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Experimental investigation on rectangular RC columns strengthened with CFRP composites under axial load and biaxial bending
Composite Structures 108 (2014) 538–546
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Experimental investigation on rectangular RC columns strengthened with CFRP composites under axial load and biaxial bending Alireza Rahai ⇑, Hamed Akbarpour Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Available online 19 September 2013 Keywords: Biaxial bending Rectangular RC columns Carbon fiber-reinforced polymer Strength Ductility
a b s t r a c t This paper presents the results of an experimental study on rectangular RC columns strengthened with carbon fiber-reinforced polymer (CFRP) composites under axial load and biaxial bending moment. A total of 8 large-scale RC columns with rectangular cross-section were cast and tested under bi-eccentric compressive loading up to failure. In this investigation, several parameters like CFRP thickness of one, two, three, and four layers, fiber orientations of ±45°, 0°, 90° and their combination, and eccentricities in the direction of both weak and main axis were studied. The effects of these parameters on the moment–curvature relationship, and load–longitudinal displacement relationship were investigated. In general, increasing longitudinal layers rather than transverse layers led to a greater load carrying and displacement capacity of the specimens, because of the overall behavior of RC wall-like columns. The results of these experimental and numerical studies showed a great improvement on the strength and ductility of confined RC columns. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, using fiber-reinforced polymer (FRP composites) has gained considerable attention in retrofitting and strengthening of reinforced concrete columns. FRP jacketing is effective with respect to strength, less stiffness and weight in comparison with steel, high ductility, resistance to corrosion, and low installation cost and repair. In this regard, FRP jackets obtained a great point in the field of civil engineering to significantly increase the compressive strength and ductility of RC columns [1–5]. To the best of the writer’s knowledge, a comprehensive study shows that the load carrying capacity of the wrapped RC columns is governed by the major influencing parameters such as the concrete compressive strength, the aspect ratio of the cross-sectional area of the specimens, the number of wrap layers, modulus and Poisson’s ratio of the wrapping sheet, fiber orientation, longitudinal steel reinforcement ratio and their orientation, and the type of loading [6–12]. Chaallal et al. [13] presented a confinement model describing the behavior of rectangular concrete columns retrofitted with FRP sheets and subjected to axial loading. This model was based on the findings of experimental studies including the testing of rectangular columns with three cross-section aspect ratio and five different numbers of FRP layers. The results of their investigation ⇑ Corresponding author. Postal Address: Hafez Ave., 15875-4413 Tehran, Iran. Tel.: +98 21 64542220. E-mail address: [email protected] (A. Rahai). 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.09.015
showed that as the cross-section aspect ratio increased, the effectiveness of FRP composites decreased. Also, they found that the stiffness of the FRP jacket is an important parameter in strengthening problems, and it is related to the number of layers, modulus and Poisson’s ratio of the wrapping jacket. Li and Hadi [14] conducted a parametric study using FEA software ANSYS. They studied the effect of FRP thickness, stiffness and fiber orientation on the strength and stiffness of the columns. They justified the analysis using experimental results that agreed reasonably with the FEA. Both results showed that mechanical parameters of the FRP jacket have a key role on the behavior of columns after reaching the unconfined concrete strength. Some researchers conducted experimental studies to investigate the effect of loading type on the load carrying capacity and ductility of wrapped RC columns. The derivation of these studies showed that the effectiveness of FRP confinement to develop the structural performance of RC columns was influenced by the load eccentricity. Increasing the eccentricity decreased the effectiveness of FRP jackets in improving the behavior of eccentrically loaded RC columns than concentrically loaded columns [15,16]. The amount and orientation of steel reinforcements influenced the flexural strength capacity of eccentrically loaded RC columns. As the longitudinal steel ratio increased, the flexural strength capacity of columns increased. Also, the compressive strength of concrete had a great effect on the effectiveness of FRP confinement and experimental studies showed that the confinement effect of the FRP jacket on the performance of low strength RC columns was more than high strength confined RC columns [17,18].
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Nomenclature ex ey f c hx hy Mx My P
eccentricity along the main axis eccentricity along the weak axis compressive strength of the concrete height of the cross-section along the weak axis, i.e. 450 mm height of the cross-section along the main axis, i.e. 150 mm bending moment about the main axis bending moment about the weak axis axial compressive load
Generally, columns are the most important part of buildings, bridges and berthing structures. These columns are usually loaded by bending moments about both principal axes. Many researchers investigated the performance of unconfined RC columns under biaxial bending moment. Short reinforced concrete columns subjected to biaxial bending have received considerable attention. As a result, there are several empirical and approximate methods, such as the Bresler method [19], available for the strength design of short columns. A few studies have also emerged for the analysis of slender reinforced concrete columns subjected to biaxial bending. On the contrary, little attention was given to the prediction of load carrying capacity and ductility of FRP-confined RC columns in the literatures [18,20,21]. Monti and Alessandri [22] presented a model for determining the flexural strength capacity and ductility of unconfined and confined RC columns under biaxial bending. This model was based on the Bresler method [19] and calculated the section capacity at the ultimate condition. The model’s results were in good agreement with the exact solution. Youcef et al. [23] investigated the behavior of CFRP-confined square RC columns under biaxial bending. They conducted an experimental study through casting and strengthening RC columns with the square cross-section (i.e., 76 mm 76 mm). All columns were wrapped with one to three FRP layers and the results showed that increasing the layers number led to improvement of the deformation capacity and section curvatures. Punurai et al. [24] prepared some specimens similar to Youcef’s experimental work with differences in both the longitudinal steel ratio and CFRP layers number. They showed that as these parameters increased, the overall flexural behavior of the strengthened specimens was improved. This paper presents the behavior of rectangular RC columns under biaxial bending (i.e., the bi-eccentric compressive loading). In this regard, a total of eight large-scale rectangular RC columns with the height to width ratio of 3:1 were built and tested up to failure. Various parameters such as the CFRP thickness, fiber orientation, and eccentricities were investigated. The results showed that strengthening RC columns with CFRP composites improved the load carrying capacity and the ultimate deformation.
