate strain or hoop failure strain. But the hoop failure strain of the FRP jacket has been shown to be less than the ultimate tensile strain in FRP when tested in conditions of pure uniaxial tension. There are a number of possible reasons for this, such as multiaxial stress state, stress concentrations due to concrete failure, or a curved shape of the jacket, especially at corners with low radius. This last parameter may be important for square or rectangular columns with rounded corners.
The ratio of hoop strain in the FRP jacket, at tensile failure, to ultimate FRP strain in uniaxial tension is called strain efficiency factor. Empirical values of strain efficiency factors found in the literature are enormously divergent. Design guides commonly propose, based on published research on Page 3 of 16 131 circular section specimens, the use of a strain efficiency factor of around 0.55-0.60. Some studies have indicated that in non-circular sections, the effective ultimate strain can be affected by factors such as the corner radius or the side aspect ratio [17,18,41,42]. Some of the more recent revisions of calculation guides, such as fib Bulletin 90 [24] and Concrete Society TR55 [25], propose using a lower value for the strain efficiency factor in rectangular sections. Strikingly, despite its importance in the calculation, this is one of the issues that the models have resolved least adequately and requires further investigation.

Research contribution
Despite the wide-ranging research that has been carried out, there is still a lack of well-instrumented experimental campaigns on full-scale or intermediate-sized specimens (meaning, in the latter case, specimens with a height that is greater than or equal to 500 mm and a ratio between column height and cross section side that is greater than two and smaller than five). Besides, the available experimental results regarding non-circular sections are more limited and there is still no consensus in the design guides for the calculation of the strength and ultimate strain of FRP-confined concrete.
For all these reasons, further research is still needed to expand the existing experimental database, improve the prediction of the main parameters and refine the calculation models for FRP-confined rectangular concrete columns.
The present work proposes an experimental programme of 31 tests on square and rectangular sections of intermediate-sized specimens. The programme analyses the influence of the main parameters on the effectiveness of the FRP jacketing, such as the side aspect ratio of the cross section and the rounding radius of the corners. The experimental results of the study are provided in detail and include the FRPconfined concrete strength and the effective strain at break of the FRP. The results are compared with the estimates given by the existing design guides. A new equation is proposed to calculate the compressive strength of FRP-confined concrete in rectangular section columns that explicitly takes into account the main parameters studied.

Specimen design
Thirty-one prismatic concrete specimens with square and rectangular cross sections were tested under centred compression. Thirty specimens had been externally strengthened with CFRP (carbon fibre reinforced polymer) and one specimen had been left unstrengthened for control purposes. None of the specimens had internal steel reinforcement.
The variables considered in the experimental programme were: -Aspect ratio (h/b) between cross section sides. Specimens with square sections (h/b = 1) and specimens with rectangular sections (h/b = 1.5 and h/b = 2) were tested. -Radius of curvature (R c ) of corners. A higher corner radius increases the value of the shape factor commonly used in design models. Three R c values were chosen: 20, 25 and 30 mm. -Degree of reinforcement. Specimens were reinforced with one, two, three and four layers of carbon fibre.
Unconfined concrete strength was not initially considered as a variable in this experimental programme. It is well known that confinement efficiency depends largely on unconfined concrete strength values and that the effect of confinement is very limited in high-and ultrahigh-strength concrete. This programme focused on low-strength concrete (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) of the type that is usually found in rehabilitation works. However, some of the manufactured batches of concrete exhibited greater values of compressive strength (around 35 MPa). Given that the effect of confinement strongly depends on concrete strength, the decision was made to include a few additional specimens in some of the test series, with a view to covering a wider range of strength values and thereby allowing a more thorough analysis of the results. This would make it possible to separate the effect of unconfined concrete strength from the other variables studied. Table 1 presents details of the test specimens, under their corresponding headings: the aspect ratio (h/b) is shown first, followed by the number of confining layers (n) and the corner radius (R c ) expressed in millimetres. Finally, in cases in which several specimens of a given type were tested, these are ascribed the letters a, b and c. For example: 1.5_2_30b is the second 1.5_2_30 specimen with an aspect ratio of 1.5; it was confined with two plies of CFRP and had a corner radius of 30 mm.

