Dissertation - UHPC - Composite beam

Behaviour of Steel-Concrete Composite Beams Made of Ultra High Performance Concrete Der Wirtschaftswissenschaftlichen Fakult¨at der Universit¨at Leipzig DISSERTATION zur Erlangung des akademischen Grades Doktor-Ingenieur (Dr.-Ing.) vorgelegt von M.Eng. Bui Duc Vinh geboren am 07 April 1972 in Vinh Phuc - Vietnam

Leipzig, 9th October 2010

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Foreword This thesis was the results of a long hard working period of the author, is would not have been possible without the contribution of a great number of people: First of all, I would like to thank to my supervisor Prof. Dr.-Ing. habil. Nguyen Viet Tue for giving me the opportunity to join his research group and giving me this challenging research project. I had learn a lot of thing from many hours discussion with him. He was not only always able to push up my spirits while I was in despair with my results but also sharing with me in sad moment which I had spent, and I am very grateful for that. The experiments of this study could not have been performed without the help and technical expertise of the laboratory personnel, as of Dipl.-Ing. Holger Busch, Dipl.-Ing. Immanuel Wojan and many staffs at MFPA-Leipzig for conducting the experiments. I would like to express my thanks for their support. My gratitude also goes to Dr.-Ing. Nguyen Duc Tung, Dr.-Ing. Jiaxin Ma, Dr.-Ing. Michael K¨ uchler, Dipl.-Ing. Jiabin Li, Dipl.-Ing. Stephan Mucha, Dipl.Ing. Gunter Schenck etc. my colleagues in IMB (Institut f¨ ur Massivbau und Baustofftechnologie, Uni-Leipzig) for many valuable suggestions and discussion hours. Grateful appreciation is also due to Mrs. Sigrid Fritzsche and Mrs. Sylvia Proksch for their warm friendship and constant help during my stay in Leipzig. I wish to thank the German Research Foundation (DFG- Deutsche Forschungsgemeinschaft) for finance support the research project SPP 1182, which allows me take up doctoral studies at University of Leipzig, Germany. Last but not least, I want to sincerely thank my parents and especially my wife Van Anh and son Nhan for their great support and patience during my study. I hope in the future I can return all their love.

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Foreword

Biography Bui Duc Vinh was born in Vinh Phuc, Vietnam, on the 7th April 1972. In October 1991 he started his studies in Civil Engineering at Ho Chi Minh University of Technology (HCMUT), where he received his Bachelor degree in 1996, specialize in Coastal Engineering. He started joint Faculty of Civil Engineering (FCE), HCMUT and worked as research assistant. Two year after, 1998, he obtained Master Degree in Mechanic of Construction from University of Liege, Belgium. He continued his studies on structural engineering and focused on high strength concrete material, modelling of concrete structures. In Dec. 2006, he jointed research team of Prof. Dr.-Ing. habil. Nguyen Viet Tue, at Institute for Structural Concrete and Building Materials, University of Leipzig (IMB, Uni-Leipzig). At here, his work concentrates on investigation structural behaviour of steel-concrete composite beams made of ultra high performance concrete. March 2010 he finished his dissertation under the supervision of Prof. Nguyen Viet Tue.

Leipzig, October 2010

Bui Duc Vinh

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Biography

Dedicated to my parents, my wife Van Anh and my son Bui Hoang Nhan

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Biography

Abstract Ultra-High Performance Concretes (hereafter, UHPC) have high mechanical strengths (fc > 150 MPa, ft > 7 MPa) and exhibit quasi-strain hardening in tension. Their very density improve durability and extend long service life. The steel-concrete composite beams with concrete slab made of UHPC possess advanced properties give significant improvement in ultimate strength of the composite beams. The research reported in this thesis aimed to determine the performance and structural behaviour of composite steel-UHPC elements in bending. In addition, the continuous Perfobond based shear connectors that belong to the beams was investigated as well. The Experimental assessment of the shear connector was conducted through 11 series Push-Out test with 27 specimens. In order to predict shear capacity, characteristic load-slip curves as well as contribution of constituents. The connectors without any reinforcement show very poor ductility, the characteristic slip reached lower 1.5mm only. They could be classified as non-ductile connector. The headed stud show better characteristic load-slip response, but this connector often failed by shanked at the base of connector. The shear connector with added reinforcement in front cover and dowel exhibits better performance than headed stud connection in both terms of load capacity and ductility. The test pointed out that embedded rebars in dowel play an important role in improvement performance of the connector. The contribution of steel fiber less important than and It is not obviously when steel fiber vary in range of 0.5% to 1.0%. The structural response of the composite members under bending with the UHPC slab in compression was investigated with four points bending test of six full scale composite beams. The concrete mix contained either 1% fibres or 0.5% (by volume) of straight steel fibres with concrete strength of approximately 150 MPa. The experimental study demonstrates that the use of UHPC slab with continuous shear connector is possible, and it enhances the performance of composite elements in terms of resistance and stiffness. The finite element analysis of the Push-Out specimens and composite beams which tested in this investigation was carried out using software ATENA. Full three dimension models for both Push-Out specimens and composite beams were developed in order to taken into account complexity of geometry. The concrete

was modelled using a Microplane M4 with parameters were calibrated accompanying to uni-axial compression and RILEM bending test. Modelling result showed a reasonable agreement with the experimental data. The FE simulation is not only provide ultimate strength, global behaviour but also explained local damage area as well process of collapse occurred in structures. However, the FE analysis need more improvement in concrete material model, in order to used for parameter studies. Finally, based on result of experimental and numerical investigation a numerous recommendations are issued for practical design. The results form this work provide to better knowledge on using new UHPC in composite structures. It also contribute to provision of design code.

Contents Foreword

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Biography

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Abstract

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Abbreviations

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List of Symbols

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List of Figures

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List of Tables

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1. Introduction 1.1. State of the art . . . . . 1.2. Context and motivation 1.3. Objectives of study . . . 1.4. Scope of work . . . . . . 1.5. Structure of the thesis .

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2. Consideration aspects of steel-concrete composite beams 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Single span composite beams under sagging moment . . . . . . . . 2.2.1. Basic Structural Behaviour . . . . . . . . . . . . . . . . . . 2.2.2. Structural composite beam with continuous shear connection 2.3. Perfobond shear connector (PSC) . . . . . . . . . . . . . . . . . . . 2.3.1. Conventional Perfobond shear connector . . . . . . . . . . . 2.3.2. Modified pefobond shear connectors . . . . . . . . . . . . . 2.4. Development of concrete technology . . . . . . . . . . . . . . . . . 2.5. Composite beam made of UHPC . . . . . . . . . . . . . . . . . . . 2.6. Finite Element modelling . . . . . . . . . . . . . . . . . . . . . . . 2.6.1. modelling of composite beams . . . . . . . . . . . . . . . . . 2.6.2. Modelling of Push-Out test . . . . . . . . . . . . . . . . . . 2.7. Design of composite beam . . . . . . . . . . . . . . . . . . . . . . .

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2.7.1. Limit state design philosophy . . . . . . . . . . . . . . . . . 2.7.2. Methods for analysis and design . . . . . . . . . . . . . . . 2.7.3. Resistant capacity of composite beam under sagging moment 2.7.4. Partial shear connection . . . . . . . . . . . . . . . . . . . . 2.7.5. Ductile and non-ductile shear connectors . . . . . . . . . . 2.8. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Characterization material properties of UHPC 3.1. Development of UHPC-A Historical perspective . . . . . . . 3.2. Constituent materials of Ultra High Performance Concrete . 3.2.1. Principle of UHPC . . . . . . . . . . . . . . . . . . . 3.2.2. Composition of UHPC . . . . . . . . . . . . . . . . . 3.2.3. Cost of UHPC . . . . . . . . . . . . . . . . . . . . . 3.2.4. Material used in this work . . . . . . . . . . . . . . . 3.3. Relevant material properties . . . . . . . . . . . . . . . . . . 3.3.1. Properties of fresh UHPC . . . . . . . . . . . . . . . 3.3.2. Time dependent properties of UHPC . . . . . . . . . 3.3.3. Durability . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Mechanical behaviour characterization . . . . . . . . . . . . 3.4.1. Development of compressive strength . . . . . . . . . 3.4.2. Stress-strain behaviour in uni-axial compression . . . 3.4.3. Bi-axial behaviour of UHPC . . . . . . . . . . . . . . 3.4.4. Flexural and direct tension behaviour of UHPC . . . 3.4.5. Fracture properties of UHPC . . . . . . . . . . . . . 3.5. Concluding remarks . . . . . . . . . . . . . . . . . . . . . .

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4. Experimental study for perfobond shear connector in UHPC 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Experimental programs and specimens . . . . . . . . . . . . . . . . 4.2.1. Push-Out test specimens . . . . . . . . . . . . . . . . . . . 4.2.2. Arrangement for Push-Out series . . . . . . . . . . . . . . . 4.2.3. Standard Push-Out test setup . . . . . . . . . . . . . . . . . 4.2.4. Loading procedure . . . . . . . . . . . . . . . . . . . . . . . 4.3. Test results and observations . . . . . . . . . . . . . . . . . . . . . 4.3.1. Resistance and slip results . . . . . . . . . . . . . . . . . . . 4.3.2. Behaviour of headed stud shear connectors in UHPC . . . . 4.3.3. General behaviour of perfobond shear connector in UHPC . 4.3.4. Influence of dowel profile and test setup . . . . . . . . . . . 4.3.5. Influence of fiber content to load slip-behaviour . . . . . . . 4.3.6. Influence of transverse reinforcement arrangement . . . . . 4.3.7. Influence of embedding reinforcement through concrete dowel

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Contents

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4.4. Summary conclusions for Push-Out test . . . . . . . . . . . . . . . 73 5. Experimental investigation on the structural behaviour of steelUHPC composite beams 75 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2. Experimental program for composite beams . . . . . . . . . . . . . 75 5.2.1. Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . 75 5.2.2. Design and construction of test specimens . . . . . . . . . . 76 5.2.3. Test set-up and instrumentation . . . . . . . . . . . . . . . 79 5.3. Analysis of the test results and observations . . . . . . . . . . . . . 81 5.3.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.2. Structural behaviour and Observations of beam B1 and B2 83 5.3.3. Structural behaviour and Observation of beam B3 and B4 . 89 5.3.4. Test results and observing of beam B5 . . . . . . . . . . . . 93 5.3.5. Test results and observing of beam B6 . . . . . . . . . . . . 97 5.4. Shear flow distribution in composite beam . . . . . . . . . . . . . . 101 5.4.1. Load-slip behaviour in composite beam versus Push-Out test101 5.4.2. Distribution of longitudinal shear forces . . . . . . . . . . . 103 5.5. Summary conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 104 6. Material models for Finite Element Modelling 107 6.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.2. Material models for structural steel and reinforcement . . . . . . . 108 6.3. Microplane M4 material model for concrete . . . . . . . . . . . . . 109 6.3.1. Aspects of concrete material model . . . . . . . . . . . . . . 109 6.3.2. Microplane M4 material model in ATENA . . . . . . . . . . 110 6.4. Parameter study of Microplane . . . . . . . . . . . . . . . . . . . . 115 6.4.1. Setting up virtual test . . . . . . . . . . . . . . . . . . . . . 115 6.4.2. Input parameter and sensitivity analysis . . . . . . . . . . . 117 6.4.3. UHPC experimental data . . . . . . . . . . . . . . . . . . . 117 6.4.4. Results of M4 model parameters investigation and discussion118 6.5. Proposed set of parameter for UHPC . . . . . . . . . . . . . . . . . 123 6.5.1. Adjustment strategy for model parameters . . . . . . . . . 123 6.5.2. Result of compression and bending modelling with M4 . . . 123 6.6. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7. Finite Element Modelling 7.1. Introduction . . . . . . . . . . . . . . 7.2. Modelling of Push Out Test . . . . . 7.2.1. Finite element model . . . . . 7.2.2. Experimental validation finite

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7.2.3. Local behaviour Push-Out specimens . . . . . . . . . . . . . 135 7.2.4. Proposed model for prediction ultimate capacity of perforbond shear connector . . . . . . . . . . . . . . . . . . . . . 141 7.3. Modelling of composite beam . . . . . . . . . . . . . . . . . . . . . 146 7.3.1. Finite element model . . . . . . . . . . . . . . . . . . . . . . 146 7.3.2. Validation of the FE model . . . . . . . . . . . . . . . . . . 149 7.3.3. Local stress distribution in steel girder and shear connectors155 7.3.4. Shear flow on concrete dowel . . . . . . . . . . . . . . . . . 157 7.4. Summary conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 157 8. Conclusions and Future Perspective 159 8.1. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.1.1. Ultra high performance concrete . . . . . . . . . . . . . . . 159 8.1.2. Composite beam members made of UHPC under static load 160 8.1.3. Perfobond based shear connectors in UHPC . . . . . . . . . 161 8.1.4. Modelling of composite beams . . . . . . . . . . . . . . . . 162 8.2. Recommendations for further research . . . . . . . . . . . . . . . . 162 A. Appendices: Concrete mix proportional 165 A.1. List of tables for constituent materials . . . . . . . . . . . . . . . . 165 B. Appendices: Standard Push-Out Test 167 B.1. Experimental results of Standard Push-Out test . . . . . . . . . . . 167 B.2. List of drawings and charts . . . . . . . . . . . . . . . . . . . . . . 167 C. Appendices: Bending test of composite beam 179 C.1. Design of steel-concrete composite beams for bending test . . . . . 179 C.2. List of drawings and charts . . . . . . . . . . . . . . . . . . . . . . 179 D. Appendices: Tool for ATENA

