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Behaviour of CFRP wrapped RC square columns under eccentric compressive loading
Structures 20 (2019) 309–323
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Behaviour of CFRP wrapped RC square columns under eccentric compressive loading
T
Faiz Uddin Ahmed Shaikh , Reza Alishahi ⁎
School of Civil and Mechanical engineering, Curtin University, GPO Box: U1987, Perth, WA6845, Australia
ARTICLE INFO
ABSTRACT
Keywords: CFRP Columns Eccentricity Strengthening Failure behaviour Compression load Load-moment interaction diagram
This paper presents the effects of carbon fibre reinforced polymer (CFRP) volumetric ratios on structural and failure behaviour of CFRP wrapped reinforced concrete (RC) square columns under concentric, eccentric and flexural loadings. The CFRP volumetric ratio is considered as the ratio of volume of CFRP to the volume of concrete. The applicability of existing confinement models to predict the load-moment interaction diagrams of such columns in eccentric loadings is also presented in this paper. Total 20 columns were tested. Dimensions of all columns were 175x175x800 mm with 20 mm rounded corners. Variable considered in this study were number of CFRP layers (e.g. 0, 1, 2 and 3 layers) which corresponds to CFRP volumetric ratio of 0, 0.3, 0.6 and 0.9%, respectively, increasing eccentricities (e.g. 0, 25, 35 and 50 mm) of the applied load and pure flexural loading. Results show that ultimate load capacity and axial deformation increase with increase in CFRP volumetric ratios irrespective of eccentricities. However, load capacity and deformation decrease with increasing eccentricities for any given CFRP volumetric ratio. Hoop strains also increase with increase in CFRP volumetric ratios and eccentricities. Stiffness of CFRP wrapped columns also increases with increase in CFRP volumetric ratio up to 0.6% and decreases with increase in eccentricities. Ductility of CFRP wrapped columns increases with increase in CFRP volumetric ratios and eccentricities. The algorithms for calculation of critical points for loadmoment (P-M) interaction diagrams using analytical as well as numerical stress integrations are developed and compared to those of the column tests. P-M interaction diagram developed using existing confinement models agree well with the experimental P-M interaction diagrams of CFRP wrapped RC square columns under eccentric loading.
1. Introduction The use of fibre reinforced polymer (FRP) for strengthening and rehabilitation of reinforced concrete (RC) structures is a common practice in the construction industry. Among various structural members, the strengthening and rehabilitation of columns by wrapping FRP fabric is most effective and efficient as the FRP does not debond prematurely and under increasing compression load the confinement efficiency of FRP is significantly increased. For circular columns, the confining pressure occurs around the entire perimeter due to the curvature of the FRP wrap produce uniform confining stress (Fig. 1a). Under concentric loading the confinement of a circular concrete column can effectively increase the strength by up to 200% [1,2]. FRP-confined rectangular columns behave in a significantly different manner due to the non-uniform distribution of hoop strains and stress concentration at the corners as shown in Fig. 1b. With the application of concentric loading, the FRP at four corners goes into tension as shown in Fig. 1b
⁎
and the confining forces are only generated at the convex corners in rectangular/square columns. Several studies have been conducted on FRP confined and strengthened RC columns under concentric loads. However, it is clear that in real situation most columns experience combination of axial compression load and bending moment (i.e. eccentric compression loading) due to construction error, moments transfer from beam to column in rigid beam-column connection, unsymmetrical loading, etc. Therefore, there is a need to understand the behaviour of FRP strengthened columns under eccentric loading. Some research has been conducted on FRP confined columns under eccentric loading. In a study performed by Parvin and Wang [3], small-scale square concrete columns having 108 mm × 108 mm in cross-section and 305 mm in height were strengthened with varying layers of carbon FRP (CFRP) and subjected to axial load at different eccentricities. The results showed that the increase in eccentricity resulted in reduction in strength capacity of the column, and the use of CFRP increased the load capacity of the
Corresponding author. E-mail address: [email protected] (F.U.A. Shaikh).
https://doi.org/10.1016/j.istruc.2019.04.012 Received 22 December 2018; Received in revised form 16 April 2019; Accepted 17 April 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
Structures 20 (2019) 309–323
F.U.A. Shaikh and R. Alishahi
Fig. 1. Confinement stress distribution around (a) circular vs (b) square column due to FRP wrapping. Table 1 Experimental program and configuration of test specimens. Series
Specimens
Eccentricity
Number of CFRP layers
CFRP volumetric ratio (%)
Longitudinal reinforcement
Transverse reinforcement
First
CR0 CF10 CF20 CF30 CR1 CF11 CF21 CF31 CR2 CF12 CF22 CF32 CR3 CF13 CF23 CF33 CRB CF1B CF2B CF3B
e = 0 mm (Pure compression)
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
0 0.3 0.6 0.9 0 0.3 0.6 0.9 0 0.3 0.6 0.9 0 0.3 0.6 0.9 0 0.3 0.6 0.9
4 N12
R6@100 mm
4 N12
R6@100 mm
4 N12
R6@100 mm
4 N12
R6@100 mm
4 N12
R6@100 mm
Second
Third
Fourth
Fifth
e = 25 mm
e = 35 mm
e = 50 mm
Pure flexure (Beam Test)
B
15 mm clear cover
4N12
A
A
800 mm
r
175 mm
R6@100
175 mm
20 mm radius
Section A - A
B t 175 mm
Fig. 3. Cross-section of RC column and reinforcement details.
column. Fam et al. [4] performed an experimental study and proposed an analytical model to describe the behavior of concrete filled FRP tubes subjected to combined axial compression loads and bending moments. Li and Hadi [5], Hadi and Li [6], and Hadi [7–10] tested several FRP-strengthened concrete columns with circular section under eccentric loading at different end conditions. The effects of concrete
Fig. 2. Definitions of geometric dimension of CFRP confined square column to calculate the CFRP volumetric ratio.
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Table 2 Properties of CFRP fabric and epoxy.
CFRP (Sikawrap 230C) Two-part epoxy (Sikadur 330)
Tensile strength (MPa)
Elongation at rupture (%)
Tensile modulus (GPa)
Thickness (mm)
4300
1.8
234
0.13
30
0.9
4.5
–
Table 3 Mechanical properties of concrete and longitudinal steel. 28 days compressive strength of concrete (MPa)
28 days tensile strength of concrete (MPa)
Steel yield strength (MPa)
Steel ultimate strength (MPa)
Steel ultimate strain
47
4
500
690
0.068
SG8
SG1
SG7
square RC columns under eccentric loading. It can be seen in above review that there are numerous studies on behaviour of RC columns strengthened by FRP materials. However, if we look into those studies it can be seen that most of them were on circular column and concentric compression loads were applied. Even some studies reported results of eccentrically loaded rectangular or square columns strengthened by FRP, most of them were short column. The present study used medium height square column to evaluate the effect of different eccentricities and pure flexure to establish load-moment interaction diagram and compared with theoretical load-moment interaction diagram using four confinement models. This paper presents the results of a comprehensive experimental program where 18 RC square columns are wrapped with various layers of CFRP fabric and are subjected to increasing eccentricities under pin-pin end conditions in compression to pure flexure under three-point bending. Effects of eccentricities and number of CFRP layers on the ultimate failure load, axial shortening at peak load, hoop strain in CFRP and mid height lateral deflection of all CFRP strengthened columns are also evaluated. Load-moment interaction diagrams are also developed based on experimental results and compared with existing models for FRP confined section in order to evaluate their suitability in predicting the load and moment capacities of CFRP confined square columns under eccentric loading.
SG2
SG3
SG6
SG4 SG5
Fig. 4. Strain gauge arrangement around the hoop at mid-height of the column.