Preparation of concrete specimens
Prismatic concrete specimens with a height of 600 mm were fabricated. Three types of cross sections were used: • Square section with 150 mm side. • Rectangular section with an aspect ratio (h/b) of 1.5 (225 mm in width and 150 mm in depth). • Rectangular section with an aspect ratio (h/b) of 2 (300 mm in width and 150 mm in depth).
Specimens were made by vertical casting. The concrete mix was prepared in the laboratory and cast into moulds with the required corner radius.
Concrete cylinders with a diameter of 150 mm and a height of 300 mm were also cast and tested under axial loading to determine the average unconfined concrete strength. The test specimens and the cylinders were cured under the same conditions.

Strengthening materials and methods
Unidirectional carbon fibre-reinforced polymer (CFRP) sheets were used for external confinement. Nominal fibre thickness was 0.129 mm per ply. The FRP was applied using the hand lay-up technique, or wrapping, with fibres oriented in the hoop direction and an overlap length of 100 mm.
To determine the material properties of the CFRP, tensile testing of six flat coupons was carried out in accordance with ISO 527-4 standard. The mean value for ultimate strength was 4161 N/mm 2 and the tensile modulus equalled 236,918 N/mm 2 (both mechanical properties having been calculated using nominal fibre thickness). The mean value for ultimate strain was 0.01776.
Specimens were fully wrapped with differing numbers of FRP plies, in accordance with the test plan shown in Table 1. To prevent local failure of the FRP material at either end of the specimens, two additional layers of 100 mm in width were applied.

Test setup and instrumentation
Axial compression tests were conducted using a hydraulic jack with a capacity of 2700 kN (Fig. 1).
Specimens were instrumented in their mid-height region to determine their stres-strain behaviour. Lateral hoop strain was measured with four electric strain gauges glued to the FRP jacket on the centre of each face. The axial strain of specimens was measured with four linear variable displacement transducers (LVDTs) with a gauge length of 200 mm. Additionally, two strain gauges were arranged axially in the central section, on either of two adjacent faces, to check the LVDT readings. The load, strains and LVDT displacements were monitored using an electronic data acquisition system.

Failure mode
The strengthened specimens failed due to tensile rupture of the CFRP jacket near the corner, usually at the curvature changing position (Fig. 1). Until loading levels close to ultimate load were reached, no visible damage or deterioration was observed in the specimens. Just before the rupture, some small noises indicated fibre breakage, followed by sudden, explosive failure as tensile rupture of the jacket within the mid-height region occurred, accompanied by complete disintegration of the concrete in that area. Failure of one specimen (1.5_2_30b) was caused by debonding of the FRP overlap.

Stress vs strain behaviour and ultimate condition
The axial stress vs axial and lateral strain curves of test specimens are shown in Figs. 2, 3 and 4. The axial stress was obtained by dividing the axial load over the cross-sectional area. The axial strain was obtained from the average value of the four LVDT displacement measurements. The transverse In specimens 1_2_30 and 1_3_20, the values of axial and lateral strain were recorded, but there was an error in the reading of the load during the test, so stress-strain curves could not be obtained.
The experimental results are summarized in Table 2, indicating for each test: -The unconfined concrete strength (f co ) obtained for the cylinders that were cast at the same time as the prismatic specimens. -The maximum load or peak load (P max ).
-The type of stress-strain curve: ascending (A) or descending (D). -The peak axial strength (f cc ) or maximum axial stress of confined concrete at the peak of the stress-strain curve. In specimens with post-peak softening behaviour, both peak stress (f cc ) and ultimate stress at failure (f ccu ) are indicated. In specimens with monotonically bilinear ascending responses, both values match. -The ratio of peak axial strength to unconfined concrete strength, or strength enhancement ratio (f cc /f co ). This is based on the strength of the control concrete cylinders (f co ). -The ultimate axial strain (ε cc ), obtained from the mean value of the four side measurements. -The ultimate strain of the FRP in the hoop direction, usually called effective FRP strain (ε f,eff ). This is also obtained from the mean value of the four side measurements. -The relationship between effective FRP strain (ε f,eff ) and ultimate fibre strain obtained through standard tensile