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Bibliography

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Abbreviations FE FEA FEM NFEA FES FEMD SG LVDT CMOD NSC CSC HPC UHPC UHPFRC RPC CB SCCB UHPCSCCB SHC SPOT HSSC PFSC ODW CDW M4 EC4 RILEM

Finite Element Finite Element Analysis Finite Element Methods Nonlinear Finite Element Analysis Finite Element Simulation Finite Element Modelling Strain gauge Linear Variable Displacement Transducer Crack Mount Opening Displacement Normal Strength Concrete Conventional Strength Concrete High performance Concrete Ultra High Performance Concrete Ultra High Performance Fiber Reinforced Concrete Reactive Powder Concrete Composite beam Steel Concrete Composite Beam Steel Concrete Composite Beam Made of UHPC Shear Connector Standard Push-Out Test Headed Stud Shear Connector Perfobon Shear Connector Open dowel Closed dowel Bazant’s Miroplane material model for concrete EuroCode 4 International Union of Laboratoies and Experts in Construction Materials, System and Structures

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Abbreviations

List of Symbols Greek characters σc δuk η κ φ

stress of concrete characteristic value of slip capacity degree of shear connection curvature diameter of concrete dowel

Latin lower case letters bo d ndw hsc tsc qu Pdw Pr Pfr Pa

bottom width of shear surface in dowel area depth of shearing cone numer of dowel in the Push-Out specimen height of steel rib thickness of steel rib shear capacity per perfobond shearing capacity of plain concrete dowel contribution of rebar in dowel to capacity of PSC contribution of rebar in front cover to capacity of PSC contribution of steel rib to capacity of PSC

Latin upper case letters A Aa Ab Abh Ac Acc

Cross-sectional area of the effective composite section neglecting concrete in tension cross-sectional area of the structural steel section cross-sectional area of bottom transverse reinforcement cross-sectional area of bottom transverse reinforcement in a haunch cross-sectional area of concrete cross-sectional area of concrete shear per connector

Acd Act Afc Ar Arf Le M D Pu Pu,test Pu,pred PRk ,1 PRk

cross-sectional area of dowel cross-sectional area of the tensile zone of the concrete cross-sectional area of the compression flange area of embedded reinforcement in concrete dowel amount area of reinforcement in front cover span of composite beam Bending moment uiameter of concrete dowel ultimate resistance of Push-Out specimen ultimate resistance of Push-out specimen from test predicted ultimate resistance of Push-out specimen characteristic value of the shear resistance of a single connector characteristic value of the shear resistance of Push-Out specimen

Mechanical Properties fc fc,cube fck fct fc,28d fy fy,r Ec Ea Ea,r Gf lch ν γv

Cylinder compressive strength Cube compressive strength (150 mm) Characteristic value of the cylinder compressive strength of concrete Tensile strength of concrete compressive strength of concrete at 28 days Nominal value of the yield strength of structural steel yield strength of reinforcement elastic modulus of concrete elastic modulus of structural steel elastic modulus of reinforcement Fracture Energy Characteristic length Possion’s ratio Partial factor for design shear resistance of a shear conector

List of Figures 1.1. Karl-Heine footbridge in Leipzig-Germany: concrete filled tube structures, after Koenig (56) (left), and the composite of a residential building in London(26) (right) . . . . . . . . 1.2. Basic mechanism of composite action . . . . . . . . . . . . . 1.3. Perfobond shear connection in composite beam . . . . . . . 2.1. 2.2. 2.3. 2.4. 2.5.

steel floor . . . . . . . . . . . .

Typical cross sections of composite beams (26) . . . . . . . . . . . Typical shear connectors, after Oehlers and Bradford (68) . . Stages of composite beam at different load levers(26) . . . . . . . Longitudinal shear force on connectors(26) . . . . . . . . . . . . . . Typified VFT-WIB composite section (above) and application in Vigaun bridge project, after Schmitt et al. (94) . . . . . . . . 2.6. Push-Out specimens and test setup, a) general specimen (Oguejiofor and Hosain (83)), b) specimen with profile steel sheet (Kim et al. (55)). . . . . . . . . . . . . . . . . . . . . . . . 2.7. Shear transfer mechanism from concrete slab to steel rib . . . . . . 2.8. Various kind of Perfobond Shear connector in composite beam . . 2.9. Push-Out test of the VFT-WIB connector (93) . . . . . . . . . . . 2.10. Discrete and continuous model for shear connector in composite beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11. Elasto-Fracture-Plastic based material models for steel and concrete in Finite element modelling of Push-Out test and composite beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12. Push-Out specimen model of Kraus and Wurzer (57) . . . . . . 2.13. Ideallized tress-strain diagrams used in the plastic method, (26; 27) 2.14. Plastic analysis of composite section under sagging moment, 1aneutral axis in concrete slab; 1b-neutral axis at the bottom of composite slab; 2a-neutral axis lies within top flange of steel section; 2b- neutral axis in the web . . . . . . . . . . . . . . . . . . . . . . 2.15. Design method for partial shear connection (47; 48) . . . . . . . .

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3.1. Historical development of UHPC . . . . . . . . . . . . . . . . . . . 32 3.2. Comonents of a typical UHPC . . . . . . . . . . . . . . . . . . . . 34

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List of Figures

3.3. Relative density vesus w/c ratio, after Richard and Cheyrezy (90) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Estimation cost of constituent materials for UHPC, (a):UHPC without steel fiber, (b) with 1% steel fiber (58) . . . . . . . . . . 3.5. Autogeneous shrinkage of UHPC with and without coarse aggregates, after Ma et al. (69; 70) . . . . . . . . . . . . . . . . . . . 3.6. Creep of UHPC with and without coarse aggregates, after Ma and Orgrass (71; 73) . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7. Porosity of UHPC with and without heat treated, after Cwirzen (23) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8. Comparison durability properties of NSC, UHP and UHPC. After Suleiman et al. (99) . . . . . . . . . . . . . . . . . . . . . . . . 3.9. Development compressive strength, after Ma (74) . . . . . . . . . 3.10. Test setup for stress-strain response under uni-axial compression 3.11. Loading procedure for uni-axial compression test . . . . . . . . . 3.12. A comparison of stress-stress curves of NSC, HPC and UHPC(left), and Poinsson’s ratio (right). After (Tue et al.) (101) . . . . . . 3.13. Relation elastic modulus vesus compressive strength.(Tue et al. (101; 70)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14. Comparison influence of grain size and fiber content to bi-axial strength increment, modified from Curbach and Hampel (22) 3.15. Proposal reduction strength under compression-tension load, modified from (Fehling et al. (29)) . . . . . . . . . . . . . . . . . . 3.16. Flexural tensile stress-deflection diagram of G7-UHPC, by Tue et al. (108) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.17. Notched beam three points bending test(left) and Wedge splitting test (right) to determine fracture energy of concrete . . . . . . . 3.18. Characteristic length versus versus compressive strength (32) . . 4.1. Behaviour of headed stud shear connector in NSC, after Johnson (47) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Standard Push-Off Test, Setup 1 (a) and Setup 1 (b) . . . . . . . 4.3. Typical stress-strain curve of structural steel at room temperature, modified Outinen et al. (85) . . . . . . . . . . . . . . . . . . . 4.4. Typical stress-strain curves of Bst500 reinforcement . . . . . . . 4.5. Material responses of G7-UHPC 1% steel fiber, stress-strain diagram in compression test (left) and stress-deflection in RILEM beam test(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6. Casting Push-Out specimens . . . . . . . . . . . . . . . . . . . .

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List of Figures

4.7. CDW (above line) and ODW (below line) shear connectors, (a & e)-without rebar, (b & f)-rebar in dowel, (c & g)-rebar in front cover, (d & h)-rebar in dowel and front cover . . . . . . . . . . . 4.8. Push-Out specimen in 4000 kN load frame and controller system 4.9. Instrumentation setup in SPOT Setup 1(left) and Setup 2 (right) 4.10. Load history for SPOT . . . . . . . . . . . . . . . . . . . . . . . . 4.11. Load-slip diagram of headed studs shear connectors in UHPC . 4.12. Crack opening in concrete surfaces . . . . . . . . . . . . . . . . . 4.13. Failure process and shanked of HSSH at footing . . . . . . . . . . 4.14. Basic mechanics of perfobond shear connector (left), stress state in concrete dowel, after Kraus and Wurzer (57)(right) . . . . 4.15. Deformation of the steel ribs after test . . . . . . . . . . . . . . . 4.16. Overview behaviour of perfobond shear contectors . . . . . . . . 4.17. Load-Slip behaviour of CDW and ODW (1 % steel fiber) . . . . . 4.18. Influence of fiber content on load-slip behaviour series 8: 0.5% and series 9: 1% vol. steel fiber . . . . . . . . . . . . . . . . . . . . . 4.19. Crack opening curves of series 8 and 9 . . . . . . . . . . . . . . . 4.20. Crack pattern of SPOT with UHPC 0.5% (left) and 1% (right) steel fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21. Crack on the concrete surface, without reinforcement in cover (left) and with reinforcement(right) . . . . . . . . . . . . . . . . . . . . 4.22. Effect of transverse reinforcement arrangement on load-slip behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23. Influence of reinforcement thought dowel . . . . . . . . . . . . . .

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66 66 66 68

. 69 . 69 . 70 . 70 . 71 . 72

5.1. Sketch layout of Beam B1 and B2 . . . . . . . . . . . . . . . . . . 5.2. Sketch layout of Beam B3 and B4 . . . . . . . . . . . . . . . . . . 5.3. Design layout of Beam B5 and B6 . . . . . . . . . . . . . . . . . . 5.4. Instrumentation for flexural test of composite beams Series 1 . . . 5.5. Instrumentation for flexural test of composite beams Series 2 . . . 5.6. Equipment for flexural test of composite beams Series 1-2 . . . . . 5.7. Force-deflection curve before and after remove residual strain . . . 5.8. Load-deflection behaviour of composite beam B1 and B2 . . . . . . 5.9. Plastic of steel girder and crushed of concrete slab . . . . . . . . . 5.10. Moment curvature relationship of beam B1 and B2 . . . . . . . . . 5.11. Strain development in concrete slab (left) and steel girder(right) of composite beam B1 and B2 . . . . . . . . . . . . . . . . . . . . . 5.12. Strain development in cross section of composite beam B1 and B2 5.13. Longitudinal slip of beam B1 (left) and B2 (right) . . . . . . . . . 5.14. Lateral strain surround hole of perforated strip . . . . . . . . . . . 5.15. Load-deflection behaviour of composite beam B3 and B4 . . . . . .

77 77 78 80 80 81 82 83 83 85 86 86 87 88 89

xxii

List of Figures

5.16. Failure of beam B3 due to collapse of shear connector in right side 5.17. Load-strain behaviour of composite beam B3 and B4, concrete slab (left) and steel girder (right) . . . . . . . . . . . . . . . . . . . . . . 5.18. Load-strain development in cross section beam B3(left) and B4 (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.19. Diagram Load-longitudinal slip in beam B3 and B4 . . . . . . . . . 5.20. Load - deflection behaviour diagrams of beam B5 . . . . . . . . . 5.21. Load - strain response of beam B5 . . . . . . . . . . . . . . . . . . 5.22. Longitudinal slip of beam B5 . . . . . . . . . . . . . . . . . . . . . 5.23. Slip development of beam B5 . . . . . . . . . . . . . . . . . . . . . 5.24. Load - deflection diagrams of beam B6, UHPC G7 0.5 % fiber content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.25. Load - slip behaviour of beam B6 . . . . . . . . . . . . . . . . . . . 5.26. Failure progress of composite beam B6 . . . . . . . . . . . . . . . . 5.27. Load-Strain at middle span section of beam B6 . . . . . . . . . . . 5.28. Strain development in middle span section (left) and one third section (right) of beam B6 . . . . . . . . . . . . . . . . . . . . . . . 5.29. Stress-strain over slab thickness . . . . . . . . . . . . . . . . . . . . 5.30. Comparison load slip behaviour of shear connector in composite beam and push out test . . . . . . . . . . . . . . . . . . . . . . . . 5.31. Comparison load slip behaviour of shear connector in composite beam and push out test . . . . . . . . . . . . . . . . . . . . . . . . 5.32. Slip distribution versus degree shear connection . . . . . . . . . . . 5.33. Longitudinal shear force in composite beams . . . . . . . . . . . . 6.1. 6.2. 6.3. 6.4. 6.5.