strength, internal steel reinforcement, wrap type, fibre orientation, and eccentricity were studied. The eccentric load was applied through a circular plate at each end of the specimens. The experimental results clearly demonstrated that the FRP wrapping enhanced strength, ductility, and energy absorption of circular concrete columns under eccentric loading. In a study performed by Chaallal and Shahawy [11], an experimental investigation was conducted on rectangular RC columns strengthened with bi-directional CFRP composites and different eccentricities. The overall length of the two haunched-head specimens was 3.6 m (200 mm wide and 350 mm high in test section). The results indicated that the strength capacity of columns improved significantly as a result of the combined action of the longitudinal and the transverse fibres of the bi-directional composite fabrics. Lignola et al. [12] reported a study where they have mainly focused their attention on square hollow columns strengthened with CFRP composites (height of 3020 mm, width of 360 mm, and wall thicknesses of 60 mm). The outcomes highlighted that composite wrapping can enhance the structural performance of concrete columns under eccentric loading in terms of strength and especially in terms of ductility. The strength improvement was more pronounced in the case of specimens loaded with smaller eccentricity, while the ductility improvement was more significant in the case of larger eccentricity. Hatami et al. [13] and Sadeghian et al. [14] in their studies evaluated the effectiveness of CFRP wrapped rectangular RC columns (200 × 300 mm) of 1.5 m long under eccentric compression loading. Lei et al. [15] and Widiarsa and Hadi [16] studied the effectiveness of CFRP strengthened RC columns of square cross-section under eccentric loading and reported that the CFRP wrapping enhanced the load carrying capacity and ductility of the
2. Experimental program In total 20 square RC columns with 175 mm in sides and 800 mm in height were cast and tested. The columns were divided in to five series according to the types of loading shown in Table 1. In the first series concentric compression load was applied in the columns wrapped with 0, 1, 2 and 3 layers of CFRP fabric. In second, third and fourth groups eccentric compression load were applied at 25, 35 and 50 mm eccentricities, respectively from the centre of the columns. In fifth series, three-point bending was applied in the above CFRP warped columns to simulate bending behaviour. Detail experimental program is shown in Table 1. The number of CFRP layers in the columns is defined as the CFRP volumetric ratio. The CFRP volumetric ratio is considered as the ratio of volume of CFRP to the volume of concrete in the column as follows. Fig. 2 shows the typical dimension of column and CFRP to calculate the CFRP volumetric ratio. Based on the proposed CFRP volumetric ratio, the CFRP volumetric ratios of 1, 2 and 3 CFRP layer are 0.3, 0.6 and 0.9%, respectively. CFRP =
[4(B 2r ) + 2 r ] t [B 2 + r 2 4r 2]
100
where, ρCFRP = CFRP volumetric ratio 311
(1)
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8 strain gauges attached transversely to measure the hoop strain in CFRP at the middle of the column. (4 at middle of sides and 4 at corners)
Three horizontal LVDTs to measure the lateral deflection of the column in the middle and approximately 200mm above and below the middle LVDT.
Two vertical LVDTs to measure the longitudinal shortening of the column. Fig. 5. Detail of instrumentation and setup of CFRP wrapped column for testing under compressive loading.
Struts attached to the load cell
LVDTs for vertical deflection measurement of the beam spaced at 200 mm
Fig. 6. Three-point bending beam test instrumentation.
Loading head Adjustable long slots to maintain eccentricity
Knife edge to represent pin support Loading cell of machine
Fig. 7. Developed ecentric loading mechanism and manufactured loading head.
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Table 4 Summary of results of all columns tested in this study. Specimens CR0 CF10 a CF20 a CF30 CR1 CF11 CF21 CF31 CR2 CF12 CF22 CF32 CR3 CF13 CF23 CF33 a
Yield load (kN)
Axial displacement at yield load (mm)
Ultimate load (kN)
Axial displacement at peak load (mm)
Ductility
Stiffness (kN/mm)
1247 894
3.55 2.56
1555 1784.5 1902 2078 1036 1229 1320 1283 840 1098 1020 998 654 798 884 840
4.5 4.95
1.27 1.93
528 610.3
– –
223 867 745 649 415 975 775 750 470 840 795 678
– –
1.89 2.2 3 1.05 2.17 0.098 5.36 0.04 2.42 1.73 1.94 3.93
– –
4.2 4.6 5.6 6.1 3.7 4.1 4.1 5.7 3.4 5.1 4.1 5.3
– –
2.24 3.94 4.18 5.82 1.69 3.51 4.48 4.94 1.38 2.97 3.69 3.74
– –
404 586 579 480 336 388 388 388 219 260 284 285
Ultimate loads are calculated values based on confinement models.
Fig. 8. Axial load-axial deformation (axial deflection) of RC square columns under (a) concentric loading (e = 0 mm) and various eccentricities at (b) e = 25 mm, (c) e = 35 mm and (d) e = 50 mm.
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Fig. 9. Axial load-hoop strain at mid-height of RC square columns under (a) concentric loading (e = 0 mm) and various eccentricities at (b) e = 25 mm, (c) e = 35 mm and (d) e = 50 mm.
B = Side of square column r = corner radius of column t = thickness of CFRP
2.2. Preparation of specimens Ready-mixed concrete was purchased from a local supplier. Slump tests were carried out immediately after the arrival of the concrete. The results from the slump tests showed that the concrete had a slump of more than 150 mm. After that, the concrete was poured into the formworks made from plywoods. All specimens were then covered with wet hessian and cured in room temperature for 28 days before they were taken out of the formwork. In order to reduce the stress concentration at four corners of the columns, a 20 mm radius round edge was created at each corner by attaching a specially manufactured foam shaper in four corners of all column moulds. After 28 days of curing all minor defects on the surface of the specimens were patched using standard mortar and then the surface of the concrete was polished and smoothed using concrete grinder. Secondly, epoxy resin was spread onto the surface of the specimen and the first layer of CFRP was attached. After that, epoxy resin was spread again on the surface of the first layer of CFRP and the second layer was attached. The same procedure was followed until three layers of CFRP were bonded. A 100 mm overlap was maintained for each layer. The specimens were left to dry for 14 days as specified by the supplier.
2.1. Detail of specimens and materials All columns had identical internal steel reinforcement. Four 12 mm deformed bars with a nominal tensile yield strength of 500 MPa were provided as longitudinal reinforcement and 6 mm plain bars were provided as transverse reinforcement with 100 mm spacing. Fig. 3 shows the cross-section and reinforcement details of the columns. Concrete cover was maintained at 15 mm thick on the surface and 20 mm thickness at top and bottom. The columns were made from normal strength concrete with a 28 days compressive strength of 47 MPa. Carbon Fibre Reinforced Polymer (CFRP) fabric was used as a primary confining material. The CFRP was 500 mm in width with unidirectional fibres. Two-part epoxy was used to bond the CFRP fabric with concrete. Properties of CFRP and two-part epoxy is provided in Table 2, while the measured mechanical properties of concrete and longitudinal steel are shown in Table 3. 314
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2.3. Loading system In total 8 electrical strain gauges of 60 mm long (wire strain gauge with polyester resin backing) were attached horizontally on CFRP at mid height of each column to measure the hoop strains as shown in Fig. 4. Four at corners and four at middle of the four sides of each column. In addition LVDTs having accuracy of ± 0.25% were also used to measure the axial shortening and lateral deflection at mid height of the columns as well as to measure the mid-span deflection of the specimens in three-point beam test. Detail instrumentation to measure the strain and displacements of concentrically and eccentrically loaded columns are show in Fig. 5, while Fig. 6 shows the instrumentation and loading arrangement in three-point bending test. Special steel frame was manufactured to hold the LVDTs in position and aluminum angels were glued to the specimens where probe tip of LVDTs were touched. 2.4. Concentric and eccentric loading All columns were tested using a 1800 kN capacity universal testing machine. An especially designed loading system was used to apply eccentric loading in the columns. The loading system consists of steel loading head at both ends of column. The loading head is connected to a thick steel plate which is then attached to a knife edge arrangement to facilitate the pin connection at both ends as shown in Fig. 7. The thick plate which was connected to loading head, contained adjustable long slots to maintain the required eccentricities in this study. Fig. 5 shows the detail of eccentric load arrangement. All specimens were capped at both ends using high strength plaster to ensure even distribution of forces. Calibration was carried out to ensure the specimen was placed in the centre. For axial loading test the loading rate of 70 kN/min which is 0.16 mm/min in the elastic range was used. 2.5. Three-point bending For the pure flexural test a three-point bending configuration was chosen. As shown in Fig. 5 the struts were attached to a load cell to apply a concentrated load at the middle of the beam. The length of the span was 700 mm and the support to the left of the picture is roller and the support to the right is a pin support. The load is being exerted on a v shaped metal plate which is attached to the surface of the specimen using rapid setting plaster. As shown in Fig. 6 three LVDTs are placed every 200 mm along the length of the beam. In order to simulate the static loading conditions, the rate of 0.16 mm/min loading was maintained during the tests. 3. Results and discussion 3.1. Load deformation behaviour of CFRP wrapped columns under increasing eccentricities All specimens were tested until failure and their results are summarised in Table 4. The load, strain and displacement data were collected using a 32 channels data-logger connected to the 1800 kN universal testing machine where the columns were tested. The effects of CFRP volumetric ratios and eccentricities on axial load – axial displacement, axial load- average hoop strain and axial load- mid-height deflection of all tested columns are shown in Figs. 8–10. A summary of ultimate load, axial shortening at peak load, and average hoop strain at peak load and mid-height lateral deflection at peak load are shown in Fig. 11. It can be seen in Fig. 11a that the use of CFRP volumetric ratio of 0.3% improved the load carrying capacity by about 15% under concentric compression load. This is due to confining pressure provided by the CFRP wrapping and by increasing the CFRP volumetric ratios this improvement is expected to increase as observed by other researches under concentric compression load. The effects of increasing CFRP volumetric ratios on the eccentrically loaded columns under
Fig. 10. Axial load-lateral deflection at mid-height of RC square columns under various eccentricities at (a) e = 25 mm, (b) e = 35 mm and (c) e = 50 mm.
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Fig. 11. Summary of (a) ultimate load, (b) axial deformation at peak load, (c) hoop strain at peak load and (d) lateral deflection at peak load of RC square columns under concentric loading and various eccentricities.
