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湘西龙里公路娃娃塘大桥施工图设计学生姓名:陈君翔 学 号:200918020132专 业:土木工程（桥梁工程方向）指导教师:余钱华长沙理工大学二零一三年六月目 录序 号图 名图 号1设计说明2 桥型布置图13 边跨一般构造图24横截面一般构造图35边跨预应力配筋图46 支点附近预应力钢筋图57 中跨附近预应力钢筋图68 下部结构一般构造图79 普通钢筋配筋图810基础配筋图911 桥面铺装钢筋图1012护栏钢筋布置图1113泄水管道构造图1214支座构造图1315横截面预应力钢筋图14（手绘）16支点附近（上部结构）一般构造图15（手绘） 设计说明第 1 页 一概况娃娃塘大桥起点桩号K0+572.42，终点桩号K0+733.58，全长161.16m。全桥设计为42m+70m+42m预应力混凝土变截面连续箱梁桥。二. 设计标准1、设计荷载：公路-II级。2、桥梁总长：154。3、桥面宽度：净-9.0+22.5m。4、设计洪水频率：无。 三. 采用规范 1、JTG D60-2004.公路桥涵设计通用规范 ；2、JTG D62-2004.公路钢筋砼及预应力砼桥涵设计规范 ；3、JTG D63-2007.公路桥涵地基与基础设计规范 ；4、JTG B01-2003 公路工程技术规范。四. 主要材料 1. 混凝土。主梁:C50混凝土桥面铺装:C50防水混凝土 防撞墙: C50混凝土桥墩、盖梁:C30混凝土 2. 预应力钢材预应力钢筋采用ASTM A416-97a标准的低松弛钢绞线（17标准型），抗拉强度标准值MPa，抗拉强度设计值MPa，公称直径15.24mm，公称面积139mm2，弹性模量MPa。3. 普通钢材普通钢筋必须符合“GB1499-84”标准的规定，其中：钢筋直径D 12mm全部采用HRB400钢筋，抗拉强度标准值fsk = 335 MPa钢筋直径D 12mm全部采用R235钢筋，抗拉强度标准值fsk =235 MPa4. 锚具采用OVM夹片式群锚。5. 预应力管道采用预埋塑料波纹管成型。6. 其它砂、石、水的质量要求应符合公路桥梁施工技术规范JTJ/T F50-2011的有关规定。五. 设计要点本桥为42m+70m+42m的预应力混凝土变截面连续梁桥；全长为161.16m，采用悬臂浇筑法施工。1. 上部构造上部构造为三跨变截面连续箱型梁，腹板宽度从跨中到支点由50cm增加到100cm，底板厚度从跨中到支点由30cm增加到60cm，顶板厚度为30cm。2. 下部构造各个桥台地面高程较低，采用桩柱式桥台，为避免基础开挖破坏河岸，桥墩采用桩柱式桥墩。(CFFT) and found a significant decrease in column load-carryingcapacity with an increase in slenderness ratio. Tested CFFT col-umns tended to be more susceptible to slenderness effects becausethe glass FRP materials used have a higher strength and lowerstiffness than steel. In addition, Pan et al. (2007) proved that thestrengthening effect decreases with an increase in the slendernessratio and that the effect of the slenderness ratio on the load-carryingcapacity of FRP-wrapped concrete columns is more significant thanthat of ordinary reinforced concrete columns because confinementenhances the strength instead of bending stiffness. The impact ofincreasing load eccentricity and column slenderness on the decreas-ing effect of the CFRP confinement on the enhancement of the col-umn load-carrying capacity was confirmed by Tao and Han (2007).The results of tests on concrete confined specimens of Tamuzset al. (2007) showed that a tangential wrapping increases the load-carrying capacity only for columns with slendernessless than 40.The effect of unidirectional and bidirectional CFRP sheets lami-nated to the surface of a square column with a slenderness ofapproximately 70 was a point of experimental investigation forTao and Yu (2008). The ultimate strength measured for columnsstrengthened only in the transverse direction is quite close to thatof nonstrengthened ones. Higher increase in load-carrying capacityis achieved by additionally strengthening in the longitudinaldirection. The longitudinal fibers become more effective whenUniversity Teacher, Dept. of Concrete Structures and Bridges, FacultyFitzwilliam and Bisby (2010) verified the strengthening ef-(columns with circular cross sections and slendernessThe more slender the column is, the lower the load-carrying capac-improve the behavior of slender CFRP wrapped circular concretethe equivalent short CFRP-wrapped columns.Full-Scale Testing of CFRP-Strengthened SlenderReinforced Concrete ColumnsKatarina Gajdosova, Ph.D.1; and Juraj Bilcik2Abstract:The paper presents an investigation into the performance of slender rectangular reinforced concrete columns strengthened withcarbon fiber-reinforced polymers (CFRPs) in two manners. The first approach is a well-known form of CFRP sheet jacketing with the effectdemonstrated in many studies, and a second one is a relatively new retrofit method of near surface mounted (NSM) CFRP strips. A total of eightfull-scale specimens with rectangular cross sections (210150mm) were tested to failure under eccentric compressive loading. The total lengthof the specimens was 4,100 mm. The results of this study demonstrate a significant difference in slender and short column strengthening inaccordance with the predominant stress manner. It was confirmed that the effect of CFRP wraps on the increase in column strength is propor-tionally greater for short RC columns subjected to predominant compression. The longitudinal fibers in CFRP strips bonded into grooves inconcrete cover are more effective in enhancing the flexural load-carrying capacity of slender reinforced concrete columns subjected to eccentricloading. The most effective approach to flexural capacity enhancement was demonstrated by a synergistic effect of NSM CFRP reinforcementensured by CFRP sheet wrapping.DOI:10.1061/(ASCE)CC.1943-5614.0000329. 