University of Bahrain College of engineering Department of Civil Engineering and Architecture Senior Project CENG490 Numerical Modelling and Design of CFST Columns using various Design Codes By Salman Salah Almajid20094818 Ali Hassan AlNasser20092446 Hesham Mohamed Abdulrahim20092299 Supervised by Dr. Esmat Kameshki A report submitted to University of Bahrain In Partial Fulfillment of the requirements of the degree of Bachelor in Civil Engineering January 2014 i Abstract ConcreteFilledSteelTube(CFST)columnswereusedinconstructionintheearly1900s. However, the research into CFSTs did not begin until the 1960s. From that time onwards, several studies were conducted on the CFSTs to fully understand their behavior with the aim of improving their performance. The proposed research presents two studies to investigate the effect of the main influencing factor on the compressive behavior of circular CFST columns. The first study is conducted using finite elementanalysisapplyingreadymadesoftware,ANSYS.Thegeometryofthecolumnswere developedusingasupplementarysoftwarecalledSolidWorkstofacilitatethemodellingin ANSYS.ThesecondstudyisdesignofCFSTcolumnsaccordingtothemostcommonlyused codes worldwide. The codes are the Euro code version is "BS EN1994-1-1", the American code versionis"AmericanInstituteforSteelConstruction(LRFD)AISC360-05"andthetwo Australiancodeswhichare"AustralianStandardofconcretestructuresAS3600-2001and Australian Standard of steel structures AS 4100-1998". The main parameter of interest is the diameter-to-thickness ratio(

). The samples used in this research are all concentrically loaded stub columns to avoid moment failure. Inthedesignstudy,spreadsheetsusingMicrosoftExcelwerecreatedtodesignCFSTcolumns accordingtothethreecodes.Detailedflowchartswerepreparedtoshowstepbystepdesign procedures using all the codes. The results of the numerical investigation and the design study were verified by comparing them with those in the published literature.In addition, a comparative study was performed using the three codes, as well as, with the numerical analysis results, ANSYS. The comparison was based on the compressive capacity of the CFST columns. The variation in the results and their causes were discussed. ii Acknowledgement First of all, we would like to thank Allah the almighty for his blessings that enabled us to submit this project. Then, our special gratitude goes to our advisor Dr. Esmat Kamashki for her tremendous support, kindnessandpatiencethroughthewholecourseofthisseniorproject.Herbackgroundinsteel structural design was our guide before, through and hopefully after concluding our project.Specialthanksgoestoourcolleagueswhoaregraduatednow,engineerAhmedandengineer Hamza. They spent big efforts with us helping in modeling finite element samples for analysis. Finally, our best thanks goes to our families. The biggest emotional supporters for us during this project. Theiremotionalsupport helped us a lot to struggle throughout this projectandfinish it with a highly motivational moods. iii Table of Contents Abstract ........................................................................................................................................ i Acknowledgement ....................................................................................................................... ii List of Figures ............................................................................................................................ vi List of tables ............................................................................................................................. viii List of Abbreviations .................................................................................................................. ix List of Symbols ........................................................................................................................... x Euro Code (EC4) ..................................................................................................................... x AISC Code (LRFD) ................................................................................................................ xi Australian Code (AS) ............................................................................................................. xi Chapter 1: Introduction ................................................................................................................... 2 1.1 Introduction ........................................................................................................................... 2 1.1.1 Advantages and Disadvantages of CFST column .......................................................... 4 1.2 Objective of the study ........................................................................................................... 6 Chapter 2 : Literature Review ......................................................................................................... 8 Chapter 3: Design using Euro code .............................................................................................. 12 3.1 Design steps using EC4 ....................................................................................................... 12 3.1.1 Design of composite columns (clause 6.7): .................................................................. 12 3.1.2 Design methods: ........................................................................................................... 12 3.1.3 Local buckling: ............................................................................................................. 12 3.1.4 Simplified method of design (clause 6.7.3): ................................................................. 13 3.2 Design Flow Chart using EC4 ............................................................................................. 19 3.3 Design Example using EC4................................................................................................. 20 3.3.1 Design strength: ............................................................................................................ 20 3.3.2 Limits of applicability of the simplified method: ......................................................... 