Bilinear Elasto-plastic material model for structural steel . . . . Calculation macro stress scheme in microplane model . . . . . . Strain component on a micro plane . . . . . . . . . . . . . . . . . Microplane boundary . . . . . . . . . . . . . . . . . . . . . . . . . FE simulation RILEM (left) bending test and uni-axial compression (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Typical stress-strain of uni-axial compression test (left) and bending stress-displacement diagram of RILEM three points bending test (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Effect of changing elastic modulus to flexural and compression specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8. Effect of k1 parameter . . . . . . . . . . . . . . . . . . . . . . . . 6.9. Influence of parameter c1 . . . . . . . . . . . . . . . . . . . . . . 6.10. Influence of parameter c3 . . . . . . . . . . . . . . . . . . . . . . 6.11. Influence of parameter c5 . . . . . . . . . . . . . . . . . . . . . . 6.12. Influence of parameter c7 . . . . . . . . . . . . . . . . . . . . . .

. . . .

90 92 92 93 94 95 95 96 97 98 99 100 100 101 102 102 103 103 108 111 111 113

. 116

. 116 . . . . . .

119 119 120 120 121 121

List of Figures

xxiii

6.13. Influence of parameter c8 . . . . . . . . . . . . . . . . . . . . . . 6.14. Influence of parameters c4 , c10 , c11 and c12 . . . . . . . . . . . . 6.15. Stress-displacement and Stress-strain response of G7-UHPC (1% vol. steel fiber) with Microplane M4 material model adjusted parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.16. Stress-displacement and Stress-strain response of B4Q-UHPC (1% vol. steel fiber) with Microplane M4 . . . . . . . . . . . . . . . .

. 122 . 122

7.1. Geometry of push-out test specimens . . . . . . . . . . . . . . . . 7.2. Finite Element model of Push-Out specimen . . . . . . . . . . . . 7.3. Loading, boundary conditions and constrain DOFs at contact surfaces between steel and concrete . . . . . . . . . . . . . . . . . . 7.4. Comparison load-slip response of experimental and FE analysis for Push-Out series 3 and 4 (open dowel) . . . . . . . . . . . . . . . 7.5. Comparison load-slip response of experimental and FE analysis for Push-Out series 6 and 7 (closed dowel) . . . . . . . . . . . . . . . 7.6. Local deformation of the series 4 - Open dowel with test setup 2 7.7. Local deformation of the series 7 - Closed dowel with test setup 1 7.8. Local stress distrubution in the steel rib . . . . . . . . . . . . . . 7.9. Local strain distribution in concrete block . . . . . . . . . . . . . 7.10. Stress concentration distribution in rebars of Series 4 (ODW) and 7 (CDW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.11. Simplified shearing cone assumption . . . . . . . . . . . . . . . . 7.12. Geometry of composite beam for FE modelling . . . . . . . . . . 7.13. Finite Element mesh of a composite beam model . . . . . . . . . 7.14. Interface between steel and concrete surface . . . . . . . . . . . . 7.15. Deformed shape of the beam B1 and FE simulation . . . . . . . . 7.16. Comparison test and modelling results of beam B1 and B2, force - deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.17. Comparison test and modelling results of beam B3 and B4, force - deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.18. Comparison test and modelling results of beam B1, force-strain 7.19. Comparison test and modelling results of beam B2, force-strain 7.20. Comparison test and modelling results of beam B3, force-strain 7.21. Comparison test and modelling results of beam B4, force-strain 7.22. Comparison local slip of beam B1 (left) and B2 (right) . . . . . . 7.23. Stress distribution in girder, beam B1 to B4 . . . . . . . . . . . . 7.24. Stress distribution in steel rib . . . . . . . . . . . . . . . . . . . . 7.25. Longgitudinal stress in steel rib of shear connector, beam B1 and B2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 128 . 129

. 123 . 124

. 131 . 134 . . . . .

134 136 136 137 138

. . . . . .

140 140 146 147 147 150

. 151 . . . . . . . .

151 152 152 153 153 154 155 156

. 156

xxiv

List of Figures

B.1. Push-Out test setup S1 and S2 . . . . . . . . . . . . . . . . . . . B.2. Rebars arrangement of Push-Out specimens . . . . . . . . . . . B.3. Push-Out test reults: Load-Slip and Crack opening, Series 1-Headed stud shear connector, specimen-1(a), specimen-2(b), specimen-3(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.4. Push-Out test reults: Load-Slip, Series 2-ODW without rebar (left), Series 3-ODW with rebar in core(right) . . . . . . . . . . . B.5. Push-Out test reults: Load-Slip and Crack opening, Series 4-Open dowel with rebar in core and front cover, specimen-1(a), specimen2(b), specimen-3(c) . . . . . . . . . . . . . . . . . . . . . . . . . . B.6. Push-Out test reults: Load-Slip and Crack opening, Series 5-CDW without Reinforcement, specimen-1(a), specimen-2(b), specimen3(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.7. Push-Out test reults: Load-Slip and Crack opening, Series 6-CDW with rebar in core, specimen-1(a), specimen-2(b), specimen-3(c) . B.8. Push-Out test reults: Load-Slip and Crack opening, Series 7-Open dowel with rebar in core and front cover, specimen-1(a), specimen2(b), specimen-3(c) . . . . . . . . . . . . . . . . . . . . . . . . . . B.9. Push-Out test reults: Load-Slip and Crack opening, Series 8CDW with rebar in cover-UHPC 0.5% steel fiber, specimen-1(a), specimen-2(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.10.Push-Out test reults: Load-Slip and Crack opening, Series 9CDW with rebar in cover-UHPC 1.0% steel fiber, specimen-1(a), specimen-2(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.11.Push-Out test reults: Load-Slip and Crack opening, Series 10-11CDW with rebar in core and front cover-UHPC 1.0% steel fiber, φ8mm-(a), φ12mm-(b) . . . . . . . . . . . . . . . . . . . . . . . .

. 168 . 169

C.1. Design of the composite beam B1 . . . . . . . . . . . . . . . . . . C.2. Design of the composite beam B2 . . . . . . . . . . . . . . . . . . C.3. Design of the composite beam B3 . . . . . . . . . . . . . . . . . . C.4. Design of the composite beam B4 . . . . . . . . . . . . . . . . . . C.5. Design of the composite beam B5 . . . . . . . . . . . . . . . . . . C.6. Design of the composite beam B6 . . . . . . . . . . . . . . . . . . C.7. Experimental setup of the composite beam B1 . . . . . . . . . . C.8. Experimental setup of the composite beam B2 . . . . . . . . . . C.9. Experimental setup of the composite beam B3 . . . . . . . . . . C.10.Experimental setup of the composite beam B4 . . . . . . . . . . C.11.Experimental setup of the composite beam B5 and B6 . . . . . . C.12.Beam B1, Load-deflection and Load-rotation (a), strain in girder section 1-1 (b) and strain in girder section 2-2 (c) . . . . . . . . .

. . . . . . . . . . .

. 170 . 171

. 172

. 173 . 174

. 175

. 176

. 177

. 178 180 181 182 183 184 185 186 187 188 189 190

. 191

List of Figures

xxv

C.13.Beam B1, Load-strain in concrete slab (a), strain in steel rib (b) and slip (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.14.Beam B2, Load-deflection and Load-rotation (a), strain in girder section 1-1 (b) and strain in girder section 2-2 (c) . . . . . . . . . C.15.Beam B2, Load-strain in concrete slab (a), strain in steel rib (b) and slip (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.16.Beam B3, Load-deflection and Load-rotation (a), strain in girder section 1-1 (b) and strain in girder section 2-2 (c) . . . . . . . . . C.17.Beam B3, Load-strain in concrete slab (a), strain in steel rib (b) and slip (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.18.Beam B4, Load-deflection and Load-rotation (a), strain in girder section 1-1 (b) and strain in girder section 2-2 (c) . . . . . . . . . C.19.Beam B4, Load-strain in concrete slab (a), strain in steel rib (b) and slip (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.20.Beam B5, Load-deflection (left), strain in girder and concrete slab at section 1-1 (right) . . . . . . . . . . . . . . . . . . . . . . . . . C.21.Beam B6, Load-deflection and Load-rotation (a), strain in girder and concrete slab section 1-1 (b) . . . . . . . . . . . . . . . . . . C.22.Beam B6, strain in girder and concrete slab section 2-2 (a), Loadlongitudinal slip along left and right side of the beam (b) . . . . D.1. D.2. D.3. D.4. D.5. D.6.

Structure of the program . . . Flow chart of calibration model Main screen of the program . . Result extraction . . . . . . . . Quick plot experiment results . Atena datafile editor . . . . . .

. . . . . . parameter . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . of microplane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . M4 . . . . . . . . . . . .

. . . . . .

. . . . . .

. 192 . 193 . 194 . 195 . 196 . 197 . 198 . 199 . 199 . 200 . . . . . .

201 202 203 203 204 204

xxvi

List of Figures

List of Tables 3.1. Diameter range of granular class for UHPC, after Richard and Cheyrezy (90) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Mixture proportion of UHPC . . . . . . . . . . . . . . . . . . . . 3.3. title of table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Fracture parameters of UHPC for different mix designs, after Ma (74) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Tensile fracture properties of UHPC with steel fiber, modified Fehling et al. (32) . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Mechanical properties of steel grade S355 and 500 . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Material properties of UHPC . . . . . . . . . 4.3. Parameter for Push-Out test program . . . . 4.4. Summary Standard Push-Out Test results . . 5.1. 5.2. 5.3. 5.4.

reinforcing bar Bst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Description of composite beams . . . . . . . . . . . . . . . . . . . Transverse reinforcement arrangement in concrete slab . . . . . Summary of test result of the composite beams . . . . . . . . . . Comparison of ultimate strength, deflection and stiffness of beams B2 with B3 and B4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Peak slip location versus actual shear connection degree . . . . .

. 34 . 38 . 41 . 50 . 52

. . . .

57 57 59 63

. 76 . 76 . 82 . 90 . 103

6.1. Boundaries for the microplane model parameters . . . . . . . . . . 117 6.2. Value of M4 model parameters for UHPC G7 and B4Q . . . . . . 124 7.1. Comparison of ultimate capacity predicted by ATENA with experimental values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.2. Push-Out test and modelling data for linear regression analysis . . 143 7.3. Push-Out test and modelling data for linear regression analysis (con’t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.4. Verification prediction model with experimental and simulation data145 7.5. Description of composite beams for experimental and modelling . . 150 7.6. Ultimate load and deflection results for the experimental and numerical analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

xxviii

List of Tables

1. Introduction 1.1. State of the art The term Composite Construction is normally understood within the context of buildings and other civil engineering structures, to imply the use of Steel and Concrete combine together as a unified component. The aim is to archive a higher level of performance than would be have been the case had the two materials functioned separately. Steel and concrete can be used in mixed structural systems, for example concrete cores encircled by steel tubes, concrete slab ”glued”’ with steel girder via shear connection in order to form composite beam which most widely used in practical construction. Moreover, composite columns offer many advantages over bare steel or reinforced columns, particularly in reducing column cross-sectional area. Another important consideration is fire resistance. Figure 1.1 shows Karl-Heine pedestrian bridge in Leipzig (Koenig (56)), and the composite floor of a residential building in London (26) . They are the typical illustration of using hybrid structures in construction.

Figure 1.1.: Karl-Heine footbridge in Leipzig-Germany: concrete filled steel tube structures, after Koenig (56) (left), and the composite floor of a residential building in London(26) (right)

The basic mechanics of composite action is best illustrated by analysis a composite beam under bending load which demonstrated in Fig. 1.2. In the case of non-composite (a), the concrete slab is not connected to the steel section and

2

1. Introduction

therefore behaves independently. As it is generally very weak in longitudinal bending it deforms to the curvature of the steel section and has its own neutral axis. The bottom surface of the concrete slab is free to slide over the top flange of the steel section and considerable slip occurs between the two. The bending resistance of the slab is often so small that it is ignored. Alternatively, if the concrete slab is connected to the steel section (b), both act together in carrying the service load. Slip between the slab and steel section is now prevented and the connection resists a longitudinal shear force. Consequently, the load bearing capacity of the second beam (b) is few times greater than the first beam (a).

slip

concrete slab steel girder

a)

Non-Composite beam

Shear connectors

b) Composite beam

Non-composite section

strain Nc

Na Composite section

stress

+ strain

stress

Figure 1.2.: Basic mechanism of composite action

The characteristic of the steel-concrete composite is exhibited by resistance of each contributed material portion and the resistance of shear connection. When the connection cannot resist all of the forces applied then considered as partial connection, otherwise full shear connection. Most frequently, composite beam is designed to carry bending load. Regarding the stress and strain distribution of composite section as shown in Fig. 1.2b,

1.2. Context and motivation

3

the neutral axis dose not often fall at the interface. Good design will attempt locate this axis close to this position. Thus whole concrete slab is subjected to compressive force, whereas steel girder to be concerned tension force. In practical constructions, the composite beam is often made of either normal strength concrete (in short NSC) or high strength concrete (in short HSC) for slab and high strength steel for girder.

