2.1 Calculation method

Axial load and bending moments are predominant in the normal concrete columns. They are called normal loads since they induce normal stress (tensile and compression) to the column´s transversal section, with maximum rates at the surface of the columns. The situation is common and, as a rule, it occurs due to the stiffness of the connection or to the eccentricity of the vertical forces caused by the imperfections of the constructions. Frequently, the columns of buildings are affected by eccentric activities, so that an initial eccentricity (e) should be taken into account for the designing of the column. The columns of buildings generally undergo uniaxial or biaxial compression due to connections between beams and columns, and to the position of them with regard to the main axes of the columns´ transversal section.

The Interaction Diagram Method was employed to calculate the uniaxial compression strength, following recommendations by ^{Wight & Macgregor (2009)} and the prescriptions and simplifications of ACI 318 (^{ACI, 2008}), coupled to parameters of NBR 6118 (^{ABNT, 2014}). As an example of the calculation methodology, Figure 1 shows a uniaxial compression transversal section in which two layers of longitudinal reinforced concrete are compressed, whilst the lower layer in the transversal section A_s3 is tensioned, where F_s1, F_s2 and F_s3 are the force in each steel layer, and F_c is the compressive force in concrete. The deformation limits adopted takes into account a concrete crushing at 3.5‰ and a steel yielding at 2.62‰ (ε_s3, experimentally obtained) for all the reinforcement bars.

Figure 1 Stress, strain and resultant forces in the transversal section of the column. 

Equation 1 determines maximum compression load applied to the column; Equation 2 determines the bending strength, taking into consideration a uniaxial compression, where: f_c is compressive strength; x is the neutral line; b is the section width; ε is the material strain; E is the modulus of elasticity of steel; A_s is the steel area; h is the section height; F is the force in the layer; d is the effective depth.

When deformation limits are established, the interaction diagram may be performed, as Figure 2 shows, where: M is the bending moment; P is the axial load. Figure 2 shows possible interactions and action plane of bending moments (M_x and M_y) and axial load (P), coupled to a simplification so that the bending moment may be considered only at the main direction (M_x), like studied in this current work.

Figure 2 Interaction diagram for biaxially and uniaxially loaded sections (^{Macgregor, 1996}). 

^{Adorno (2004)} developed a research of rectangular reinforced concrete columns submitted to uniaxial compression, in order to prove the calculation method developed by ^{Mello (2003)}. The concrete presented average 40 MPa compressive strength and the experimental program was composed of 12 specimens, divided into two series: PSA and PCA. The PSA series consisted of four columns and the PCA was composed of eight columns. All of them had a rectangular cross section of (250 × 120) mm², subjected to axial load plus uniaxial bending. The bar spacing, and the minimum concrete cover followed the recommendations of NBR 6118 (2007).

By analyzing the ultimate loads, it is possible to observe that the PSA columns crushed with a higher load than the PCA series, due to the increased compressive strength. According to ^{Adorno (2004)}, the initial eccentricity variation had poor influence on the critical tensile stress which was evidenced by the advanced cracking stage. The author concluded that the models tested kept the proportionality between the longitudinal deformation and the distance from the neutral axis to the rupture, confirming the validity of the Bernoulli’s principle, that the plane sections before bending remain plane after bending, which validates the model used in the present research.

^{Melo (2009)} developed an experimental and numerical study of the behavior of hinged reinforced concrete (40 MPa) columns submitted to axial load plus uniaxial moment. In order to continue the research developed by ^{Adorno (2004)}, columns with the same cross section and longitudinal reinforcement rate (1.57%) were used. The experimental program composed 24 columns divided into three series according to its length, where the main variable was the uniaxial eccentricity. The columns had a cross section of (250 x 120) mm² and bar spacing and minimum concrete cover according to NBR 6118 (^{ABNT, 2007}) recommendations.

The experimental results showed a proper functioning of the test system, which validates the methodological procedures applied in this present research, with columns failure occurring at half height, as expected. Also, the main variable of the tests performed was the uniaxial eccentricity, what shows great influence on the columns ultimate load. A nonlinear response of the bending strength was observed as a function of the slenderness and eccentricity of the force application in the columns. ^{Melo (2009)} verified that the conservatism of the ultimate force predictions methods increases as the uniaxial eccentricity is reduced.

3.1 General characteristics

Six partially jacketed concrete columns were analyzed and submitted to axial load plus uniaxial bending. All columns were monitored by electrical resistance strain gauges (extensometers), placed longitudinally to the column to register concrete and steel’s deformation. Digital comparative monitors were employed to obtain displacements. Variables comprised the position of partial jacketing and the presence or absence of a cement-sand mortar coating. Transversal section, longitudinal reinforcement rate, compression strength, and positioning of extensometers used in the tests setup, were constant for all columns.

The eccentricity of axial load was 100 mm when compared to the longitudinal axis of the column´s span. The columns were divided into two groups: a group of columns strengthened in the compression zone (PCR, PCS and PCSR) and another group of columns strengthened in the tensile zone (PTR, PTS and PTSR). A control column was cast in each group, one simulating the column strengthening without the removal of the mortar coating of the original section and the other with the complete removal. Control columns featured a transversal section of (200 × 200) mm² and total length of 1.600 mm, with slenderness index of approximately 28. Strengthened columns had an initial section of (120 × 200) mm² and total length of 1.600 mm, with 80 mm of strengthening layer. After the retrofit, the columns showed a final transversal section identical to that of the reference columns. Figure 3 demonstrates the columns´ size, and the concrete corbel made to prevent premature concrete cracking in the strengthened specimens.