21 3.3.3 Local buckling: ............................................................................................................. 21 3.3.4 Design checks at ultimate limits state: ......................................................................... 21 3.3.5 Check on limits of simplified method: ......................................................................... 22 3.3.6 Buckling resistance of the composite column in axial compression: ........................... 22 3.4 Spread Sheet Solver using EC4 ........................................................................................... 24 3.4.1 Keywords: ..................................................................................................................... 24 iv 3.4.2 Inputs: ........................................................................................................................... 24 3.4.3 Process and outputs: ..................................................................................................... 25 Chapter 4: Design using AISC/LRFD code .................................................................................. 29 4.1 Design steps using LRFD .................................................................................................... 29 4.1.1General provisions: ........................................................................................................ 29 4.1.2 Material Limitations (clause I1.2.): .............................................................................. 29 4.1.3 Axial member (clause I2): ............................................................................................ 29 4.2 Design Flow Chart using LRFD.......................................................................................... 32 4.3 Design Example using LRFD ............................................................................................. 33 4.3.1 Material limitation: ....................................................................................................... 33 4.3.2 Nominal axial compressive strength without consideration of length effects ........ 34 4.3.3 Euler buckling load ................................................................................................. 34 4.3.4 Factored nominal axial strength ......................................................................... 35 4.4 Spread Sheet Solver using LRFD........................................................................................ 36 4.4.1 Keywords: ..................................................................................................................... 36 4.4.2 Input: ............................................................................................................................. 36 4.4.3 Process and outputs: ..................................................................................................... 37 Chapter 5: Design using Australian code ...................................................................................... 40 5.1 Design steps using A.S. ....................................................................................................... 40 5.1.1 Strength of Short Columns: .......................................................................................... 40 5.1.2 Australian standard concrete structures AS 3600-2001: .............................................. 40 5.1.3 Australian Standard Steel structures AS 4100-1998: ................................................... 42 5.2 Design Flow Chart using A.S. ............................................................................................. 47 5.3 Design Example Using A.S. ................................................................................................ 48 5.3.1 Standard AS 3600-2001 (concrete structure) ............................................................... 48 5.3.2 Standard AS 4100-1998 (steel structure)...................................................................... 49 5.3.3 Ultimate capacity .................................................................................................... 52 5.4 Spread Sheet Solver using A.S. ........................................................................................... 53 5.4.1 Key word: ..................................................................................................................... 53 5.4.2 Input: ............................................................................................................................. 53 5.4.3 Process and output: ....................................................................................................... 54 Chapter 6: Finite Element Analysis .............................................................................................. 58 v 6.1 General ................................................................................................................................ 58 6.2 Model .................................................................................................................................. 58 6.3 Finite Element Mesh ........................................................................................................... 58 6.4 Boundary Conditions and Load Application ....................................................................... 59 6.5 Concrete-Steel tube interaction ........................................................................................... 60 6.6 Steps of Design.................................................................................................................... 61 6.6.1 Defining the analysis system ........................................................................................ 62 6.6.2 Entering the Engineering data ...................................................................................... 63 6.6.3 Modelling the Geometry ............................................................................................... 63 6.6.4 Assigning the properties, connections and mesh of the model ..................................... 