2013 American Society of Civil Engineers.CE Database subject headings:Concrete columns; Fiber reinforced polymer; Slenderness ratio; Eccentric loads; Full-scale tests.Author keywords:Concrete rectangular column; Carbon fiber-reinforced polymer; Slenderness ratio; Eccentric loads.IntroductionStrengthening of concrete structures with the use of traditionalmaterials (concrete, reinforcement) as used in the past not only in-creases the load-carrying capacity, but also the dimensions of thecross section. In the last few decades, new progressive compositematerials for strengthening have been recognized. The most widelyknown and used are carbon fiber-reinforced polymers (CFRPs) be-cause of their properties, especially their resistance to corrosion,high strength to weight ratio, and easy handling and installation.The field of application of FRPs in the strengthening of concretestructures is extended to each type of stress. This paper focuses onthe strengthening of slender concrete columns, in which compres-sion and bending stresses are applicable. The load-carrying capac-ity and ductility enhancement effect of FRP sheet wrapping onaxially loaded short concrete columns was demonstrated with anumber of tests.In comparison with the large database of publications dealingwith confined short columns, the investigation of eccentricallyloaded slender columns is insufficient. The extension of thismethod of application is restricted because there are apparentdifferences between the behavior of short and slender columns.Research in this field was started by Mirmiran et al. (2001), whoinvestigated concretefilled fiber-reinforced polymer tubesbending becomes dominant.1of Civil Engineering, Slovak Univ. of Technology, 813 68 Bratislava,fects of lamination with two and four CFRP sheet layers in bothSlovakia (corresponding author). E-mail: katarina.gajdosovastuba.skthe transverse and longitudinal directions on small-scale specimens2Head, Dept. of Concrete Structures and Bridges, Faculty of CivilE-mail: juraj.bilcikstuba.skindividual papers. This paper is part of theJournal of Composites for Con-struction2-239-248/$25.00.JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013 /239J. Compos. Constr. 2013.17:239-248.e0=40mm31 88 31150Fig. 1.Geometry of specimens (dimensions in mm)CFRP CFRP strip in groove150210(a)(b)Fig. 2.Strengthening configuration: (a) C3, C4; (b) C5, C6 (dimen-sions in mm)Table 1.Properties of CFRP MaterialsCFRP sheet, weight ofC-fiber in primaryProperty CFRP strip direction (300g=m2)Modulus of elasticity (GPa) 168 240The same concrete mix was used for all columns. During theconcreting of the columns, cubic, cylindrical, and prismatic spec-imens were also prepared and tested after 28 days and immediatelybefore the columns were tested. The results are summarized inTable2. The average 28-day cylindrical concrete strength wassheet150150In the investigations of Tao and Yu (2008) and Fitzwilliam andBisby (2010), only CFRP sheet wraps were used for strengtheningin the longitudinal direction. Within the last three or four years,a limited number of studies dealing with NSM FRP reinforce-ment have appeared; see Barros et al. (2008) and Bournas andTriantafillou (2009). In these studies, small- or large-scale speci-mens with small slenderness (17and 22) were tested. This isthe first time that CFRP strips such as near surface mounted (NSM)reinforcement additionally secured with CFRP sheet jacketing arestudied for strengthening of full-scale rectangular columns withconsiderable high slenderness (95).This paper is focused on the investigation the effectiveness ofCFRP