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Stress Strain Behavior of Concrete in Circular Concrete Col 2018 Composite S

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Stress Strain Behavior of Concrete in Circular Concrete Col 2018 Composite S
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  Contents lists available at ScienceDirect Composite Structures  journal homepage: www.elsevier.com/locate/compstruct Stress-strain behavior of concrete in circular concrete columns partiallywrapped with FRP strips Jun-Jie Zeng a,b , Yong-Chang Guo a, ⁎ , Wan-Yang Gao c , Wei-Peng Chen a , Li-Juan Li a a  School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China b  Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, China c  School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China A R T I C L E I N F O  Keywords: FRPCircular columnFRP partially wrapped concreteStress-strain modelCon 󿬁 nementFRP strip/ring A B S T R A C T Fiber-reinforced polymer (FRP) wrapping has become an attractive strengthening technique for concrete col-umns. Within this strengthening technique, FRP jackets are wrapped around the concrete column with the  󿬁 bersin the jacket being oriented in the hoop direction. In practice, the FRP jackets can be either continuous ordiscontinuous along the column height and thus the resulting column is referred to as FRP fully or partiallywrapped concrete columns. Existing research has demonstrated that the FRP partial wrapping strengtheningtechnique by discrete FRP strips (rings) is a promising and economic alternative to the FRP full wrappingstrengthening technique. Although a number of experimental investigations have been conducted on FRP par-tially wrapped concrete columns, the stress-strain behavior of FRP-con 󿬁 ned concrete in partially wrappedconcrete columns is not yet completely understood. This paper presents an experimental program to investigatethe axial compressive behavior of circular concrete columns partially wrapped with FRP strips. The test resultsare presented and compared with  󿬁 ve existing representative stress-strain models to examine the reliability andaccuracy of each model. It has been demonstrated that the Teng et al. ’ s (2007) model is superior to the other fourrepresentative models and it provides reasonably accurate predictions of the ultimate axial stress of FRP partiallywrapped concrete while it usually underestimates the ultimate axial strain. 1. Introduction Over the past three decades,  󿬁 ber-reinforced polymer (FRP) hasemerged as a favorite material for the strengthening of existing concretecolumns. The columns are usually wrapped with FRP jacket along theentire column height, and the resulting column is referred to as an FRPfully wrapped concrete column. Existing research has demonstratedthat the full FRP con 󿬁 nement can signi 󿬁 cantly enhance the compressivestrength and deformation capacities of circular concrete columns[3,6,9 – 12,15 – 17,20,24,26 – 28,32,36,40 – 42,45,48]. Alternatively, theconcrete column can be wrapped with longitudinally discrete (i.e.,spaced) FRP strips/rings (Fig. 1), which is referred to as a FRP partiallywrapped concrete column. Although most of the existing studies arerelated to FRP fully wrapped concrete columns, FRP partially wrappedconcrete columns have also been demonstrated to process an adequateincrease in strength and a remarkable increase in axial deformationcapacity compared with their counterparts (i.e., un-con 󿬁 ned