68 6.6.5 Setting up the Model..................................................................................................... 71 6.6.6 Setting up the solution .................................................................................................. 72 6.6.7 Viewing the results ....................................................................................................... 75 Chapter 7: Results and Discussion ................................................................................................ 77 7.1 Verification of the results .................................................................................................... 77 7.1.1 Verification of FEM results .......................................................................................... 77 7.1.2 Verification of Euro code (EC4) results ....................................................................... 78 7.1.3 Verification of American code (AISC/LRFD) results .................................................. 78 7.1.4 Verification of Australian code (AS) results ................................................................ 79 7.2 Comparison of the results .................................................................................................... 80 7.2.1 Comparison of the results for the three codes .............................................................. 80 7.2.2 Comparison of FEM results with the codes.................................................................. 81 Chapter 8: Conclusion and Recommendations ............................................................................. 84 8.1 Conclusion ........................................................................................................................... 84 8.2 Recommendations ............................................................................................................... 85 References ................................................................................................................................. 86 Appendix ....................................................................................................................................... 89 vi List of Figures Figure 1: Steel sections encased with concrete ............................................................................... 2 Figure 2: Steel Sections in-filled with concrete .............................................................................. 2 Figure 3: Cross-section of CFST column with rebars .................................................................... 3 Figure 4: Installation of CFST column during construction ........................................................... 4 Figure 5: Column buckling curves (based on figure 6.4, EC3) [18] ............................................. 18 Figure 6: Excel keyword ............................................................................................................... 24 Figure 7:Material properties for concrete and steel ...................................................................... 24 Figure 8: Loads and geometric properties .................................................................................... 25 Figure 9: Cross-section properties ................................................................................................ 25 Figure 10: Material Limitation...................................................................................................... 26 Figure 11: Local buckling check................................................................................................... 26 Figure 12: Plastic resistance and effective flexural stiffness calculation ..................................... 26 Figure 13: Buckling resistance check ........................................................................................... 27 Figure 14: Excel keyword ............................................................................................................. 36 Figure 15: Material properties for concrete and steel ................................................................... 36 Figure 16: Loads and geometric properties .................................................................................. 37 Figure 17: Cross-section properties .............................................................................................. 37 Figure 18: Material limitation ....................................................................................................... 37 Figure 19: Compressive strength calculation ................................................................................ 38 Figure 20: Excel key word ............................................................................................................ 53 Figure 21: Material properties for concrete and steel ................................................................... 53 Figure 22: Loads and geometric properties .................................................................................. 54 Figure 23: Cross-section properties .............................................................................................. 54 Figure 24: Concrete calculation .................................................................................................... 55 Figure 25: Steel tube calculation................................................................................................... 55 Figure 26:Steel tube calculation.................................................................................................... 56 Figure 27: Total capacity and final check ..................................................................................... 56 Figure 28: Meshed CFST column in ANSYS .............................................................................. 59 Figure 29: CFST column with loading and base plate; force applied on the loading plate .......... 60 Figure 30: Seperation of Steel and concrete after the application of load .................................... 61 Figure 31: Steps of ANSYS design .............................................................................................. 