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Effects of wrap thickness and ply configuration on composite-confined concrete cylinders
Composite Structures 67 (2005) 437–442 www.elsevier.com/locate/compstruct
Effects of wrap thickness and ply configuration on composite-confined concrete cylinders Azadeh Parvin *, Aditya S. Jamwal Department of Civil Engineering, The University of Toledo, Toledo, OH 43606, USA Available online 25 March 2004
Abstract The behavior of small-scale fiber reinforced polymer (FRP) wrapped concrete cylinders under uniaxial compressive loading was investigated through nonlinear finite element analysis. Two parameters were considered for this numerical study: the FRP wrap thickness, and the ply configuration. Performances of numerical models with ‘‘hoop-angle-hoop’’ and ‘‘angle-hoop-angle’’ ply configurations were compared, where the terms ‘‘hoop’’ and ‘‘angle’’ indicate that wraps were oriented at an angle of 0 and 45 in reference to circumferential direction, respectively. The finite element analysis results showed substantial increase in the axial compressive strength and ductility of the FRP confined concrete cylinders as compared to the unconfined ones. The cylinders with ‘‘hoop-angle-hoop’’ ply configuration in general exhibited higher axial stress and strain capacities as compared to the cylinders with the ‘‘angle-hoop-angle’’ ply configuration. The increase in wrap thickness also resulted in enhancement of axial strength and ductility of the concrete cylinders. 2004 Elsevier Ltd. All rights reserved. Keywords: Columns; Concrete; Fibers; Composite wrap; Uniaxial compression; Strength; Ductility; Ply angle; Wrap thickness
1. Introduction Although a concrete-filled steel tube is an effective retrofit technique and has been used widely in practice, fiber composite jackets have recently shown great potential as a desirable alternative to steel jackets for retrofitting as well as new construction since fiber composite materials are lightweight, noncorrosive, and exhibit high tensile strength [1–9]. The composite jacket provides enhancement in compressive strength and ductility due to confining the concrete core. Studies performed on fiber reinforced polymer (FRP) confined concrete columns are more infrequent and limited compared to extensively available database on FRP-strengthened concrete beams. Many of the studies on FRP-confined concrete columns involve evaluation of experimental results with available confinement models in the literature [1,2] while others focus on prediction of bilinear stress–strain response of FRPconfined concrete columns under uniaxial compression: employment of analytical models and subsequent *
Corresponding author. Tel.: +1-419-530-8134; fax: +1-419-5308116. E-mail address: [email protected] (A. Parvin). 0263-8223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.02.002
validation with experiments of their own or other researchers [3–5] is widely adopted. As an on-going deficiency in the literature, parametric studies related to the effect of ‘‘hoop-angle-hoop’’ and ‘‘angle-hoopangle’’ ply configurations have not been taken into account in most of the studies of FRP-jacketed columns reported. On the other hand, limited investigations suggest this parameter influences the strength and ductility of FRP-wrapped columns subjected to the axial load [7]. In presence of the perceived deficiency in current literature and significance of the issue, this research indeed explores the effects of ply angle and ply stacking sequence combined with wrap thickness on FRPconfined short columns through nonlinear finite element analysis: the expectation is to develop a better understanding and consequently to be able to leverage this understanding to fine-tune these parameters in design. A literature survey of significant research studies relevant to this research thrust will be presented next. A number of studies on FRP-confined concrete columns subjected to uniaxial compression, where the wrap angle orientation was 0 with respect to circumferential direction, appeared in the recent literature. Nanni and Bradford [1] tested 152.5 · 305 mm (6 · 12 in.) FRPconfined concrete cylinders to verify the validity of
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existing analytical models. Their experimental results indicated that the jacket increased the ductility and strength significantly and the analytical models were accurate for the prediction of strength, but underestimated the ultimate strain of FRP-confined columns. Saafi et al. [4] tested short concrete columns confined with FRP tubes under uniaxial compressive load to investigate the effects of FRP jacket thickness as well as fiber type and concrete strength. Significant improvement in strength, ductility, and energy capacity was reported and the axial strain of confined concrete increased as the jacket thickness increased. Parvin and Wang [6] performed experimental and numerical analysis of FRP-jacketed square concrete columns under eccentric loading, where the effects of various eccentricities and FRP jacket thickness were investigated. The results showed that strength and ductility of concrete FRP-jacketed columns under eccentric loading can greatly increase and that the strain gradient decreases the retrofit efficiency of the FRP jacket for concrete columns. Additionally, similar to short columns subjected to concentric axial load, the strength and ductility of the eccentrically loaded columns increased as the jacket thickness increased. Although this study involved the effects of the wrap and its thickness on short columns it was limited to 0 ply orientation configuration. A number of researchers employed a ply orientation different than just 0 with respect to circumferential direction in FRP-confined concrete columns while not necessarily studying variations in ply angle and ply stacking sequence. Mirmiran and Shahawy [2] conducted experiments on axially loaded 152.5 · 305 mm (6 · 12 in.) concrete-filled FRP tubes made of unidirectional E-glass fibers at ±15 winding angle. Various jacket thicknesses of 6, 10, and 14 plies were examined, while winding angle was fixed. Their findings indicated that, as the jacket thickness increased, the strength and ductility increased as well. However, their study was concentrated on one winding angle configuration (±15 winding angle) with no further discussion on this parameter. Rochette and Labossiere [7] axially tested the effect of wrap thickness and cross-section shape of short column on its strength (circular, square, and rectangular). The wraps had 0 angle orientation with horizontal axis with the exception of one square specimen being wrapped with [±15/0] ‘‘angle-hoop’’ configuration. Their results indicated that confinement enhanced the strength of axially loaded short columns as much as 92%. The variation of number of plies on square columns wrapped with carbon or aramid improved the strength and ductility as the number of plies increased. The column with ‘‘angle-hoop’’ configuration exhibited a peculiar behavior. Although the maximum strength of five-layer ‘‘angle-hoop’’ confinement increased as compared to four-layer circumferential confinement, its ductility decreased: the number of layers were chosen