ULon ULatx ULaty eLtop eLbottom
ux uy
longitudinal displacement lateral displacement at the midheight section along the weak axis lateral displacement at the midheight section along the main axis longitudinal strain of the tension face longitudinal strain of the compression face curvature about the main axis curvature about the weak axis
In this paper, some parameters such as the CFRP thickness, fiber orientation and the eccentricities were considered as variables. The different CFRP thickness as 0.5, 1, 1.5 and 2 mm (1–4 layers respectively) and the fiber orientations as the combination of 0° and 90° were investigated. 90° referred to the orientation of fibers along the column axis and 0° referred to the orientation of fibers perpendicular to the column axis. For this reason, six fiber orientation as (0°), (90°), (90°/0°), (90°/90°/0°), (0°/0°/0°/0°) and (45°/45°) were investigated. The test program and column properties are summarized in Table 1. All columns were divided into two different groups. The first group labeled ‘‘S’’ included strengthened columns and another group labeled ‘‘U’’ as an unstrengthened column served as a control column. Six columns were strengthened with four CFRP layers: 90° as the longitudinal layer, 0° as the transverse layer, and the combination of 45° and 45° as the diagonal layers with respect to an axis perpendicular to the column axis. Eccentricities both in X, and Y directions were changed from 70 to 75 mm, and 225 to 300 mm respectively and were constant during the tests. 2.2. Material properties All columns were cast from one batch of concrete. A concrete with an average compressive strength of f c ¼ 35 MPa and a slump of 80 mm was used in this study. The longitudinal steel reinforcements were 6u12 mm with yield and ultimate strengths of 375 and 580, respectively. The transverse reinforcement was provided with rectangular ties of u6@150 mm. The yield and ultimate strength of the transverse reinforcement were 215 and 326, respectively. The reinforcement details for the columns were depicted in Fig. 1. It is noted that extra reinforcement was provided in each bracket in order to prevent local failure. Unidirectional carbon fiber-reinforcement sheets (CFRP) were used and adopted with the resin epoxy. According to the data sheet provided by tension testing on CFRP coupons, a cured CFRP composite sheet has a thickness of 0.5 mm, a tensile strength of 336 MPa, and an ultimate elongation of 0.93%. Mechanical properties of the CFRP were shown in Table 2. 2.3. Specimen preparation and test setup
2. Experimental program 2.1. Specimens layout A total of 8 large-scale RC columns with the rectangular crosssection (150 mm 450 mm) were built and tested under axial load and biaxial bending up to failure. The test portion of each column had a height of 1500 mm. Two brackets with a height of 400 mm were designed for each head. To avoid stress concentration and make the use of CFRP easier, each corner was chamfered to a radius of 15 mm. Fig. 1 shows the geometry of the columns.
The concrete was cast in one batch and after a 28-day humid condition curing, the surface of specimens were cleaned and prepared for strengthening. The CFRP fibers were saturated with epoxy resin and applied to the surface. The resin content must be sufficient to ensure that enough bonds between the CFRP sheet and concrete surface were developed. In order to prevent anchorage rupture in the transverse layer, a 100 mm overlap was considered in the fiber direction. The load was applied on specimens by means of a 1000 KN nominal load capacity hydraulic jack. Both end supports were designed as hinged condition to apply the
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Section B-B
Section A-A
Fig. 1. Geometry and reinforcement detailing of columns (units in mm).
Table 1 Specimens design layouts. Specimens
Strengthening
Number of layers
Fiber orientation
Eccentricity Y-direction (mm)
Eccentricity X-direction (mm)
U-225-75 U-300-70 S-225-75-L S-225-75-T S-225-75-LT S-300-70-LLT S-300-70-TTTT S-300-70-DD0
Unstrengthened Unstrengthened Strengthened Strengthened Strengthened Strengthened Strengthened Strengthened
– – 1 1 2 3 4 2
– – 90° 0° 90°/0° 90°/90°/0° 0°/0°/0°/0° 45°/45°
225 300 225 225 225 300 300 300
75 70 75 75 75 70 70 70
Table 2 Mechanical properties of the CFRP coupon. Test direction
Ultimate strength (MPa)
Initial modulus (MPa)
Ultimate strain (mm/m)
CFRP thickness (mm/layer)
Dry thickness (mm/layer)
Fiber direction Matrix direction
336 32
39,944 2338
9.3 9
0.5 0.5
0.166 0.166
incremental load in the predefined eccentricity. Two end supports consisted of a rectangular steel frame (350 mm 700 mm) from an angle section member and a roller welded to the frame. The lateral deflection in the direction of each principal axis was measured using 4 Linear Variable Displacement Transducers (LVDTs). The longitudinal and transverse strains were measured by 40 foil strain gauges for each specimen. The specimens were tested under axial load and biaxial bending up to failure. All strains, displacements, and loads were saved by a computer program. Figs. 2–4 showed the test setup and the schematic arrangement of LVDTs and strain gauges, respectively.
3. Experimental results and discussions 3.1. Overall behavior The overall behavior of unstrengthened columns was similar. Specimens failed suddenly by crushing at the load point and producing tensile cracks on the tension side. Tensile cracks were propagated along two adjacent sides with an increase of compressive loading simultaneously with producing and progressing a pyramid on the compression side. The cracks were opened extensively on midheight of the specimens when the tensile/compressive steel
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Fig. 2. Test setup and loading condition.