1.2. Context and motivation Recent development of concrete technology resulting a new type of concrete with many advanced properties, it is called in common name Ultra High Performance Concrete (in short UHPC). The key benefits of UHPC are considered in application point of view as follows: very high in compressive strength and tensile strength which are ideal to carry compression load in the composite beams. addition steel fiber will enhanced ductility behaviour reduce total weight of structural member with high flow ability properties, concrete can be complete fulled for complex geometry members. extraordinary durability compare to conventional concrete, reduce maintain cost during service time. most disadvantage of UHPC is highly cost at the moment, it may be decreasing in the near future when increasing amount of applications. The detail characteristic of UHPC will be mentioned in the chapter 3.

In the structural member behaviour outlook, with NSC the resistance of concrete slab is often less than steel girder, the neutral line lie in the web. By substituting UHPC to NSC/HSC, the resistance of concrete materials could be reached resistance capacity of steel easily. Consequently obtaining optimal load caring of each contribute material. The replacement is not only increase the stiffness and overall ultimate strength but also reduce cross section of the composite beams. Fig. 1.3 illustrates the idea using perforated steel rib as continuous shear connection in the composite beam. This type of shear connector was first introduced by Leonhardt (62). Perforation strip are welded on top flange of steel girder or cut

4

1. Introduction

directly from web. At construction phase, UHPC will be flowed through perforated hole the dowels formed. Under loading, interaction is developed by concrete engaging with perforations strip, the working mechanism of shear connector can be illustrated similar to the action of a dowel. In principle, this method brings to many advantages in practical construction, while load transfer performance is still guaranteed.

Figure 1.3.: Perfobond shear connection in composite beam

It is well known that, at interaction area between perforated strip and UHPC dowel, the behaviour is combination of tension-shear and compression. The UHPC with very high compressive strength but less ductility must be treated to satisfy characteristic ductility requirement of shear connector in composite beam. The application of this device for shear connection incorporating steel girder still requires further verification. Due to the high cost of UHPC material and testing, the experimental study is unable to cover all range of interested problems. Consequently, numerical simulation play an important role in this works. However, the behaviour of UHPC is different with conventional concrete, therefore suitable material model is required to illustrate mechanism of beam as well concerned problems.

1.3. Objectives of study The present study aims to investigate performance and structural behaviour of steel-concrete composite beam made of UHPC under bending, and it also provide

1.4. Scope of work

5

a better knowledge of perfobond shear connector response in Push-Out test and conjugate with steel girder. More precisely, the following points are explored: Characteristic of UHPC would be better known and understood, especially focus on basic mechanical properties. A better knowledge on response of the perfobond shear connectors in UHPC, appropriate choice of shear connector for UHPC composite member would be achieved. Experimental investigation of UHPC composite beam subjected flexural load, which provides structural behaviour of member under serviceability and ultimate limit state, in order to answer the following questions: - Is it possible to build composite ”UHPC-Steel” elements with monolithic behaviour; and how can the advantageous UHPC properties be exploited in such composite elements? - What do resistance and failure modes of ”UHPC-Steel” elements would be shown under bending? - How do local deformations, stresses and cracking evolve in the composite members under monotonic load?

Nonlinear finite element models must be evaluated and developed in order to predict the structural behaviour of shear connectors and ”UHPC-Steel” composite beams. The simulation should be explored following aspects: - Are existing material models appropriate to simulate behaviour of UHPC? - How to construct suitable structural models for shear connector and composite beams? - What do local behaviour would be shown? - How to improve performance of the ”UHPC-Steel” composite beam?

On the basis of the results, a design model and guidelines are developed for practical application of UHPC composite members.

1.4. Scope of work This work is part of priority research program SPP 1182: ”Sustainable Building with Ultra High Performance Concrete”, which collaborate by numerous of universities in Germany. The concrete material and design of composite were prior planned, and oriented to the trend of this project. The flexural behaviour of single span composite beams were limited to sagging moment only. The continuous

6

1. Introduction

beam with hogging moment (negative moment) at support is not considered in this work.

1.5. Structure of the thesis The thesis consists of eight chapters. Chapter one is the outline introduction to innovation context of development of UHPC and its application into hybrid steel-concrete structures. The main aspect and objective of this research work was also mentioned. Chapter two presents relevant literature review of the behaviour of steel-concrete composite beams made of UHPC. The content includes material properties aspect, load transfer mechanism in the beam, as well as experiment and modelling of composite beams. In Chapter three, the state of the art of UHPC are brief introduced, properties of UHPC are characterized and main properties which influence on behaviour of structures under loading service are to be discussed in details. Chapters four and five present an experimental program to investigate the behaviour of shear connectors and composite beams. The structural tests are conducted on standard Push-Out test (SPOT) specimens according to guideline of Euro Code 4 (EC4), the beams are performed on large scale. Experimental framework is divided into two phases namely Push-Out test of shear connectors, then bending test for composite beam. The discussion and analysis of the experimental results are presented. The first part of chapters six presents briefly material the model for structural steel and reinforcement was well. Principally, this chapter focuses on the Microplane M4 material model for concrete. Based on parameter investigation, a set of model parameters for UHPC was introduced. Chapter seven describe a development of three dimension model for simulation of Push-Out specimens and composite beams. The parameter study was carried out for various type of shear connectors (SHC) and steel-concrete composite beams (SCCB). Discussion on modeling results and conclusion were drawn. The last chapter of this dissertation presents final conclusion based on this research project and provide future prospective concerning to SCCB and hybrid structures made of UHPC.

2. Consideration aspects of steel-concrete composite beams 2.1. Introduction The most important and most frequently encountered combination of construction materials is that of steel and concrete, with applications in multi-storey buildings and constructions, as well as in bridges. These materials can be used in mixed structural systems, for example concrete slab glued with steel girder, as well as in composite structures where members consisting of steel and concrete act together. Steel and concrete have the same expansion coefficient, and each materials is strong in either compression or tension. Concrete also provides corrosion protection and thermal insulation to the steel at elevated temperatures and additionally can restrain slender steel sections from local or lateral-torsional buckling. These essentially different materials are completely compatible and complementary to each other. Composite beams, subjected mainly to bending, consist of a steel section acting compositely with one (or two) flanges of reinforced concrete. The two materials are interconnected by means of mechanical shear connectors. For single span beams, sagging bending moments, due to applied vertical loads, cause tensile forces in the steel section and compression in the concrete deck thereby allowing optimum use of each material. Fig. 2.1 and Fig.2.2 show several composite beam cross-sections and shear connectors respectively, which are widely used in practical construction.

I-beam with steel girder

Haunched-slab with steel sheet

Steel box girder

Figure 2.1.: Typical cross sections of composite beams (26)

I beam with precast concrete slab

8

2. Consideration aspects of steel-concrete composite beams

Figure 2.2.: Typical shear connectors, after Oehlers and Bradford (68)

The shear connectors in composite beams are used to develop the composite action between steel girder and concrete. They are provided mainly to resist longitudinal shear force, therefore must meet a various requirements, such as (26): transfer direct shear at their base. create a tensile link into the concrete. economic to manufacture and welding.

The most common type of mechanical shear connector is the headed stud shown in Fig. 2.2a. It can be welded to the upper flange either directly in the factory or through thin galvanised steel sheeting on site. The Behaviour and ultimate strength of connectors can be examined by Push-Out test according to available standards such as EuroCode4 (27). For the design of headed stud, the following aspects are considered; shear strength of stud shank, bearing strength of concrete, additional contribution of chemical bonding and friction. In spite of its wide application, the headed stud has many deficiencies such as a slip Behaviour between stud and concrete, and fatigue failure at welding zone. (26; 80; 47; 55) Recently, a very high strength cement based composite called Ultra High Performance Concrete (UHPC) has been developed. It provides many enhancements in properties compared to conventional and high strength concrete (HSC). In

2.2. Single span composite beams under sagging moment

9

the composite beams, the replacement of normal strength concrete (NSC) with UHPC lead to an improvement in the load carrying in the compression zone. Generally, a significant increase in load bearing capacity and stiffness of the beam is achieved, resulting in saving dead load, reducing construction depth as well as construction time. However, as reported in Johnson (47), Hegger et al., Tue et al. (105) the headed stud shear connector is not appropriate in the HSC/UHPC slab due to restrict deformation surrounding stud area. The combination of perfobond shear connector in UHPC will be optimized in both term of material and structural system. This chapter aims to review researches relevant to the Behaviour of composite beams under bending load, which focuses to composite beam/slab with perfobond shear connector. Different aspects of the problem are discussed such as the basic Behaviour of composite beams, innovation of concrete technology, mechanical shear connection. The numerical modelling of the structural composite beams and the currently available design procedures will be also mentioned.

2.2. Single span composite beams under sagging moment 2.2.1. Basic Structural Behaviour The way in which a composite beam behaves under the action of low load, medium and the final failure load can be briefly described in stages as follows (26): Stage 1 Under very low loads the steel and concrete behaves in an approximately linear way. The connection between the two materials carries very low shear stresses and it is unlikely that appreciable longitudinal slip will occur. The beam deforms so that the strain distribution at mid span is linear, as in Fig. 2.3a, and the resulting stress is also linear. It can be seen from the strain diagram that, if the slab is thick enough then the neutral axis lies within the concrete. As a result some of the concrete is in tension. If the slab was thin, it is possible that the neutral axis would be in the steel and then the area of steel above the axis would be in compression. This stage corresponds to the service load situation in the sagging moment region of most practical composite beams.

10


strain stress -

Shear force Bending moment

+

a) stage 1

strain stress Shear force b) stage 2

Bending moment Shear force

strain stress

Bending moment c) Stage 3

Figure 2.3.: Stages of composite beam at different load levers(26) Load on shear connector Longitudinal shear d a

b

c

d

c a)

b a

slip

Load on shear connector d c

Longitudinal shear

b a

b

c

d

a b)

slip Load on shear connector c d a b

Longitudinal shear a

b

c

d c)

slip

Figure 2.4.: Longitudinal shear force on connectors(26)

Stage 2 In this stage applied load was increased, thus caused rise to deformation in the shear connection. This deformation is known as slip and contributes to the overall


11

deformation of the beam. Fig. 2.3b shows the influence of slip on the strain and stress distribution. This stage corresponds to the service load stage that composite beams class has been designed as partially shear connection. However, for many composite beams slip is very small and may be neglected. Stage 3 The steel girder achieves yield limit strain first, plasticity develops and then almost part of steel section becomes plastic. It occurs as similar fashion in concrete slab. Stress block of whole section changes from triangular to shape shown in Fig. 2.3c that is very difficult to express in mathematical form. In ultimate limit state (ULS) it is assumed to be a rectangular block. If longitudinal shear resistance is big enough the slip can be neglected. The strain in concrete slab could lead to over stress, then it is potentially possible that explosive brittle failure of the slab would occur. However, in most practical case this situation could ever arise due to the deformation of shear connectors. The response of shear connector in load stage is illustrated as follows: As the load increases the shear strain, the longitudinal shear force between the concrete slab and steel girder increases in proportion. For single span composite beam under uniformly load, it is assumed to deform in an elastic manner and the longitudinal shear force between slab and steel section can be expressed as T = VS /I (96). Hence longitudinal shear force is directly proportional to the vertical shear force, thus the force on the end connectors is the greatest. For low loads the force acting on a connector produces elastic deformation. The slip between the slab and the steel section will be greatest at the end of the beam. The longitudinal shear and deformation of a typical composite beam, at this stage of loading, are shown in Fig. 2.4a. If the load is further increased the longitudinal shear force increases too, and the load on the end stud may cause plastic deformation. The ductility of the connectors means that the connectors are able to deform plastically whilst maintaining resistance to longitudinal shear force. Fig. 2.4b shows the situation when the end connectors are deforming plastically. By increasing applied load, the connectors near to the midspan section also begin sequentially to deform plastically. Failure occurs when once all of the connectors have reached their ultimate resistance as shown in Fig. 2.4c. The failure pattern is dependent upon the plastic deformation of shear connector. As exhibited, the end connector must be considered before other one close to the midspan area reaches its ultimate capacity. The requirement for ductility of shear connector is necessary.