strengthening for eccentrically loaded slender columns.The majority of reinforced concrete columns in practice isconstructed as slender columns with a rectangular cross sectionand is loaded eccentrically, so it is necessary to derive and verifythe design procedures for including the strengthening effects offiber-reinforced polymers. The purpose of this study is to verifythe effectiveness of NSM CFRP reinforcement for flexuralstrengthening of slender reinforced concrete columns and providea methodology for the calculations for practical design applica-tions. Experimental and numerical investigations are describedin the following sections.150Experimental ProgramTesting was performed on eight full-scale slender rectangular rein-forced concrete columns in four series. The series differed with re-spect to the method of strengthening. The first, a reference series,consisted of nonstrengthened columns, and the remaining serieswere strengthened by CFRPs, i.e., longitudinal NSM CFRP strips,transverse CFRP sheet wrapping, and a combination of these twomethods. To achieve very slender columns that largely approximateload-bearing members in real structures, the specimens were de-signed as columns 4,100 mm long, with rectangular cross sections210150mm, symmetrically reinforced with2410mm lon-gitudinal bars, and with hinged supports at both ends (Fig.1). Four-shear stirrups of 6 mm diameter at a spacing of 150-mm centerswere mounted lengthwise and reduced to 30-mm centers at theends. At both column ends, 30-mm thick steel plates were set toassist in better load distribution. The corners of the cross sectionwere beveled by embedding triangular laths (1010mm) in theformwork edges. For columns strengthened by confining, thesecorners were additionally chamfered to a radius of 20 mm.First, two columns (C1 and C2) were tested as nonstrengthenedcolumns. Two other columns (C3 and C4) were strengthened by thenear surface mounted reinforcement method, i.e., in the form ofCFRP strips (1.410mm) mounted into grooves (three on eachof the longer side of the cross section) in concrete cover Fig.2(a).The next two columns (C5 and C6) were strengthened by confine-ment of one layer of transverse CFRP sheet (300-mm width) in theform of stirrups at 50 mm centers Fig.2(b). The remaining twocolumns (C7 and C8) were strengthened with a combination of thepreviously noted methods.Tensile strength (MPa) 2,500 3,900MaterialsFor the purpose of the comparison of experimental and analyticalmodeling results, the material properties of the concrete and steelspecimens were laboratory tested. The properties of the CFRPsheets and strips provided by the manufacturer (Table1) were notverified, following a good agreement with the results of previousexperimental tests carried out at our department during a formerinvestigation.240/ JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013J. Compos. Constr. 2013.17:239-248.the steel angle section members (welded to a bottom steel plate) toensure a hinged connection (Fig.4).The strains of the concrete, steel, and CFRP reinforcement, andthe deflection from the increasing bending moment at midheight,were monitored during loading. The primary objective of the ex-perimental study was the examination of the relationship betweension force. In total, three linear variable displacement transducers(LVDTs) were used as they are considered the most accurate meas-urement method for this purpose, one at midheight and two controlsat the ends of column (Fig.5). Indirect methods for checking themidheight deflection were based on deflection calculations fromconcrete or by geodetic surveying in a direction perpendicular toLVDTs. Strains of all materials were measured by strain gauges(T1T4, steel; T5T8, concrete; T9T10, CFRP strips; T11T12,CFRP sheet), and strains at concrete face in midheight crosssectionwere controlled with removable deformeters (D1D4) at bothsides (compressed, tensile). At column height, five geodetic points(G1G5) were used to control the deformation of a column.Measure tapes 150-mm long