Stress-strain behaviour
It is widely accepted that the stress-strain behaviour of FRPconfined concrete displays an approximately bilinear ascending response. The first branch of the curve is similar to that of plain concrete and the slope of the second branch depends on the stiffness and amount of FRP reinforcement. However, if the confinement level is low, the stress-strain response may have a descending branch and the compressive or peak axial strength is reached before FRP rupture (Fig. 5a). Available design oriented models are usually empirical, based on tests performed on "well-confined" concrete with monotonically ascending curves. Commonly, design guidelines define a minimum amount of FRP to ensure that the stress-strain response is of the ascending type, but consensus has currently not been reached regarding this issue (see Fig. 5b).
The experimental stress-strain curves shown in Figs. 2, 3 and 4 are described below and some considerations are made about the minimum confinement ratios proposed in the design recommendations.
Although all the specimens tested in this study exceeded the minimum confinement level described in Concrete Society TR55 [25] and ACI-440.2R-17 [26], a second descending branch was observed in some rectangular section specimens. In contrast, no rectangular specimens (not even those exhibiting an ascending curve) reached the minimum confinement ratio recommended in fib Bulletin 90 [24].

Square specimens
Bilinear ascending stress-strain responses were observed in the specimens with a square cross section (Fig. 2) except for specimen 1_1_20, whose curve shows an almost horizontal branch. Specimen 1_1_20 had an unconfined concrete strength of f co = 35.3 MPa and was wrapped with only one layer of CFRP, so its confinement ratio is quite low, below the minimum value that is recommended in CNR and fib guidelines. In all the other square specimens, the confinement ratio was greater than the minimum recommended value in all guides and their curves exhibit an upward behaviour, indicating increased resistance. The confinement ratio of specimens with an f co of 35 MPa, wrapped with two layers of CFRP, was below the value recommended in the CNR and fib guidelines. These specimens exhibited post-peak softening behaviour as the load was reduced, which continued until tensile rupture of the FRP jacket took place. However, for specimens with f co = 35 MPa and three layers of strengthening, the confinement ratio was greater and their ascending type stress-strain curves reveal the typical behaviour of well-confined concrete. In these "well-confined" specimens, confinement efficiency increased with larger corner radiuses. Specimens with f co equal to 27 MPa and two confining layers also exhibited an ascending behaviour, their confinement ratio being greater than the values recommended by most guides [25][26][27]. Figure 3b shows the curves for specimens with an aspect ratio (h/b) of 1.5 and a f co value of around 20 MPa. These specimens with low unconfined concrete strength were wrapped with one and two layers of FRP. The confinement ratio of specimens strengthened with one layer is low. The second branch of stress-strain curves is horizontal or slightly ascending. When increasing the confinement ratio by wrapping the specimens with three layers of FRP, a bilinear ascending behaviour was observed. In this case, the curves show no differences in specimens with divergent rounding radiuses. Figure 4 shows the stress-strain curves of rectangular specimens with an aspect ratio (h/b) of 2. These specimens were strengthened with three and four layers of FRP to achieve an adequate level of confinement. Though the confinement ratio was greater than the minimum value recommended in ACI-440.2R-17, CNR-DT200_R1 and Concrete Society TR55, the specimens did not exhibit the typical behaviour of well-confined concrete. The curves have a different shape: after reaching a resistance peak, a drop in resistance occurs, followed by recovery and an ascending curve section, but without reaching peak resistance. This behaviour can be considered typical of a lack of confinement effectiveness and has been shown in other works on confinement of high-strength concrete [9].

Rectangular specimens with an aspect ratio (h/b) of 2
Specimens with an unconfined concrete strength of around 30 MPa, confined with three and four plies, exhibited the stress-strain behaviour described above, although the strength enhancement ratio achieved with four plies is greater.
In the curves corresponding to specimens with low unconfined concrete strength (23 MPa approximately), a slight improvement in performance was observed as the rounding radius increased, specimen 2_30_3b being the only one with an ascending curve. Table 2 shows the strength enhancement ratio obtained in the tested specimens.