such that the overall confinement stiffness of five-layers ‘‘angle-hoop’’ would be approximately equivalent to four-layer circumferential confinement. They concluded that the effect of ‘‘angle-hoop’’ wrap as a candidate for obtaining more strength and ductility should be investigated. Their study on the ply orientation was limited to one specimen and one ‘‘angle-hoop’’ configuration. Pessiki et al. [8] performed experiments on small-scale square and circular plain concrete specimens as well as large-scale square and circular reinforced concrete FRPjacketed columns under axial load. The FRP jackets were made of (a) 0/±45 multidirectional E-glass fiber reinforced polymer (GFRP) jackets E-glass fabric with 50% of its fibers oriented at 0 angle with respect to circumferential direction and 25% of fibers oriented at each of ±45), (b) 0 unidirectional GFRP jackets, and (c) 0 unidirectional carbon fiber reinforced polymer (CFRP) jackets. The compressive strength increased by 128% for small-scale circular specimens with one-ply 0/ ±45 GFRP jacket and 244% for circular specimens with two-ply 0 CFRP jackets. Additionally, as compared to unjacketed specimens, axial strains at peak stress have increased approximately seven times. Their investigation on fiber orientation was limited to a single configuration for fiber orientation at 0/±45. It would be a reasonable assessment to state that practically all studies presented thus far have not adequately looked at the effects of angle and hoop plies and their staking sequence such as ‘‘hoop-angle-hoop’’ and ‘‘angle-hoop-angle’’ combined with various wrap thicknesses. Some have just investigated one ‘‘angle’’ wrap configuration, while others performed limited studies on ‘‘hoop-angle’’ or ‘‘angle-hoop’’ ply configurations combined with various thicknesses without any concentration on stacking sequence effect. When fibers are oriented with an angle with respect to circumferential direction, they provide effective modulus and strength in both axial and hoop directions, and this may eliminate the use of conventional steel reinforcement from the column altogether. Also, since shear cracks usually happen at ±45 angle, the ±45 wrap angle combination will possibly ensure reinforcement perpendicular to the shear crack and suppress shear failure. For instance, in the case of column of a joint subject to both axial and transverse loadings, the shear capacity and/or flexural capacity might increase when using ±45 ply for the wrap [9]. Furthermore, the axial strength capacity might increase due to existence of ‘‘hoop-angle-hoop’’ plies and their confinement effect, while the rate of increase for each capacity might vary. The objective of our study is to characterize the increase in stress–strain response of FRP-confined concrete cylinders due to the jacket thickness and staking sequence of plies with various angles in the jacket. The MSCMARCTM 2001 nonlinear finite element analysis (FEA) software will be employed for modeling and
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simulation [10]. Such FEA models will facilitate fine tuning the values of these parameters in design to maximize the axial strength and ductility of FRP-confined concrete cylinders.
2. Finite element analysis models The small-scale circular columns considered in this study had dimensions of 152.5 · 305 mm (6 · 12 in.). Fig. 1 illustrates the boundary conditions of a typical circular column. The bottom of the concrete column is fixed in x-, y-, and z-directions. To prevent the slippage of FRP jacket in the z-direction between the concrete and the FRP jacket in the vertical direction, a gap of 0.1016 mm (0.004 in.) was established on top and bottom of the column. This assures that FRP does not carry any axial load. The axial load is applied at the top crosssection of the column and increases until failure occurs. Fig. 2 shows the plot of load increment on the x-axis versus the axial load on the y-axis. The load factor of ‘1’ on y-axis corresponds to the actual applied load for a typical circular column. The distributed load multiplier is at least 1.5 times the maximum axial strength of the unconfined concrete column. Thus, the failure load is the distributed load multiplier times the number of load increments at the time of failure divided by 50, the maximum value on x-axis. The concrete was modeled as an isotropic material: the concrete strength was specified as 27.58 MPa (4000 psi). The modulus of elasticity ffiffiffiffi confined concrete was pof calculated using E ¼ 47; 586 fc0 where fc0 is the compressive strength of the concrete in psi [11]. A Poisson’s ratio of 0.17 was employed for all concrete column models. Along with Mohr–Coulomb failure criterion, isotropic work hardening rule defined the concrete
Fig. 2. Loading sequence for uniaxial load.
material’s plastic behavior. The failure criterion for the unconfined concrete was the crushing strain of 0.003. In this case, the small strain analysis option in MSCMARCTM 2001 was utilized. However, since it is expected to have large deformation in the confined concrete, the large strain option was selected. For all confined concrete cases, the wrap was unidirectional E-glass with a modulus of elasticity value of 41,370 MPa (6 · 106 psi) and a Poisson’s ratio of 0.24 obtained through tensile tests of flat coupons using ASTM D 3029 [12]. The failure strain was 0.019 and controlled the failure of the confined column. The unidirectional FRP composite was modeled as an orthotropic material.