concretecolumns) (e.g., [4,25,43,5,28,46,47]. As a result, FRP partially wrappedconcrete columns are comparatively favorable, especially for columnsonly requiring a considerable increase in axial deformation capacity. Inaddition, strengthening columns with discrete FRP strips is expected tobe able to avoid FRP buckling failure which will easily occurred inconcrete- 󿬁 lled FRP tubes as the axial sti ff  ness of the FRP tube cannot beneglected. Also, less FRP materials are needed for FRP partiallywrapped concrete columns and thus FRP partial wrapping strength-ening can be applied easier and faster than FRP full wrappingstrengthening [28,46].The interest to understand the behavior of FRP partially wrappedconcrete has led to a few experimental studies on the behavior of concrete in FRP partially wrapped columns [4,25,5,28,37,29,46,47,18].The con 󿬁 nement in the axially loaded circular columns fully wrappedby FRP jackets is uniform. However, as for the con 󿬁 ned concrete in FRPpartially wrapped circular columns, the con 󿬁 nement is non-uniform(Fig. 2) within the concrete between two adjacent FRP strips [30,19]. The usage of discrete FRP strips results in the less e ffi cient con 󿬁 nementto the concrete between the two adjacent FRP strips. The con 󿬁 nementmechanism is similar to the concrete con 󿬁 ned by steel hoops or spirals,in which the reduced con 󿬁 nement e ff  ect between two adjacent strips https://doi.org/10.1016/j.compstruct.2018.05.001Received 12 October 2017; Received in revised form 11 March 2018; Accepted 2 May 2018 ⁎ Corresponding author at: Room 203, Structural Laboratory, School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou Higher Education MegaCenter, Guangzhou, China.  E-mail address:  guoyc@gdut.edu.cn (Y.-C. Guo). Composite Structures 200 (2018) 810–828Available online 04 May 20180263-8223/ © 2018 Elsevier Ltd. All rights reserved.    can be considered through the  “ arching action ” . Based on the archingaction assumption, a parabola with an initial slope of 45° covering aclear vertical spacing (  ′ s  f  ) between two FRP strips is de 󿬁 ned to separatethe e ff  ectively con 󿬁 ned part from the ine ff  ectively con 󿬁 ned part of theconcrete section (Fig. 2a). As illustrated in Fig. 2b, the ine ff  ectivecon 󿬁 nement area is located between two adjacent FRP strips. Subse-quently, the axial deformation of FRP partially wrapped concrete col-umns is believed to concentrate at the ine ff  ectively-con 󿬁 ned concretebetween the FRP strips and some experimental evidence of the axialdeformation distribution has been observed experimentally by the au-thors (e.g., [46,47]). The di ff  erence of con 󿬁 nement mechanisms be-tween FRP fully and partially wrapped concrete implies di ff  erent be-haviors between them, which may lead to the di ff  erence in stress-straincurves between the con 󿬁 ned concrete in FRP partially wrapped con-crete columns and that in FRP fully wrapped concrete columns. As aresult, the reliability and accuracy of existing theoretical models forFRP fully wrapped concrete need to be carefully examined for theirapplicability for FRP partially wrapped concrete.The stress-strain behavior of FRP-con 󿬁 ned concrete can be appro-priately described by either a design-oriented stress-strain model whichhas closed-form equations or an analysis-oriented stress-strain modelwhich is based on an incremental numerical procedure. Based on ex-isting experimental observations, the stress-strain response of FRP-con 󿬁 ned concrete can be classi 