12


It can be seen that the failure of the composite beam is dictated by the resistance of its three main components: steel girder, concrete slab as well as shear connector. the interaction of these components is very complex, in design the stress-strain relation of these materials are usually assumed as elastic- perfect plasticity (27). 2.2.2. Structural composite beam with continuous shear connection Steel-concrete composite beam with perforbond shear connectors have been rarely investigated. Jurkiewiez and Hottier (50; 51) studied Behaviour of simple support composite beams whose steel beam is an Tee girde without upper flange. Horizontal shear connection was designed as dovetail-shape (a variant of perfobond) and cut directly on the web of I steel section. By taking symmetric characteristic of shear connector, two steel beams obtained with only a cutting line. To improve the shear capacity and ductility, concrete dowel and horizontal was combined acting together to resist longitudinal shear force. Normal strength concrete with compressive strength of 48 MPa at 28 days was used for slab. Numerous large scale specimens were constructed, three points bending tests were conducted under static and fatigue load. Experimental results shows global Behaviour of the beam with novel shear connector is similar to that with usual connectors. The response includes elasticity, yielding and plasticity domains as well. A flexural failure occurred with a plastic hinge in the mid-span cross section accompanied by yielding of the steel girder and crushing of the concrete. The shear connectors did not fail during the test and allowed to efficiently transmit shear forces from the slab to the girder. The new proposed shear connector is satisfactory in the bending Behaviour in accordance with requirements of design codes. In different context, Kim and Jeong (53; 46; 54) carried out experimental investigations on the ultimate strength of steel-concrete composite bridge deck with profiled steel sheeting and perfobond rib shear connectors. In fact, composite action of one way bridge deck behaves similar to composite beam in flexural mode. The perforate steel rib with holes of 50mm diameter was welded directly into steel sheet and form continuous shear connectors. The parameters such as steel deck profile, perfobond rid, reinforcement as well as concrete strength were considered. The Push-Out with the same shear connection of the deck was carried out to determine the capacity of shear connector. The proposed deck system outperforms a typical cast in place (CIP) reinforce concrete deck in several ways: its ultimate load-carrying capacity is approximately 2.5 times greater; its initial concrete cracking load is 7.1 times greater;


13

and it weighs about 25% less. Cconsequently, reduction in the permanent load may lead to lighter superstructures and extend longer span deck. The test results also confirm that the perfobond rib shear connection designed in this study can be effectively used for the proposed deck system. However, in the Push-out test specimens was taken into account the resistance of concrete at bottom of the perforated strip 1 , this is not accompanying to continuous shear connection which used in the deck specimens. Therefore, ultimate strength result from Push-Out test gives higher than its real capacity. The conclusion on the estimated horizontal shear resistance greater than two times of the required horizontal shear strength is not exact. Composite truss girders having longer spans that requires higher resistance capacity. Machacek and Cudejko (76) have proposed to use CTU perforate shear connector for shear connection system. The ultimate capacity of composite truss system as well as longitudinal shear distribution was investigate by experiment and three dimensional finite element analysis. The test and numerical results were compared to approximate solution according to EuroCode4 (27). According to test results the perforate shear connector show excellent performance in both case of full and part shear connection. Within elastic region the distribution of longitudinal shear is generally highly non-uniform, exhibiting peaks above nodes of the composite truss. And within the yielding region, longitudinal shear is redistributed and depending on characteristic load-slip diagram of the connector. Recent development of composite beam in Germany with continuous shear connection was introduced and have been applied in practical construction. The commercial product lines namely VFT-WIB (also known as VFT-construction method) which developed by Schmitt et al., Seidl et. al. (93; 94; 39). In fact, The cross-section of composite beam is composed of two prefabricated elements with halved rolled girders, working as bottom flange. The composite dowels are manufactured by cutting directly from web of rolled steel profiles. The height of section was designed relatively low to reduce slender of the section. Steel girder works as external reinforcement as shown in Fig. 2.5. In the VFT-WIB composite beam, the failure mode of shear connector was identified in three modes: the shear resistance, yielding due to bending of the dowel and in the fatigue limit state by fatigue cracks due to dynamic loading. The experimental study on Standard Push-Out test (SPOT) according EuroCode4(27) was carried out with static and fatigue load. In the tests failure of concrete as well as steel was observed, It indicated that, the ultimate strength of the steel part is almost independent on the shape of the dowel. Fatigue cracks caused by a very

©

©

1 reaction

force Rbr in Fig. 2.6

14


high level of stress amplitude. And the fatigue cracks has limited propagation due to steel part is compressed in the SPOT. The optimize shape of dowel has been performed by finite element simulation. The several beam test was also taken to verify load bearing capacity of structural VFT-WIB beams (39). Concrete casted in place

Reinforcement

Concrete beam

Steel girder

shear connector

©

Figure 2.5.: Typified VFT-WIB composite section (above) and application in Vigaun bridge project, after Schmitt et al. (94)

©

The VFT-WIB construction method was successfully applied in the road bridge over the railway line to Poecking (Bavaria, Germany) in 2004 (93). And other road bridge project in Vigaun (Austria) which used the same structural system was done and service began 2008 (94).

2.3. Perfobond shear connector (PSC) 2.3.1. Conventional Perfobond shear connector To overcome the disadvantages of headed stud connector, several new type of shear connector has been developed and used as alternative solutions. Among

2.3. Perfobond shear connector (PSC)

15

of them Perfobond shear connector is known to be a highly effective method in term of construct ability and fatigue resistance. Conventional Perfobond rib shear connector is made from a rectangular plate with perforated holes as indicated in Fig. 2.8a. During casting concrete slab, concrete will flow through holes and concrete dowels formed. (62; 83). A considerable amount of experimental tests have been done to establish the Behaviour of different types of perfobond shear connectors. Leonhardt et al. (62) proposed a formula to evaluate strength of the PSC as given in equation 2.1. It depends on the compressive strength of concrete rather than yield strength of steel. qu = 1.6ld 2 fck /γv

(2.1)

Hosaka et al. (44) have proposed another expression for the calculation of a Perfobond connector resistance, corresponding to each hole’s contribution: r tsc qu = 3.38D 2 fck − 39 (2.2) D Oguejiofor and Hosain (83; 83) performed an extensive experimental study with different Perfobond connector geometries on normal strength concrete. In fact that specimens and Push-Out test setup are shown in Fig. 2.6. The thickness of concrete slab, diameter of rib holes as well as spacing between holes was taken into account, the thickness and transverse reinforcement are not changed in all of the specimens. The full size of composite beam with discrete shear connectors was tested to verify performance of the shear connectors. Additionally, a numerical study of the Behaviour of PSC was established. The three dimension model was generated and nonlinearity was taken into account, in order to consider complexity of material and geometry of specimens. Numerical models were validated and showed good agreement with test data. Through parameter study and linear regression analysis the prediction model was obtained and given in equation 2.3. q 0 (2.3) qu = 4.47htfc + (3.30Acd + 0.01Acc ) fc0 + 0.90Atr fyr or qu = 4.50hsc tsc fck + 0.91Atr fy + 3.31nD 2

p fck

(2.4)

where qu is the shear capacity per Perfobond; h and t are height and thickness of steel rib respectively; Acd is concrete area of the dowel; Acc is the concrete shear

16


per connector that equals to the slab longitudinal area minis the connector area; Atr is reinforcement areas presents in the concrete dowel. P

a)

337

100

Concrete slabs

375

Rdw

Rbr

712

W 200 X 59

thickness-t

100

d

P

b)

Figure 2.6.: Push-Out specimens and test setup, a) general specimen (Oguejiofor and Hosain (83)), b) specimen with profile steel sheet (Kim et al. (55)).

In a similar manner based on Push-Out test results, Medberry and Shahrooz (79) have proposed a more general formula for estimation strength of PSC as given in equation 2.5. qu = 0.747bh

p D2 p fck + 0.413bf Lc + 0.9Atr fy + 1.66nπ fck 4

(2.5)

where b is slab thickness; h is slab height downward the connector; bf steel section


17

flange width; Lc is contact length between the concrete and the flange of the steel section. Kim et al. (55) conducted test of with Perfobond connectors on normal weight concrete for building structures. The influence of dimension of steel rib and reinforcing bars placement on load carrying capacity were investigated. Jeong et al. (46; 53) conducted several tests of perfobond connector with profile sheeting, fig. 2.6 shows specimen for POT. Subsequently, the test results was used to designed shear connection for concrete composite bridge decks. Neves et al. (110; 14) investigated Behaviour and strength of PSG as well as TPerfobond which derived from original PSG. The specimens and test setup as well as evaluation results were performed according to EuroCode4. A comparison experimental result with other authors was established. Through research work mentioned above, it can be seen that the contributions for the shear resistance of perfobond rib shear connector can be evaluated as summation of three terms; dowel action of the concrete holes, shear resistance of hole crossing reinforcement, and the concrete end-bearing resistance. Vc +dV c Mc +dMc

Mc Vc Nc

Ps Ma

Ps

Ps VL

VL

Nc +dNc

δ

δ

Nc

Rsh

Rst

Rsh

Nc

Ma +dMa

Na

Na +dNa Va

Va +dV a dx

a)

b)

c)

Figure 2.7.: Shear transfer mechanism from concrete slab to steel rib

The mechanism of shear transfer between concrete slab in composite beam is illustrated in Fig. 2.7. In fact, if continuous shear is used (Fig.2.7b) then the resistance is generated by only concrete dowel (included reinforcement if any). The prediction equation 2.3 to 2.5 as well as test data can not be used in this case. The predicted shear strength of shear connector overestimate its actual capacity, there are some misunderstanding in translating from Push-Out test result to design shear connection such as (53; 54). The end-bearing resistance components being accounted if and only if discrete shear connector is used (Fig. 2.7c). The advantage is that the shear strength of each PCS is increased, but the number of shear connector along beam is reduced due to essential space between shear connectors. Consequently, the overall shear connection degree may not higher than continuous shear connector.

18


2.3.2. Modified pefobond shear connectors From practical application point of view the traditional PSC have disadvantages in construction, especially for placing reinforcement into concrete dowel during form works are enclosed. However, the concrete dowel has small diameter is not optimal in term of using material by follow reasons: failure always occurs in concrete dowel rather than steel rib large amount of wasted material after cutting high producing cost for cutting by special equipment required

If the diameter of dowel is increased, then thickness of concrete slab is also greater than requirement, particularly in the case of high strength concrete is used. There are several different types shear connectors which are modified from original PSC have been studied, proposed and used as shown in Fig. 2.8.

a) Perfobond

d) Puzzle saw/VFT-WIB

b) CTU Perfobond

e) Puzzle strip/crestbond

c) Open dowel

f) CR connector/crestbond

Figure 2.8.: Various kind of Perfobond Shear connector in composite beam

The CTU Perfobond connector was early developed by Studnicka and Machacek at 1994, it was modified from original PSC and the half holes were added in the front side of steel rib which contacts with concrete, aimed to increase resistant capacity (Fig. 2.8b). The Behaviour of CTU connector was elevated for other geometries, hole size, concrete strength. Several Push-Out test series was conducted with full size of specimens (98; 75). Chromiak and Studnicka (21) adapted CTU PSC for slightly modified on half opening to use with standard welded reinforcing mesh. Verissimo et al (109)) have developed a new type of connector as an alternative to the Perfobond, named Crestbond (or CR). This new shear connector was formed by an indented steel rib. Fig. 2.8e and 2.8f) shown CR connector as well as its variation. The open holes provides resistance to longitudinal shear and makes the assembly of the reinforcing bar into concrete slab easier. The structural Behaviour of Crestbond connector was studied by Push-Out test and compare to other existing connectors. Tracing back experimental work, it can be seen that the specimens and test setup was designed that reaction force at ending steel plate is accounted as early mentioned (Fig. 2.6). According to test


19

results the connector CR50 with reinforcement φ12mm and concrete compressive strength of 28.5 MPa gives ultimate capacity over of 350kN per connector and excellent characteristic slip also derived. This result is 45% higher than the corresponding open dowel shear connector made of UHPC which tested by Tue et al. (108). Once again, it can be noted that, the data obtained from above test setup is not able to used in the composite beam with continuous shear connector.

Figure 2.9.: Push-Out test of the VFT-WIB connector (93)

Schmitt et al. (93) introduced a connector called Puzzle saw (Fig. 2.8d) that possibility used for bridges. The ultimate capacity is achieved from Push-Out test as described in sketch 2.9. Based on test data, the cutting line for Puzzle connector was modified, in order to achieve better fatigue resistance performance under dynamic load. The Puzzle connector was used in composite beam of the Vigaun bridge project (94). It can be seen from figure two foam blocks are placed at bottom of steel rib. Thus the end-plate bearing component is ignored in summation of resistance of the connector. This test setup is different from other POT as above mentioned. Hottier and Jurkiewiez (51)) have proposed the Dovetail-shape connection type which similar Puzzle saw connector. The connector exhibits efficient in load carrying, reducing wasted material by utilize symmetric of geometry. The beam test was taken to verify possibility of proposed connector.

20


Beside many advantages, in the production point of view the modified Perfobond connector more difficult to make a cutting line, especially if profile contains many round angles. Generally, it requires high precision cutting machine with automatic controller (CNC cutting machine). The cutting work may be performed in factory only.

2.4. Development of concrete technology During the 1970s, concrete having a compressive strength of 60 to 70 MPa began specified for column in high rise buildings , because of reduced column cross section that offers more architectural space (4). The concrete properties is not only offer high strength but also high durability and other desirable characteristics. Therefore the name has been change to High Performance concrete (HPC). For the few past decades, HPC has demonstrated its superior performance in engineering applications such as Water Tower Place (Chicago, USA), Petronas Twin Tower (Kuala Lumpur, Malaysia), Tsing Ma Bridge (Hong Kong, China) etc. The advent of Ultra High Strength (UHSC) and Ultra High Performance Concrete (UHPC) is a relatively recent development in concrete technology. The excellent properties of UHPC could be briefly explained as follow: very high strength in compression (>150MPa) and tension (> 10MPa), high elastic modulus (> 45GPa), the stress - train relation linearly up to 70% or 80% of strength. The extremely dense matrix allows increasing significantly durability, reducing permeability to structures working in extreme condition. Properties of fresh UHPC with high self compacting, fast development strength at early age and does not require any heat or pressure curing condition (74; 34). The details on UHPC will be discussed in chapter 3. The increases of strength and extraordinary properties is accompanying increase material cost and a general reluctance to use new materials in practical applications. To reduce the gap between material development and application of new materials in routine design, researchers must optimize the use of UHPC in structural design to take advantage of the incredible increase in strength and other material properties. Then the use of UHPC and other high performance materials can become more common in structural applications.