Fig. 12. Stiffness of RC square columns under concentric loading and various eccentricities.
increasing eccentricities on the axial load-displacement behaviour of CFRP wrapped square columns can be seen in Fig. 8b–d. It can be seen that the load carrying capacities of eccentrically loaded columns increase with increase in CFRP volumetric ratios under all eccentricities except at e = 35 mm, where the load capacities of CFRP wrapped
columns containing CFRP volumetric ratios of 0.6% and 0.9% are slightly lower than that containing CFRP volumetric ratio of 0.3%. It is also interesting to see that the improvement in load carrying capacities of columns containing CFRP volumetric ratios of 0.6% and 0.9% is very similar in all eccentricities. In the case of axial shortening at peak loads 316
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Fig. 13. Ductility of RC square columns under concentric loading and various eccentricities.
e=0 mm
e=25 mm
e=35 mm
e=50 mm
Fig. 14. Failure behaviour of CFRP wrapped columns containing CFRP volumetric ratio of 0.3% under various eccentricities (close-up of buckling of steel and rupturing of CFRP are shown at bottom).
a similar trend is observed in Fig. 10b where the axial deformation increases with increase in CFRP volumetric ratios in all eccentricities and decreases with increase in eccentricities, except for CFRP volumetric ratio of 0.6% at e = 50 mm eccentricity. Unlike ultimate loads, no similarities can be seen in the axial deformation in CFRP volumetric ratios of 0.6% and 0.9%. By comparing results in Fig. 11a we can see that significant improvement in ultimate axial load is observed at all eccentricities due to CFRP wrapping and increase in CFRP volumetric ratios. However, beyond CFRP volumetric ratio of 0.6% the improvement was not significant but the ultimate axial load were still higher than un-wrapped columns at all eccentricities. Inconsistencies in increase in axial load capacity of columns with increase in FRP volumetric ratios is also reported in numerous studies even without eccentric loading [17,18]. The hoop strains on CFRP at mid-height of all columns as well as the lateral deflection of columns at mid-height are also measured until
failure. The hoop strain values indicate the confining efficiency where higher hoop strains indicate higher confining pressure provided by the CFRP under load. It can be seen in Fig. 11c that the average hoop strain at mid-height of columns increases with increase in CFRP volumetric ratio up to 0.6% except in the case of CFRP volumetric ratio of 0.9% in all eccentricities. The reduction in hoop strains of columns containing CFRP volumetric ratio of 0.9% than those of 0.6% coincide with the axial shortening values where the columns containing CFRP volumetric ratio of 0.9% shorten excessively than those containing CFRP volumetric ratio of 0.6%. These might be the reason for lower ultimate load of those columns containing CFRP volumetric ratio of 0.9% than those of volumetric ratio of 0.6%. Because, under eccentric loading the CFRP might have debonded in the compression side which do not contribute to the confinement and hence no contribution in load capacity. With regard to the mid-height lateral deflection no trend can be seen in Fig. 11d with regards to the CFRP volumetric ratios and increasing 317
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e=25 mm
e=35 mm
e=50 mm
Fig. 15. Failure behaviour of CFRP wrapped columns containing CFRP volumetric ratio of 0.6% under various eccentricities (close-up of buckling of steel and rupturing of CFRP are shown at bottom).
eccentricities. Nevertheless, the experimental results show that the square RC columns strengthened using CFRP volumetric ratio of 0.6% exhibited higher load carrying capacity and confining efficiency in terms of higher hoop strains.
displacement at peak load to that at yield load [19] and is shown in Fig. 13. It can be seen that the ductility increases with increase in CFRP volumetric ratios and decreases with increase in eccentricity irrespective of CFRP volumetric ratios.
3.2. Stiffness and ductility of CFRP wrapped columns under increasing eccentricities
3.3. Failure behaviour of CFRP wrapped columns under increasing eccentricities
The stiffness is calculated by considering the slope of the liner portion of ascending branch of axial load-displacement curves of all columns and are shown in Fig. 12. It can be seen that the column containing CFRP volumetric ratio of 0.3% improves the stiffness by about 16% under concentric load. Improvement in stiffness of columns is also observed under all three eccentricities due to confinement of column using various CFRP volumetric ratios. In the case of 25 mm eccentricity a decreasing trend of increase in stiffness is observed with increase in CFRP volumetric ratios, however, at higher eccentricities e.g. at e = 35 mm a stable trend and at e = 50 mm an increasing trend is observed. Nevertheless, for any CFRP volumetric ratio, the stiffness of strengthened columns decreases with increase in eccentricities. Ductility is considered as one of the important parameter for structural members as it provides insight on the deformability and energy absorption of structural members during failure. The ductility of all columns was analysed as well to evaluate the effect of number of CFRP volumetric ratios on the efficiency of strengthened columns under eccentric loading. The ductility is calculated as the ratio of axial
With regard to the failure behaviour of CFRP wrapped columns, it can be seen a relatively longer softening branch in load-axial displacement curves of all CFRP wrapped columns compared to unstrengthened columns for all eccentricities and the softening tail increases with increase in CFRP volumetric ratios. However, the stiffness of the softening branches decreases with increase in eccentricities regardless of CFRP volumetric ratios. This indicates that the CFRP fabrics ruptured and longitudinal reinforcement buckled (reinforcement buckling is intensifying delamination as well as rupture of the FRP wraps in higher eccentricities) due to bending of columns with increase in eccentricities, which are evidenced in the failure modes of columns containing CFRP volumetric ratio of 0.3% under increasing eccentricities as shown in Fig. 14. It can be seen buckling of longitudinal steels and spalling of concrete in the close-up of failure zones of respective columns in Fig. 14. Similar buckling of longitudinal steels and rupturing of CFRP are observed in columns wrapped with CFRP volumetric ratios of 0.6% and 0.9% shown in Figs. 15 and 16, respectively, however, the level of buckling and the spalling area of concrete are much smaller
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e=25 mm
e=35 mm
e=50 mm
Fig. 16. Failure behaviour of CFRP wrapped columns containing CFRP volumetric ratio of 0.9% under various eccentricities (close-up of buckling of steel and rupturing of CFRP are shown at bottom).
Fig. 17. Moment-mid span deflection behaviour of RC square columns wrapped with CFRP layers under three-point bending.
than that containing CFRP volumetric ratio of 0.3% under all eccentricities.
in CFRP volumetric ratios (as shown in Fig. 17). This insignificant improvement in moment in pure flexure of CFRP wrapped columns is due to the fact that the CFRP used in this study was uni-directional and was wrapped in transverse direction. As a result the CFRP did not contribute to the tensile stress developed in the tension side of the specimen under pure flexure, which can be seen in Fig. 18 where carbon fibres in CFRP were relatively intact. The failure behaviour of wrapped columns become ductile in a sense that the columns CF1B, CF2B, and CF3B
3.4. Failure and moment-deflection behaviour of CFRP wrapped columns under three-point bending In the case of wrapped columns CF1B, CF2B, and CF3B there was a slight improvement in the ultimate moment of about 8% due to increase
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Fig. 18. Rupturing of CFRP in three-point bending.
Fig. 21. Strain distribution of critical points in load-moment interaction diagram of column.
3.5. Load-moment interaction diagram of CFRP wrapped columns In this analytical study it is assumed that the behaviour of CFRP confined concrete is similar to that of the unconfined concrete except the constitutive stress-strain equation of CFRP-confined concrete is adopted to develop the interaction diagram. All of the interaction diagrams herein are developed by connecting five critical points with straight lines as shown in Fig. 21 the state of each critical point is as follows:
Fig. 19. Propagation and localization of diagonal shear cracks in control column withour CFRP wrap.
• Point A: This point corresponds to column under pure compression • • • •
and a uniform distribution of ultimate strain (εccu for FRP-confined concrete and εcu for unconfined concrete) exists all over the column cross section. Point B: This point corresponds to ultimate compressive strain (εccu for confined concrete) at outmost compressive part of the cross section and zero strain at the level of longitudinal rebar closest to the tensile part of the cross section. Point C: This point corresponds to balanced failure of the column with maximum compressive strain of εccu at the extreme compressive fibre of the cross section and yield tensile strain εfy at steel reinforcement layer closest to extreme tensile fibre of the cross section. Point D: This point is located at the limit of tensile-controlled failure with a compressive strain of εccu at the extreme compressive fibre and the tensile strain of 0.005 at the longitudinal reinforcement layer closest to the extreme tensile fibre of the cross section. Point E: This point represents the bending state of the column and the value of the moment corresponds to the ultimate flexural capacity of the column.
In calculation of moment as well as compressive force of the columns, contribution of the CFRP confinement is only considered compression controlled regions (Points A, B, and C in Fig. 20). Since in this study no CFRP fibres are arranged in the longitudinal direction of the column the contribution of transverse CFRP wraps in flexural resistance is negligible. For points B and C the location of neutral axis (c) is found by applying similar triangle method for the strain distribution and the corresponding axial and flexural capacity is found by integration of stresses (or first moment of inertia of stresses) over the cross section of the column. In the case of point E the moment is found by applying the
Fig. 20. Failure of CFRP wrapped columns under three-point bending.
undergo 18 mm, 27 mm, and 35 mm, respectively of mid-span deflection compared to 5 mm of control column without CFRP wrap. Another observation is that CFRP wrapping changed the failure mode of the beams from brittle shear failure in control column (shown in Fig. 19) to a ductile flexural mode accompanied by longitudinal rebar yielding and rupturing of CFRP for the wrapped specimens (as shown in Fig. 20).