Fig. 3. Arrangement of LVDTs (units in mm).
bars yielded and buckled respectively. The load carrying capacity of the specimens was dropped through a smooth path until the formation of a plastic hinge. It is noted that because of a large aspect ratio of the cross-section (3:1), the failure mode of specimens was affected greatly by the weak axis and all columns were failed at a tension mode of failure. At first, the behavior of strengthened columns was similar to the corresponding unstrengthened ones. At the early levels of loading, microcracking of concrete was initiated by transferring the tensile stress from the concrete to the CFRP composite. The CFRP composite was stretched and ruptured suddenly at the failure point. The rupture of the CFRP was started through longitudinal layers to reach the exterior transverse layers. This process took place near the two opposite corners. The main rupture of the CFRP and the formation of the plastic hinge were produced at the midheight of the strengthened specimens. After the rupture of the CFRP layers, the lateral deflection was increased suddenly and the decrease of the load was clearly seen. In addition, no debonding took place between the concrete and the CFRP composite during the tests. At the failure point, the tensile steel bars were yielded in the tension side and the compressive steel bars were buckled in the compression side. The postpeak behavior of the strengthened columns was related significantly to the fiber orientation. After reaching the maximum strength, a sudden drop in both strength and stiffness occurred. This occurred rapidly for the longitudinal layers, but as the number of the transverse layers was increased, the behavior of the strengthened specimens would tend to increase gradually. For example, -TTTT and -DD0 series had a bilinear load–displacement curve up to failure. Fig. 5 shows the failure region and the cracking pattern of the unstrengthened and strengthened specimens. Generally, the strength and ductility of all strengthened specimens were increased in comparison with the unstrengthened columns. The failure mechanism of the CFRP-confined biaxially loaded RC columns is mainly similar to the mechanism which is occurred in Punurai et al.’s experimental study [25]. For the columns wrapped with transverse fabrics there, the concrete in the compression zone has been greatly strengthened and thus helps increase its midheight deflection and overall energy absorption capacity of the columns.
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Fig. 4. Arrangement of strain gauges (units in mm).
Fig. 5. Failure regions and cracking pattern of unstrengthened and strengthened specimens.
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3.2. Load–displacement relationship Fig. 6a shows the load–displacement curves of all specimens with 225 and 75 mm eccentricities in Y and X directions, respectively. The longitudinal displacement of ULon was obtained from the actuator displacement gauge. The unstrengthened specimen U-225-75 had a nearly linear load–displacement behavior up to the yield point (i.e., Y) and the tensile steel bars were yielded at a load of 156.24 KN and the corresponding longitudinal displacement of 8.35 mm. The secant stiffness is equal to 24.72 KN/mm. After the yield point, load carrying of the column was increased with a lower rate. Finally, this behavior was ended with the formation of the plastic hinge along with buckling of the compressive steel bars at a load level of 215.04 KN corresponding to the displacement of 11.82 mm. The postpeak behavior of the specimen included a softening branch along with buckling of the compressive steel bars up to failure. All strengthened specimens under the compressive loading with the above eccentricities such as S-225-75-T showed a similar
behavior to the counterpart unstrengthened columns. The first region is approximately linear up to the yield point (i.e., Y). Strengthening with CFRP composites improved the secant stiffness, yield point, and the total load carrying capacity of the unstrengthened specimen. For example, the yield point of S-225-75-LT is equal to 277.46 KN corresponding to the displacement of 11.92 mm. A 78% increase in the load level of the yield point of the tensile steel bars is revealed. Table 3 shows the longitudinal secant stiffness, yield point, and the failure point of all specimens. It is being noted that after the yield point, the tensile stress started transferring from the concrete to the composite. Thus, the CFRP was activated gradually up to the failure point (i.e., F) and ruptured totally with a sudden loud noise. Improving the CFRP stiffness by increasing the ratio of the longitudinal layers to the transverse layers would access a greater load carrying capacity, but decrease the ductility. Fig. 6b shows the load–displacement curves of all specimens with 300 and 70 mm eccentricities in Y and X directions respectively. The behavior of the unstrengthened specimen (i.e., U-30070) is similar to U-225-75 series. The first region is linear and after reaching the peak load, a softening behavior is cleared through buckling of the compressive steel bars. All strengthened specimens’ behavior was dependent on the fiber orientation. For -LLT series, an approximately bilinear behavior was shown up to the peak load, and then the stiffness of the specimen was decreased gradually in the plastic region. The specimens of -TTTT and -DD0 showed a nearly elastoplastic behavior. Generally, for both strengthened and unstrengthened columns, the load–displacement behaviors consist of three parts including linear, ascending and descending branches which are similar to ones obtained in an experimental investigation on the behavior of biaxially loaded CFRP-confined RC slender columns by Punurai et al. [25]. The deformation capacity of the specimen was changed greatly with a negligible increase of the load carrying capacity in the plastic region. Based on the failure observations, all strengthened columns were failed in tension-controlled failure. 3.3. Moment–curvature relationship
Fig. 6. Load–displacement behavior of specimens: (a) e (225, 75 mm) and (b) e (300, 70 mm).
All specimens were under bi-eccentric compressive load producing biaxial bending, and moment–curvature behavior of the specimens was investigated around the weak and main axes of the cross-section. Fig. 7a and b shows the moment–curvature relationship about the weak axis of the specimens and Fig. 8a and b show the moment–curvature relationship about the main axis. The bending moments about the weak and main axes, My and Mx respectively, were determined by multiplying the compressive load P by the actual eccentricities in two main directions. The actual eccentricities were calculated by predefined eccentricities ey, and ex plus midheight lateral deflection ULaty, and ULatx at the previous step. The bending moment relationship is described as Eq. (1). By substituting x with y in Eq. (1), My would be determined:
Table 3 Specimen design details. Specimen
U-225-75 U-300-70 S-225-75-L S-225-75-T S-225-75-LT S-300-70-LLT S-300-70-TTTT S-300-70-DD0
Secant stiffness (KN/mm)
24.72 19.9 26.34 25.03 25.73 32.97 22.33 25.6
Yield point
CFRP failure point
Load (KN)
ULon (mm)
Load (KN)
ULon (mm)
156.24 158.66 250.34 194 277.46 242.92 206.32 220.84
8.35 8.93 10.31 7.75 11.92 8.93 9.80 10.02
215.04 231.96 296.69 274.62 352.78 372.62 257.30 285.60
11.82 14.30 13.28 13.72 17.06 19.14 24.85 25.01
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Fig. 7. Moment–curvature behavior about the weak axis: (a) e (225, 75 mm) and (b) e (300, 70 mm).