3. Finite element analysis results In this section, stress–strain responses of unconfined and confined circular columns are presented. Parameters considered are the wrap thickness, and the wrap configuration (including combination of hoop and angle plies and their stacking sequence) listed in Table 1. The subscripts in the table indicate the number of alternating layers of FRP for each ply configuration. For example, in the case of 04 = 456 =04 , there are six layers of FRP with alternating angles of þ45= 45= þ 45= 45= þ45= 45= sandwiched by four-layers of 0 ply forming the wrap. 3.1. Unconfined concrete column (control model)
Fig. 1. Boundary conditions for a typical FRP wrapped circular column.
The column was subjected to the increasing axial load until the failure. The model showed maximum axial stress at 27.91 MPa (4048 psi) with an axial strain of 0.0032 at failure. Thus, the observed behavior depicted in Fig. 3 was as expected for unconfined concrete.
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Table 1 Columns with various ply configurations and thicknesses Case no. 1, 2 3, 4 5, 6
Ply configuration 02 = 452 =02 02 = 456 =02 04 = 456 =04
Wrap thickness mm (in.) 452 =02 = 452 452 =06 = 452 454 =06 = 454
1.3 (0.051) 2.1 (0.083) 3.0 (0.118)
3.3. Case 2: Confined column with ply configuration of 452 =02 = 452 and wrap thickness of 1.3 mm (0.051 in.) As compared to the Case 1, the model with ply configuration of 452 =02 = 452 and the same wrap thickness of 1.3 mm (0.051 in.) exhibited a lower confinement as seen in Fig. 5 due to modifying the ply stacking sequence to ‘‘angle-hoop-angle’’ from ‘‘hoopangle-hoop’’. However, with respect to the control model, there was a gain in strength and ductility. The axial stress increased by 29% and the axial strain was 6 times larger than that of the unconfined column. Fig. 3. Stress versus strain response at mid-height of the unconfined column.
3.2. Case 1: Confined column with ply configuration of 02 = 452 =02 and wrap thickness of 1.3 mm (0.051 in.) Analysis results for the model with the ply configuration of 02 = 452 =02 and wrap thickness of 1.3 mm (0.051 in.) are presented in Fig. 4, where the axial strength increased to 42.51 MPa (6165 psi) which is much beyond the unconfined concrete strength of 27.58 MPa (4000 psi). Thus, the 02 = 452 =02 ply configuration provided a very good confinement for the concrete column.
Fig. 4. Stress versus strain response at mid-height of the column with ply configuration of 02 = 452 =02 and wrap thickness of 1.3 mm.
3.4. Case 3: Confined column with ply configuration of 02 = 456 =02 and wrap thickness of 2.1 mm (0.083 in.) Fig. 6 shows that concrete column with ply configuration of 02 = 456 =02 and a wrap thickness of 2.1 mm (0.083 in.) has a tri-linear response. The column failed at an axial stress of 81.57 MPa (11830 psi) and an axial strain of 0.04133. This is attributed to the ‘‘hoopangle-hoop’’ ply configuration with 2 layers of 0 for the outermost layers, and 6 layers of ±45 sandwiched in the middle. The 02 = 456 =02 ply configuration resulted in excellent confinement. As compared to Case 1, which possesses similar ply configuration, both axial stress and strain improved due to the increase in the wrap thickness.
Fig. 5. Stress versus strain response at mid-height of the column with ply configuration of 452 =02 = 452 and wrap thickness of 1.3 mm.
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3.6. Case 5: Confined column with ply configuration of 04 = 456 =04 and wrap thickness of 3.0 mm (0.118 in.) The axial stress and axial strain for this case were 106.94 MPa (15,510 psi) and 0.04014, respectively (Fig. 8). This response was similar to the response for the column wrapped with ply configuration of 02 = 456 =02 and wrap thickness of 2.1 mm (0.083 in.). The higher axial stress and axial strain might be due to the two additional layers with 0 ply angle sandwiching the 456 layers.
Fig. 6. Stress versus strain response at mid-height of the column with ply configuration of 02 = 456 =02 and wrap thickness of 2.1 mm.