Strength enhancement ratio
In specimens 1_1_20, 1.5_2_20a and 1.5_2_30a, the improvement in resistance was marginal (3-5%). These are specimens with an unconfined concrete strength of 35.3 MPa and with a very small confinement ratio. In all the other specimens, significant increases in resistance were achieved.
The graph in Fig. 6 shows the strength enhancement ratio achieved in specimens with different numbers of layers and aspect ratios equal to 1, 1.5 and 2. To analyse the influence of these parameters, specimens with similar values of unconfined concrete strength (f co ) must be compared with each other, so the results are presented in the graph as a function of f co . It can be seen from the figure that the effectiveness of confinement in terms of strength improvement decreases with increasing aspect ratios.
In general, it is also observed that the degree of improvement in compressive strength increases with corner radius, as can be seen when comparing the results corresponding to groups of specimens with the same values of f co , aspect ratio, number of layers and different corner radius (Fig. 7).
Finally, it should be noted that in columns of low-strength concrete such as those tested in this work, significant   Fig. 7 Effect of corner radius on the strength enhancement ratio increases in strength can be obtained even with low confinement ratios. It is also noteworthy that in specimens with an aspect ratio (h/b) of 2, which in principle would have responded very unfavourably to confinement, significant increases in strength were obtained, although high levels of FRP reinforcement had to be applied to achieve the purpose. In practical applications, the need for such high amounts of FRP could limit the competitiveness of the strengthening technique.

Ultimate axial strain
As can be seen in the ε cc values given in Table 2, the increased concrete strain achieved in confinement conditions is very high (ε cc values between 1.2 and 3.7%). This was even observed in specimens with a very small confinement ratio, or in rectangular sections with a h/b of 2.
It should be mentioned that very high values of concrete strain must be avoided in practical applications, since even if the FRP jacket is far from breaking point, the concrete core will be highly cracked, making it impossible for the column to withstand transverse forces. With this in mind, some guidelines [25,26] recommend limiting the maximum value of concrete strain to 1%.
In addition, the effects of these high deformations of the FRP-confined columns on adjacent elements of the structure may have to be taken into account.

Effective strain in the FRP at failure
Regarding ultimate lateral strain, or FRP effective strain, values much lower than the ultimate tensile strain obtained using the tensile coupon test method were recorded in all specimens.
An accurate estimation of the FRP effective strain is needed to predict the compressive strength of FRP-confined columns, but there is no consensus among the current design guidelines on this issue. ACI-440.2R-17 proposes a strain efficiency factor (ε f,eff /ε f ) equal to 0.55, for both circular and rectangular sections, based on the average value reported by several researchers. CNR-DT200_R1 also does not distinguish between circular and rectangular sections and recommends an FRP effective strain equal to 0.004 to avoid excessive cracking on the concrete core. fib Bulletin 90 proposes a value of ε f,eff /ε f equal to 0.5 for circular sections and lower values, depending on the radius of the corners, for rectangular columns. The Concrete Society TR55 guideline also recommends lower values for ε f,eff /ε f in rectangular sections, depending in this case on the corner radius and the longest side of the section. Table 2 gives the registered FRP rupture strain and the corresponding strain efficiency factor (ε f,eff /ε f ) for each specimen, which ranges from 0.32 to 0.74, with an average value of 0.53. Figure 8 shows the average value of the strain efficiency factor as a function of the aspect ratio. The higher the crosssectional aspect ratio (h/b), the lower is the value of ε f,eff /ε f . The average value of ε f,eff /ε f was 0.64 in the square specimens, while in the rectangular specimens with an aspect ratio of 1.5 and 2 the average values obtained were 0.52 and 0.39, respectively.
The influence of corner radius is also represented in Fig. 8. Some studies have shown that fibre curvatures are one of the potential causes of small FRP failure strain values [17,18,43,44]. Figure 8 shows that the value of ε f,eff /ε f increases with corner radius in square specimens. However, this effect was not found in the rectangular specimens tested in the present study, which may be due to the softening behaviour exhibited by some of these specimens.