󿬁 ed into two types [15,25,46], as shownin Fig. 3. For the concrete with su ffi cient FRP con 󿬁 nement, the stress-strain curve usually exhibits two segments (Type I):  󿬁 rst ascendingsegment and second linear ascending segment (Fig. 3a). During the  󿬁 rstsegment, the concrete is initially in the elastic stage where the stressincreases linearly with strain and the load is predominantly sustainedby the concrete core. When near the turning point, the concrete beginsto crack and the dilation of concrete during the second segment isconstrained by the FRP jacket, leading to substantial increases in theaxial stress and strain of concrete. However, the stress-strain curve of concrete with insu ffi cient FRP con 󿬁 nement exhibits a strain softeningresponse (Fig. 3b and c) (Type II). In this type of stress-strain response,the stress at ultimate strain is smaller than the peak stress. The strainsoftening behavior of Type II can be further divided into Type II-I with ′ ⩾ ′  f f  cu c 0  (Fig. 3b) and Type II-I with  ′ < ′  f f  cu c 0  (Fig. 3c) [15]. It is seen that the performances are di ff  erent for the two di ff  erent types of stress-strain responses [44,46]. However, most of the existing models estab-lished based on FRP fully wrapped concrete do not distinguish theabovementioned two types, and thus some of them are only applicableto Type-I stress-strain curve. Therefore, the reliability and accuracy of the existing stress-strain models need to be examined for FRP partiallywrapped concrete.In addition, the existing test results enable the evaluation and ver-i 󿬁 cation of available design guidelines (e.g., [8,7]) for FRP partiallywrapped concrete columns (e.g., [46,47]). As per these codes, a long-itudinal con 󿬁 nement e ff  ectiveness factor is suggested for determiningthe compressive strength and ultimate axial strain of FRP partiallywrapped concrete, and therefore, the FRP partially wrapped concretecolumns can be designed with an acceptable accuracy. In other words,the di ff  erent combinations of the FRP thickness and the FRP strip clearspacing can obtain identical e ff  ective FRP con 󿬁 nements which are sameto those occurred in FRP fully wrapped concrete. However, an increasein the FRP strip clear spacing may lead to the concrete crushing failure,as found in a previous experimental study conducted by the authors[46], which in turn in 󿬂 uences the stress-strain behavior of FRP partiallywrapped concrete. Therefore, as stated in Zeng et al. [46], the accuracy '  f   s  f   s  f  b '  f   D-s /2 D Fig. 1.  Schematic of an FRP partially wrapped concrete column.  (a) Arching action (b) Effective confinement area '  f   s  f   s FRP '  D  D  f  b A A Section A-A Fig. 2.  Arching action and e ff  ective con 󿬁 nement area in a circular column partially wrapped with FRP.  J.-J. Zeng et al. Composite Structures 200 (2018) 810–828 811  of the longitudinal con 󿬁 nement e ff  ectiveness factor needs to be furtherexamined using more test data.To this end, an experimental program was conducted to study theaxial compressive behavior of circular columns wrapped with CFRPstrips. In total 60 columns were prepared and tested. The main testvariable examined in this experimental program included the clearspacing and width of FRP strips. The test results, in term of the e ff  ects of the clear spacing and width of FRP strips on the axial compressivebehavior of FRP partially wrapped concrete, were presented and dis-cussed. A widely accepted analysis-oriented stress-strain model pro-posed by Teng et al. [33] was used to predict the stress-strain behaviorof FRP partially wrapped concrete;  󿬁 ve representative models wereemployed to predict the ultimate condition of FRP partially wrappedconcrete. The reliability and accuracy of these models were examinedby the comparisons between the test results and the model predictions. 