Test specimens were formed by a central part with a length of 600 mm and a square section of 150×150 mm² and two 400×400×140 mm³ heads on the ends (Figure 1). The heads simulated the connection with the top and bottom floor slabs or foundations, and served to prevent premature failure at the extremes of specimen. The cross-section of the column had rounded corners with a 25 mm radius of curvature.

The value of the concrete compressive strength was obtained by testing at 28 days after casting cylindrical normalized specimens (150 mm diameter and 300 mm height) for each series (5 series). The longitudinal reinforcement was made up of four 6 mm diameter steel bars, and 6 mm diameter stirrups were spaced at 100 mm. The yield stress of the steel reinforcement was 500 N/mm².

Each series consisted of two specimens cast with the same concrete: one specimen was strengthened with two layers of glass fibre and the other one with a layer of carbon fibre. The FRP was applied by the hand lay-up technique which is the most common strengthening method. After removing the dust and dirt from the surface of the specimen, a layer of epoxy resin was placed on the specimen, then the fibre was wrapped around it with a length of 100 mm overlap and finally another layer of resin epoxy was applied. Fibres were placed perpendicularly to the axis of the column, in what is called a 0° orientation. Table 1 shows the fibres mechanical properties according to the manufacturer technical data sheets, and the FRP properties obtained by means of tensile testing of flat coupons according to (24).

Thereafter the specimens were named as follows: a letter indicating the type of jacket (C for carbon and G for glass) followed by a number from 1 to 5 indicating the series number, with series 1 with the lowest strength (f_co=8.8 MPa) and series 5 the larger one (f_co=17.5 MPa).

The specimens were tested with centred compression load in a 1000 kN capacity INSTRON press. The specimens were placed in the press with a thin layer of plaster applied to both ends (between the lower end and the base of the press and between the upper end and the load application plate) for the purpose of levelling the specimen and eliminating irregularities at the end surfaces.

The load was applied on a 150×150×20 mm³ steel plate centred on the head of the jack coinciding with the section of the column. The test was carried out in displacement controlled way until failure.

To measure the axial deformation of the column four linear transducers (LVDT) with a 5 mm range and 0.001 mm precision were used. The transducers were placed between the heads of the column, 160 mm away from its axis, centred to each face (Figure 2).

To measure the transverse strain, electrical strain gauges were glued onto the FRP jacket at half the height of the specimen. Four strain gauges were used centred at each face, perpendicularly to the column axis, that is, in the fibre direction.

The measurements of the transducers, strain gauges, and the applied load were continuously recorded during the tests. In series 1 and 3 lateral deformation was not measured, and also in specimen C1 one error occurred and the axial strain was not recorded.

The results are summarized in Table 2. Indicated for each specimen is: the unconfined concrete strength obtained from cylindrical standard samples (f_co), the ultimate axial stress (f_cc), the relationship between these two magnitudes (f_cc/f_co), the ultimate axial (ε_cc) and lateral (ε_l) strain and the relationship between this last and the ultimate deformation obtained in the tensile coupon test (ε_l/ε_j).

The ultimate concrete axial stress was calculated by subtracting the contribution of the longitudinal reinforcement (area of the four bars multiplied by their yielding stress) from the ultimate load, and dividing the result by the area of the net concrete cross-section. The values of the ultimate axial and transverse strains were obtained as the mean value of the readings of the four transducers or four gauges, respectively, located in the midsection of the specimen. Positive values indicate compressive strain and negative values tension.

Shown for each specimen in Figure 3 are the axial stress vs. average longitudinal and lateral strain curves obtained as average readings of displacement transducers and strain gauges respectively. During the loading of specimen C4, the test had to be stopped, and the specimen was unloaded and reloaded again. Only the second part of the test is shown in the figure.

The failure of the specimens was caused in all cases by the jacket rupture, usually near a corner (Figure 4). The failure occurred suddenly, although previously some warning signals such as noise and “wrinkles” in the jacket were noted. These wrinkles were more visible on glass jackets (where can be appreciated whiter areas indicating debonding of the jacket).

The test results (Table 2) show that confinement with FRP significantly improves the axial load capacity and ductility in all specimens.

The lower the unconfined concrete strength (f_co), the greater the strength enhancement ratio (f_cc/f_co). It also increases with the stiffness of the jacket (it is higher for carbon fibre strengthening than for glass fibre). The value of the ratio f_cc/f_co obtained in the test varies between 1.40 for the concrete strength of 17 MPa confined with glass fibres and 2.53 for the 8.8 MPa concrete strength confined with carbon.

In Figure 3 it can be seen that the axial and lateral stress-strain curves obtained in all the tests have a very similar pattern, approximately a bilinear form, as predicted by the models, with a smooth transition zone. In the first part of the curve, behaviour is very similar to what unconfined concrete would have. In this part, with axial stress below the unconfined concrete strength, the lateral expansion of the concrete core is small and not enough to put the fibre strengthening in tension. In the second part of the curves, with the concrete already cracked, the confinement due to the FRP jacket significantly influences the behaviour of the specimens. In all cases, the second branch is also upward, reaching the maximum load and deflection at the time of failure. It is observed that the slope of the second branch is approximately equal in all specimens confined with glass, and equally in those with carbon.