Comparison of test results with predictions of design guidelines
The experimental results of this study were compared with theoretical predictions calculated on the basis of the following design recommendations: fib bulletin 90, by the International Federation for Structural Concrete [24]; ACI-440.2R-17, by the American Concrete Institute [26]; CNR-DT200_R1, by the National Research Council of Italy [27]; Concrete Society TR55 [25] f ccd f c0 and Technical Report TR55, by the British Concrete Society [25]. Table 3 presents the equations provided for the calculation of compressive strength in confined concrete columns with a rectangular cross section. The symbols of the variables are those used in the respective guideline. The comparison between experimental confined concrete strength (f cc ) and the predictions made on the basis of the guidelines is shown in Table 4 and Fig. 9. Partial safety factors for materials have not been included in the calculation of the predictions. The guidelines provided by fib, ACI and CNR set a maximum side aspect ratio of 2. In cases where the aspect ratio is greater than 2 the formulations should be used with caution unless the effectiveness of confinement is experimentally demonstrated.
The Concrete Society TR55 guide restricts the use of the model to columns with and aspect ratio (h/b) ≤ 1.5. Despite this, specimens with a h/b of 2 have been included in Fig. 9 for comparative purposes. The guide also indicates that equations are only valid for cases in which the confinement has sufficient stiffness ( k ≥ 0.01∕k e ) to result in an increased capacity of strength to failure. All the tested specimens comply with this condition.
It should be noted that only 8 of the 30 specimens tested in the present work meet condition b (Table 3). These were the square specimens that had been strengthened with 2 and 3 plies of FRP, and one of the rectangular specimens (1.5_30_2b). In the remaining specimens, according to the fib 90 recommendation, no strength enhancement should be expected. As shown in Table 4, a considerable divergence between theoretical predictions and test results can be found in some specimens. Predictions determined using the reviewed guidelines also differ from one another, particularly in the case of specimens with rectangular sections. For specimens with aspect ratios (h/b) of 1 and 1.5, the predictions of the Concrete Society guide were the most congruent with test results. Results confirmed that, as indicated in the guide, it is appropriate to limit the use of this model to sections whose aspect ratio is less than or equal to 1.5. The model notably overestimated strength enhancement in the case of rectangular columns with a h/b of 2.
The CNR guide predictions were reasonably in line with values obtained for rectangular section specimens, but underestimated the resistance of square section specimens. In rectangular section specimens, the CNR formulation overestimated experimental resistance in cases in which no ascending stress-strain behaviour was observed. In this regard, it should be pointed out that the minimum confinement criterion proposed in the CNR guide was the most congruent with the ascending or descending shape of the experimental curves.
Predictions resulting from the ACI and the fib recommendations were more conservative. In the case of the ACI guide, experimental results for confined concrete strength were higher than the theoretical values in all tests except four. It should be noted that these four tests corresponded to specimens associated with a softening behaviour.  The fib predictions underestimated strength in all cases. According to the fib guide, an improvement in strength was not to be expected in the tested rectangular sections. However, strength enhancement ratios (f cc /f co ) of up to 1.81 and 1.36 were achieved for aspect ratios of 1.5 and 2 respectively. The minimum confinement ratio that the guide recommends, in order to achieve some degree of improvement in strength, is too conservative. In practice, meeting the minimum confinement ratio in rectangular sections would require an unfeasible number of FRP layers, both from the financial point of view and in terms of difficulty of application.

Predictive equation for axial compressive strength
The present paper proposes a new equation for the calculation of maximum strength of FRP-confined concrete f cc in square and rectangular columns. It is based on the Eq. (6.1) given in the design oriented model by Lam and Teng [33], which as described in the previous section is the reference used for two of the main calculation guidelines (ACI-440.2R-17 and fib Bulletin 90): where f lef f f co is the effective confinement ratio; k s the shape factor of the cross section and 3 is a constant value derived from experimental and regression analysis which was equal to 3.3 in Lam and Teng [33]. Equation (6.2) is used in this work for the calculation of effective confinement pressure and Eq. (6.3) for calculation of FRP effective strain.
where D eq is the equivalent diameter equal to √ h 2 + b 2 in Lam and Teng's model [33]; eff is the FRP effective strain; fu is the ultimate FRP jacket strain and k is the strain efficiency factor.