2. Experimental program  2.1. Test specimens Totally sixty FRP-con 󿬁 ned cylindrical column specimens weretested to investigate the e ff  ects of FRP strip width, clear spacing andFRP thickness. All specimens had a diameter of 150mm and a height of 300mm. Note that the clear spacing and width of FRP strips are themain parameters studied in the current study and they represent thecoe ffi cient of FRP vertical e ffi ciency. Note that the vertical con 󿬁 nemente ff  ectiveness coe ffi cient, which is a coe ffi cient representing the coe ffi -cient of FRP vertical e ffi ciency, is given by  − ′ s D (1 /2 )  f  2 where  ′ s  f   is the  (a) Type I: increasing type (b) Type II-I: decreasing type (>) (c) Type II-II: decreasing type (<) Fig. 3.  Classi 󿬁 cations of stress-strain curves of FRP fully wrapped concrete. Fig. 4.  Illustration of the FRP strip spacings considered in the experimental program.  J.-J. Zeng et al. Composite Structures 200 (2018) 810–828 812  clear spacing of two adjacent FRP strips and  D  is the diameter of thecolumn [8]. The variation of coe ffi cient of FRP vertical e ffi ciency wasachieved by wrapping concrete columns with FRP strips (3, 4 and 5strips) with di ff  erent widths (i.e., 25, 30, and 35mm) (Fig. 4). For easeof reference, the specimens were divided into four series and thenumber of FRP strips in each series is identical, as is shown in Table 1.The design of strip number and strip width led to several di ff  erent clearspacing ratios in present study (Table 1). It is noted that the ratio be-tween the clear spacing of two adjacent FRP strips and the columndiameter is referred to as clear spacing ratio (i.e.,  ′ s D /  f   ), as shown inFig. 1. Each column has two nominally identical specimens. The detailsabout the test columns (including the width of FRP strips, the FRP Table 1 Key information of test columns and key test results. Series Specimen Width of FRP strips Thickness of FRP strips Number of FRP strips  ′ s D /  f   ′  f  co  ′  f  cc  ε  cc  ′  f  cu  ε  cu  ′ ′  f f  / cu co  ε ε  / cu co  ε  h rup , / SC-1  — — —  / 23.27 / / / / / / /SC-2 / 22.98 / / / / / / /SC-3 / 23.86 / / / / / / /I SP-1-1 / 0.167 / 0.00 23.40 62.13 0.0295 / / 2.66 10.54  − 0.0141SP-1-2 / 0.167 / 0.00 23.40 59.06 0.0293 / / 2.52 10.46  − 0.0158SP-2-1 / 0.334 / 0.00 23.40 88.55 0.0395 / / 3.78 14.11  − 0.0156SP-2-2 / 0.334 / 0.00 23.40 88.10 0.0389 / / 3.76 13.89  − 0.0150SP-3-1 / 0.501 / 0.00 23.40 108.98 0.0516 / / 4.66 18.43  − 0.0154SP-3-2 / 0.501 / 0.00 23.40 110.62 0.0507 / / 4.73 18.11  − 0.0164II S-1-3-25-1 25 0.167 3 0.75 23.40 25.70 0.0039 21.27 0.0116 0.91 1.39  − 0.0107S-1-3-25-2 25 0.167 3 0.75 23.40 25.38 0.0035 19.38 0.0140 0.83 1.25  − 0.0122S-1-3-30-1 30 0.167 3 0.70 23.40 25.48 0.0060 22.12 0.0135 0.95 2.14  − 0.0098S-1-3-30-2 30 0.167 3 0.70 23.40 25.26 0.0047 22.03 0.0097 0.94 1.68  − 0.0110S-1-3-35-1 35 0.167 3 0.65 23.40 25.21 0.0039 21.24 0.0160 0.91 1.39  − 0.0138S-1-3-35-2 35 0.167 3 0.65 23.40 26.60 0.0034 24.63 0.0142 1.05 1.21  − 0.0115S-2-3-25-1 25 0.334 3 0.75 23.40 27.43 0.0034 22.34 0.0134 0.95 1.21  − 0.0109S-2-3-25-2 25 0.334 3 0.75 23.40 