M x ¼ Pðex þ U Latx Þ
Fig. 8. Moment–curvature behavior about the main axis: (a) e (225, 75 mm) and (b) e (300, 70 mm).
ð1Þ
As mentioned above, the specimens had two curvature variations in the direction of both the main and weak axes of the cross-section (i.e., ux and uy respectively). The curvatures were calculated using Eq. (2) based on the plane section assumption. By substituting x with y in Eq. (2), uy would be determined:
ux ¼
ðeLtop Þx ðeLbottom Þx h
ð2Þ
where eLtop is the longitudinal strain of the tension face; eLbottom the longitudinal strain of the compression face; and h is the height of the cross-section corresponding to each axis (i.e., 450 mm and 150 mm for the main and weak axis, respectively). Observations showed that strengthening improved the moment capacity of the specimens. It was clear that the longitudinal layers in comparison to the transverse ones had a greater effect on the moment stiffness and moment capacity of the specimens. For example, in -L series, the moment capacity became approximately 3.25 times. As the number of longitudinal layers was increased, the CFRP stiffness also increased. Thus, the curvatures were not enhanced significantly. The moment–curvature behavior of the specimens was dependent on the cross-section shape, fiber orientation and eccentricities. The rectangularity of the cross-section and large eccentricities decreased the effect of the strengthening technique. 3.4. Longitudinal strain Figs. 9a,b and 10a,b showed the variation of longitudinal strain on the compression and tension sides at the midheight section respectively. Figs. 11a,b and 12a,b showed the variation of longitudinal
Fig. 9. Longitudinal strains on the compression sides along the: (a) main axis and (b) weak axis; e (225, 75).
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Fig. 10. Longitudinal strains on the tension sides along the: (a) main axis and (b) weak axis; e (225, 75).
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Fig. 12. Longitudinal strains on the tension sides along the: (a) main axis and (b) weak axis; e (300, 70).
strain on the compression and tension sides at the midheight section of the second group of specimens, respectively. For the first group, a bilinear relationship between load and longitudinal strain was shown. The behavior of unstrengthened columns, both first and second groups, indicated that the maximum longitudinal strain at the failure point was 250 lm/m on the compression sides. This was compatible with the ultimate strain of plain concrete. The maximum longitudinal strains for strengthened columns with transverse layers were similar to the unstrengthened specimens on the compression side, so transverse layers made no significant confinement on these sides. On the tension sides, there was no significant difference in the initial stiffness of specimens. The bilinear relationship was also shown. It was clear that the high aspect ratio of specimens (i.e. 3:1) caused an increasing effect of the weak axis rather than the main axis on the total behavior of columns under biaxial bending. For this reason, the effect of FRP strengthening on the tension sides along the main axis was much greater than the weak axis. On the tension sides, using transverse layers led to improvement in the ductility. The behavior of diagonal fibers was the same as the coupon test results which were nearly elastic–plastic, and its effect along the weak axis was great. 4. Conclusions
Fig. 11. Longitudinal strains on the compression sides along the: (a) main axis and (b) weak axis; e (300, 70).
This paper expressed an experimental investigation on rectangular RC columns strengthened with CFRP composites under the combination of the axial load and biaxial bending moment. Eight large-scale rectangular RC columns with two brackets at each head were built and tested under bi-eccentric compression loading up to failure. Various parameters such as the CFRP thickness, eccentricities, and fiber orientation were considered. The effects of these
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parameters on the load–displacement, moment–curvature, and longitudinal and transverse strains were discussed in detail. The following conclusions were derived: 1. The overall behavior of the strengthened and unstrengthened specimens was similar with an exception of -TTTT and -DD0 series. All specimens showed an approximately linear behavior up to the yield point, when the tensile steel bars were yielded in the tension region. After the yield point, the concrete cracking was propagated from one corner along with the concrete crushing at the opposite corner. At this level of load, the CFRP composite was effectively activated causing an improvement of the secant stiffness and yield strength. The load carrying capacity of the specimens was increased at a lower rate than the first region up to reach to the CFRP failure point. The maximum load was obtained when the rupture of the CFRP occurred. The rupture of the CFRP was started through longitudinal layers to reach the exterior transverse layer or in a diagonal path for DD0 series. The postpeak behavior of the specimens included a softening branch until the formation of a plastic hinge. Two series of the specimens had a bilinear load–displacement curve with a sudden drop of the stiffness at the failure point. This behavior is significantly similar to an elastoplastic treatment in a plastic region. The overall behavior of the specimens revealed an increase in the moment capacity and stiffness with an improvement of ductility causing a greater level of energy dissipation. 2. The moment–curvature relationships about the main and weak axis of the cross-section presented an improvement of the bending stiffness and the moment capacity of the specimens. The effect of the longitudinal layers in comparison to the transverse layers was significant for enhancing moment capacity of the specimens. Increasing the number of longitudinal layers would improve the CFRP stiffness decreasing the curvatures. It is noted that the weak axis had a greater role for controlling the overall behavior of specimens. 3. All specimens failed in the tension-controlled failure region. When this process occurred the transverse layers could not produce an effect on the confinement of the compression sides. The transverse layers improved the anchorage of the longitudinal layers.