2.5. Composite beam made of UHPC

21

2.5. Composite beam made of UHPC The UHPC filled tube with high bearing capacities and sufficient ductility have been investigated by Tue et al. (101; 106). Generally, the hybrid structural member can be applied to buildings and bridges. In this work, the UHPC filled steel tube columns was compared to composite column with steel core and shows benefit in the costs per load unit as well as possibility to the realization. In addition, some structural solutions for joint element which needed to transfer loading from UHPC composite columns to conventional concrete slab were proposed as well. Several tests were conducted to evaluate performance of joint elements. Fehling et al. (31; 28) introduced the pedestrians bridge project cross Fulda river in Kassel-Germany. This is the first construction in European using UHPC composite structure. The bridge deck consists of precast prestressed UHPC slab elements. The longitudinal structure comprise of a continuous truss girder system with triangular cross section. The truss girder was made of two upper chords of precast prestressed UHPC and a lower chord and diagonals made of tubular steel sections. Glued connections are used between the upper chords and the deck as well as between the deck plates. The project have been built in period 2005-2006 and began service since the end of 2006. In the same manner, the combination of UHPC panel and steel girder in bridge have been successfully applied to retrofit the Kaag bridges Netherlands, further detail can be found in Kaptijn and Blom (52). Within a collaborative research project SPP1182, the study on shear connection and composite beam made of UHPC was performed at University of Leipzig (Uni-Leipzig) and RWTH Aachen University (Uni-Aachen). In fact, the composite beam with continuous Perfobond based shear connectors was used. Hegger et al. (40; 105; 42) investigated shear connector with puzzle and saw tooth shapes, while Tue et al. (105; 108) deals with closed and opened circles connectors. Many series of Push-Out test was conducted to assess general Behaviour, load bearing capacity, local deformation and influence of reinforcement to performance of shear connectors. Furthermore, the bending test of composite beam with various design were conducted. Ultimate strength, load-defection, local slip, strain as well as mode of failure could be determined and compared to existing design codes.

22


2.6. Finite Element modelling 2.6.1. modelling of composite beams Composite structures exhibit complex Behaviour in both term of geometry as well as material response. It is not possible for one individual to be master of all the required inputs. They must, recognize,appreciate and know how best to utilize the contributions of others so that the whole is considerably more than just the sum of the parts. In the structural engineering research, experimental study is most important and often used in study a new type of structures. However, the condition for testing is not always available by many reasons. Even if in the case of testing would be able to perform then it also may not cover all respected problems due to highly cost of materials, labour work and time. Consequently, a numerical simulation is carried out correspondingly to experiment research. Today with faster and cheaper of computer hardware, Nonlinear Finite Element modelling is a powerful tool to analysis general structures as well as specially in composite constructions. The modelling of composite beam can be divided into primary approach according geometry items: One dimensional element or full three dimensional. The first approach is usually in practical design by advantages in computation time and reasonable precision of results. While the achieved results from last approach can give more detail of Behaviour and local response. Moreover result is generally higher accuracy than simple model. Therefore it is favoritelly used in research. Ranzi and Zona (87) presented an analytical model for full/partial shear connection including deformability of the of steel girder. The formulation is obtained by coupling the Euler-Bernoulli’s beam for concrete slab to Timoshenko’s beam for the steel girder. The composite action is provided by a continuous shear connection which enables relative longitudinal displacements to occur between the two components. The structural steel and reinforcement are modelled by using linear elastic laws, while linear viscous-elastic integral-type constitutive law is used to taken into account time dependent Behaviour of the concrete slab. Gatteso (33) proposed a numerical procedure for the analysis of composite beams. In particular the most refined stress-strain constitutive relationships of materials were used as input parameters. For shear connectors distributed bond model is used (Fig. 2.10) and the nonliear load-slip relationship adapted from Push-Out test. The favorable comparisons between the proposed method with experimental results was done. This procedure is capable in predicting the structural Behaviour of composite beams over the whole loading range up to failure. The program may be helpful in design as well as parameter study.

2.6. Finite Element modelling

23

Figure 2.10.: Discrete and continuous model for shear connector in composite beams

Compression

σc

σs,2

σs fy

Esh Es I Tension

Compression εd εc

ε1 ε0 Tension

σs,1

ε

Compression

fct

σc,2

Tension fct

ε

σc,1

Ec Esh

Uni-axial loading

fck

Eo

fy Bi-axial loading

fck Uni-axial loading

Bi-axial loading

Figure 2.11.: Elasto-Fracture-Plastic based material models for steel and concrete in Finite element modelling of Push-Out test and composite beam

Queiroz et al. (86) used commercial finite element software ANSYS to analyze composite beam with full and partial shear connection. Quadrilateral shell element (SHELL43) and 8 nodes brick concrete element (SOILD65) was employed to simulate the steel section and concrete slab, respectively. Discrete stud shear connector was represented by nonlinear spring element, the load slip curves for stud are obtained from push-out tests (Fig. 2.10a). The effect of full or partial shear connection were taken into account. In the analysis model, both longitudinal and transverse reinforcement are modeled as smeared reinforcement throughout the solid elements. Bilinear Elasticity-Plastic material model is used for structural steel and reinforcement (Fig. 2.11a) and fracture plastic based model describes for nonlinear Behaviour of concrete (Fig. 2.11b). The proposed Finite Element (FE) model was validated with test data, some parameter study for various case of composite have been performed. Liang et al. (64) investigated ultimate flexural and shear strength of simple support composite beams in combined bending and shear actions. By using the general purpose ABAQUS software, a three dimension (3D) FE model has been developed to account for geometric and nonlinear material of composite beams. The concrete slab and steel girder were modeled by four-node doubly curved thick/thin shell elements with reduced integration. 3D beam was used to represent for discrete stud shear connectors. The material models for both

24


steel and concrete are the same with Queiroz’s work. The developed model was made valid with experiment and then performed case studies of composite beam. Based on analysis results, a design model has been proposed for the composite beam subjected combined bending and shear load. 2.6.2. Modelling of Push-Out test A numerical study of the Perfobond rib shear connector was early conducted by Oguejiofor and Hosain (82). In fact the general purpose FE software ANSYS was used to generate the model and analysis. Taking advantage of symmetry to reduce the size of the problem, only one-quarter of the specimen was selected and modeled. The push-out test specimen was modeled using two types of elements from the ANSYS element library: SOLID65 for concrete slab; SHELL41 for both steel section and perfobond rib connectors. The reinforcing bars were smeared into the three-dimensional reinforced concrete solid elements. Coincident nodes on the contact surface were either constrained in particular directions or merged completely. In order to make appropriated relative movement between steel and concrete under applied load. Afterwards the Push-Out model was calibrated with the test data before used to study shear capacity of PSC. Finally, linear regression analysis was conducted to achieve formula for prediction ultimate strength of PSC as expressed in equation 2.4. It can be seen that Oguejiofor’s model was simplified up to possible, the concrete dowel and thickness of steel rib were ignored in the model. Therefore it can not capture the local damage at concrete dowel which caused by tension-shear stress state. And contribution of bearing reaction at bottom plate is not accounted correctly in general case. From FE modelling point of view, the Oguejiofor’s model can not be used to assess local Behaviour well as evaluation load-slip relation of the PO specimens. In the independent work, Kraus and Wurzer (57) developed 3D layered PushOut model for open dowel specimen within Finite Element code ADINA (Fig. fig:Kraus-POT-model). In fact that concrete slab, steel flange and ribs are modelled by 3D solid element. The FE mesh used very small element size had to be used in concrete dowel as well as the area that near contact surface. The nonliear stress-strain relationship based material model which includes postfailure Behaviour and three dimensional failure envelope are used for concrete. The plastic-Multilinear was used for reinforcement and structural steel. Only three components was taken into account in contribution to resistance capacity: concrete dowel; embedded reinforcing bars in dowel as well as transverse reinforcement in front cover.

2.7. Design of composite beam

25

Figure 2.12.: Push-Out specimen model of Kraus and Wurzer (57)

The Kraus and Wurzer model successfully reproduced the characteristic damage state of the concrete dowel with increasing shear force as well as splitting and failure load level. The load-slip achieved from simulation showed more stiffness than test results. The full 3D model of Push-Out specimen can be used to predict Behaviour of perforated shear connectors.

2.7. Design of composite beam 2.7.1. Limit state design philosophy Several design codes for composite structures were developed in early and widely used practical engineering such as EuroCode4, BS 5090, AISC LRFD etc. The design of composite beams is generally based upon limit state principles with two class should be taken in design process (47; 80): ultimate (denoted ULS), which are associated with structural failure, whether by rupture, crushing, buckling, fatigue or overturning serviceability (SLS), such as excessive deformation, vibration, or width of cracks in concrete.

And there are three types of design situation must be considered: persistent, corresponding to normal use; transient, for example during construction, refurbishment or repair; accidental, such as fire, explosion or earthquake.

26


Verification for an ultimate limit state consists of checking that: Ed ≤ Rd

or

Sd ≤ Rd

(2.6)

where Ed or Sd express for actions which caused internal forces or moment, Rd is the relevant design resistance of the system or member or cross-section considered. The safety factor are accounted for actions while resistances are calculated using design values of materials. The detail of safety factors can be found in many design codes or manuals as well as textbooks. 2.7.2. Methods for analysis and design

Figure 2.13.: Ideallized tress-strain diagrams used in the plastic method, (26; 27)

In the global analysis for the determination of internal forces, the steel is assumed to be behave in a linear elastic manner, however rigid-plastic analysis can sometimes be used. Resistance of cross section are determined using plastic analysis wherever possible. This assumes that steel and concrete behave in elastic perfect plasticity, as illustrated in Fig.2.13. Subsequently, the entire depth of concrete is subject to its maximum design stress and the whole depth of steel is subject to yield stress. Plastic stress are rectangular, unlike elastic block which are triangular. The reduction factor of 0.85 is used for concrete in calculation its resistance. 2.7.3. Resistant capacity of composite beam under sagging moment According EuroCode4 (27), the ultimate capacity of a simply supported beam is determined by the moment of resistance of the critical cross-section. It is based on the following assumptions:

2.7. Design of composite beam

27

the shear connectors are able to transfer the forces occurring between the steel and the concrete at failure (full shear connection). no slip occurs between the steel and the concrete (complete interaction). tension in concrete is neglected. the strains caused by bending are directly proportional to the distance from the neutral axis stress-strain relation of concrete and steel are idealized as perfectly elasticplasticity ( Fig. 2.13) Rc

Rc

hc

Rc

Rc

x ha-yc

ha yc

z

Rs

Rft

Rw Rs

Rs

Rft ha-yc

1b)

es z

yc

Rfb 1a)

Rw Rs

ec

2a

2b

Figure 2.14.: Plastic analysis of composite section under sagging moment, 1a-neutral axis in concrete slab; 1b-neutral axis at the bottom of composite slab; 2a-neutral axis lies within top flange of steel section; 2b- neutral axis in the web a) 1.0

C

Partial shear connection B

Plastic Method

MRd Mpl.Rd

0

b)

0.8 ductile Simplified Method

Mpl.a.Rd A Mpl.Rd

η = Nc/Ncf 1.0

0.6

Full shear connection

non-ductile

0.4

Lower limit on Nc/Ncf (EC4) 0.4

η = Nc/Ncf

span, m 1.0

0

5

10

Figure 2.15.: Design method for partial shear connection (47; 48)

15

20

25

28


Fig. 2.14 shows the stress block and equivalent force in the composite section, moment resistance is determined by taking moment equilibrium at the cross section. It depends upon to situation of the yield line (neutral axis). 2.7.4. Partial shear connection Most beams are designed with the assumtion that the deformation of shear connector is infinite. However, in some certainly and uncertainly situations the partial shear connection must be taken. EuroCode4 offer two methods to plastic moment (Mpl.Rd ) of the section: Plastic method (stress block method) and simplified (linear interaction method) as shown in Fig. 2.15a. Specified formulas to determine plastic moment is given in Johnson (47), Lawson and Chung (61). It can be seen from figure that, the plastic moment is mostly dependent on the degree of shear connection η as well as plastic moment of steel girder. Limitation on the use of partial shear connection in beams for buildings is given in Clause 6.6.1.2 of EuroCode4 (27)as follows: Le ≤ 5m 5m ≤ Le ≤ 25m Le ≥ 5m

η ≥ 0.4 η ≥ 0.25 + 0.03Le η ≥ 1.0

(2.7)

Where: Le is the beam span in meter. 2.7.5. Ductile and non-ductile shear connectors Slip of connector enables longitudinal shear to be redistributed between the connectors in a critical length, before any of them fail. The slip required for this purpose increases at low degrees of shear connection, and as the critical length increases (a scale effect). A connector that is ductile (has sufficient slip capacity) for a short span becomes non-ductile in a long span, for which a more conservative design method must be used Johnson (47). For headed stud connectors EuroCode4 (Section 6.6.1.1) requires slip capacity δuk at least 6mm and definition are shown in Fig. 2.15b. The design data for shear connectors other than headed studs are not specified. Where partial shear connection is used and the connectors are ductile, the bending resistance of cross-sections in Class 1 or 2 may be found by plastic theory. Otherwise, elastic theory is required, which gives a lower resistance. Also, ductile connectors may be spaced uniformly along a critical length whereas, for nonductile connectors, the spacing must be based on elastic analysis for longitudinal shear.