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Fig. 22. Experimental load-moment interaction diagrams of warped square columns containing CFRP volumetric ratios of 0, 0.3, 0.6 and 0.9%.
conservative estimation of those columns which yield about 1880 kN and 2002 kN axial load capacity, respectively. The estimated axial loads are very close to the predicated by Youssef et al. [21] and Eid and Paultre [22] in the case of CFRP volumetric ratios of 0.6% and 0.9% as shown in Fig. 20. The other two models e.g. Lam and Teng [20] and Faustino et al. [22] underestimate the axial capacity. In the case of columns with CFRP volumetric ratios of 0.6% and 0.9%, models by Lam and Teng [20], Faustino et al. [23], and Eid & Paultre [22] estimate the flexural capacity with a good accuracy while model by Youssef et al. [21] overestimates the flexural capacity especially at balanced failure point which is not conservative. Model by Lam and Teng [20] underestimates the axial capacity by a considerable margin while model by Faustino et al. [23] has a better prediction of axial capacity, it still is conservative and is underestimating the axial force. Models by Youssef et al. [21] and Eid & Paultre [22] have the closest estimation of axial capacity of the columns. The considerable underestimation of axial forces in model by Lam and Teng [20] can be attributed to the fact that in the compression controlled zone for points that resemble a combined flexural and axial state of stress (Points B and C) the ultimate strain of the concrete is limited to 0.004 following the recommendation by Rocca et al. [26]. Overall by comparing the test results to the models it can be witnessed that the model developed by Eid & Paultre [22] exhibit the best performance in calculation of P-M diagram. This close fit can be attributed to the fact that in this model the full 3D interaction of the internal reinforcement and CFRP wraps are considered in modelling the behaviour of CFRP confined RC columns.
conventional beam theory to calculate the ultimate flexural capacity. Four different FRP-confined concrete models are considered to develop load-moment interaction diagram of CFRP wrapped columns with compared to the experimental results in order to study their applicability in predicting load-moment interaction diagram of CFRP wrapped RC square columns. These models were by Lam and Teng [20], Youssef et al. [21], Eid and Paultre [22] and Faustino et al. [23]. Experimental load-moment (P-M) interaction diagrams of control column and CFRP wrapped columns containing CFRP volumetric ratios of 0.3%, 0.6% and 0.9% are shown in Fig. 22. It should be noted that due to limitation of testing machine the columns wrapped by 2 and 3 layers CFRP corresponding to CFRP volumetric ratios of 0.6% and 0.9%, respectively were not tested in pure compression instead their theoretical capacities were calculated based on existing confinement models and are used in this interaction diagram. By comparing the wrapped columns with that of un-wrapped column it can be seen that the load and moment capacities of wrapped columns are higher than those of un-wrapped column and increase with increase in CFRP volumetric ratios. Experimental load-moment (P-M) interaction diagrams are also compared to those of the models in Fig. 23 for CFRP wrapped columns. In the case of columns containing CFRP volumetric ratio of 0.3%, models by Lam and Teng [20], Youssef et al. [21] and Faustino et al. [23] predict the ultimate flexural capacity of the column in the compression controlled zone with good accuracy however in these models the axial capacity is underestimated. On the contrary, the model proposed by Eid and Paultre [22] yields a closer estimation of axial capacity while flexural capacity is underestimated. It can be seen in Fig. 10a that the CFRP volumetric ratio of 0.3% increased the axial load capacity of RC square column by about 15%. Due to limitation of testing machine of the columns wrapped by two and three layer CFRP were not tested. However, based on reported results on RC square columns wrapped by CFRP the axial capacity for two and three layer can be conservatively estimated. For example, Darby et al. [24] reported about 22% increase in axial load capacity of two CFRP layers wrapped 150 mm square RC column. Benzaid et al. [25] observed 15% improvement in axial load capacity of two GFRP layers wrapped 100 mm square RC column. Therefore, based on reported results and observed improvement for CFRP volumetric ratio of 0.3%, 22% and 30% improvements in axial load capacity of RC square columns wrapped CFRP layer with CFRP volumetric ratios of 0.6% and 0.9% are
4. Conclusions This paper presents experimental results on the behaviour of CFRP wrapped RC square columns with CFRP volumetric ratios of 0.3%, 0.6% and 0.9% under various eccentric loadings. Based on available experimental results the following conclusions are summarised: 1. Regardless of eccentricities the load carrying capacities of columns increased due to wrapping by CFRP. An increasing trend of load carrying capacities is observed with increase in CFRP volumetric ratios at all eccentricities except at e = 35 mm where a slight reduction is observed. Load carrying capacities are also decreased
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3.
4.
5.
6.
eccentricities due to confinement of column using CFRP fabric layers. In the case of 25 mm eccentricity, a decreasing trend is observed with increase in CFRP volumetric ratios, however, at e = 35 mm a stable trend and at e = 50 mm an increasing trend is observed. Average hoop strain values at mid height of column increased with increase in CFRP volumetric ratios at all eccentricities. Hoop strains are also increased with increase in eccentricities for CFRP volumetric ratios of 0.3% and 0.6%, however for CFRP volumetric ratio of 0.9% an opposite trends is observed. No trend is observed in lateral deflection at mid height of columns with regards to eccentricities and CFRP volumetric ratios. Among the models Eid & Paultre [22] model demonstrated the best performance in prediction of P-M interaction diagram of CFRP wrapped RC square columns containing CFRP volumetric ratios of 0.3% and 0.6%. Whereas Faustina et al. [23] model predicts the P-M interaction diagram for CFRP volumetric ratio of 0.9%. Among the wrapped columns a clear increasing pattern is observed in the ductility of specimens when increasing the CFRP volumetric ratios. This trend in ductility improvement indicates the energy absorption capacity of columns can be increased by providing thicker jackets and higher confinement pressures as a result. There is little evidence that CFRP wrapping increases the ultimate flexural capacity of the beam specimens, although their deformability is increased significantly. Also the brittle shear failure mode in unwrapped beams is changed to a ductile flexural failure mode in the CFRP wrapped specimens.
References [1] Campione G, Miraglia N. Strength and strain capacities of concrete compression members reinforced with FRP. Cem Concr Compos 2003;25:31–41. [2] Pessiki S, Harries KA, Kestner JT, Sause R, Ricles JM. Axial behaviour of reinforced concrete columns confined with FRP jackets. J Compos Constr 2001;5(4):237–45. [3] Parvin A, Wang W. Behaviour of FRP jacketed concrete columns under eccentric loading. J Compos Constr 2001;5(3):146–52. [4] Fam A, Flisak B, Rizkalla S. Experimental and analytical modeling of concrete-filled fiber-reinforced polymer tubes subjected to combined bending and axial loads. ACI Struct J 2003;100(4):1–11. [5] Li J, Hadi MNS. Behaviour of externally confined high strength concrete columns under eccentric loading. Compos Struct 2003;62(2):145–53. [6] Hadi MNS, Li J. External reinforcement of high strength concrete columns. Compos Struct 2004;65(3–4):279–87. [7] Hadi MNS. Behaviour of FRP wrapped normal strength concrete columns under eccentric loading. Compos Struct 2006;72(4):503–11. [8] Hadi MNS. Comparative study of eccentrically loaded FRP wrapped columns. Compos Struct 2006;74(2):127–35. [9] Hadi MNS. Behaviour of FRP strengthened concrete columns under eccentric compression loading. Compos Struct 2007;77(1):92–6. [10] Hadi MNS. The behaviour of FRP wrapped HSC columns under different eccentric loads. Compos Struct 2007;78(4):560–6. [11] Chaallal O, Shahawy M. Performance of fiber-reinforced polymer wrapped reinforced concrete column under combined axial-flexural loading. ACI Struct J 2000;97(4):659–88. [12] Lignola GP, Prota A, Manfredi G, Cosenza E. Experimental performance of RC hollow columns confined with CFRP. J Compos Constr 2007;11(1):42–9. [13] Hatami F, Saadat H, Saba HR. Comparison experimental behaviour of RC column with and without carbon fiber polymer (CFRP) layer under eccentric loading. Proceedings of the 13th East Asia Pacific conference on structural engineering and construction (EASEC-13), September 11–13, 2013, Sapporo, Japan. 2013. [14] Sadeghian P, Rahai A, Ehsani MR. Experimental study of rectangular RC columns strengthened with CFRP composites under eccentric loading. J Compos Constr 2010;14(4):443–50. [15] Lei X, Pham TM, Hadi MNS. Behaviour of CFRP wrapped square RC columns under eccentric loading. Australasian structural engineering conference, Perth, Australia. 2012. [16] Widiarsa IBR, Hadi MNS. Performance of CFRP wrapped square reinforced concrete columns subjected to eccentric loading. Proc Eng 2013;54:365–76. [17] Mirmiran et al. (1998) Effect of column parameters on FRP-confined concrete, J Compos Constr, 2(4):175–185. [18] Munteanu, et al. Structural behaviour of eccentrically loaded FRP confined square RC columns. Recent advances in urban planning and construction. 2011. [19] Wang LM, Wu YF. Effect of corner radius on the performance of CFRP-confined square concrete columns: test. Eng Struct 2008;30:493–505.