were mounted at these points and thehorizontal displacement of each point was measured by theodolite.Parameters obtained during the testing were recorded bycomputer software. The test was stopped after cross-section failure,following achievement of buckling resistance, and a decrease incompression force (the descending branch was noted).weld joint of steel roller plate welded to the bottom steel plate Fig. 4.Detail of hinged connectiontop steel bottom steel plate Table 2.Material Properties of ConcreteProperty 28th day 316th dayCube strength (MPa) 35.6 42.1Cylindrical strength (MPa) 32.0 34.2Static modulus of elasticity (GPa) Not measured 36.8deflection at midheight and the eccentrically acting compres-32 MPa. Three bars of each diameter of the reinforcing steel weretested for their material properties, the results of which are shown inTable3. The measured yield strength of longitudinal reinforcementwas approximately 560 MPa.the curvature. This was determined from the strain in the steel andSpecimensThe columns were cast in a horizontal position in prepared form-work. After 14 days the columns were demolded, and after 28 daysthe columns were prepared for strengthening (Fig.3). Along theentire length of columns C3, C4, C7, and C8, three grooves(315mm) on each of the longer sides of the cross section werecut, cleaned, and filled with epoxy adhesive MBrace Epoxikleber220, into which CFRP strips, MBrace S&P CFK 150/2000, wereinserted Fig.3(a).The beveled corners of columns C5C8 were chamfered, andcolumns were confined by one layer of CFRP sheet MBrace,S&P C-Sheet 240, with the help of MBrace epoxy resin, in the formof 300-mm wide stirrups anchored with an overlap of 170 mm onthe longer side of the cross section Fig.3(b).Items of InvestigationAll eight columns were tested in the same manner, i.e., by increas-ing the compression force applied at an initial eccentricity of40 mm. This eccentricity was predefined by the position of a steelroller (welded to a top steel plate at column ends) placed betweensteel angles Table 3.Material Properties of SteelProperty 6mm 10mmYield strength (MPa) 605 562Tensile strength (MPa) 625 637Modulus of elasticity (GPa) 237 208Ultimate tensile strain (%) 6.64 10.75Fig. 3.Strengthening of specimens: (a) NSM CFRP strips; (b) CFRP sheet confinementJOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013 /241J. Compos. Constr. 2013.17:239-248.G1theodolite View FD3 D4 Strain gauges in midheightT1T7D3 DT8T2emeasuredkm2 wherel=column length (4,100 mm); andk= curvaturekc strain at compressed face of mid height cross section;=tensile strain at the face of cross section (by deformeters) or in=steel reinforcement (by strain gauges); andhct=distance betweenpoints with strainscandt.A comparison of results from all measurement methods isshown in Fig.6. Good agreement was obtained. Directly measuredvalues from geodetic theodolites and indirectly calculated valuesfrom strains measured with strain gauges and deformeters showthe deflections of the most stressed cross section at the middleof the column height close to the LVDT measurements.Column Resistancedeflection in midheight cross section measuredforce beside the nonstrengthened reinforced concrete column,a combination of CFRP strips and CFRP sheet (Fig.7).G5T3T94T4l10thwherec=T10T112T12View B: LVDT2G2View BG3deformeters G4LVDT1D1 D2 View F: cross section: 3x70T5LVDT3T6150Fig. 5.Column during experimental testingTest ResultsGeneralThe loaddeflection curves were measured by LVDTs for all ofthe tested columns. The value of measured deflection is calculatedas a difference between deflection at midheight (LVDT1) and theaverage of the top and bottom deflection (LVDT2 and LVDT3).Strains needed for the calculation of curvature and deflection weremeasured by strain gauges. When two gauges are mounted on theinvestigated side of a cross section, the average value is calculatedand used. Checking methods (deformeters, theodolite) were onlyapplied to the last step before peak load achievement, as after thispoint, the deflection