3.5. Case 4: Confined column with ply configuration of 452 =06 = 452 and wrap thickness of 2.1 mm (0.083 in.) As illustrated in Fig. 7, the concrete column with ply angle and stacking sequence of 452 =06 = 452 and a wrap thickness of 2.1 mm (0.083 in.) also has a tri-linear response similar to the column in Case 3 with the ply angle and stacking sequence of 02 = 456 =02 , while carrying lower level of axial stress and strain due to its ‘‘angle-hoop-angle’’ wrap configuration. The axial strength and strain of this case were also compared to the column with similar ply configuration but lower wrap thickness (Case 2). This comparison demonstrates an increase in axial stress and strain due to the wrap thickness.
Fig. 7. Stress versus strain response at mid-height of the column with ply configuration of 452 =06 = 452 and wrap thickness of 2.1 mm.
3.7. Case 6: Confined column with ply configuration of 454 =06 = 454 and wrap thickness of 3.0 mm (0.118 in.) This case shows maximum axial stress of 100.05 MPa (14510 psi) and an axial strain of 0.04194 at failure and has a similar response pattern as the Case 5 (see Fig. 9). The axial stress capacity decreased when the ply configuration changed from 04 = 456 =04 to 454 =06 = 454 . Thus, the ‘‘hoop-angle-hoop’’ ply configuration appears to be superior to ‘‘angle-hoop-angle’’ in providing axial strength and ductility. Analysis results showed that the compressive strength increased as the wrap thickness increased from 1.3 mm (0.051 in.) to 3.0 mm (0.118 in.). Additionally, concrete cylinders with ‘‘hoop-angle-hoop’’ wrap configuration consistently provided higher compressive strength as compared to ‘‘angle-hoop-angle’’ configuration, as seen from Table 2. As an example, the short column with wrap thickness of 1.3 mm (0.051 in.) and ‘‘hoop-anglehoop’’ wrap configuration of 02 = 452 =02 (Case 1) provided 18% additional axial strength capacity than the column with ‘‘angle-hoop-angle’’ of 452 =02 = 452 and the same wrap thickness (Case 2). The wrap
Fig. 8. Stress versus strain response at mid-height of the column with ply configuration of 04 = 456 =04 and wrap thickness of 3.0 mm.
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Fig. 9. Stress versus strain response at mid-height of column with ply configuration of 454 =06 = 454 and wrap thickness of 3.0 mm.
Table 2 Analysis results for column case studies 1 through 6 Case no.
Maximum axial stress MPa (psi)
Axial strain
1 2 3 4 5 6
42.51 (6165) 35.96 (5216) 81.57 (11,830) 76.05 (11,030) 106.94 (15,510) 100.05 (14,510)
0.02226 0.02362 0.04133 0.03174 0.04014 0.04194
‘‘hoop-angle-hoop’’ ply configuration of 04 = 456 =04 with the highest wrap thickness of 3.00 mm (0.118 in.) (Case 6) greatly enhanced the axial stress and axial strain capacities of the FRP-confined small-scale concrete columns. In this case, the compressive strength increased 258% (the highest of all cases) and the axial strain at failure point increased 12 times compared to unconfined concrete columns.
4. Conclusions The finite element analysis performed in this study demonstrated that externally bonded E-glass FRP reinforcement is a viable solution towards enhancing the strength and ductility of concrete cylinders subjected to axial load. Parameters considered include the wrap thickness and the wrap configuration, which includes combination of 0 and ±45 ply angles with respect to the circumferential direction and the ply stacking sequence. Wrapping configurations studied indicated angle and hoop plies and their stacking sequence: first
hoop, second angle, and third hoop versus first angle, second hoop, and third angle provide different enhancement levels of strength and ductility for the same thickness. Therefore, it is critical to investigate which upgrade scheme furnishes the enhancement in strength and/or ductility desired for the design purposes. Considering all six cases studied, columns with the ‘‘hoop-angle-hoop’’ wrap configuration consistently exhibited higher axial stress capacity as compared to the columns with the ‘‘angle-hoop-angle’’ configuration with the same wrap thickness. Additionally, in general columns with the same ply angle and ply stacking sequence exhibited increases in both axial stress and strain as the wrap thickness increased. Consequently, as a preliminary conclusion the ‘‘hoop-angle-hoop’’ wrap configuration is recommended for FRP-confined short circular columns in practice. However, in order to fully understand the effect of ply configuration on enhancement of strength and ductility, a more comprehensive study incorporating further options for wrap angle and other short columns such as square or rectangular where combination of hoop and angle ply configurations may prevent possible premature punching at the corners should be pursued.