62 Figure 32: Types of analysis systems in ANSYS Workbench ..................................................... 62 Figure 33: Engineering data source in ANSYS Workbench ........................................................ 63 Figure 34: Properties for concrete material in ANSYS Workbench ............................................. 63 Figure 35: Solidworks new files interface .................................................................................... 64 Figure 36: Input parameters for cirles ........................................................................................... 64 Figure 37: Plan view of a steel tube .............................................................................................. 65 Figure 38: Extruded steel tube ...................................................................................................... 65 Figure 39: Extruded concrete core ................................................................................................ 66 Figure 40: Extruded steel plate ..................................................................................................... 66 Figure 41: parts of a column inserted in assemly file ................................................................... 67 vii Figure 42: Command "Mate" properties ....................................................................................... 67 Figure 43: Finallized model using Solidworks ............................................................................. 68 Figure 44: Outline of ANSYS Mehcanical ................................................................................... 69 Figure 45: Defining the properties of each part in ANSYS Mechanical ...................................... 69 Figure 46: Properties of each part of the model in ANSYS Mechanical ...................................... 69 Figure 47: Contacts between each part of the model in ANSYS Mechanical .............................. 70 Figure 48: Details of the contact between Concrete Core and Steel tube in ANSYS Mechanical 70 Figure 49: Details of Mesh in ANSYS Mechanical...................................................................... 70 Figure 50: Setting up the model under Static Structural in ANSYS Mechanical ......................... 71 Figure 51: Details of force in ANSYS Mechanical ...................................................................... 71 Figure 52: Details of Fixed Support in ANSYS Mechanical ........................................................ 72 Figure 53: Details of Remote Displacement in ANSYS Mechanical ........................................... 72 Figure 54: Solution options in ANSYS Mechanical ..................................................................... 72 Figure 55: Equivalent (von-Mises) Stress in Ansys Mechanical .................................................. 73 Figure 56: Stress ratio in ANSYS Mechanical ............................................................................. 74 Figure 57: Stress Probe in ANSYS Mechanical ........................................................................... 75 viii List of tables Table 1: Comparison of Column Costs [4] ..................................................................................... 5 Table 2:Maximum values (d/t), (h/t) and (b/t) with fy N/mm2 (based on Table 6.3, EC4) [16] .. 13 Table 3: Buckling curves and member imperfections for composite columns(based on table 6.5, EC4)[16] ....................................................................................................................................... 17 Table 4: Values of plate element yield slenderness limit (based on table 6.2.4, AS4100) [21] ... 43 Table 5 values of member section for kf = 1.0 (based on table 6.3.3(1), AS4100) [21] ............... 45 Table 6 values of member section constant (b) for kf < 1.0 (based on table 6.3.3(2),AS4100)[21]....................................................................................................................................................... 46 Table 7: Verification of FE results................................................................................................ 77 Table 8: Verification of Euro code results .................................................................................... 78 Table 9: Verification of American code results ............................................................................ 79 Table 10: Verification of Australian code results ......................................................................... 79 Table 11: Comparison of the results with different codes ............................................................ 80 Table 12: Comparison of FE with the codes ................................................................................. 81 ix List of Abbreviations AISCAmerican Institute of Steel Construction ANSIAmerican National Standards Institute ASCEAmerican Society of Civil Engineers ACIAmerican Concrete Institute ASAustralian Standard CFTConcrete Filled Tube CFSTConcrete Filled Steel Tube EC4Euro Code FEFinite Element FEMFinite Element Model HSSHollow Structural Section LRFDLoad and Resistance Factor Design x List of Symbols Euro Code (EC4) Aa Cross-sectional area of the structural steel section Ac Cross-sectional area of concrete AsCross-sectional area of reinforcement Ea Modulus of elasticity of structural steel Ecm Secant modulus of elasticity of concrete Es Design value of modulus of elasticity of reinforcing steel (EI)eff Effective flexural stiffness for calculation of relative slenderness Ia Second moment of area of the structural steel section Ic Second moment of area of the uncracked concrete section Is Second moment of area of the steel reinforcement Ke ,Ke,II Correction factors to be used in the design of composite columns LLength; span; effective span MEd Design bending moment Ncr Elastic critical normal force NEd Design value of the compressive normal force Npl,Rd Design value of the plastic resistance of the composite section to compressive normal force Npl,Rk Characteristic value of the plastic resistance of the composite section to compressive normal force b Width of the flange of a steel section width of slab d Clear depth of the