increases without any force increase and thesteps after peak load was achieved cannot be controlled withoutcontinuous computer measurement.Loadmoment curves are used for comparison of various mea-surements and for determination of increase in resistance attribut-able to strengthening. Bending moment acting in a midheight crosssection is calculated from applied force and total deflection of aninvestigated cross sectionMNemeasuredNm1All columns tested in the experimental investigation failed in buck-ling. The increase in resistance attributable to strengthening can bee0expressed as an enhancement of maximum achieved compressionwhereemeasured=deformeters); ande0=initial end eccentricity40mm.strips, 2.4% for columns strengthened by confining with one layerture following the strains242/ JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013J. Compos. Constr. 2013.17:239-248.C1-300-250-200LVDTtensometersstrain gaugesdeformeterstheodolite0102030400Calculated bending moment kNmC3-300-250-200LVDTstrain tensometersgaugesdeformeterstheodolite0102030400Calculated bending moment kNmC5-300-250-200LVDTtensometersstrain gaugesdeformeterstheodolite0102030400Calculated bending moment kNmC7-300-250-200LVDTstrain gaugestensometersdeformeterstheodolite theodolite010203040010203040Calculated bending moment kNmFailure ModesFailure mode of all columns was specified by crushing andspalling of the concrete. At nonstrengthened columns, severalbigger cracks were observed at the middle of the height of acolumn on the tensile side of a cross section Figs.8(a and b).-350-150-100-50theodolite010203040-350-150-100-50theodolite010203040-350-150-100-50theodolite010203040-350-150-100-50C2LVDTstrain gaugestensometersdeformetersC4LVDTstrain gaugestensometersdeformetersC6LVDTstrain gaugestensometersdeformetersC8LVDTstrain gaugestensometersdeformeters-350-300-250-200-150-100-500Calculated bending moment kNm-350-300-250-200-150-100-500Calculated bending moment kNm-350-300-250-200-150-100-500Calculated bending moment kNm-350-300-250-200-150-100-500 0Calculated bending moment kNmFig. 6.Comparison of direct and indirect measurement methodsFor confined columns, no significant variation in the behaviorduring loading was observed. More ductile postpeak behavioroccurred at columns strengthened with longitudinal NSM CFRPstrips. The difference between deflection at peak load and finaldeflection is 1.5 times greater for strengthened columns.JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013 /243J. Compos. Constr. 2013.17:239-248.is recommended to wrap a specimen continuously or with coveringof particular stirrups in the middle segment of a column for furtherinvestigation.nonstrengthened column - average column strengthened with CFRP strips - average of C3 and C4column strengthened with CFRP sheet - average of C5 and C6column strengthened withcombination - average of C7 and C89. Ultimate strains from tension tests werefive times higher. This decrease can be caused by different stressand the CFRP strips are stressed in the direct and bending stressmanner rather than pure tension during the tension test, so the strainwere lower by 40% in comparison with tensile strains. No signifi-cant buckling of strips in compression was observed. In specimenswith CFRP wraps there was no difference in the behavior of CFRPstrips in tension and compression; compared with specimens with-out wraps, the failure strains were higher by 15% for CFRP strips atboth sides.The confinement effect of transverse CFRP sheet strengtheningon slender columns with large curvature at the midheight crosssection is very small and the expected concrete strength enhance-ment could not be reached, which results from very low, almostzero, measured values of CFRP sheet strains on the compressedface and a maximum 0.01% on the tensile face of the columnRelative StrainsStrains of all used materials at the column midheight wereobserved. The strains of CFRP materials served the purpose ofevaluating their capacity utilization.The rupture of the NSM longitudinal CFRP strips was observedat ultimate strains of 0.250.28%. Similar values were measured by-350-300-250-200of C1 and C2-150-100-500010203040Olivova (2007); see Fig.Bending moment kNmpaths, as there is a large curvature at the midheight cross sectionFig. 