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Experimental investigation on rectangular RC columns strengthened with CFRP composites under axial load and biaxial bending Alireza Rahai ⇑, Hamed Akbarpour Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Available online 19 September 2013 Keywords: Biaxial bending Rectangular RC columns Carbon fiber-reinforced polymer Strength Ductility
a b s t r a c t This paper presents the results of an experimental study on rectangular RC columns strengthened with carbon fiber-reinforced polymer (CFRP) composites under axial load and biaxial bending moment. A total of 8 large-scale RC columns with rectangular cross-section were cast and tested under bi-eccentric compressive loading up to failure. In this investigation, several parameters like CFRP thickness of one, two, three, and four layers, fiber orientations of ±45°, 0°, 90° and their combination, and eccentricities in the direction of both weak and main axis were studied. The effects of these parameters on the moment–curvature relationship, and load–longitudinal displacement relationship were investigated. In general, increasing longitudinal layers rather than transverse layers led to a greater load carrying and displacement capacity of the specimens, because of the overall behavior of RC wall-like columns. The results of these experimental and numerical studies showed a great improvement on the strength and ductility of confined RC columns. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, using fiber-reinforced polymer (FRP composites) has gained considerable attention in retrofitting and strengthening of reinforced concrete columns. FRP jacketing is effective with respect to strength, less stiffness and weight in comparison with steel, high ductility, resistance to corrosion, and low installation cost and repair. In this regard, FRP jackets obtained a great point in the field of civil engineering to significantly increase the compressive strength and ductility of RC columns [1–5]. To the best of the writer’s knowledge, a comprehensive study shows that the load carrying capacity of the wrapped RC columns is governed by the major influencing parameters such as the concrete compressive strength, the aspect ratio of the cross-sectional area of the specimens, the number of wrap layers, modulus and Poisson’s ratio of the wrapping sheet, fiber orientation, longitudinal steel reinforcement ratio and their orientation, and the type of loading [6–12]. Chaallal et al. [13] presented a confinement model describing the behavior of rectangular concrete columns retrofitted with FRP sheets and subjected to axial loading. This model was based on the findings of experimental studies including the testing of rectangular columns with three cross-section aspect ratio and five different numbers of FRP layers. The results of their investigation ⇑ Corresponding author. Postal Address: Hafez Ave., 15875-4413 Tehran, Iran. Tel.: +98 21 64542220. E-mail address: [email protected] (A. Rahai). 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.09.015
showed that as the cross-section aspect ratio increased, the effectiveness of FRP composites decreased. Also, they found that the stiffness of the FRP jacket is an important parameter in strengthening problems, and it is related to the number of layers, modulus and Poisson’s ratio of the wrapping jacket. Li and Hadi [14] conducted a parametric study using FEA software ANSYS. They studied the effect of FRP thickness, stiffness and fiber orientation on the strength and stiffness of the columns. They justified the analysis using experimental results that agreed reasonably with the FEA. Both results showed that mechanical parameters of the FRP jacket have a key role on the behavior of columns after reaching the unconfined concrete strength. Some researchers conducted experimental studies to investigate the effect of loading type on the load carrying capacity and ductility of wrapped RC columns. The derivation of these studies showed that the effectiveness of FRP confinement to develop the structural performance of RC columns was influenced by the load eccentricity. Increasing the eccentricity decreased the effectiveness of FRP jackets in improving the behavior of eccentrically loaded RC columns than concentrically loaded columns [15,16]. The amount and orientation of steel reinforcements influenced the flexural strength capacity of eccentrically loaded RC columns. As the longitudinal steel ratio increased, the flexural strength capacity of columns increased. Also, the compressive strength of concrete had a great effect on the effectiveness of FRP confinement and experimental studies showed that the confinement effect of the FRP jacket on the performance of low strength RC columns was more than high strength confined RC columns [17,18].
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Nomenclature ex ey f c hx hy Mx My P
eccentricity along the main axis eccentricity along the weak axis compressive strength of the concrete height of the cross-section along the weak axis, i.e. 450 mm height of the cross-section along the main axis, i.e. 150 mm bending moment about the main axis bending moment about the weak axis axial compressive load
Generally, columns are the most important part of buildings, bridges and berthing structures. These columns are usually loaded by bending moments about both principal axes. Many researchers investigated the performance of unconfined RC columns under biaxial bending moment. Short reinforced concrete columns subjected to biaxial bending have received considerable attention. As a result, there are several empirical and approximate methods, such as the Bresler method [19], available for the strength design of short columns. A few studies have also emerged for the analysis of slender reinforced concrete columns subjected to biaxial bending. On the contrary, little attention was given to the prediction of load carrying capacity and ductility of FRP-confined RC columns in the literatures [18,20,21]. Monti and Alessandri [22] presented a model for determining the flexural strength capacity and ductility of unconfined and confined RC columns under biaxial bending. This model was based on the Bresler method [19] and calculated the section capacity at the ultimate condition. The model’s results were in good agreement with the exact solution. Youcef et al. [23] investigated the behavior of CFRP-confined square RC columns under biaxial bending. They conducted an experimental study through casting and strengthening RC columns with the square cross-section (i.e., 76 mm 76 mm). All columns were wrapped with one to three FRP layers and the results showed that increasing the layers number led to improvement of the deformation capacity and section curvatures. Punurai et al. [24] prepared some specimens similar to Youcef’s experimental work with differences in both the longitudinal steel ratio and CFRP layers number. They showed that as these parameters increased, the overall flexural behavior of the strengthened specimens was improved. This paper presents the behavior of rectangular RC columns under biaxial bending (i.e., the bi-eccentric compressive loading). In this regard, a total of eight large-scale rectangular RC columns with the height to width ratio of 3:1 were built and tested up to failure. Various parameters such as the CFRP thickness, fiber orientation, and eccentricities were investigated. The results showed that strengthening RC columns with CFRP composites improved the load carrying capacity and the ultimate deformation.