References [1] Nanni A, Bradford NM. FRP jacketed under uniaxial compression. Constr Build Mater 1995;9(2):115–24. [2] Mirmiran A, Shahawy M. Behavior of concrete columns confined by fiber composites. J Struct Eng ASCE 1997;123(5):583– 90. [3] Samaan M, Mirmiran A, Shahawy M. Model of concrete confined by fiber composites. J Struct Eng ASCE 1998;124(9):1025–31. [4] Saafi M, Toutanji HA, Li Z. Behavior of concrete columns confined with fiber reinforced polymer tubes. ACI Mater J 1999;96(4):500–9. [5] Lam L, Teng JG. Strength models for fiber-reinforced plasticconfined concrete. J Struct Eng ASCE 2002;128(5):612–23. [6] Parvin A, Wang W. Behavior of FRP jacketed concrete columns under eccentric loading. J Compos Constr ASCE 2001;5(3):146– 52. [7] Rochette P, Labossiere P. Axial testing of rectangular column models confined with composites. J Compos Constr ASCE 2000; 4(3):129–36. [8] Pessiki S, Harries K, Kestner JT, Sause R, Ricles J. Axial behavior of reinforced concrete columns confined with FRP jackets. J Compos Constr 2001;5(4):237–45. [9] Parvin A, Wu S. Ply angle effect on fiber composite wrapped reinforced concrete beam-column connections under combined axial and cyclic loads. J Compos Constr ASCE, under revision. [10] MSC.MARC 2001. MSC Software Corporation, Palo Alto, CA. [11] Ahmad SH, Shah SP. Complete triaxial stress–strain curves for concrete. J Struct Div ASCE 1982;108(4):728–42. [12] Wang W. Behavior of fiber reinforced plastic jacketed concrete columns under eccentric loading. MS thesis. University of Toledo, Toledo, OH, 1999.
Effects of wrap thickness and ply configuration on composite-confined concrete cylinders Azadeh Parvin *, Aditya S. Jamwal Department of Civil Engineering, The University of Toledo, Toledo, OH 43606, USA Available online 25 March 2004
Abstract The behavior of small-scale fiber reinforced polymer (FRP) wrapped concrete cylinders under uniaxial compressive loading was investigated through nonlinear finite element analysis. Two parameters were considered for this numerical study: the FRP wrap thickness, and the ply configuration. Performances of numerical models with ‘‘hoop-angle-hoop’’ and ‘‘angle-hoop-angle’’ ply configurations were compared, where the terms ‘‘hoop’’ and ‘‘angle’’ indicate that wraps were oriented at an angle of 0 and 45 in reference to circumferential direction, respectively. The finite element analysis results showed substantial increase in the axial compressive strength and ductility of the FRP confined concrete cylinders as compared to the unconfined ones. The cylinders with ‘‘hoop-angle-hoop’’ ply configuration in general exhibited higher axial stress and strain capacities as compared to the cylinders with the ‘‘angle-hoop-angle’’ ply configuration. The increase in wrap thickness also resulted in enhancement of axial strength and ductility of the concrete cylinders. 2004 Elsevier Ltd. All rights reserved. Keywords: Columns; Concrete; Fibers; Composite wrap; Uniaxial compression; Strength; Ductility; Ply angle; Wrap thickness
1. Introduction Although a concrete-filled steel tube is an effective retrofit technique and has been used widely in practice, fiber composite jackets have recently shown great potential as a desirable alternative to steel jackets for retrofitting as well as new construction since fiber composite materials are lightweight, noncorrosive, and exhibit high tensile strength [1–9]. The composite jacket provides enhancement in compressive strength and ductility due to confining the concrete core. Studies performed on fiber reinforced polymer (FRP) confined concrete columns are more infrequent and limited compared to extensively available database on FRP-strengthened concrete beams. Many of the studies on FRP-confined concrete columns involve evaluation of experimental results with available confinement models in the literature [1,2] while others focus on prediction of bilinear stress–strain response of FRPconfined concrete columns under uniaxial compression: employment of analytical models and subsequent *
Corresponding author. Tel.: +1-419-530-8134; fax: +1-419-5308116. E-mail address: [email protected] (A. Parvin). 0263-8223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.02.002
validation with experiments of their own or other researchers [3–5] is widely adopted. As an on-going deficiency in the literature, parametric studies related to the effect of ‘‘hoop-angle-hoop’’ and ‘‘angle-hoopangle’’ ply configurations have not been taken into account in most of the studies of FRP-jacketed columns reported. On the other hand, limited investigations suggest this parameter influences the strength and ductility of FRP-wrapped columns subjected to the axial load [7]. In presence of the perceived deficiency in current literature and significance of the issue, this research indeed explores the effects of ply angle and ply stacking sequence combined with wrap thickness on FRPconfined short columns through nonlinear finite element analysis: the expectation is to develop a better understanding and consequently to be able to leverage this understanding to fine-tune these parameters in design. A literature survey of significant research studies relevant to this research thrust will be presented next. A number of studies on FRP-confined concrete columns subjected to uniaxial compression, where the wrap angle orientation was 0 with respect to circumferential direction, appeared in the recent literature. Nanni and Bradford [1] tested 152.5 · 305 mm (6 · 12 in.) FRPconfined concrete cylinders to verify the validity of