Fig. 23. Comparison of experimental load-moment interaction diagrams with those predicated by various models for columns with CFRP volumetric ratios of (a) 0.3%, (b) 0.6% and (c) 0.9%.
with increase in eccentricities for all CFRP volumetric ratios. 2. Axial deformation is increased with increase in CFRP volumetric ratios in all eccentricities. However, it slightly decreased at higher eccentricities e.g. at e = 35 and 50 mm at any given CFRP volumetric ratios. Stiffness of columns is increased under all three
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F.U.A. Shaikh and R. Alishahi [20] Lam L, Teng J. Oriented stress–strain model for FRP-confined concrete in design rectangular columns. J Reinf Plast Compos 2003;22(13):1149–86. [21] Youssef MN, Feng QF, Mosallam AS. Stress-strain model for concrete confined by FRP composites. Compos Part B 2007;38:614–28. [22] Eid R, Paultre P. Compressive behavior of FRP-confined reinforced concrete columns. Eng Struct 2017;132:518–30. [23] Faustino P, Chastre C, Paula R. Design model for square RC columns under compression confined with CFRP. Compos Part B 2014;57:187–98.
[24] Darby AP, Coonan R, Tim I, Mark E. FRP confined square columns under concentric and eccentric loading. Proceedings of 5th international conference on advanced composite in construction, 6-8th sept. 2011, Warwick, UK. 2011. [25] Benzaid R, Chikh NE, Mesbah H. Behaviour of square concrete column confined with GFRP composite wrap. J Civ Eng Manag 2008;14(2):115–20. [26] Rocca S, Galati N, Nanni A. Interaction diagram methodology for design of FRPconfined reinforced concrete columns. Construct Build Mater 2009;23:1508–20.
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Behaviour of CFRP wrapped RC square columns under eccentric compressive loading
T
Faiz Uddin Ahmed Shaikh , Reza Alishahi ⁎
School of Civil and Mechanical engineering, Curtin University, GPO Box: U1987, Perth, WA6845, Australia
ARTICLE INFO
ABSTRACT
Keywords: CFRP Columns Eccentricity Strengthening Failure behaviour Compression load Load-moment interaction diagram
This paper presents the effects of carbon fibre reinforced polymer (CFRP) volumetric ratios on structural and failure behaviour of CFRP wrapped reinforced concrete (RC) square columns under concentric, eccentric and flexural loadings. The CFRP volumetric ratio is considered as the ratio of volume of CFRP to the volume of concrete. The applicability of existing confinement models to predict the load-moment interaction diagrams of such columns in eccentric loadings is also presented in this paper. Total 20 columns were tested. Dimensions of all columns were 175x175x800 mm with 20 mm rounded corners. Variable considered in this study were number of CFRP layers (e.g. 0, 1, 2 and 3 layers) which corresponds to CFRP volumetric ratio of 0, 0.3, 0.6 and 0.9%, respectively, increasing eccentricities (e.g. 0, 25, 35 and 50 mm) of the applied load and pure flexural loading. Results show that ultimate load capacity and axial deformation increase with increase in CFRP volumetric ratios irrespective of eccentricities. However, load capacity and deformation decrease with increasing eccentricities for any given CFRP volumetric ratio. Hoop strains also increase with increase in CFRP volumetric ratios and eccentricities. Stiffness of CFRP wrapped columns also increases with increase in CFRP volumetric ratio up to 0.6% and decreases with increase in eccentricities. Ductility of CFRP wrapped columns increases with increase in CFRP volumetric ratios and eccentricities. The algorithms for calculation of critical points for loadmoment (P-M) interaction diagrams using analytical as well as numerical stress integrations are developed and compared to those of the column tests. P-M interaction diagram developed using existing confinement models agree well with the experimental P-M interaction diagrams of CFRP wrapped RC square columns under eccentric loading.
1. Introduction The use of fibre reinforced polymer (FRP) for strengthening and rehabilitation of reinforced concrete (RC) structures is a common practice in the construction industry. Among various structural members, the strengthening and rehabilitation of columns by wrapping FRP fabric is most effective and efficient as the FRP does not debond prematurely and under increasing compression load the confinement efficiency of FRP is significantly increased. For circular columns, the confining pressure occurs around the entire perimeter due to the curvature of the FRP wrap produce uniform confining stress (Fig. 1a). Under concentric loading the confinement of a circular concrete column can effectively increase the strength by up to 200% [1,2]. FRP-confined rectangular columns behave in a significantly different manner due to the non-uniform distribution of hoop strains and stress concentration at the corners as shown in Fig. 1b. With the application of concentric loading, the FRP at four corners goes into tension as shown in Fig. 1b
⁎
and the confining forces are only generated at the convex corners in rectangular/square columns. Several studies have been conducted on FRP confined and strengthened RC columns under concentric loads. However, it is clear that in real situation most columns experience combination of axial compression load and bending moment (i.e. eccentric compression loading) due to construction error, moments transfer from beam to column in rigid beam-column connection, unsymmetrical loading, etc. Therefore, there is a need to understand the behaviour of FRP strengthened columns under eccentric loading. Some research has been conducted on FRP confined columns under eccentric loading. In a study performed by Parvin and Wang [3], small-scale square concrete columns having 108 mm × 108 mm in cross-section and 305 mm in height were strengthened with varying layers of carbon FRP (CFRP) and subjected to axial load at different eccentricities. The results showed that the increase in eccentricity resulted in reduction in strength capacity of the column, and the use of CFRP increased the load capacity of the
Corresponding author. E-mail address: [email protected] (F.U.A. Shaikh).
https://doi.org/10.1016/j.istruc.2019.04.012 Received 22 December 2018; Received in revised form 16 April 2019; Accepted 17 April 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Confinement stress distribution around (a) circular vs (b) square column due to FRP wrapping. Table 1 Experimental program and configuration of test specimens. Series
Specimens
Eccentricity
Number of CFRP layers
CFRP volumetric ratio (%)
Longitudinal reinforcement
Transverse reinforcement
First
CR0 CF10 CF20 CF30 CR1 CF11 CF21 CF31 CR2 CF12 CF22 CF32 CR3 CF13 CF23 CF33 CRB CF1B CF2B CF3B
e = 0 mm (Pure compression)
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
0 0.3 0.6 0.9 0 0.3 0.6 0.9 0 0.3 0.6 0.9 0 0.3 0.6 0.9 0 0.3 0.6 0.9
4 N12
R6@100 mm
4 N12
R6@100 mm
4 N12
R6@100 mm
4 N12
R6@100 mm
4 N12
R6@100 mm
Second
Third
Fourth
Fifth
e = 25 mm
e = 35 mm
e = 50 mm
Pure flexure (Beam Test)
B
15 mm clear cover
4N12
A
A
800 mm
r
175 mm
R6@100
175 mm
20 mm radius
Section A - A
B t 175 mm
Fig. 3. Cross-section of RC column and reinforcement details.
column. Fam et al. [4] performed an experimental study and proposed an analytical model to describe the behavior of concrete filled FRP tubes subjected to combined axial compression loads and bending moments. Li and Hadi [5], Hadi and Li [6], and Hadi [7–10] tested several FRP-strengthened concrete columns with circular section under eccentric loading at different end conditions. The effects of concrete
Fig. 2. Definitions of geometric dimension of CFRP confined square column to calculate the CFRP volumetric ratio.
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Table 2 Properties of CFRP fabric and epoxy.
CFRP (Sikawrap 230C) Two-part epoxy (Sikadur 330)
Tensile strength (MPa)
Elongation at rupture (%)
Tensile modulus (GPa)
Thickness (mm)
4300
1.8
234
0.13
30
0.9
4.5
–
Table 3 Mechanical properties of concrete and longitudinal steel. 28 days compressive strength of concrete (MPa)
28 days tensile strength of concrete (MPa)
Steel yield strength (MPa)
Steel ultimate strength (MPa)
Steel ultimate strain
47
4
500
690
0.068
SG8
SG1
SG7
square RC columns under eccentric loading. It can be seen in above review that there are numerous studies on behaviour of RC columns strengthened by FRP materials. However, if we look into those studies it can be seen that most of them were on circular column and concentric compression loads were applied. Even some studies reported results of eccentrically loaded rectangular or square columns strengthened by FRP, most of them were short column. The present study used medium height square column to evaluate the effect of different eccentricities and pure flexure to establish load-moment interaction diagram and compared with theoretical load-moment interaction diagram using four confinement models. This paper presents the results of a comprehensive experimental program where 18 RC square columns are wrapped with various layers of CFRP fabric and are subjected to increasing eccentricities under pin-pin end conditions in compression to pure flexure under three-point bending. Effects of eccentricities and number of CFRP layers on the ultimate failure load, axial shortening at peak load, hoop strain in CFRP and mid height lateral deflection of all CFRP strengthened columns are also evaluated. Load-moment interaction diagrams are also developed based on experimental results and compared with existing models for FRP confined section in order to evaluate their suitability in predicting the load and moment capacities of CFRP confined square columns under eccentric loading.