web of the structural steel section; diameter of the shank of a stud connector; overall diameter of circular hollow steel section; minimum transverse e Eccentricity of loading; distance from the centroidal axis of profiled steel sheeting to the extreme fibre of the composite slab in tension fcd Design value of the cylinder compressive strength of concrete fck Characteristic value of the cylinder compressive strength of concrete at 28 days fsd Design value of the yield strength of reinforcing steel fsk Characteristic value of the yield strength of reinforcing steel fy Nominal value of the yield strength of structural steel h Overall depth thickness tAge; thickness tf Thickness of a flange of the structural steel section Factorparameter C Partial factor for concrete S Partial factor for reinforcing steel Factor steel contribution ratio 235/ y , where fy is in N/mm2 a, ao Factors related to the confinement of concrete c, co, Factors related to the confinement of concrete Relative slenderness Diameter (size) of a steel reinforcing bar; damage equivalent impact factor Reduction factor for flexural buckling LT Reduction factor for lateral torsional buckling xi AISC Code (LRFD) Ac Area of concrete, in.2 (mm2) As Area of steel cross section, in.2 (mm2) Asr Area of continuous reinforcing bars, in.2 (mm2) D Outside diameter, in. (mm) EModulus of elasticity of steel = 29,000 ksi (200 000 MPa) Ec modulus of elasticity of concrete = wc1.5, ksi Ecm Modulus of elasticity of concrete at elevated temperature, ksi (MPa) EIeff Effective stiffness of composite section, kip in.2 (N-mm2) Es Modulus of elasticity of steel = 29,000 ksi (200 000 MPa) Fy Specified minimum yield stress of the type of steel being used, ksi (MPa). As used in this Specification, yield stress denotes either Ic Moment of inertia of the concrete section, in.4 (mm4) Is Moment of inertia of steel shape, in.4 (mm4) Isr Moment of inertia of reinforcing bars, in.4 (mm4) K Effective length factorL Length of the member, in. (mm) PeEuler buckling load, kips (N) Pn Nominal axial strength, kips (N) Po Nominal axial compressive strength without consideration of length effects, kips (N) fc'Specified minimum compressive strength of concrete, ksi (MPa) t Thickness of element, in. (mm) wc Weight of concrete per unit volume (90 wc 155 lbs/ft3 or 1500 wc 2500 kg/m3) cResistance factor for axially loaded composite columns cSafety factor for axially loaded composite columns Australian Code (AS) AgGross area of a cross-sectionAsThe cross-sectional area of reinforcement Ae Effective area of a cross-section An Net area of a cross-section DThe overall depth of a cross-section E Youngs modulus of elasticity, 200 103 MPa EsThe mean value of the modulus of elasticity of concrete at 28 daysGNominal dead load I Second moment of area of a cross-section LeThe effective length of column LuThe unsupported length of a column M1*,M2* The smaller and larger design bending moment respectively at the ends of a column N* The axial compressive or tensile force on a cross-section NuoThe ultimate strength in compression without bending; of an axially loaded cross-section NcNominal member capacity in compression Ns Nominal section capacity of a compression member xii Q Nominal live load b Widthbe Effective width of a plate element doOutside diameter of a circular hollow section f'cThe characteristic compressive cylinder strength of concrete at 28 days fyYield stress used in design kf Form factor for members subject to axial compression kb Elastic buckling coefficient for a plate element kbo Basic value of kb le Effective length of a compression member Le/rGeometrical slenderness ratio rRadius of gyration of a cross-section tWall thickness of a circular hollow section aCompression member factor bCompression member section constant cCompression member slenderness reduction factor Compression member factor Slenderness ratio ePlate element slenderness eyPlate element yield slenderness limit nModified compression member slenderness Capacity factor 1 CHAPTER 1 2 Chapter 1: Introduction 1.1 Introduction Composite construction as we know it today was first used in the construction of a building and a bridge in the U.S. over a century ago. The first forms of composite structures incorporated the use ofsteelandconcreteforflexuralmembers,andtheissueoflongitudinalslipbetweenthese elementswassoonidentified.Compositesteelconcretebeamsaretheearliestformofthe composite construction method. In the U.S. a patent by an American engineer was developed for the shear connectors at the top flange of a universal steel section to prevent longitudinal slip. This was the beginning of the development of fully composite systems in steel and concrete.Concrete-encasedsteelsectionswasusedatthebeginningtoovercometheproblemoffire resistance and to ensure that the stability of the steel section was maintained throughout loading. The steel section and concrete act compositely to resist axial force and bending moments. Composite tubular columns were developed much later during the last century. They were used becausetheyprovidedpermanentandintegralformworkforacompressionmemberandwere instrumental in reducing construction times and consequently costs. [1] Thus, 2 types of steel-concrete columns were developed: 1.Steel section in-filled with concrete 2.Steel section encased with concrete Figure 1: Steel sections encased with concrete Figure 2: Steel Sections in-filled with concrete Nowadays, the composite structural elements are increasingly used in tall buildings, bridges and other types of structures. It is still based on the fundamental principle that steel is most effective 3 in tension and concrete is most effective in compression. Thus, the disadvantage of two materials can be compensated for and the advantages can be combined, providing efficient structural system. The steel-concrete composites are considered as an advantageous system for carrying large axial load benefitting from the interaction between the concrete and the steel section. The steel section reinforces the concrete to resist any bending moments, tensile and shear forces. The concrete in a composite column reduces the potential for buckling of the steel section in