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existing analytical models. Their experimental results indicated that the jacket increased the ductility and strength significantly and the analytical models were accurate for the prediction of strength, but underestimated the ultimate strain of FRP-confined columns. Saafi et al. [4] tested short concrete columns confined with FRP tubes under uniaxial compressive load to investigate the effects of FRP jacket thickness as well as fiber type and concrete strength. Significant improvement in strength, ductility, and energy capacity was reported and the axial strain of confined concrete increased as the jacket thickness increased. Parvin and Wang [6] performed experimental and numerical analysis of FRP-jacketed square concrete columns under eccentric loading, where the effects of various eccentricities and FRP jacket thickness were investigated. The results showed that strength and ductility of concrete FRP-jacketed columns under eccentric loading can greatly increase and that the strain gradient decreases the retrofit efficiency of the FRP jacket for concrete columns. Additionally, similar to short columns subjected to concentric axial load, the strength and ductility of the eccentrically loaded columns increased as the jacket thickness increased. Although this study involved the effects of the wrap and its thickness on short columns it was limited to 0 ply orientation configuration. A number of researchers employed a ply orientation different than just 0 with respect to circumferential direction in FRP-confined concrete columns while not necessarily studying variations in ply angle and ply stacking sequence. Mirmiran and Shahawy [2] conducted experiments on axially loaded 152.5 · 305 mm (6 · 12 in.) concrete-filled FRP tubes made of unidirectional E-glass fibers at ±15 winding angle. Various jacket thicknesses of 6, 10, and 14 plies were examined, while winding angle was fixed. Their findings indicated that, as the jacket thickness increased, the strength and ductility increased as well. However, their study was concentrated on one winding angle configuration (±15 winding angle) with no further discussion on this parameter. Rochette and Labossiere [7] axially tested the effect of wrap thickness and cross-section shape of short column on its strength (circular, square, and rectangular). The wraps had 0 angle orientation with horizontal axis with the exception of one square specimen being wrapped with [±15/0] ‘‘angle-hoop’’ configuration. Their results indicated that confinement enhanced the strength of axially loaded short columns as much as 92%. The variation of number of plies on square columns wrapped with carbon or aramid improved the strength and ductility as the number of plies increased. The column with ‘‘angle-hoop’’ configuration exhibited a peculiar behavior. Although the maximum strength of five-layer ‘‘angle-hoop’’ confinement increased as compared to four-layer circumferential confinement, its ductility decreased: the number of layers were chosen
such that the overall confinement stiffness of five-layers ‘‘angle-hoop’’ would be approximately equivalent to four-layer circumferential confinement. They concluded that the effect of ‘‘angle-hoop’’ wrap as a candidate for obtaining more strength and ductility should be investigated. Their study on the ply orientation was limited to one specimen and one ‘‘angle-hoop’’ configuration. Pessiki et al. [8] performed experiments on small-scale square and circular plain concrete specimens as well as large-scale square and circular reinforced concrete FRPjacketed columns under axial load. The FRP jackets were made of (a) 0/±45 multidirectional E-glass fiber reinforced polymer (GFRP) jackets E-glass fabric with 50% of its fibers oriented at 0 angle with respect to circumferential direction and 25% of fibers oriented at each of ±45), (b) 0 unidirectional GFRP jackets, and (c) 0 unidirectional carbon fiber reinforced polymer (CFRP) jackets. The compressive strength increased by 128% for small-scale circular specimens with one-ply 0/ ±45 GFRP jacket and 244% for circular specimens with two-ply 0 CFRP jackets. Additionally, as compared to unjacketed specimens, axial strains at peak stress have increased approximately seven times. Their investigation on fiber orientation was limited to a single configuration for fiber orientation at 0/±45. It would be a reasonable assessment to state that practically all studies presented thus far have not adequately looked at the effects of angle and hoop plies and their staking sequence such as ‘‘hoop-angle-hoop’’ and ‘‘angle-hoop-angle’’ combined with various wrap thicknesses. Some have just investigated one ‘‘angle’’ wrap configuration, while others performed limited studies on ‘‘hoop-angle’’ or ‘‘angle-hoop’’ ply configurations combined with various thicknesses without any concentration on stacking sequence effect. When fibers are oriented with an angle with respect to circumferential direction, they provide effective modulus and strength in both axial and hoop directions, and this may eliminate the use of conventional steel reinforcement from the column altogether. Also, since shear cracks usually happen at ±45 angle, the ±45 wrap angle combination will possibly ensure reinforcement perpendicular to the shear crack and suppress shear failure. For instance, in the case of column of a joint subject to both axial and transverse loadings, the shear capacity and/or flexural capacity might increase when using ±45 ply for the wrap [9]. Furthermore, the axial strength capacity might increase due to existence of ‘‘hoop-angle-hoop’’ plies and their confinement effect, while the rate of increase for each capacity might vary. The objective of our study is to characterize the increase in stress–strain response of FRP-confined concrete cylinders due to the jacket thickness and staking sequence of plies with various angles in the jacket. The MSCMARCTM 2001 nonlinear finite element analysis (FEA) software will be employed for modeling and
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simulation [10]. Such FEA models will facilitate fine tuning the values of these parameters in design to maximize the axial strength and ductility of FRP-confined concrete cylinders.