SG2
SG3
SG6
SG4 SG5
Fig. 4. Strain gauge arrangement around the hoop at mid-height of the column.
strength, internal steel reinforcement, wrap type, fibre orientation, and eccentricity were studied. The eccentric load was applied through a circular plate at each end of the specimens. The experimental results clearly demonstrated that the FRP wrapping enhanced strength, ductility, and energy absorption of circular concrete columns under eccentric loading. In a study performed by Chaallal and Shahawy [11], an experimental investigation was conducted on rectangular RC columns strengthened with bi-directional CFRP composites and different eccentricities. The overall length of the two haunched-head specimens was 3.6 m (200 mm wide and 350 mm high in test section). The results indicated that the strength capacity of columns improved significantly as a result of the combined action of the longitudinal and the transverse fibres of the bi-directional composite fabrics. Lignola et al. [12] reported a study where they have mainly focused their attention on square hollow columns strengthened with CFRP composites (height of 3020 mm, width of 360 mm, and wall thicknesses of 60 mm). The outcomes highlighted that composite wrapping can enhance the structural performance of concrete columns under eccentric loading in terms of strength and especially in terms of ductility. The strength improvement was more pronounced in the case of specimens loaded with smaller eccentricity, while the ductility improvement was more significant in the case of larger eccentricity. Hatami et al. [13] and Sadeghian et al. [14] in their studies evaluated the effectiveness of CFRP wrapped rectangular RC columns (200 × 300 mm) of 1.5 m long under eccentric compression loading. Lei et al. [15] and Widiarsa and Hadi [16] studied the effectiveness of CFRP strengthened RC columns of square cross-section under eccentric loading and reported that the CFRP wrapping enhanced the load carrying capacity and ductility of the
2. Experimental program In total 20 square RC columns with 175 mm in sides and 800 mm in height were cast and tested. The columns were divided in to five series according to the types of loading shown in Table 1. In the first series concentric compression load was applied in the columns wrapped with 0, 1, 2 and 3 layers of CFRP fabric. In second, third and fourth groups eccentric compression load were applied at 25, 35 and 50 mm eccentricities, respectively from the centre of the columns. In fifth series, three-point bending was applied in the above CFRP warped columns to simulate bending behaviour. Detail experimental program is shown in Table 1. The number of CFRP layers in the columns is defined as the CFRP volumetric ratio. The CFRP volumetric ratio is considered as the ratio of volume of CFRP to the volume of concrete in the column as follows. Fig. 2 shows the typical dimension of column and CFRP to calculate the CFRP volumetric ratio. Based on the proposed CFRP volumetric ratio, the CFRP volumetric ratios of 1, 2 and 3 CFRP layer are 0.3, 0.6 and 0.9%, respectively. CFRP =
[4(B 2r ) + 2 r ] t [B 2 + r 2 4r 2]
100
where, ρCFRP = CFRP volumetric ratio 311
(1)
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8 strain gauges attached transversely to measure the hoop strain in CFRP at the middle of the column. (4 at middle of sides and 4 at corners)
Three horizontal LVDTs to measure the lateral deflection of the column in the middle and approximately 200mm above and below the middle LVDT.
Two vertical LVDTs to measure the longitudinal shortening of the column. Fig. 5. Detail of instrumentation and setup of CFRP wrapped column for testing under compressive loading.
Struts attached to the load cell
LVDTs for vertical deflection measurement of the beam spaced at 200 mm
Fig. 6. Three-point bending beam test instrumentation.
Loading head Adjustable long slots to maintain eccentricity
Knife edge to represent pin support Loading cell of machine
Fig. 7. Developed ecentric loading mechanism and manufactured loading head.
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Table 4 Summary of results of all columns tested in this study. Specimens CR0 CF10 a CF20 a CF30 CR1 CF11 CF21 CF31 CR2 CF12 CF22 CF32 CR3 CF13 CF23 CF33 a
Yield load (kN)
Axial displacement at yield load (mm)
Ultimate load (kN)
Axial displacement at peak load (mm)
Ductility
Stiffness (kN/mm)
1247 894
3.55 2.56
1555 1784.5 1902 2078 1036 1229 1320 1283 840 1098 1020 998 654 798 884 840
4.5 4.95
1.27 1.93
528 610.3
– –
223 867 745 649 415 975 775 750 470 840 795 678
– –
1.89 2.2 3 1.05 2.17 0.098 5.36 0.04 2.42 1.73 1.94 3.93
– –
4.2 4.6 5.6 6.1 3.7 4.1 4.1 5.7 3.4 5.1 4.1 5.3
– –
2.24 3.94 4.18 5.82 1.69 3.51 4.48 4.94 1.38 2.97 3.69 3.74
– –
404 586 579 480 336 388 388 388 219 260 284 285
Ultimate loads are calculated values based on confinement models.
Fig. 8. Axial load-axial deformation (axial deflection) of RC square columns under (a) concentric loading (e = 0 mm) and various eccentricities at (b) e = 25 mm, (c) e = 35 mm and (d) e = 50 mm.
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Fig. 9. Axial load-hoop strain at mid-height of RC square columns under (a) concentric loading (e = 0 mm) and various eccentricities at (b) e = 25 mm, (c) e = 35 mm and (d) e = 50 mm.
B = Side of square column r = corner radius of column t = thickness of CFRP
2.2. Preparation of specimens Ready-mixed concrete was purchased from a local supplier. Slump tests were carried out immediately after the arrival of the concrete. The results from the slump tests showed that the concrete had a slump of more than 150 mm. After that, the concrete was poured into the formworks made from plywoods. All specimens were then covered with wet hessian and cured in room temperature for 28 days before they were taken out of the formwork. In order to reduce the stress concentration at four corners of the columns, a 20 mm radius round edge was created at each corner by attaching a specially manufactured foam shaper in four corners of all column moulds. After 28 days of curing all minor defects on the surface of the specimens were patched using standard mortar and then the surface of the concrete was polished and smoothed using concrete grinder. Secondly, epoxy resin was spread onto the surface of the specimen and the first layer of CFRP was attached. After that, epoxy resin was spread again on the surface of the first layer of CFRP and the second layer was attached. The same procedure was followed until three layers of CFRP were bonded. A 100 mm overlap was maintained for each layer. The specimens were left to dry for 14 days as specified by the supplier.
2.1. Detail of specimens and materials All columns had identical internal steel reinforcement. Four 12 mm deformed bars with a nominal tensile yield strength of 500 MPa were provided as longitudinal reinforcement and 6 mm plain bars were provided as transverse reinforcement with 100 mm spacing. Fig. 3 shows the cross-section and reinforcement details of the columns. Concrete cover was maintained at 15 mm thick on the surface and 20 mm thickness at top and bottom. The columns were made from normal strength concrete with a 28 days compressive strength of 47 MPa. Carbon Fibre Reinforced Polymer (CFRP) fabric was used as a primary confining material. The CFRP was 500 mm in width with unidirectional fibres. Two-part epoxy was used to bond the CFRP fabric with concrete. Properties of CFRP and two-part epoxy is provided in Table 2, while the measured mechanical properties of concrete and longitudinal steel are shown in Table 3. 314
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2.3. Loading system In total 8 electrical strain gauges of 60 mm long (wire strain gauge with polyester resin backing) were attached horizontally on CFRP at mid height of each column to measure the hoop strains as shown in Fig. 4. Four at corners and four at middle of the four sides of each column. In addition LVDTs having accuracy of ± 0.25% were also used to measure the axial shortening and lateral deflection at mid height of the columns as well as to measure the mid-span deflection of the specimens in three-point beam test. Detail instrumentation to measure the strain and displacements of concentrically and eccentrically loaded columns are show in Fig. 5, while Fig. 6 shows the instrumentation and loading arrangement in three-point bending test. Special steel frame was manufactured to hold the LVDTs in position and aluminum angels were glued to the specimens where probe tip of LVDTs were touched. 2.4. Concentric and eccentric loading All columns were tested using a 1800 kN capacity universal testing machine. An especially designed loading system was used to apply eccentric loading in the columns. The loading system consists of steel loading head at both ends of column. The loading head is connected to a thick steel plate which is then attached to a knife edge arrangement to facilitate the pin connection at both ends as shown in Fig. 7. The thick plate which was connected to loading head, contained adjustable long slots to maintain the required eccentricities in this study. Fig. 5 shows the detail of eccentric load arrangement. All specimens were capped at both ends using high strength plaster to ensure even distribution of forces. Calibration was carried out to ensure the specimen was placed in the centre. For axial loading test the loading rate of 70 kN/min which is 0.16 mm/min in the elastic range was used. 2.5. Three-point bending For the pure flexural test a three-point bending configuration was chosen. As shown in Fig. 5 the struts were attached to a load cell to apply a concentrated load at the middle of the beam. The length of the span was 700 mm and the support to the left of the picture is roller and the support to the right is a pin support. The load is being exerted on a v shaped metal plate which is attached to the surface of the specimen using rapid setting plaster. As shown in Fig. 6 three LVDTs are placed every 200 mm along the length of the beam. In order to simulate the static loading conditions, the rate of 0.16 mm/min loading was maintained during the tests. 3. Results and discussion 3.1. Load deformation behaviour of CFRP wrapped columns under increasing eccentricities All specimens were tested until failure and their results are summarised in Table 4. The load, strain and displacement data were collected using a 32 channels data-logger connected to the 1800 kN universal testing machine where the columns were tested. The effects of CFRP volumetric ratios and eccentricities on axial load – axial displacement, axial load- average hoop strain and axial load- mid-height deflection of all tested columns are shown in Figs. 8–10. A summary of ultimate load, axial shortening at peak load, and average hoop strain at peak load and mid-height lateral deflection at peak load are shown in Fig. 11. It can be seen in Fig. 11a that the use of CFRP volumetric ratio of 0.3% improved the load carrying capacity by about 15% under concentric compression load. This is due to confining pressure provided by the CFRP wrapping and by increasing the CFRP volumetric ratios this improvement is expected to increase as observed by other researches under concentric compression load. The effects of increasing CFRP volumetric ratios on the eccentrically loaded columns under
Fig. 10. Axial load-lateral deflection at mid-height of RC square columns under various eccentricities at (a) e = 25 mm, (b) e = 35 mm and (c) e = 50 mm.