ULon ULatx ULaty eLtop eLbottom
ux uy
longitudinal displacement lateral displacement at the midheight section along the weak axis lateral displacement at the midheight section along the main axis longitudinal strain of the tension face longitudinal strain of the compression face curvature about the main axis curvature about the weak axis
In this paper, some parameters such as the CFRP thickness, fiber orientation and the eccentricities were considered as variables. The different CFRP thickness as 0.5, 1, 1.5 and 2 mm (1–4 layers respectively) and the fiber orientations as the combination of 0° and 90° were investigated. 90° referred to the orientation of fibers along the column axis and 0° referred to the orientation of fibers perpendicular to the column axis. For this reason, six fiber orientation as (0°), (90°), (90°/0°), (90°/90°/0°), (0°/0°/0°/0°) and (45°/45°) were investigated. The test program and column properties are summarized in Table 1. All columns were divided into two different groups. The first group labeled ‘‘S’’ included strengthened columns and another group labeled ‘‘U’’ as an unstrengthened column served as a control column. Six columns were strengthened with four CFRP layers: 90° as the longitudinal layer, 0° as the transverse layer, and the combination of 45° and 45° as the diagonal layers with respect to an axis perpendicular to the column axis. Eccentricities both in X, and Y directions were changed from 70 to 75 mm, and 225 to 300 mm respectively and were constant during the tests. 2.2. Material properties All columns were cast from one batch of concrete. A concrete with an average compressive strength of f c ¼ 35 MPa and a slump of 80 mm was used in this study. The longitudinal steel reinforcements were 6u12 mm with yield and ultimate strengths of 375 and 580, respectively. The transverse reinforcement was provided with rectangular ties of u6@150 mm. The yield and ultimate strength of the transverse reinforcement were 215 and 326, respectively. The reinforcement details for the columns were depicted in Fig. 1. It is noted that extra reinforcement was provided in each bracket in order to prevent local failure. Unidirectional carbon fiber-reinforcement sheets (CFRP) were used and adopted with the resin epoxy. According to the data sheet provided by tension testing on CFRP coupons, a cured CFRP composite sheet has a thickness of 0.5 mm, a tensile strength of 336 MPa, and an ultimate elongation of 0.93%. Mechanical properties of the CFRP were shown in Table 2. 2.3. Specimen preparation and test setup
2. Experimental program 2.1. Specimens layout A total of 8 large-scale RC columns with the rectangular crosssection (150 mm 450 mm) were built and tested under axial load and biaxial bending up to failure. The test portion of each column had a height of 1500 mm. Two brackets with a height of 400 mm were designed for each head. To avoid stress concentration and make the use of CFRP easier, each corner was chamfered to a radius of 15 mm. Fig. 1 shows the geometry of the columns.
The concrete was cast in one batch and after a 28-day humid condition curing, the surface of specimens were cleaned and prepared for strengthening. The CFRP fibers were saturated with epoxy resin and applied to the surface. The resin content must be sufficient to ensure that enough bonds between the CFRP sheet and concrete surface were developed. In order to prevent anchorage rupture in the transverse layer, a 100 mm overlap was considered in the fiber direction. The load was applied on specimens by means of a 1000 KN nominal load capacity hydraulic jack. Both end supports were designed as hinged condition to apply the
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Section B-B
Section A-A
Fig. 1. Geometry and reinforcement detailing of columns (units in mm).
Table 1 Specimens design layouts. Specimens
Strengthening
Number of layers
Fiber orientation
Eccentricity Y-direction (mm)
Eccentricity X-direction (mm)
U-225-75 U-300-70 S-225-75-L S-225-75-T S-225-75-LT S-300-70-LLT S-300-70-TTTT S-300-70-DD0
Unstrengthened Unstrengthened Strengthened Strengthened Strengthened Strengthened Strengthened Strengthened
– – 1 1 2 3 4 2
– – 90° 0° 90°/0° 90°/90°/0° 0°/0°/0°/0° 45°/45°
225 300 225 225 225 300 300 300
75 70 75 75 75 70 70 70
Table 2 Mechanical properties of the CFRP coupon. Test direction
Ultimate strength (MPa)
Initial modulus (MPa)
Ultimate strain (mm/m)
CFRP thickness (mm/layer)
Dry thickness (mm/layer)
Fiber direction Matrix direction
336 32
39,944 2338
9.3 9
0.5 0.5
0.166 0.166
incremental load in the predefined eccentricity. Two end supports consisted of a rectangular steel frame (350 mm 700 mm) from an angle section member and a roller welded to the frame. The lateral deflection in the direction of each principal axis was measured using 4 Linear Variable Displacement Transducers (LVDTs). The longitudinal and transverse strains were measured by 40 foil strain gauges for each specimen. The specimens were tested under axial load and biaxial bending up to failure. All strains, displacements, and loads were saved by a computer program. Figs. 2–4 showed the test setup and the schematic arrangement of LVDTs and strain gauges, respectively.
3. Experimental results and discussions 3.1. Overall behavior The overall behavior of unstrengthened columns was similar. Specimens failed suddenly by crushing at the load point and producing tensile cracks on the tension side. Tensile cracks were propagated along two adjacent sides with an increase of compressive loading simultaneously with producing and progressing a pyramid on the compression side. The cracks were opened extensively on midheight of the specimens when the tensile/compressive steel
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Fig. 2. Test setup and loading condition.