Strain efficiency factor
Lam and Teng's model assumed that k was a constant value equal to 0.586 for all cross sections, which is the average derived from extensive experimental work.
Nevertheless, for square and rectangular columns, smallscale tests in the literature have determined that k varies depending on geometrical factors that influence confinement 3) ef f = fu k , effectiveness, such as the corner radius ratio ( 2R c b ) [18,27,42] and the side ratio h b . However, intermediate-sized rectangular column data that can be used to quantify these parameters are scarce.
Based on the analysis of the 30 tests results included in Fig. 10, the present study shows the strain efficiency factor of FRP for square and rectangular sections to be a function of: side ratio h b ; corner radius ratio as and geometric reinforcement ratio f .
Then the proposed strain efficiency factor (k * ) is given by Eq. (6.4): where the constant 1 isequalto0.46 ; 2 isequalto0.32 and f is the geometric reinforcement ratio calculated as The maximum recommended value for k * is limited to 0.7.

Shape factor
The proposed shape factor ( k * s ) is given by Eq. (6.5).
The value of k * s depends on two parameters: the effective confinement area ratio  area adopted by Refs. [33], which is contained by four parabolas whose initial slopes are the same adjacent diagonal lines.
As the side ratio increases, the compressive strength decreases. This observation is confirmed by the analysis in Fig. 11, illustrating the results obtained from the relationship between strength enhancement f cc f co and shape factor k * s . By using the factors proposed above, k * and k * s , the equation for the calculation of f cc is shown in Eq. (6.6), where new value of 3 , derived from the regression analysis of the 30 tests results, is equal to 5.75. When R c is zero then f cc f co will be equal to 1.

Conclusions
The present study describes the results of an investigation on the behaviour of FRP-confined concrete in axially loaded columns with square and rectangular cross sections. The study examined low-and medium-strength concrete (between 20 and 35 MPa) and its conclusions cannot be extrapolated to high-strength concrete without further verification.
The following conclusions are drawn from the study.
(1) FRP confinement efficiency decreases as the aspect ratio of the rectangular section increases. In the experimental study, specimens with three CFRP plies and f co = 34.4 MPa reached an average strength enhance- It was also observed that improvement in compressive strength increased with corner radius. (2) Despite this, in rectangular sections with an aspect ratio (h/b) of 1.5, and even 2, significant improvements in concrete properties, especially for low-strength concrete, can be obtained by increasing the amount of FRP reinforcement. Strength enhancement ratios (f cc /f co ) of up to 1.81 and 1.36 were achieved in the experimental study for aspect ratios of 1.5 and 2, respectively. (3) The recommended values obtained by the design guides do not have a good fit, in general, with the ultimate FRP strain achieved in the tests. This parameter is crucial for predicting the compressive strength of the retrofitted column.
In the experimental study, the value of the strain efficiency factor (ε f,eff /ε f ) was found to decrease with an increase in cross-sectional aspect ratios. In the square specimens, an average ε f,eff /ε f value of 0.64 was obtained, while in the rectangular specimens with aspect ratios of 1.5 and 2 the average value was 0.52 and 0.39, respectively. (4) Regarding the minimum confinement ratio, a poor congruency was observed between the criteria described in the design guidelines and the shape of experimental curves, except in the case of CNR recommendations.
The fib bulletin proposal about the minimum confinement criterion resulted too conservative, a review of this criterion is deemed advisable. This area, which has not received adequate attention so far, is important, since existing models are usually based on the assumption of hardening behaviour. (5) The confined concrete strength values resulting from the rectangular tests were compared with predictions based on the four international guidelines. Such comparisons reveal that considerable differences exist between them. The predictions from the Concrete Society TR55 were the most congruent with the test results for specimens with aspect ratios (h/b) of 1 and 1.5. The fib bulletin proposal is the most conservative, underestimating the FRP confinement for rectangular concrete columns. (6) With a view to improving the estimation of the bearing capacity of FRP-confined rectangular columns, a new predictive equation is proposed, based on Lam and Teng's model [33]. Strain efficiency factor and shape factor are critically examined in the context of the experimental programme's results, leading to a more refined formulation for these factors in rectangular columns (Eqs. 6.4 and 6.5).