26.89 0.0057 20.20 0.0124 0.86 2.04  − 0.0115S-2-3-30-1 30 0.334 3 0.70 23.40 29.54 0.0058 23.37 0.0165 1.00 2.07  − 0.0126S-2-3-30-2 30 0.334 3 0.70 23.40 30.14 0.0070 23.18 0.0178 0.99 2.50  − 0.0145S-2-3-35-1 35 0.334 3 0.65 23.40 29.23 0.0099 24.27 0.0224 1.04 3.54  − 0.0126S-2-3-35-2 35 0.334 3 0.65 23.40 29.08 0.0088 20.27 0.0248 0.87 3.14  − 0.0117S-3-3-25-1 25 0.501 3 0.75 23.40 29.72 0.0078 20.44 0.0279 0.87 2.79  − 0.0108S-3-3-25-2 25 0.501 3 0.75 23.40 28.19 0.0105 19.41 0.0214 0.83 3.75  − 0.0109S-3-3-30-1 30 0.501 3 0.70 23.40 27.93 0.0085 22.93 0.0200 0.98 3.04  − 0.0110S-3-3-30-2 30 0.501 3 0.70 23.40 29.28 0.0085 24.15 0.0282 1.03 3.04  − 0.0106S-3-3-35-1 35 0.501 3 0.65 23.40 33.37 0.0074 25.20 0.0154 1.08 2.64  − 0.0093S-3-3-35-2 35 0.501 3 0.65 23.40 32.23 0.0062 27.30 0.0207 1.17 2.21  − 0.0084III S-1-4-25-1 25 0.167 4 0.44 23.40 27.55 0.0092 / / 1.18 3.29  − 0.0109S-1-4-25-2 25 0.167 4 0.44 23.40 26.41 0.0092 / / 1.13 3.29  − 0.0115S-1-4-30-1 30 0.167 4 0.40 23.40 28.73 0.0132 / / 1.23 4.71  − 0.0128S-1-4-30-2 30 0.167 4 0.40 23.40 29.06 0.0099 / / 1.24 3.54  − 0.0104S-1-4-35-1 35 0.167 4 0.36 23.40 32.92 0.0099 32.60 0.0106 1.39 3.54  − 0.0111S-1-4-35-2 35 0.167 4 0.36 23.40 33.55 0.0117 33.36 0.0121 1.43 4.18  − 0.0118S-2-4-25-1 25 0.334 4 0.44 23.40 30.74 0.0098 30.64 0.0119 1.31 3.50  − 0.0132S-2-4-25-2 25 0.334 4 0.44 23.40 34.95 0.0106 34.54 0.0118 1.48 3.79  − 0.0112S-2-4-30-1 30 0.334 4 0.40 23.40 35.65 0.0142 / / 1.52 5.07  − 0.0109S-2-4-30-2 30 0.334 4 0.40 23.40 35.95 0.0154 / / 1.54 5.50  − 0.0107S-2-4-35-1 35 0.334 4 0.36 23.40 40.14 0.0207 / / 1.72 7.39  − 0.0111S-2-4-35-2 35 0.334 4 0.36 23.40 40.19 0.0161 / / 1.72 5.75  − 0.0110S-3-4-25-1 25 0.501 4 0.44 23.40 35.97 0.0193 35.52 0.0235 1.52 6.89  − 0.0139S-3-4-25-2 25 0.501 4 0.44 23.40 35.92 0.0248 35.25 0.0296 1.51 8.86  − 0.0116S-3-4-30-1 30 0.501 4 0.40 23.40 41.04 0.0328 / / 1.75 11.71  − 0.0162S-3-4-30-2 30 0.501 4 0.40 23.40 40.38 0.0280 / / 1.30 10.00  − 0.0139S-3-4-35-1 35 0.501 4 0.36 23.40 48.64 0.0397 / / 2.08 14.18  − 0.0154S-3-4-35-2 35 0.501 4 0.36 23.40 45.00 0.0448 / / 1.92 16.00  − 0.0164IV S-1-5-25-1 25 0.167 5 0.29 23.40 31.09 0.0187 / / 1.33 6.68  − 0.0106S-1-5-25-2 25 0.167 5 0.29 23.40 28.88 0.0177 / / 1.23 6.32  − 0.0110S-1-5-30-1 30 0.167 5 0.25 23.40 35.41 0.0228 / / 1.51 8.14  − 0.0126S-1-5-30-2 30 0.167 5 0.25 23.40 36.22 0.0224 / / 1.55 8.00  − 0.0138S-1-5-35-1 35 0.167 5 0.21 23.40 38.53 0.0232 / / 1.65 8.29  − 0.0156S-1-5-35-2 35 0.167 5 0.21 23.40 38.51 0.0232 / / 1.65 8.29  − 0.0133S-2-5-25-1 25 0.334 5 0.29 23.40 42.49 0.0365 / / 1.82 13.04  − 0.0137S-2-5-25-2 25 0.334 5 0.29 23.40 41.99 0.0304 / / 1.79 10.86  − 0.0144S-2-5-30-1 30 0.334 5 0.25 23.40 42.03 0.0238 / / 1.80 8.50  − 0.0120S-2-5-30-2 30 0.334 5 0.25 23.40 47.53 0.0331 / / 2.03 11.82  − 0.0136S-2-5-35-1 35 0.334 5 0.21 23.40 51.62 0.0287 / / 2.21 10.25  − 0.0143S-2-5-35-2 35 0.334 5 0.21 23.40 52.03 0.0323 / / 2.22 11.54  − 0.0168S-3-5-25-1 25 0.501 5 0.29 23.40 47.98 0.0507 / / 2.05 18.11  − 0.0134S-3-5-25-2 25 0.501 5 0.29 23.40 46.83 0.0541 / / 2.00 19.32  − 0.0148S-3-5-30-1 30 0.501 5 0.25 23.40 58.80 0.0381 / / 2.51 13.61  − 0.0140S-3-5-30-2 30 0.501 5 0.25 23.40 59.63 0.0365 / / 2.55 13.04  − 0.0137S-3-5-35-1 35 0.501 5 0.21 23.40 64.74 0.0422 / / 2.77 15.07  − 0.0157S-3-5-35-2 35 0.501 5 0.21 23.40 63.17 0.0369 / / 2.70 13.18  − 0.0141  J.-J. Zeng et al. Composite Structures 200 (2018) 810–828 813
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