Fig. 3. Arrangement of LVDTs (units in mm).
bars yielded and buckled respectively. The load carrying capacity of the specimens was dropped through a smooth path until the formation of a plastic hinge. It is noted that because of a large aspect ratio of the cross-section (3:1), the failure mode of specimens was affected greatly by the weak axis and all columns were failed at a tension mode of failure. At first, the behavior of strengthened columns was similar to the corresponding unstrengthened ones. At the early levels of loading, microcracking of concrete was initiated by transferring the tensile stress from the concrete to the CFRP composite. The CFRP composite was stretched and ruptured suddenly at the failure point. The rupture of the CFRP was started through longitudinal layers to reach the exterior transverse layers. This process took place near the two opposite corners. The main rupture of the CFRP and the formation of the plastic hinge were produced at the midheight of the strengthened specimens. After the rupture of the CFRP layers, the lateral deflection was increased suddenly and the decrease of the load was clearly seen. In addition, no debonding took place between the concrete and the CFRP composite during the tests. At the failure point, the tensile steel bars were yielded in the tension side and the compressive steel bars were buckled in the compression side. The postpeak behavior of the strengthened columns was related significantly to the fiber orientation. After reaching the maximum strength, a sudden drop in both strength and stiffness occurred. This occurred rapidly for the longitudinal layers, but as the number of the transverse layers was increased, the behavior of the strengthened specimens would tend to increase gradually. For example, -TTTT and -DD0 series had a bilinear load–displacement curve up to failure. Fig. 5 shows the failure region and the cracking pattern of the unstrengthened and strengthened specimens. Generally, the strength and ductility of all strengthened specimens were increased in comparison with the unstrengthened columns. The failure mechanism of the CFRP-confined biaxially loaded RC columns is mainly similar to the mechanism which is occurred in Punurai et al.’s experimental study [25]. For the columns wrapped with transverse fabrics there, the concrete in the compression zone has been greatly strengthened and thus helps increase its midheight deflection and overall energy absorption capacity of the columns.
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Fig. 4. Arrangement of strain gauges (units in mm).
Fig. 5. Failure regions and cracking pattern of unstrengthened and strengthened specimens.
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3.2. Load–displacement relationship Fig. 6a shows the load–displacement curves of all specimens with 225 and 75 mm eccentricities in Y and X directions, respectively. The longitudinal displacement of ULon was obtained from the actuator displacement gauge. The unstrengthened specimen U-225-75 had a nearly linear load–displacement behavior up to the yield point (i.e., Y) and the tensile steel bars were yielded at a load of 156.24 KN and the corresponding longitudinal displacement of 8.35 mm. The secant stiffness is equal to 24.72 KN/mm. After the yield point, load carrying of the column was increased with a lower rate. Finally, this behavior was ended with the formation of the plastic hinge along with buckling of the compressive steel bars at a load level of 215.04 KN corresponding to the displacement of 11.82 mm. The postpeak behavior of the specimen included a softening branch along with buckling of the compressive steel bars up to failure. All strengthened specimens under the compressive loading with the above eccentricities such as S-225-75-T showed a similar
behavior to the counterpart unstrengthened columns. The first region is approximately linear up to the yield point (i.e., Y). Strengthening with CFRP composites improved the secant stiffness, yield point, and the total load carrying capacity of the unstrengthened specimen. For example, the yield point of S-225-75-LT is equal to 277.46 KN corresponding to the displacement of 11.92 mm. A 78% increase in the load level of the yield point of the tensile steel bars is revealed. Table 3 shows the longitudinal secant stiffness, yield point, and the failure point of all specimens. It is being noted that after the yield point, the tensile stress started transferring from the concrete to the composite. Thus, the CFRP was activated gradually up to the failure point (i.e., F) and ruptured totally with a sudden loud noise. Improving the CFRP stiffness by increasing the ratio of the longitudinal layers to the transverse layers would access a greater load carrying capacity, but decrease the ductility. Fig. 6b shows the load–displacement curves of all specimens with 300 and 70 mm eccentricities in Y and X directions respectively. The behavior of the unstrengthened specimen (i.e., U-30070) is similar to U-225-75 series. The first region is linear and after reaching the peak load, a softening behavior is cleared through buckling of the compressive steel bars. All strengthened specimens’ behavior was dependent on the fiber orientation. For -LLT series, an approximately bilinear behavior was shown up to the peak load, and then the stiffness of the specimen was decreased gradually in the plastic region. The specimens of -TTTT and -DD0 showed a nearly elastoplastic behavior. Generally, for both strengthened and unstrengthened columns, the load–displacement behaviors consist of three parts including linear, ascending and descending branches which are similar to ones obtained in an experimental investigation on the behavior of biaxially loaded CFRP-confined RC slender columns by Punurai et al. [25]. The deformation capacity of the specimen was changed greatly with a negligible increase of the load carrying capacity in the plastic region. Based on the failure observations, all strengthened columns were failed in tension-controlled failure. 3.3. Moment–curvature relationship
Fig. 6. Load–displacement behavior of specimens: (a) e (225, 75 mm) and (b) e (300, 70 mm).
All specimens were under bi-eccentric compressive load producing biaxial bending, and moment–curvature behavior of the specimens was investigated around the weak and main axes of the cross-section. Fig. 7a and b shows the moment–curvature relationship about the weak axis of the specimens and Fig. 8a and b show the moment–curvature relationship about the main axis. The bending moments about the weak and main axes, My and Mx respectively, were determined by multiplying the compressive load P by the actual eccentricities in two main directions. The actual eccentricities were calculated by predefined eccentricities ey, and ex plus midheight lateral deflection ULaty, and ULatx at the previous step. The bending moment relationship is described as Eq. (1). By substituting x with y in Eq. (1), My would be determined:
Table 3 Specimen design details. Specimen
U-225-75 U-300-70 S-225-75-L S-225-75-T S-225-75-LT S-300-70-LLT S-300-70-TTTT S-300-70-DD0
Secant stiffness (KN/mm)
24.72 19.9 26.34 25.03 25.73 32.97 22.33 25.6
Yield point
CFRP failure point
Load (KN)
ULon (mm)
Load (KN)
ULon (mm)
156.24 158.66 250.34 194 277.46 242.92 206.32 220.84
8.35 8.93 10.31 7.75 11.92 8.93 9.80 10.02
215.04 231.96 296.69 274.62 352.78 372.62 257.30 285.60
11.82 14.30 13.28 13.72 17.06 19.14 24.85 25.01
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Fig. 7. Moment–curvature behavior about the weak axis: (a) e (225, 75 mm) and (b) e (300, 70 mm).