2.8. Summary

29

2.8. Summary This chapter focus on the Behaviour as well as performance of composite beams under bending load. Many research work has been attempt on improve load carrying capacity of the beam through structural solution rather than using new advanced materials. Most of the experimental and finite element studies conducted on shear connectors and composite beams have focused on combination of steel and normal strength concrete. The literature pointed out that the design code which most widely used also limited on a traditional headed stud connector, all of other type which recently developed are not considered yet. Moreover, the strength of concrete slab which used in composite beam is not exceed 50 MPa. The contribution of steel fiber on improvement ductility of shear connectors was also not reported in the standard and other research works. The literature review shows that UHPC is recently development in concrete technology which has many advanced properties, especially in compressive and tensile strength. The replacement of conventional concrete to UHPC and combine with perfobond based continuous shear may provide an improvement performance in both terms of strength and service life. However, the experiences and knowledge as well as design guide is not sufficient for applying in construction engineering. It can be seen that, the number of research and published work on using UHPC in composite structures is very little. In this study, experimental and nonlinear FE analysis is carried, for both shear connector solution and structural Behaviour of composite beam under static load. The original Perfobond shear and a variant type were focused, the composite beam with I and Tee girder will be conducted. Various shear connection degree will be taken in order to evaluate performance of the shear connectors.

30


3. Characterization material properties of UHPC 3.1. Development of UHPC-A Historical perspective The development of high strength concrete began in 1970s, when the first time the compressive strength of the concrete used in the columns of some high rise building was higher than that of concrete usually used in construction. The concrete was made using the same technology as that for normal strength concrete expect that the materials were carefully selected and controlled (4). The new concept High Strength Concrete-HSC was called for this concrete. With the development of superplasticizers and the usage of pozzolannic admixtrure such as silica fume, it is possible to produce concrete with compressive strength more than 150 MPa (4). Moreover, the concrete has also improved characteristics such as higher flowability, elastic modulus, flexural strength, low permeability and better durability over NSC. The expression High Strength Concrete can no longer adequately describe the overall improvement in the properties. Therefore, the new expression High Performance Concrete - HPC became more widely used early 1990s (78; 4; 81; 1). ACI 363 committee defined HPC as follows: HPC is concrete meeting special combinations of performance and uniformity requirements that can not always be archived routinely using only conventional constituent and normal mixing, placing and curing practices. These requirements may involve enhancements of the following (43): easy of placement and compaction without segregation long term mechanical properties early age strength toughness volume stability long life in sever environments

32

3. Characterization material properties of UHPC

The development of material technology in the early 2000s not only enhance quality but also reduce significantly their cost. In fact, HPC was used widely in many applications. Up to now, in the normal curing condition a compressive strength can be reach over 200 MPa. However, in this case, the concrete is very brittle. Consequently, the addition of fiber is necessary to improve the ductility. Since, the the new concept Ultra High Performance Concrete-UHPC began widely used (56; 111; 4), Fig. 3.1 summarize the historical development of concrete. Time 1916

1943

1972

2000

2005

Compressive strength (MPa)

250 UHPC 200

150 HSC C55~C100 100

NSC C10~C50

50

0 1,0

0,8

0,6

0,4

0,2

0

Water-cement ratio Figure 3.1.: Historical development of UHPC

Several types of UHPC have been developed in different countries by different manufactures or research institutions. Some product lines have been marketed and became commercialize. There are few major types of UHPC those namely Ceracem/BSI (by Sika)(77), compact reinforced composites (CRC) by CRC Technology (52), multi-scale cement composite (MSCC) by Laboratoire Central des Ponts et Chausees (France) (91), and reactive powder concrete (RPC) by Lafarge as known with commercial name DUCTAL (3). This count is by no means a complete overview of all mixtures, as more mixtures are being developed and entering the market from different laboratories and universities. All the above described mixtures were designed with the main aim to reach a high compressive strength, while the improvement of the tensile and flexural tensile strength was of secondary interest. Another, different group of fibre reinforced concretes has also been developed where instead of the compressive strength,

3.2. Constituent materials of Ultra High Performance Concrete

33

the focus was set on improving the tensile load bearing capacity, and especially the tensile deformation capacity. These ductile concretes are often called High Performance Fibre Reinforced Cementitious Composites-HPFRCC or commonly UHPC (60; 63). In Germany, the research program on UHPC was carried out early ten years ago(56). Especially, the priority research project SPP 1182 - Sustainable Building with Ultra High Performance Concrete has been performed with the collaboration of many research institutions. This work is also a part of this project.

3.2. Constituent materials of Ultra High Performance Concrete 3.2.1. Principle of UHPC Several authors have been identified the basic principles to produce UHPC, which can be summarized as follows (99): enhancement of homogeneity by elimination of coarse aggregate. enhancement of the packing density by optimization of the granular mixture through a wide distribution of powder size classes. improvement of the properties of the matrix by the addition of pozzolanic admixture, such as silica fume. improvement of the matrix properties by reducing water/binder ratio. enhancement of the microstructure by post-set heat-treatment, and enhancement of ductility by addition of micro steel fibers.

The application of the fist five principles lead to very high compressive strength, however without any improvement in ductility. UHPC could be cured with high temperature and pressure condition after setting. High pressure treatment increases density by reducing entrapped air, removing excess water and accelerating chemical shrinkage. Heat treatment accelerates the cement hydration and puzzolanic reaction as well as modifies micro structures of the hydrates (36; 88). The addition of the steel fibers that noted in the last principle helps to improve both the tensile strength and ductility, whereas polymer and carbon fiber enhance fire resistance. The UHPC in this work contains steel fiber but without using any special treatment.

34


3.2.2. Composition of UHPC A typical UHPC consists of cement, silica fume, coarse aggregate, sand, crushed quatz, superplasticizer, fiber, crushed quartz, fibers, superplasticizer, and water as well. (90). silica fume

superplasticizer

quartz sand (basalt split)

UHPC water

cement

steel fibres quartz powder

Figure 3.2.: Comonents of a typical UHPC

Table 3.1.: Diameter range of granular class for UHPC, after Richard and Cheyrezy (90) Components Steel fiber Aggregate Sand Cement Crushes Quartz Silica fume

Mean diameter

Typical diameter range

0.15mm 5mm 500µm 15µm 10µm 0.15µm

0.1 - 0.2mm 1 - 5mm 250 - 1000µm < 50µm 5 - 20µm 0.10 - 1.0µm

Figure 3.2 shows typical components for make an UHPC and their sizes are presented in table 3.1. The role of the each constituent is briefly summarized as follows: Cement: Usually ordinary Portland cement type I (CEM I 42.5R/52.5R) or Portland cement with high sulphate resistance (CEM I 42.5R HS/52.5R HS) can be used to produce UHPC. The cement used should be low to medium fineness and not rich in C3 A content. Thus, reducing water need ettringite formation and heat of hydration (37). Low shrinkage cements may also be preferred since the high cement content of UHPC can make it more susceptible to high shrinkage (99).


35

Sand: It plays the role of reducing the matrix volume fraction under condition of enough flowability. Its strength is higher than the matrix and provides good paste-aggregate interfacing bonding. A variety of sand is usually used, however, it is not chemically active in the cement hydration reaction at room temperature. The mean particle size is often smaller than 1mm. It is noted that, the grain size of the silica fume, cement and sand must have to be optimized in oder to get high compact, dense matrix and low permeability. Crushed Quartz: In fact, not all of cement in the concrete mix is hydrated, some of which can be replaced by crushed quartz powder. Ma and Schneider (72) pointed out that, up to 30 percent of cement can be replaced by quartz power without reduction in compressive strength. Besides that, it also improves flowability of fresh UHPC. The improvement of flowability may due to the filling effect, since the crushed quartz particles are smaller than cement particles. Silica fume: Silica fume is composed of very small of glassy silica particle which are perfectly spherical, whose mean particles is in the range of 0.1 to 1.0 µm. Silica fume has three main roles in UHPC (99): filling the voids between coarser particles; reducing the friction between angular particles due to imperfect sphericity of them production secondary hydrates by puzzolanic reaction with the Ca(OH )2 from cement hydration (81).

Consequently, silica fume not only contributes to the increase of mechanical strength, but also to compact material density, and contribute to enhance micro structure. Ma and Schneider (72), Ma et al. (69) noted that, the optimal silica fume content could increases up to 25% to get the densest mixture, and some other test data shown that the greatest compressive strength could be achieved with 30% of silica fume. Fiber: Steel fiber is most commonly used in UHPC. Generally the diameter of steel fibers is in the range of 0.1mm to 0.2mm, and the length from 6mm to 30mm with various shapes. Its tensile strength is often greater than 2.4 GPa. In material matrix, the steel fibers are generally fulled out. The flexural tensile strength of the concrete increase with the fiber volume. Meanwhile, the ductile post fracture behaviour is also improved. Especially, the combination of several fibers with different lengths give better ductility and toughness, even if in the case when fiber volume fraction is less than 1% vol. (84). However, fiber nearly no significant effect on either the compressive strength or the

36


modulus of elasticity of UHPC. The flexural strength decreases when the fibers are preferentially aligned perpendicular to the principal flexural tensile forces. In UHPC, the workability is reciprocal with fiber content, in the case without coarse aggregates, the limit is about 10% vol. for φ0.15 × 6mm of fibers in CRC type. With the longer fibers of φ0.15 × 13mm, an upper limit of 2% to 4% exists. fiber volume of 2% represents the most commonly and was regards as the most economic content identified by Richard and Cheyrezy (90). Superplasticizer: Superplasticizer based on polycarboxylates and polycarboxylathers are popular used in producing UHPC. Superplasticizers disperse fine particles, thus improving the flowability of UHPC. The dosage of superplasticizers ranges from 2% to 4% of the volume fraction. 0.880

Relative Desnsity

0.875 0.870 0.865 0.860 0.855 0.850 0.845 0.06

Minimum 0.08

0.10

Optimum 0.12

0.14

0.16

0.18

0.20

Water /Binder Ratio (w/b) Figure 3.3.: Relative density vesus w/c ratio, after Richard and Cheyrezy (90)

Water: As known, water play key a role in the hydration reaction of cement. The water/cement ratio (w/c) does affects the porosity and have a signification effect on the compressive strength. The goal in UHPC mix is not to minimize the water content, but to maximize relative density. Richard and Cheyrezy (90) identified 0.14 as the optimal w/b ratio for UHPC as shown in Fig. 3.3. Investigation on set of mix proportional by several authors indicate that 0.15 to 0.25 are common range value for w/b ratio. 3.2.3. Cost of UHPC Currently, UHPC is much more expensive than NSC or HPC. The cost of a typical UHPC without steel fiber is around 513euro/m 3 , and it to be increased depend on addition volume of steel fiber. With 1.2 % vol. fiber the cost increases


37

up to 683euro/m 3 . Based on experiment in laboratory, Kuechler (58) pointed out the details of the cost of each material constituent given in Figure 3.4. It can be seen that, a large portion comes from silica fume and steel fiber. In fact, silica fume take about 55% and 72% total cost for UHPC with and without steel fiber, respectively. 72.6%

Silica fume

7.4%

Quart powder

5.7% 5.4%

Coarse aggregate

24.9%

Steel fiber

9.9%

Quart powder Plasticity admixtures

54.5%

Silica fume

Plasticizers

4.3%

Coarse aggregate

4.1%

5.1%

Cement

3.9%

Cement

1.1%

Quart sand Water

a)

0.2% 0

50

100

150

200

250

300

350

400

price in €/meter cubic

Quart sand

0.8%

Water

0.1% 0

b) 50

100

150

200

250

300

350

400

price in €/meter cubic

Figure 3.4.: Estimation cost of constituent materials for UHPC, (a):UHPC without steel fiber, (b) with 1% steel fiber (58)

Very high cost is main disadvantage for the application of UHPC in practical construction. As a result, currently, the practical use of UHPC is very limited absolutely compare to NSC/HPC, only for small structures or few structural members . In the near future, with the development of material production technology and the extension of application range, the cost of UHPC may be reasonable and widely accepted. 3.2.4. Material used in this work As mentioned in the previous part, many kinds of UHPC products have been developed by several laboratories during the last few years. As a part of collaboration research project SPP1182, two UHPC mixtures derived from University of Kassel (B4Q) and University of Leipzig (G7) are used in this work. Table 3.2 presents the mix proportion of the G7 and B4Q. In all experiments, the fiber volume range from 0.5% to maximum 1.25%, the target compressive strength reaches values of 140 MPa after 7 days and 150 MPa after 28 days in dry curing condition, the details of mechnical properties will given in chapter 5.