2. Finite element analysis models The small-scale circular columns considered in this study had dimensions of 152.5 · 305 mm (6 · 12 in.). Fig. 1 illustrates the boundary conditions of a typical circular column. The bottom of the concrete column is fixed in x-, y-, and z-directions. To prevent the slippage of FRP jacket in the z-direction between the concrete and the FRP jacket in the vertical direction, a gap of 0.1016 mm (0.004 in.) was established on top and bottom of the column. This assures that FRP does not carry any axial load. The axial load is applied at the top crosssection of the column and increases until failure occurs. Fig. 2 shows the plot of load increment on the x-axis versus the axial load on the y-axis. The load factor of ‘1’ on y-axis corresponds to the actual applied load for a typical circular column. The distributed load multiplier is at least 1.5 times the maximum axial strength of the unconfined concrete column. Thus, the failure load is the distributed load multiplier times the number of load increments at the time of failure divided by 50, the maximum value on x-axis. The concrete was modeled as an isotropic material: the concrete strength was specified as 27.58 MPa (4000 psi). The modulus of elasticity ffiffiffiffi confined concrete was pof calculated using E ¼ 47; 586 fc0 where fc0 is the compressive strength of the concrete in psi [11]. A Poisson’s ratio of 0.17 was employed for all concrete column models. Along with Mohr–Coulomb failure criterion, isotropic work hardening rule defined the concrete
Fig. 2. Loading sequence for uniaxial load.
material’s plastic behavior. The failure criterion for the unconfined concrete was the crushing strain of 0.003. In this case, the small strain analysis option in MSCMARCTM 2001 was utilized. However, since it is expected to have large deformation in the confined concrete, the large strain option was selected. For all confined concrete cases, the wrap was unidirectional E-glass with a modulus of elasticity value of 41,370 MPa (6 · 106 psi) and a Poisson’s ratio of 0.24 obtained through tensile tests of flat coupons using ASTM D 3029 [12]. The failure strain was 0.019 and controlled the failure of the confined column. The unidirectional FRP composite was modeled as an orthotropic material.
3. Finite element analysis results In this section, stress–strain responses of unconfined and confined circular columns are presented. Parameters considered are the wrap thickness, and the wrap configuration (including combination of hoop and angle plies and their stacking sequence) listed in Table 1. The subscripts in the table indicate the number of alternating layers of FRP for each ply configuration. For example, in the case of 04 = 456 =04 , there are six layers of FRP with alternating angles of þ45= 45= þ 45= 45= þ45= 45= sandwiched by four-layers of 0 ply forming the wrap. 3.1. Unconfined concrete column (control model)
Fig. 1. Boundary conditions for a typical FRP wrapped circular column.
The column was subjected to the increasing axial load until the failure. The model showed maximum axial stress at 27.91 MPa (4048 psi) with an axial strain of 0.0032 at failure. Thus, the observed behavior depicted in Fig. 3 was as expected for unconfined concrete.
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Table 1 Columns with various ply configurations and thicknesses Case no. 1, 2 3, 4 5, 6
Ply configuration 02 = 452 =02 02 = 456 =02 04 = 456 =04
Wrap thickness mm (in.) 452 =02 = 452 452 =06 = 452 454 =06 = 454
1.3 (0.051) 2.1 (0.083) 3.0 (0.118)
3.3. Case 2: Confined column with ply configuration of 452 =02 = 452 and wrap thickness of 1.3 mm (0.051 in.) As compared to the Case 1, the model with ply configuration of 452 =02 = 452 and the same wrap thickness of 1.3 mm (0.051 in.) exhibited a lower confinement as seen in Fig. 5 due to modifying the ply stacking sequence to ‘‘angle-hoop-angle’’ from ‘‘hoopangle-hoop’’. However, with respect to the control model, there was a gain in strength and ductility. The axial stress increased by 29% and the axial strain was 6 times larger than that of the unconfined column. Fig. 3. Stress versus strain response at mid-height of the unconfined column.
3.2. Case 1: Confined column with ply configuration of 02 = 452 =02 and wrap thickness of 1.3 mm (0.051 in.) Analysis results for the model with the ply configuration of 02 = 452 =02 and wrap thickness of 1.3 mm (0.051 in.) are presented in Fig. 4, where the axial strength increased to 42.51 MPa (6165 psi) which is much beyond the unconfined concrete strength of 27.58 MPa (4000 psi). Thus, the 02 = 452 =02 ply configuration provided a very good confinement for the concrete column.
Fig. 4. Stress versus strain response at mid-height of the column with ply configuration of 02 = 452 =02 and wrap thickness of 1.3 mm.
3.4. Case 3: Confined column with ply configuration of 02 = 456 =02 and wrap thickness of 2.1 mm (0.083 in.) Fig. 6 shows that concrete column with ply configuration of 02 = 456 =02 and a wrap thickness of 2.1 mm (0.083 in.) has a tri-linear response. The column failed at an axial stress of 81.57 MPa (11830 psi) and an axial strain of 0.04133. This is attributed to the ‘‘hoopangle-hoop’’ ply configuration with 2 layers of 0 for the outermost layers, and 6 layers of ±45 sandwiched in the middle. The 02 = 456 =02 ply configuration resulted in excellent confinement. As compared to Case 1, which possesses similar ply configuration, both axial stress and strain improved due to the increase in the wrap thickness.
Fig. 5. Stress versus strain response at mid-height of the column with ply configuration of 452 =02 = 452 and wrap thickness of 1.3 mm.