7. Load-moment relationship measured with LVDT duringexperimental testingcapacity utilization of the CFRP strips is limited.Measured compression strains of CFRP strips during failureTensile cracks at columns strengthened with longitudinal NSMCFRP strips were not continuous over the entire side of crosssection; they primarily appeared near the edges Fig.8(c). Afterfalling off of a concrete layer, buckling of the longitudinalsteel reinforcing bar and rupture of CFRP strips were observedFig.8(d). At columns strengthened with transverse CFRP wrap-ping, the primary tensile crack appeared up or down the middleCFRP stirrup and several smaller cracks were found under thesheet after its removal Figs.8(eg). The same cracking mecha-nism was achieved at columns strengthened with a combinationof NSM CFRP strips and a CFRP sheet jacket Fig.8(h). Toprevent the cracking over or below the middle CFRP stirrup, itFig. 8.Columns after failure: (a and b) cracks at the middle of the height of a column on the tensile side of a cross section; (c) tensile cracks nearcolumn edges; (d) buckling of steel reinforcing bar and rupture of CFRP strips; (eg) tensile crack up or down the middle CFRP stirrup with cracksunder the sheet; (h) cracks on columns strengthened with NSM CFRP strips and CFRP sheet jacket244/ JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013J. Compos. Constr. 2013.17:239-248.XMRFcczcFsizsiNm6whereFcc=compression force in concrete;zc=distance of com-pression force in concrete from gravity center axis of concretecross section;Fsi=force in steel reinforcement in rowi; andcenter axis of concrete cross section.The interaction diagrams are calculated by assuming a seriesof strain distributions. Stresses for force calculations are thendetermined from stress-strain relationships of each material andEqs. (5) and (6) are quantified. In each point of the sectioninteraction diagram, the real reduced bending stiffnessEIrcanbe calculated and used for determination of curvature, includingsecond-order effects. Following this curvature, a first-order bendingmoment can be derived to present a slender column interactiondiagram.The second part of the analytical procedure involves the inclusionof the strengthening effects to the column resistance. NSM CFRPstrips in the grooves are considered as additional reinforcement nearthe cross-section surface and the values of their strains are determinedbased upon concrete strains, depending on their distance from theneutral axis (Fig.11). From the strain values of the CFRP strips, thestress is determined from a linear stress-strain relationship. The samestress-strain diagram is used both in tension and compression. It isvery important to make provision for initial strains in the reinforcedslender columnening the structure is maximally relieved, even though there are somelow strains in the concrete and steel reinforcement, and it is necessaryfor them to be included. The theoretical initial strain values of CFRPstrips after unloading (f;un) are subtracted. Equilibrium equationsMR,0RX XMforce in rowiof CFRP strips from gravity center axis of concretecross section.Xconcrete section when the CFRP strips are applied. During strength-MIIFcc Fsi FfiN7whereFfi=force in CFRP strips in rowi;andzfidistance of=B1are then adjusted as follows:Xthe most convenient method for discussing the effects of variableson column resistance. The load-maximum moment curves (at themidheight for columns with hinged supports at both ends), for agiven slendernessand initial end eccentricitye01, is shown byline0-B1. The column fails when this line intersects the ID, at pointB1. At this point, the load and moment at the column ends are givenby pointA1. The same relationship holds for line0-B2at endeccentricitye02. This indicates that the