M x ¼ Pðex þ U Latx Þ
Fig. 8. Moment–curvature behavior about the main axis: (a) e (225, 75 mm) and (b) e (300, 70 mm).
ð1Þ
As mentioned above, the specimens had two curvature variations in the direction of both the main and weak axes of the cross-section (i.e., ux and uy respectively). The curvatures were calculated using Eq. (2) based on the plane section assumption. By substituting x with y in Eq. (2), uy would be determined:
ux ¼
ðeLtop Þx ðeLbottom Þx h
ð2Þ
where eLtop is the longitudinal strain of the tension face; eLbottom the longitudinal strain of the compression face; and h is the height of the cross-section corresponding to each axis (i.e., 450 mm and 150 mm for the main and weak axis, respectively). Observations showed that strengthening improved the moment capacity of the specimens. It was clear that the longitudinal layers in comparison to the transverse ones had a greater effect on the moment stiffness and moment capacity of the specimens. For example, in -L series, the moment capacity became approximately 3.25 times. As the number of longitudinal layers was increased, the CFRP stiffness also increased. Thus, the curvatures were not enhanced significantly. The moment–curvature behavior of the specimens was dependent on the cross-section shape, fiber orientation and eccentricities. The rectangularity of the cross-section and large eccentricities decreased the effect of the strengthening technique. 3.4. Longitudinal strain Figs. 9a,b and 10a,b showed the variation of longitudinal strain on the compression and tension sides at the midheight section respectively. Figs. 11a,b and 12a,b showed the variation of longitudinal
Fig. 9. Longitudinal strains on the compression sides along the: (a) main axis and (b) weak axis; e (225, 75).
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Fig. 10. Longitudinal strains on the tension sides along the: (a) main axis and (b) weak axis; e (225, 75).
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Fig. 12. Longitudinal strains on the tension sides along the: (a) main axis and (b) weak axis; e (300, 70).
strain on the compression and tension sides at the midheight section of the second group of specimens, respectively. For the first group, a bilinear relationship between load and longitudinal strain was shown. The behavior of unstrengthened columns, both first and second groups, indicated that the maximum longitudinal strain at the failure point was 250 lm/m on the compression sides. This was compatible with the ultimate strain of plain concrete. The maximum longitudinal strains for strengthened columns with transverse layers were similar to the unstrengthened specimens on the compression side, so transverse layers made no significant confinement on these sides. On the tension sides, there was no significant difference in the initial stiffness of specimens. The bilinear relationship was also shown. It was clear that the high aspect ratio of specimens (i.e. 3:1) caused an increasing effect of the weak axis rather than the main axis on the total behavior of columns under biaxial bending. For this reason, the effect of FRP strengthening on the tension sides along the main axis was much greater than the weak axis. On the tension sides, using transverse layers led to improvement in the ductility. The behavior of diagonal fibers was the same as the coupon test results which were nearly elastic–plastic, and its effect along the weak axis was great. 4. Conclusions
Fig. 11. Longitudinal strains on the compression sides along the: (a) main axis and (b) weak axis; e (300, 70).
This paper expressed an experimental investigation on rectangular RC columns strengthened with CFRP composites under the combination of the axial load and biaxial bending moment. Eight large-scale rectangular RC columns with two brackets at each head were built and tested under bi-eccentric compression loading up to failure. Various parameters such as the CFRP thickness, eccentricities, and fiber orientation were considered. The effects of these
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parameters on the load–displacement, moment–curvature, and longitudinal and transverse strains were discussed in detail. The following conclusions were derived: 1. The overall behavior of the strengthened and unstrengthened specimens was similar with an exception of -TTTT and -DD0 series. All specimens showed an approximately linear behavior up to the yield point, when the tensile steel bars were yielded in the tension region. After the yield point, the concrete cracking was propagated from one corner along with the concrete crushing at the opposite corner. At this level of load, the CFRP composite was effectively activated causing an improvement of the secant stiffness and yield strength. The load carrying capacity of the specimens was increased at a lower rate than the first region up to reach to the CFRP failure point. The maximum load was obtained when the rupture of the CFRP occurred. The rupture of the CFRP was started through longitudinal layers to reach the exterior transverse layer or in a diagonal path for DD0 series. The postpeak behavior of the specimens included a softening branch until the formation of a plastic hinge. Two series of the specimens had a bilinear load–displacement curve with a sudden drop of the stiffness at the failure point. This behavior is significantly similar to an elastoplastic treatment in a plastic region. The overall behavior of the specimens revealed an increase in the moment capacity and stiffness with an improvement of ductility causing a greater level of energy dissipation. 2. The moment–curvature relationships about the main and weak axis of the cross-section presented an improvement of the bending stiffness and the moment capacity of the specimens. The effect of the longitudinal layers in comparison to the transverse layers was significant for enhancing moment capacity of the specimens. Increasing the number of longitudinal layers would improve the CFRP stiffness decreasing the curvatures. It is noted that the weak axis had a greater role for controlling the overall behavior of specimens. 3. All specimens failed in the tension-controlled failure region. When this process occurred the transverse layers could not produce an effect on the confinement of the compression sides. The transverse layers improved the anchorage of the longitudinal layers.
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