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3.6. Case 5: Confined column with ply configuration of 04 = 456 =04 and wrap thickness of 3.0 mm (0.118 in.) The axial stress and axial strain for this case were 106.94 MPa (15,510 psi) and 0.04014, respectively (Fig. 8). This response was similar to the response for the column wrapped with ply configuration of 02 = 456 =02 and wrap thickness of 2.1 mm (0.083 in.). The higher axial stress and axial strain might be due to the two additional layers with 0 ply angle sandwiching the 456 layers.
Fig. 6. Stress versus strain response at mid-height of the column with ply configuration of 02 = 456 =02 and wrap thickness of 2.1 mm.
3.5. Case 4: Confined column with ply configuration of 452 =06 = 452 and wrap thickness of 2.1 mm (0.083 in.) As illustrated in Fig. 7, the concrete column with ply angle and stacking sequence of 452 =06 = 452 and a wrap thickness of 2.1 mm (0.083 in.) also has a tri-linear response similar to the column in Case 3 with the ply angle and stacking sequence of 02 = 456 =02 , while carrying lower level of axial stress and strain due to its ‘‘angle-hoop-angle’’ wrap configuration. The axial strength and strain of this case were also compared to the column with similar ply configuration but lower wrap thickness (Case 2). This comparison demonstrates an increase in axial stress and strain due to the wrap thickness.
Fig. 7. Stress versus strain response at mid-height of the column with ply configuration of 452 =06 = 452 and wrap thickness of 2.1 mm.
3.7. Case 6: Confined column with ply configuration of 454 =06 = 454 and wrap thickness of 3.0 mm (0.118 in.) This case shows maximum axial stress of 100.05 MPa (14510 psi) and an axial strain of 0.04194 at failure and has a similar response pattern as the Case 5 (see Fig. 9). The axial stress capacity decreased when the ply configuration changed from 04 = 456 =04 to 454 =06 = 454 . Thus, the ‘‘hoop-angle-hoop’’ ply configuration appears to be superior to ‘‘angle-hoop-angle’’ in providing axial strength and ductility. Analysis results showed that the compressive strength increased as the wrap thickness increased from 1.3 mm (0.051 in.) to 3.0 mm (0.118 in.). Additionally, concrete cylinders with ‘‘hoop-angle-hoop’’ wrap configuration consistently provided higher compressive strength as compared to ‘‘angle-hoop-angle’’ configuration, as seen from Table 2. As an example, the short column with wrap thickness of 1.3 mm (0.051 in.) and ‘‘hoop-anglehoop’’ wrap configuration of 02 = 452 =02 (Case 1) provided 18% additional axial strength capacity than the column with ‘‘angle-hoop-angle’’ of 452 =02 = 452 and the same wrap thickness (Case 2). The wrap
Fig. 8. Stress versus strain response at mid-height of the column with ply configuration of 04 = 456 =04 and wrap thickness of 3.0 mm.
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Fig. 9. Stress versus strain response at mid-height of column with ply configuration of 454 =06 = 454 and wrap thickness of 3.0 mm.
Table 2 Analysis results for column case studies 1 through 6 Case no.
Maximum axial stress MPa (psi)
Axial strain
1 2 3 4 5 6
42.51 (6165) 35.96 (5216) 81.57 (11,830) 76.05 (11,030) 106.94 (15,510) 100.05 (14,510)
0.02226 0.02362 0.04133 0.03174 0.04014 0.04194
‘‘hoop-angle-hoop’’ ply configuration of 04 = 456 =04 with the highest wrap thickness of 3.00 mm (0.118 in.) (Case 6) greatly enhanced the axial stress and axial strain capacities of the FRP-confined small-scale concrete columns. In this case, the compressive strength increased 258% (the highest of all cases) and the axial strain at failure point increased 12 times compared to unconfined concrete columns.
4. Conclusions The finite element analysis performed in this study demonstrated that externally bonded E-glass FRP reinforcement is a viable solution towards enhancing the strength and ductility of concrete cylinders subjected to axial load. Parameters considered include the wrap thickness and the wrap configuration, which includes combination of 0 and ±45 ply angles with respect to the circumferential direction and the ply stacking sequence. Wrapping configurations studied indicated angle and hoop plies and their stacking sequence: first
hoop, second angle, and third hoop versus first angle, second hoop, and third angle provide different enhancement levels of strength and ductility for the same thickness. Therefore, it is critical to investigate which upgrade scheme furnishes the enhancement in strength and/or ductility desired for the design purposes. Considering all six cases studied, columns with the ‘‘hoop-angle-hoop’’ wrap configuration consistently exhibited higher axial stress capacity as compared to the columns with the ‘‘angle-hoop-angle’’ configuration with the same wrap thickness. Additionally, in general columns with the same ply angle and ply stacking sequence exhibited increases in both axial stress and strain as the wrap thickness increased. Consequently, as a preliminary conclusion the ‘‘hoop-angle-hoop’’ wrap configuration is recommended for FRP-confined short circular columns in practice. However, in order to fully understand the effect of ply configuration on enhancement of strength and ductility, a more comprehensive study incorporating further options for wrap angle and other short columns such as square or rectangular where combination of hoop and angle ply configurations may prevent possible premature punching at the corners should be pursued.
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