The strains measured on the fibres at the time of rupture are significantly lower than the ultimate strains obtained by standard tensile testing of FRP flat coupons. This fact is shown in most of the published experimental studies (11, 25–26) and may be related to the triaxial stress state on jackets, the curvature of the fibres and also to local stress concentrations in the fibres caused by the cracked concrete. Several design guidelines and authors have proposed introducing a coefficient of efficiency applied to the ultimate strain to account for this fact, although there is no unanimity in the proposed value.

The value of the ultimate lateral strains shown in Table 2 is the average value measured at the four faces, which corresponds to the last point of the stress-strain curves of Figure 3. The relationship between this value and the ultimate strain obtained in tensile tests on coupons ranges approximately between 14 and 37%, with a mean value of 29%. However, it is difficult to propose a coefficient of efficiency of the ultimate strain that would apply generally, due to the fact that if we observe the measured strains for each gauge just before the failure, some gauges reach values well above these mean values, and besides, the number of tests is small.

As mentioned before, all the specimens failed in a similar manner due to the rupture of the jackets. There has been no failure due to debonding in the jacket overlap. The overlap length of 100 mm is sufficient for the size of the specimens.

In fib Bulletin 14 Spoelstra & Monti's model is proposed as the most versatile despite its operational complexity. It is an analytical model which combines the Mander's model (27), for concrete confined with steel, with a model expressing the lateral strain as a function of the axial strain, to take into account the specific behaviour of FRP. The complete stress-strain curve may be considered as formed by the points of a curve crossing a family of Mander's curves, each one belonging to the pressure level corresponding to the lateral confinement strain at each moment, while the ultimate stress and strain can be obtained from the confining pressure exerted by the jacket at the ultimate load.

The model considers that the ultimate axial strain occurs when the lateral strain of the concrete reaches the value of the ultimate strain of the FRP (subjected to a multiaxial state of stress) and the jacket fails. It gives no indication as to how to obtain the value of the ultimate strain. In this comparison we have calculated this strain using a strain efficiency factor k_ε=0.6, i.e., expressed as the ratio of the jacket ultimate hoop strain to the failure strain determined according to flat coupon tensile tests. This value of k_ε was chosen because it is approximately equal to that obtained by several authors from analysis of tests from the literature (11, 28).

Regarding the influence of the shape of the cross-section, we have calculated this by introducing two different form factors into the model:

Table 3 shows the experimental and theoretical values of f_cc/f_co and ε_cc for both values of α_e.

When considering α_e=0.695, the strength in all specimens is overestimated, with an average error of 40.8% in f_cc/f_co and 86.9% in ε_cc. The best estimates of strength and strain are achieved with α_e=0.333, where the absolute error is 8.3% in the strength and 52.6% in the axial strain.

Figure 6 shows the axial stress versus axial and transverse strain curves obtained experimentally in two specimens of the series 2 compared with those obtained by the iterative procedure given by Spoelstra & Monti with the two values of α_e: α_e=0.695 and α_e=0.333. It is observed that the model reproduces well the shape of the experimental curves, and the slope of the second branch, while overestimating the ultimate strength and strain when adopting α_e=0.695, and fits much better adopting α_e=0.333. The graphs for other specimens show a very similar pattern and are not included.

Lam and Teng (23) proposed a model for rectangular sections derived from the model by the same authors for circular sections (11), based on an extensive database obtained from experimental results in the literature. In the model the stress-strain curve is formed by a first parabolic and a second linear branch.

The ultimate strength and strain of concrete for rectangular cross-sections is calculated by the following equations [1] [2]: 1 f c c = f c o + 3.3 k s 1 f 1 2 ε c c ε c o = 1.75 + 12 k s 2 f 1 f 2 ( ε j u ε c o ) 0.45

In these equations f_l is the maximum confining pressure given by the FRP jacket to an equivalent circular column with a diameter equal to the length of the diagonal of the rectangular section. In calculating the values of the ultimate FRP effective strain to be used in the jacket, from the analysis of experimental results from the literature, Lam and Teng proposed a value of k_ε=0.586 for carbon and k_ε=0.624 for glass fibres, while indicating the large observed dispersion.

k_s1 and k_s2 are the two shape factors that depend on the relationship between the dimensions of the sides of the section and the effectively confined area ratio, whereas this model considers the area bounded by the parabolas intersecting the sides of the rectangle parallel to the slope of the diagonal section. For the particular case of square sections, k_s1 and k_s2 have the same value and also match the factor α_e proposed in fib Bulletin 14. In the specimens tested k_s1=k_s2=0.695.

Table 4 shows the experimental values of f_cc/f_co and ε_cc compared with the theoretical ones according to this model, considering an effective strain coefficient k_ε=0.6. The error in estimating the compressive strength ranges between −3% and +29%, with a mean error of +12.2%. The ultimate theoretical strain is lower than the experimental strain in all cases with an average error of −35.3%.

The use of a form factor α_e=k_s1=k_s2=0.333 leads to larger errors underestimating the resistance with an average error of −19%.

Figure 7 shows the stress-strain curves recorded in the tests for specimens of series 2 and 3, and the theoretical curves according to the model. The model gives a good prediction for the strength, but the predicted slope of the second branch is greater than the experimental slope and thus the ultimate axial strain is underestimated.