interaction diagram for aslender column with a given slendernesscan be obtained by re-peating this process a number of times with different end eccen-tricitiese0i. The maximum load capacityNRcan be determinedfrom the linear relationship between the compression forceNandthe first order bending momentM0. Compression forceNRand to-tal bending momentMRact in the most stressed crosssection. Thismoment is the sum of bending moments of first (MR;0) and secondorders (MR;II)MRMR;0MR;IINm4The resistance of reinforced concrete cross section, defined byMR, is calculated as follows from the equilibrium equations:NRFccFsiN5Fig. 9.CFRP strips ruptured in failurecross section. This confirms measurements reported by Tao andYu (2008).zsi=distance of force in rowiof steel reinforcement from gravityAnalytical ProcedureAlong with the experimental investigation, a numerical model wasconducted using the program ATENA 3D. More information aboutcomputer modeling can be found in the original thesis (Gajdosova2010). Material properties and static actions were adapted from thefull-scale tests. Numerical and experimental procedures yieldedidentical results.Theoretical analysis was carried out before column testing withmeasured material properties according to a number of analyticalmodels found from various sources, which were then modified fol-lowing the results of the experimental investigation. The models,which primarily corresponded with experimental results, are furtherrecommended for typical use.In the preliminary part of the analytical procedure, interactiondiagrams (IDs) were developed for slender columns (Fig.10)asshort columnNN0Ne01MRNRNeB2MRFcczcFsizsi FfizfiNm80Fig. 10.Interaction diagrams for short and slender columnsJOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013 /245J. Compos. Constr. 2013.17:239-248.-1600slender column ID (=95)end eccentricitypeak load-1000d2-N010203040Fs1bdance with Fig.10is a factor of confinement effectiveness in a cross sectionForces in cross section strengthened with longitudinalthe total area of the cross section; andkehcolumns, e.g., Eqs. (5) and (6), but the concrete compression forceincludes confined concrete compressive strength.An example of theoretical analysis results for a chosen columnis shown in Fig.12.Discussion of Results13.5 flf10ffco11adhesive, additional CFRP sheet jacketing was provided through=of the column load-carrying capacity in comparison with usingonly the NSM method.was carried out. By changing the column length whilecolumn strengthened with combinationshort column ID (=0)fcFf2Fs2M0M kNmd1wherekeis a factor of confinementflf calculations. This is a product of many simplifications in the theo-modeling, and experimental tests is shown in Fig.13, in which onlywhenfl0.07fco1.2obvious. In a flexural stress path, longitudinal NSM CFRP stripsretrofitting methods results in a slight increase in the enhancementTable4-600-400NFf1+fthe lower parts of the interaction diagrams (to the peak load ofslender column) are displayed.ened with transverse CFRP sheet jacketing in stirrup form yield aresponse similar to slender nonstrengthened RC columns and it isFccInteraction diagram of chosen column calculated in accor-200-312Fig. 12.fy-1400-1200fc-800f2Mh+f1syflfl;okekehMPa12fycalculated like a ratio of effectively confined cross-section area toFig. 11.CFRP strips effectiveness along column height, making provision for sectionswith a reduced confinement effect.Equilibrium equations are the same as for nonstrengthenedCFRP sheet confinement is included as an increase in concretestrength and with a modified stress-strain relationship. Lam andTengs stress-strain model (cited inHollaway and Teng 2008) pri-marily correspondents with experimental results. This diagram con-sists of a parabolic part followed by a linear section ending at apoint defined by the confined concrete strength and ultimate strain.These values are calculated in accordance with Teng (cited inHollaway and Teng 2008)The measured results of column resistance from the experimentalfccfcoretical