Figure 3 Sizes of columns. 

3.2 Reinforcement

Representing conventional situation, the longitudinal reinforcement of reference columns featured 6 Ø 10.0 mm (A_s = 4.71 mm²), with stirrups measuring Ø 5.0 mm spaced at every 100 mm at the center, and Ø 5.0 mm for every 50 mm at the edges. Further, additional open stirrups were employed with epoxy adhesive, measuring Ø 5.0 mm for every 100 mm, later fixed in the hardened concrete to help in adherence between new and old concrete. Initial reinforcement of all columns measured 4 Ø 10.0 mm (A_s= 314 mm²), with two longitudinal bars added for reinforcement, meeting the number of bars used in the reference columns without any reinforcement, or rather, 6 Ø 10.0 mm (A_s = 4.71 mm²). Transversal reinforcement were of the same specification as that in the reference columns (Figure 4).

Figure 4 Reinforcement of columns. 

3.3 Instrumentation

3.3.1 Concrete

For reinforcement at the tensile and compression region of the columns, the transversal reinforcement (open stirrups) was fixed into the hardened concrete with an epoxy-based structural adhesive in 60 mm-deep holes. It comprised Ø 5.0 mm stirrups every 100 mm, simulating procedures in civil work. Posterior to the fixing of open stirrups (Figure 5), extensometers were placed on the concrete. A cement-sand mortar coating was applied to the PTSR and PCSR columns prior to the installation of the open stirrups. Another extensometer was placed on the coating surface. Longitudinal reinforcements (2 Ø 10.0 mm) were positioned to complete the positioning of the reinforcement by placing the wooden moldings and for the casting of concrete. The instrumentation of the concrete surface was finalized by placing an extensometer on the strengthening layer.

Figure 5 Extensometers installed in the concrete (PTS; PTSR; PCS; PCSR respectively). 

3.3.2 Reinforcements

Electrical resistance strain gauges were used on concrete and reinforcement bars to monitor deformations during the tests. Figure 6 shows the positioning of sensors in the columns PTR, PTS and PTSR and Figure 7 displays the placement of sensors in columns PCR, PCS and PCSR. Extensometers were positioned half way the columns´ length.

Figure 6 Extensometers on the rebar and concrete of the tensile zone strengthened columns. 

Figure 7 Extensometers on the rebar and concrete of the compression zone strengthened columns. 

3.4 Test system

Figure 8 details the test setup used in the experimental analysis of the columns. The system comprised a highly rigid metallic frame fixed to the reaction slab, a 2000 kN hydraulic jack driven by a hydraulic pump for loading, and a 2000 kN load cell with a 0.5 kN precision, locked to a digital indicator for load recording. Columns were coupled in pinned supports, simulating hinges placed eccentrically to the columns´ axis and thus making viable the expected uniaxial compression. Extensometers were read by a computer-connected data logger, for sensors installed in the rebars and for those fixed on the concrete surface.

Figure 8 Testing setup system. 

4.1 Steel and concrete

The columns were pour simultaneously. Column was reinforced after 28 days of cement-sand mortar coating. Three cylindrical specimens were casted at each concreting stage and tested according to NBR 5739 (^{ABNT, 2007}), with compressive strength (f_c) 7.0 MPa and 32.0 MPa respectively for coating mortar and concrete. Concrete modulus (E_cs) was equivalent to 28.1 GPa. In the case of the steel bars, tests were performed following NBR 8522 (^{ABNT, 2008}). Results for yielding stress (f_ys) and modulus (E_s) were 662.0 MPa and 218.4 GPa for 5.0 mm diameter bars and 548.1 MPa and 209.2 GPa for 10.0 mm diameter bars, respectively.

4.2 Loads and failure modes

Control columns PTR (reference tensile strengthened column) and PCR (reference compressive strengthened column) revealed the concrete´s fragile failure in the compression zone near the middle span. PCR also showed failure close to edge, in the compression zone. Reinforced columns also revealed different failure modes, even though they demonstrated a monolithic behavior during tests immediately before failure. PTS reinforced column behaved monolithically immediately before failure, even though, on this occasion, the loosening of reinforcement occurred at the zone close to the upper end. A similar behavior has been registered for the mortar cover of column PTSR. PCS column, reinforced at the compression zone, revealed monolithic behavior up to column failure, without any loss or crack at the strengthening layer or the concrete interface.

The crushing of the concrete at the zone close to the edge occurred. PCRS column showed cracking pattern on the surface between reinforcement and substrate immediately prior to failure.

Table 1 displays failure loads, maximum tensile strain of the steel (ε_s) and maximum compression strain of the concrete (ε_c), the ultimate axial load (N_u), and the comparison between ultimate load and the load prediction (N_Ref) for PTR and PCR columns, and the columns´ failure modes. Failure modes were defined taking into account deformation and failure characteristics, observed experimentally. Control column PTR failed at 340 kN axial load, revealing steel deformations higher than yield (ε_s≥ε_ys=2.62‰). Reference column PCR crushed at 400 kN axial load, corresponding to approximately 120% of last load provided by column PTR. Tensile strengthened columns PTS and PTSR presented failure by detachment of strengthening layer. Further, compression-reinforced columns PCS and PCSR were failed at the tensile zone with steel yielding and crushing of concrete at the compression zone, no signs of detachment were registered.