addition to resisting compressive loading. Figure 3: Cross-section of CFST column with rebars The use of composite columns, encased or in-filled, results in significant reduction of the column size when compared to regular reinforced concrete columns needed to carry the same load. Hence, considerable economic savings can be obtained. Also, the column size reduction is advantageous where floor space is at a premium, such as in office blocks and car parkings. In addition, closely spaced composite columns connected with spandrel beams can be used around the outsides of the high rise buildings for lateral loads resistance by the tabular concept [2].4 Figure 4: Installation of CFST column during construction Concrete encased steel composite sections are favored for many seismic resistant structures. When theconcreteencasementcracksundersevereflexuraloverloading,thestiffnessofthesection reduces but the steel core provides shear capacity and ductileresistance to subsequent cycles of overload.Additionally,thesurfaceareaoftheenclosedsteelsectionsisintactbytheconcrete cover, thus required no painting and fireproofing costs.Concrete filled steel tube (CFST) columns are favored for many earthquake resistant structures, columns in high rise buildings, bridge piers subject to high strainratefrom trafficand railways decks.Concretefilledsteeltubesnecessitatesupplementaryfireresistantinsulationiffire protection of the structure is crucial. The CFST structures have better constructability because the steel tubes can be used as the formwork and the shoring system for casting concrete in construction. Moreover,CFSTsprovidehighcompressiveandtorsionalresistanceaboutallaxeswhen compared with concrete encased steel composite sections [3]. 1.1.1 Advantages and Disadvantages of CFST column 1.Maintenance Cost: Whenexposedtoairandhumidity,thesteelstructuresarevulnerabletocorrosion,thus they have to be painted periodically. This issue occurs in the case of CFST structures but not in the case of encased concrete composite element, because the steel section is protected by the surrounding concrete. 2.Buckling Failure: The steel sections are considered economical because of their low strength to weight ratio. However,withtheincreasedslendernessofthesteelcolumnthecarryingcapacity 5 decreasesbecauseofthebucklingfailuredomination.Inthecompositecolumnsthe concrete delays the buckling when compressively loaded which enhances the capacity of the element. Also, thinner steel section would be required in the presence of concrete thus the cost is reduced. 3.Fireproofing Costs: Thesteelsectionshashighloadcarryingcapacityatnormalrangetemperatures,butits strengthreducesimmenselywhenexposedtohightemperatures,thusfireproofingis essential. This issue occurs in the case of CFST structures but not in the encased concrete composite element because the steel section is protected by the surrounding concrete. 4.Construction: The structural steel tube in the CFST acts as in-place framework. Fixing the steel tube for casting concrete is much easier and less time consuming than fixing and removing frame work. Also, the presence of steel tube minimizes the need for rebar fixing, which is one of the most tedious works in the RC construction. 5.Ecology: Thereductioninwoodconsumptionneededfortheformworkisenvironmentally advantageous. Also, it is much easier to reuse the concrete and the steel of CFST elements compared to regular RC members. 6.Cost: AcomparisonoftypicalcostsofcolumnconstructionhasbeencompiledbyAustralian consulting engineers, Webb and Peyton [4], and this is summarized in Table 1. This reveals thecompetitivenatureoftheconcrete-filledsteelcolumnwhencomparedwith conventional reinforced concrete columns for buildings over 30 levels. This statistic will be more favorable for concrete-filled steel columns in buildings of over 50 stories, which are becoming common in many densely populated cities throughout the world. Table 1: Comparison of Column Costs [4] Type of column Reinforced Concrete Concrete with steel erection column Concrete-Encased Steel Strut Tube Filled with Reinforced Concrete Steel Tube Filled with Concrete Full Steel Column Relative cost, 10 levels 1.01.221.531.141.102.27 Relative cost, 30 levels 1.01.131.851.111.022.61 6 1.2 Objective of the study 1-Design of CFST columns using various codes to compute their compressive capacities. The codes are: Euro code "BS EN1994-1-1". American code "American Institute for Steel Construction (LRFD) AISC 360-05". Australiancode"AustralianStandardofconcretestructuresAS3600-2001and Australian Standard of steel structures AS 4100-1998". 2-Develop a spreadsheet using Microsoft Excel for each one of the design codes to compute the compressive capacity of CFST columns. 3-PreparethegeometryofCFSTcolumnsusingSolidWorksandthenlinkingthemto ANSYS to perform the rest of the finite element analysis process. 4-Verification and comparison of the results achieved in this study with those in the published literature. 7 CHAPTER 2 8 Chapter 2: Literature Review Test to investigate the axial strength of CFT columns have been performed on a variety of cross-sectional shapes and D/t and L/D ratios. Furlong (1967) investigated 13 specimens with D/t ratios ranging from 29 to 98. Results indicated that each component of the composite column resisted load independent of each other, and consequently there was no increase in the load bearing capacity due to the confinement of the concrete core [5].Gardner and Jacobson (1967) investigated 22 composite columns with D/t ratios between 30 and 40. These results suggested that at ultimate load the steel tube was at failure but the concrete core was not. However, an increased strain level was noted for the steel tube without local buckling, suggesting that the concrete stabilized the tube wall [6]. Knowles and Park (1969) studied 12 circular and seven square columns with D/t ratios of 15, 22 and 59, and L/D ratios ranging from 2 to 21. Results indicated that the tangent modulus method accuratelypredictedthecapacityforcolumnswithL/Dratiosgreaterthan11butwasslightly conservativeforcolumnswithsmallslendernessratios.Itwasconcludedthatthislargerthan expectedcapacityforcompositecolumnswithL/D