analysis. A comparison of theoretical predictions, computerccco 117.5 Given that the behavior and loss of the load-carrying capacity ofall the columns were controlled by bending, the columns strength-ccco 117.5 whenfl0.07fcotend to be more effective. To prevent eventual debonding of CFRPstrips in compression and to ensure the stability of the epoxywherefcc=confined concrete compressive strength;fco=uncon-fined concrete compressive strength;fl =pressure;cc=confined concrete ultimate strain; andco=uncon-fined concrete ultimate strain.Confined concrete strength and strain result from the lateralconfining pressure provided by the CFRP jacket, which depends onmany factors, for which provision must be made. The most impor-Effects of Slendernesstant factors are material properties of the CFRP sheet, cross-sectionhighly dependent on these strains.a reduction of the initial valuefl;ocalculated from geometricalratiosof approximately 25, 48, 71, 95, and 118 (lengths fromaverage of pressures in two directions of rectangular cross section1,0005,000 mm) were achieved.246/ JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013J. Compos. Constr. 2013.17:239-248.nonstrengthened column-300-250-200-150-100-50010203040 010203040M kNmcolumn strengthened with CFRP sheet-300-250-200-150-100-50010203040010203040M kNmNonstrengthenedcolumnEffect of Steel Reinforcement RatioAnother parameter changed for a theoretical parametric studywas the longitudinal steel reinforcement ratio. By changing thediameter of steel reinforcement in the range from 6, 8, 10, and12 mm, the reinforcement ratios 0.0072, 0.0128, 0.0199, and0.0287 were achieved. With a quadruple increase in reinforce-ment ratio (from 0.00720.0287), the final increase in columnload-carrying capacity is reduced from 28 to 8.4%. This observa-tion confirms the conclusions of Barros et al. (2008), that columns-350-350Column strengthenedwith NSM CFRP strips SEcolumn strengthened with CFRP stripscolumn strengthened with combinationColumn strengthenedwith CFRP sheet SEColumn strengthenedwith combination SE-350-300-250-200-150-100-500 0M kNm-350-300-250-200-150-100-500 0M kNm-150theoretical predictions (Fig. 17)computer modeling (software ATENA 3D)-100experimental test (average of two same columns)Fig. 13.Comparison of theoretical predictions, computer modeling, and experimental testsTable 4.Slenderness Effect on Column Resistance in KiloNewtonsColumnslenderness0 704 713 1 780 11 793 1325 679 687 1 745 10 762 1248 594 610 3 638 7 667 1271 428 460 7 438 2 490 1495 265 296 12 266 1 312 18118 137 196 13 174 1 207 20Note: SE=strength enhancement (%).The slenderness is calculated as the length to concrete cross-section radius of inertia ratio, whereas the length is consideredthe length between the hinges.Resistance of all four columns types decreases in more or lessthe same proportion with an increase in slenderness. The basic dif-ference is in the increase in resistance for the different strengthen-ing methods; the higher the slenderness, the higher the increasein resistance for columns strengthened with longitudinal NSMCFRP strips and vice-versa with respect to the smaller increase forconfined columns.JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE / MARCH/APRIL 2013 /247J. Compos. Constr. 2013.17:239-248.AcknowledgmentsThe research described in this paper was developed within and withthe support of research project VEGA No. 1/0306/09, Applicationof Probabilistic Methods to Improve the Reliability of ConcreteStructures.ReferencesBarros, J. A. O., Varma, R. K., Sena-Cruz, J. M., and Azevedo, A. F. M.(2008).“Near surface mounted CFRP strips for the flexural strengthen-ing of RC columns: Experimental and numerical research. ”Eng. Struct.,30(12), 34123425.Bournas, D. A., and Triantafillou, T. C. (2009). “Flexural strengthening ofRC columns with NSM FRP or stainless steel.”ACI Struct. J., 106(4),495505.Fitzwilliam, J., and Bisby, L. A. (2010). “Slenderness effects on circularCFRP confined reinforced concrete columns.”J. Compos. Constr.,14(3), 280288.G