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Fig. 11. Summary of (a) ultimate load, (b) axial deformation at peak load, (c) hoop strain at peak load and (d) lateral deflection at peak load of RC square columns under concentric loading and various eccentricities.
Fig. 12. Stiffness of RC square columns under concentric loading and various eccentricities.
increasing eccentricities on the axial load-displacement behaviour of CFRP wrapped square columns can be seen in Fig. 8b–d. It can be seen that the load carrying capacities of eccentrically loaded columns increase with increase in CFRP volumetric ratios under all eccentricities except at e = 35 mm, where the load capacities of CFRP wrapped
columns containing CFRP volumetric ratios of 0.6% and 0.9% are slightly lower than that containing CFRP volumetric ratio of 0.3%. It is also interesting to see that the improvement in load carrying capacities of columns containing CFRP volumetric ratios of 0.6% and 0.9% is very similar in all eccentricities. In the case of axial shortening at peak loads 316
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Fig. 13. Ductility of RC square columns under concentric loading and various eccentricities.
e=0 mm
e=25 mm
e=35 mm
e=50 mm
Fig. 14. Failure behaviour of CFRP wrapped columns containing CFRP volumetric ratio of 0.3% under various eccentricities (close-up of buckling of steel and rupturing of CFRP are shown at bottom).
a similar trend is observed in Fig. 10b where the axial deformation increases with increase in CFRP volumetric ratios in all eccentricities and decreases with increase in eccentricities, except for CFRP volumetric ratio of 0.6% at e = 50 mm eccentricity. Unlike ultimate loads, no similarities can be seen in the axial deformation in CFRP volumetric ratios of 0.6% and 0.9%. By comparing results in Fig. 11a we can see that significant improvement in ultimate axial load is observed at all eccentricities due to CFRP wrapping and increase in CFRP volumetric ratios. However, beyond CFRP volumetric ratio of 0.6% the improvement was not significant but the ultimate axial load were still higher than un-wrapped columns at all eccentricities. Inconsistencies in increase in axial load capacity of columns with increase in FRP volumetric ratios is also reported in numerous studies even without eccentric loading [17,18]. The hoop strains on CFRP at mid-height of all columns as well as the lateral deflection of columns at mid-height are also measured until
failure. The hoop strain values indicate the confining efficiency where higher hoop strains indicate higher confining pressure provided by the CFRP under load. It can be seen in Fig. 11c that the average hoop strain at mid-height of columns increases with increase in CFRP volumetric ratio up to 0.6% except in the case of CFRP volumetric ratio of 0.9% in all eccentricities. The reduction in hoop strains of columns containing CFRP volumetric ratio of 0.9% than those of 0.6% coincide with the axial shortening values where the columns containing CFRP volumetric ratio of 0.9% shorten excessively than those containing CFRP volumetric ratio of 0.6%. These might be the reason for lower ultimate load of those columns containing CFRP volumetric ratio of 0.9% than those of volumetric ratio of 0.6%. Because, under eccentric loading the CFRP might have debonded in the compression side which do not contribute to the confinement and hence no contribution in load capacity. With regard to the mid-height lateral deflection no trend can be seen in Fig. 11d with regards to the CFRP volumetric ratios and increasing 317
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e=25 mm
e=35 mm
e=50 mm
Fig. 15. Failure behaviour of CFRP wrapped columns containing CFRP volumetric ratio of 0.6% under various eccentricities (close-up of buckling of steel and rupturing of CFRP are shown at bottom).
eccentricities. Nevertheless, the experimental results show that the square RC columns strengthened using CFRP volumetric ratio of 0.6% exhibited higher load carrying capacity and confining efficiency in terms of higher hoop strains.
displacement at peak load to that at yield load [19] and is shown in Fig. 13. It can be seen that the ductility increases with increase in CFRP volumetric ratios and decreases with increase in eccentricity irrespective of CFRP volumetric ratios.
3.2. Stiffness and ductility of CFRP wrapped columns under increasing eccentricities
3.3. Failure behaviour of CFRP wrapped columns under increasing eccentricities
The stiffness is calculated by considering the slope of the liner portion of ascending branch of axial load-displacement curves of all columns and are shown in Fig. 12. It can be seen that the column containing CFRP volumetric ratio of 0.3% improves the stiffness by about 16% under concentric load. Improvement in stiffness of columns is also observed under all three eccentricities due to confinement of column using various CFRP volumetric ratios. In the case of 25 mm eccentricity a decreasing trend of increase in stiffness is observed with increase in CFRP volumetric ratios, however, at higher eccentricities e.g. at e = 35 mm a stable trend and at e = 50 mm an increasing trend is observed. Nevertheless, for any CFRP volumetric ratio, the stiffness of strengthened columns decreases with increase in eccentricities. Ductility is considered as one of the important parameter for structural members as it provides insight on the deformability and energy absorption of structural members during failure. The ductility of all columns was analysed as well to evaluate the effect of number of CFRP volumetric ratios on the efficiency of strengthened columns under eccentric loading. The ductility is calculated as the ratio of axial
With regard to the failure behaviour of CFRP wrapped columns, it can be seen a relatively longer softening branch in load-axial displacement curves of all CFRP wrapped columns compared to unstrengthened columns for all eccentricities and the softening tail increases with increase in CFRP volumetric ratios. However, the stiffness of the softening branches decreases with increase in eccentricities regardless of CFRP volumetric ratios. This indicates that the CFRP fabrics ruptured and longitudinal reinforcement buckled (reinforcement buckling is intensifying delamination as well as rupture of the FRP wraps in higher eccentricities) due to bending of columns with increase in eccentricities, which are evidenced in the failure modes of columns containing CFRP volumetric ratio of 0.3% under increasing eccentricities as shown in Fig. 14. It can be seen buckling of longitudinal steels and spalling of concrete in the close-up of failure zones of respective columns in Fig. 14. Similar buckling of longitudinal steels and rupturing of CFRP are observed in columns wrapped with CFRP volumetric ratios of 0.6% and 0.9% shown in Figs. 15 and 16, respectively, however, the level of buckling and the spalling area of concrete are much smaller
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e=25 mm
e=35 mm
e=50 mm
Fig. 16. Failure behaviour of CFRP wrapped columns containing CFRP volumetric ratio of 0.9% under various eccentricities (close-up of buckling of steel and rupturing of CFRP are shown at bottom).
Fig. 17. Moment-mid span deflection behaviour of RC square columns wrapped with CFRP layers under three-point bending.
than that containing CFRP volumetric ratio of 0.3% under all eccentricities.
in CFRP volumetric ratios (as shown in Fig. 17). This insignificant improvement in moment in pure flexure of CFRP wrapped columns is due to the fact that the CFRP used in this study was uni-directional and was wrapped in transverse direction. As a result the CFRP did not contribute to the tensile stress developed in the tension side of the specimen under pure flexure, which can be seen in Fig. 18 where carbon fibres in CFRP were relatively intact. The failure behaviour of wrapped columns become ductile in a sense that the columns CF1B, CF2B, and CF3B
3.4. Failure and moment-deflection behaviour of CFRP wrapped columns under three-point bending In the case of wrapped columns CF1B, CF2B, and CF3B there was a slight improvement in the ultimate moment of about 8% due to increase
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Fig. 18. Rupturing of CFRP in three-point bending.
Fig. 21. Strain distribution of critical points in load-moment interaction diagram of column.
3.5. Load-moment interaction diagram of CFRP wrapped columns In this analytical study it is assumed that the behaviour of CFRP confined concrete is similar to that of the unconfined concrete except the constitutive stress-strain equation of CFRP-confined concrete is adopted to develop the interaction diagram. All of the interaction diagrams herein are developed by connecting five critical points with straight lines as shown in Fig. 21 the state of each critical point is as follows:
Fig. 19. Propagation and localization of diagonal shear cracks in control column withour CFRP wrap.
• Point A: This point corresponds to column under pure compression • • • •
and a uniform distribution of ultimate strain (εccu for FRP-confined concrete and εcu for unconfined concrete) exists all over the column cross section. Point B: This point corresponds to ultimate compressive strain (εccu for confined concrete) at outmost compressive part of the cross section and zero strain at the level of longitudinal rebar closest to the tensile part of the cross section. Point C: This point corresponds to balanced failure of the column with maximum compressive strain of εccu at the extreme compressive fibre of the cross section and yield tensile strain εfy at steel reinforcement layer closest to extreme tensile fibre of the cross section. Point D: This point is located at the limit of tensile-controlled failure with a compressive strain of εccu at the extreme compressive fibre and the tensile strain of 0.005 at the longitudinal reinforcement layer closest to the extreme tensile fibre of the cross section. Point E: This point represents the bending state of the column and the value of the moment corresponds to the ultimate flexural capacity of the column.
In calculation of moment as well as compressive force of the columns, contribution of the CFRP confinement is only considered compression controlled regions (Points A, B, and C in Fig. 20). Since in this study no CFRP fibres are arranged in the longitudinal direction of the column the contribution of transverse CFRP wraps in flexural resistance is negligible. For points B and C the location of neutral axis (c) is found by applying similar triangle method for the strain distribution and the corresponding axial and flexural capacity is found by integration of stresses (or first moment of inertia of stresses) over the cross section of the column. In the case of point E the moment is found by applying the
Fig. 20. Failure of CFRP wrapped columns under three-point bending.
undergo 18 mm, 27 mm, and 35 mm, respectively of mid-span deflection compared to 5 mm of control column without CFRP wrap. Another observation is that CFRP wrapping changed the failure mode of the beams from brittle shear failure in control column (shown in Fig. 19) to a ductile flexural mode accompanied by longitudinal rebar yielding and rupturing of CFRP for the wrapped specimens (as shown in Fig. 20).
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Fig. 22. Experimental load-moment interaction diagrams of warped square columns containing CFRP volumetric ratios of 0, 0.3, 0.6 and 0.9%.
conservative estimation of those columns which yield about 1880 kN and 2002 kN axial load capacity, respectively. The estimated axial loads are very close to the predicated by Youssef et al. [21] and Eid and Paultre [22] in the case of CFRP volumetric ratios of 0.6% and 0.9% as shown in Fig. 20. The other two models e.g. Lam and Teng [20] and Faustino et al. [22] underestimate the axial capacity. In the case of columns with CFRP volumetric ratios of 0.6% and 0.9%, models by Lam and Teng [20], Faustino et al. [23], and Eid & Paultre [22] estimate the flexural capacity with a good accuracy while model by Youssef et al. [21] overestimates the flexural capacity especially at balanced failure point which is not conservative. Model by Lam and Teng [20] underestimates the axial capacity by a considerable margin while model by Faustino et al. [23] has a better prediction of axial capacity, it still is conservative and is underestimating the axial force. Models by Youssef et al. [21] and Eid & Paultre [22] have the closest estimation of axial capacity of the columns. The considerable underestimation of axial forces in model by Lam and Teng [20] can be attributed to the fact that in the compression controlled zone for points that resemble a combined flexural and axial state of stress (Points B and C) the ultimate strain of the concrete is limited to 0.004 following the recommendation by Rocca et al. [26]. Overall by comparing the test results to the models it can be witnessed that the model developed by Eid & Paultre [22] exhibit the best performance in calculation of P-M diagram. This close fit can be attributed to the fact that in this model the full 3D interaction of the internal reinforcement and CFRP wraps are considered in modelling the behaviour of CFRP confined RC columns.
conventional beam theory to calculate the ultimate flexural capacity. Four different FRP-confined concrete models are considered to develop load-moment interaction diagram of CFRP wrapped columns with compared to the experimental results in order to study their applicability in predicting load-moment interaction diagram of CFRP wrapped RC square columns. These models were by Lam and Teng [20], Youssef et al. [21], Eid and Paultre [22] and Faustino et al. [23]. Experimental load-moment (P-M) interaction diagrams of control column and CFRP wrapped columns containing CFRP volumetric ratios of 0.3%, 0.6% and 0.9% are shown in Fig. 22. It should be noted that due to limitation of testing machine the columns wrapped by 2 and 3 layers CFRP corresponding to CFRP volumetric ratios of 0.6% and 0.9%, respectively were not tested in pure compression instead their theoretical capacities were calculated based on existing confinement models and are used in this interaction diagram. By comparing the wrapped columns with that of un-wrapped column it can be seen that the load and moment capacities of wrapped columns are higher than those of un-wrapped column and increase with increase in CFRP volumetric ratios. Experimental load-moment (P-M) interaction diagrams are also compared to those of the models in Fig. 23 for CFRP wrapped columns. In the case of columns containing CFRP volumetric ratio of 0.3%, models by Lam and Teng [20], Youssef et al. [21] and Faustino et al. [23] predict the ultimate flexural capacity of the column in the compression controlled zone with good accuracy however in these models the axial capacity is underestimated. On the contrary, the model proposed by Eid and Paultre [22] yields a closer estimation of axial capacity while flexural capacity is underestimated. It can be seen in Fig. 10a that the CFRP volumetric ratio of 0.3% increased the axial load capacity of RC square column by about 15%. Due to limitation of testing machine of the columns wrapped by two and three layer CFRP were not tested. However, based on reported results on RC square columns wrapped by CFRP the axial capacity for two and three layer can be conservatively estimated. For example, Darby et al. [24] reported about 22% increase in axial load capacity of two CFRP layers wrapped 150 mm square RC column. Benzaid et al. [25] observed 15% improvement in axial load capacity of two GFRP layers wrapped 100 mm square RC column. Therefore, based on reported results and observed improvement for CFRP volumetric ratio of 0.3%, 22% and 30% improvements in axial load capacity of RC square columns wrapped CFRP layer with CFRP volumetric ratios of 0.6% and 0.9% are
4. Conclusions This paper presents experimental results on the behaviour of CFRP wrapped RC square columns with CFRP volumetric ratios of 0.3%, 0.6% and 0.9% under various eccentric loadings. Based on available experimental results the following conclusions are summarised: 1. Regardless of eccentricities the load carrying capacities of columns increased due to wrapping by CFRP. An increasing trend of load carrying capacities is observed with increase in CFRP volumetric ratios at all eccentricities except at e = 35 mm where a slight reduction is observed. Load carrying capacities are also decreased
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3.
4.
5.
6.
eccentricities due to confinement of column using CFRP fabric layers. In the case of 25 mm eccentricity, a decreasing trend is observed with increase in CFRP volumetric ratios, however, at e = 35 mm a stable trend and at e = 50 mm an increasing trend is observed. Average hoop strain values at mid height of column increased with increase in CFRP volumetric ratios at all eccentricities. Hoop strains are also increased with increase in eccentricities for CFRP volumetric ratios of 0.3% and 0.6%, however for CFRP volumetric ratio of 0.9% an opposite trends is observed. No trend is observed in lateral deflection at mid height of columns with regards to eccentricities and CFRP volumetric ratios. Among the models Eid & Paultre [22] model demonstrated the best performance in prediction of P-M interaction diagram of CFRP wrapped RC square columns containing CFRP volumetric ratios of 0.3% and 0.6%. Whereas Faustina et al. [23] model predicts the P-M interaction diagram for CFRP volumetric ratio of 0.9%. Among the wrapped columns a clear increasing pattern is observed in the ductility of specimens when increasing the CFRP volumetric ratios. This trend in ductility improvement indicates the energy absorption capacity of columns can be increased by providing thicker jackets and higher confinement pressures as a result. There is little evidence that CFRP wrapping increases the ultimate flexural capacity of the beam specimens, although their deformability is increased significantly. Also the brittle shear failure mode in unwrapped beams is changed to a ductile flexural failure mode in the CFRP wrapped specimens.
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Fig. 23. Comparison of experimental load-moment interaction diagrams with those predicated by various models for columns with CFRP volumetric ratios of (a) 0.3%, (b) 0.6% and (c) 0.9%.
with increase in eccentricities for all CFRP volumetric ratios. 2. Axial deformation is increased with increase in CFRP volumetric ratios in all eccentricities. However, it slightly decreased at higher eccentricities e.g. at e = 35 and 50 mm at any given CFRP volumetric ratios. Stiffness of columns is increased under all three
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