38


Table 3.2.: Mixture proportion of UHPC Weight per cubic meter (kg/m 3 ) Components

Volume fraction (%)

G7(Leipzig) Tue (101)

B4Q(Kassel) Schmidt (30)

G7

B4Q

567.00 102.00 305.61 831.03 487.35 39.0 39.0 26.81 142.82 0.242 68-71 150

660.0 180.00 463.00 607.40 360.00 70.0 32.00 161.46 0.221 65 150

18.59 4.4 11.62 28.00 18.40 0.5 0.5 4.73 14.28 -

20.75 7.82 12.45 22.4 13.58 1.0 4.8 16.14 -

CEM I 42,5R HS CEM I 52,5R HS Silica fume Quart powder Aggregate 2-5 mm(G7) Aggregate 5-8mm (B4Q) Quart sand (0.3-0.8mm Steel fiber (0.16 × 13mm) Steel fiber (0.16 × 6mm) Steel fiber (0.15 × 17.5mm) Superplasticizer Water Water/binder W/(C+SF) Slum flow (cm) Target comp. strength (MPa)

3.3. Relevant material properties 3.3.1. Properties of fresh UHPC The workability is usually taken into account for fresh UHPC mixtures. It is verified by using the flow cone, U-box or block ring apparatus. The workability depend on many factors: the water/binder ratio, type and dosage of superplasticizer, steel fiber content and aspect ratio as well as mixing method etc. Ma and Dietz (69; 70) reported that, with a right choice of w/b and superplasticizer, the slump flow of UHPC in 600mm to 800mm range. Neither segregation nor bleeding occurred, even though mixed with high fraction of coarse aggregates. The negative effect of steel fibers on workability of UHPC could be improved by using hybrid fibers (cocktail) consisting of fiber of different aspect ratios (84). The properties of fresh UHPC are also effected by the mixing method. The investigation of Tue et al. (104), Ingo et al. (45) indicate that, the fluidity of fresh UHPC can be significantly enhanced through stepwise addition of superplasticizer. The superplasticizer is divided into two parts, the first part is added to mixture following water, and then the remaining part is added after 60 to 120 second later. Such an approarch leads to an increase of 20% to 30% the slump flow, and a decrease of 2.5% to 1% of air contain in comparision with one time

3.3. Relevant material properties

39

addition. The mixing procedure with 6 steps also introduced to obtained more optimal results (45). 3.3.2. Time dependent properties of UHPC

autogenous shrinkage after T max (µm/m)

0 UHPC with coarse aggregates UHPC without coarse aggregates

-100

-200

251.3

-300 404.4

-400

-500 0

48

96

144

192

240

288

336

384

432

480

528

time after Tmax (hours)

Figure 3.5.: Autogeneous shrinkage of UHPC with and without coarse aggregates, after Ma et al. (69; 70) −2500

−1500

Creep of free UHPC

Creep of sealed UHPC

0,70fc

0,85fc −1200 Creep strain (µmm)

Creep strain (µmm)

−2000 −1500

0,70fc −1000

0,60fc

0,55fc

0,47fc

−500

0,60fc −900

0,53fc 0,47fc

−600

0,28fc

−300

0,28fc 0

0

20

40

60

Loading duration (days)

80

100

0

0

20

40

60

80

100

Loading duration (days)

Figure 3.6.: Creep of UHPC with and without coarse aggregates, after Ma and Orgrass (71; 73)

Shrinkage: The shrinkage of UHPC is caused by two sources: the autogeneous and dry shrinkage. UHPC can exhibit large shrinkage values. The autogenous shrinkage takes a larger portion in the total shrinkage than the drying shrinkage (36; 34). Collaborating in this study, Ma et al. (69; 70) evaluated the shrinkage

40


of UHPC on a large number of mixtures with and without coarse aggregate as well. The experimental results exhibited very high autogeneous shrinkage with rapid development. This resulted from the accelerated self desiccation due to very low w/c ratio and very fine capillary pore. The test also indicated that, after casting three weeks, the autogeneous shrinkage of UHPC containing coarse aggregate is 40% lower than that of UHPC without coarse aggregate. Fig. 3.5 shows the autogeneous shrinkage for both UHPCs. Creep: Creep is defined as additional deflection or strain in addition to the initial instantaneous strain that occurs when a load is applied to the concrete (εcreep = εel .ϕcr ). Ma and Orgrass (71; 73) stutied the creep of UHPC with coarse aggregates with cylindrical specimens of φ100 × 300mm. The compressive load was applied at the age of 28 days, the stress level were about 25% to 85% of the compressive strength. The ultimate creep coefficient of UHPC was found to be 0.92, which is noticeably smaller than that of normal strength concrete which is in the range 2.0 to 4.0 (81). Experiences from the test also indicated that: The dry environment has only a small influence on the creep behaviour; the drying creep of UHPC is so small that it can be neglected. 3.3.3. Durability As well know, UHPC exhibits not only high compressive strength but also superior durability. The low porosity of UHPC (particularly capillary porosity) leads to a great improvement in the durability properties of UHPC. The porosity and then various durability properties for UHPC are presented in this section, they are also compared to HPC as well as normal strength concrete. Porosity: The porosity is intrinsically related to the durability properties of all concretes, including UHPC. Both the total pore volume and the size of the pores as well as their connections in concrete are important for the durability. The peability, the resistance against chemical aggression and the freeze-thaw are relative to the pores in concrete. Many durability parameters, such as the rate and depth of ingress of contaminants and the freeze-thaw damage, are greatly improved if a low volume of disconnected pores can be developed in the material. The total porosity range from 4.0% to 11.1% for UHPC without heat treatment (2; 92; 100). Otherwise, UHPC has total porosity ranging from 1.1% to 6.2% when heat treated (23). Figure 3.7 shows the cumulative porosity of UHPC corresponding to UHPC with and without heat treated. It indicates the total porosity of the untreated UHPC are approximately 8.4%, but heat treatment

3.3. Relevant material properties

41

Table 3.3.: Total porosity, capillary porosity and NSC, HPC and UHPC, after Teichmann and Schmidt (100) UHPC Parameter

HPC

NSC

(heat treated)

Value

Ratio to UHPC

Value

Ratio to UHPC

6.0% 1.5%

8.3% 5.2%

1.4 3.5

15.0% 8.3%

2.5 5.5

Total porosity Capillary porosity

reduces the total porosity of the UHPC sample to only 1.5%. Table 3.3 presents some results on total porosity of UHPC, HPC and NSC(99). Por e Diameter , mm 2.54E-05

0.000254

0.00254

0.0254

0.254

Cumulative Por osity

9% 8%

Non-Heat Treated

7%

Heat Treated

6% 5% 4% 3% 2% 1% 0% 0.1

1

10

100

1000

10000

Por e Diameter, µin

NSC Abrasion Resistance Relative Vol. Loss Index

HPC

NSC Reinforcement Corrosion Rate

NSC UHPC

HPC

UHPC

HPC UHPC Carbonation Depth (3 years)

Water Absorption

UHPC HPC

UHPC Nitrogen Permeability

UHPC HPC Oxygen Permeabilty

Chloride Ion Permeability, Total Charge Passed

UHPC HPC

HPC Chloride Ion Penetration Depth

UHPC

UHPC Chloride Ion Diffusion Coefficient

0

UHPC HPC

0.4 0.2

NSC

HPC

HPC

0.6

NSC

NSC

NSC

NSC

NSC

0.8

Salt Scaling Mass Lost (28 cycles)

Parameter relative to Normal Concrete

1

NSC

Figure 3.7.: Porosity of UHPC with and without heat treated, after Cwirzen (23)

Figure 3.8.: Comparison durability properties of NSC, UHP and UHPC. After Suleiman et al. (99)

The durability properties of UHPC compared to other concrete was sumarized

42


by Suleiman et al. (99). Fig. 3.8 shows the relative durability parameters of UHPC and HPC respect to NSC (low values identify favorable material).

3.4. Mechanical behaviour characterization 3.4.1. Development of compressive strength The time dependent compressive behaviour of UHPC was investigated through a series of tests, including the strength, modulus of elasticity, and compressive strain capacity both before and after the application of curing treatment (74; 34; 30; 37). Fig. 3.9 depicts the strength development spectrum on cylinder specimens with φ100×200mm (74). It can be seen that, the compressive strength of UHPC reached more than 65% of fc28 (80 to 120 MPa) only after 3 days. The strength increase slowly in the period of 7 to 14 days and reached about 80% to 90% of fc28 . Since 28 day after casting, the measured strength increment is approximate 15%. In addition, the strength development for two mixtures with silica fume of 18 % and 30 % cement replacement are almost identical. The great decrease of the silicafume has no remarkable influence on the development of compressive strength. In practical applications, UHPC is fairly interesting for pre-stress and pre-cast concrete industries, which require short production time. The rapid strength development is also very useful in repair or improving existing structures, especially for structures in service state. 1.4

Silicafume: 30% of Cement Silikafume: 18% of Cement

200

MC90 Experiment

1.2 175 150

fc(t) / fc,28d

Cylinder comp. strength (MPa)

225

125

1.0 fc(t)=exp[s*(1−(28/t)n)]*fc,28d

0.8

n=0.549

100

s=0.217

0.6 75 50

1

3

9

27

81

243

729

2187

0.4

1

3

Concrete age (days)

Figure 3.9.: Development compressive strength, after Ma (74)

9

27

81

243

Concrete age (days)

729

2187

3.4. Mechanical behaviour characterization

43

The development of compressive strength can be estimated by using MC-90 equation 3.1, as also presented in Fig. 3.9 (Ma (74; 102)). " 0.5 !# 28 fc (t) = exp s 1 − fc,28d (3.1) t where: fc (t) is the mean concrete compressive strength at an age of t days, fc,28d is the mean concrete compressive strength at 28 days, s is coefficient which depends on type of cement, s = 0.2 for rapid hardening high strength cement. In another work, in the analysis of a set of untreated cylinders tested between 1 and 57 days, Graybeal (35) introduced estimate an equation by using linear regression method as follows: " 0.6 !# t − 0.9 fc,28d (3.2) fc (t) = 1 − exp − 3 The author noticed that, the development of compressive strength is dependent on the age of the mixture and the environmental conditions, the above equation may not applicable to all cases. 3.4.2. Stress-strain behaviour in uni-axial compression Stress-strain behaviour under uni-axial compression is obtained from φ150mm×300mm cylinder specimens. The test setup includes a couple strain gages (60mm gages length) attached in vertical direction to capture the axial deformation, other pair of the same strain gages was also attached in the horizontal direction to measure radial strain (Fig. 3.10). The axial and lateral strain of the cylinder can be measured accurately from initiation of loading up to failure. Compression force was generated by servo hydraulic system with maximum capacity of 4000kN. The loading procedure and rate were programmed and controlled according force and displacement as shown in Fig. 3.11. Measured data of all channels were recorded automatically by external digital data acquisition system. A typical stress-strain behaviour of UHPC under compression are shown in Figure 3.12 and to be discussed detailed as follows.


60mm

300mm

120mm

44

120mm

4 strain gage with 60mm gage length o 180

o 180

Figure 3.10.: Test setup for stress-strain response under uni-axial compression 160 Vertical strain Horizontal strain

Disp. Control 0.03mm/min

Force Control (0.5MPa/sec)

0.8

120

0.6 Stress (MPa)

Relative compressive stress

1.0

80 0.4

40

0.2

Ec = 48 GPa

0.0

0

310

620

930

1240

0.5

1550

0

-0.5

Time in second

-1. 5 Strain (‰.)

-2.5

-3.5

Figure 3.11.: Loading procedure for uni-axial compression test 180

0.50 0.45

140

0.40

NSC HPC UHPC

120

Poisson's ratio ν

Compressive Stress (MPa)

160

100 80 60 40 20 0 3.0

0.35 0.30 0.25 0.20 0.15 0.10

lateral strain 2.0

1.0

0.05

axial strain 0.0 −1.0 Strain %o

−2.0

−3.0

(a) σ − ε-curves of NSC, HPC and UHPC

−4.0

NSC HPC UHPC

0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Relative compressive strength

Poisson's ratio of NSC, HPC and UHPC

Figure 3.12.: A comparison of stress-stress curves of NSC, HPC and UHPC(left), and Poinsson’s ratio (right). After (Tue et al.) (101)


45

Linearity and compressive stress-strain response As well know, the stress-strain response of concrete under uni-axial compression reflects the micro crack development in concrete under increasing of compressive stress. The linearity property exhibit resistance of material matrix and aggregate at interface zone. At low load level, the strain increases proportionally which is expressed in linear branch of stress-strain behaviour. The nonlinearity usually begin when the first crack in the contact zone occurs. There is no standard method to determine the linear range of the concrete. For the present experiments, the linear range of stress-strain curve of UHPC was determined through comparing measured stress and calculated stress which obtained from elastic modulus and corresponding axial strain, the derivative is limited lower than 5%. The investigated from concrete which used in this work show that, linear range of UHPC approximate 70-80% of compressive strength for untreated specimens. Graybeal (35) also pointed out that, the linear range of specimens underwent stream streatmen could be reach 80% to 90% of the compressive strength. Relationship between elastic modulus and compressive strength As show in figure 3.13, the initial stiffness of UHPC is alway higher than conventional concrete at the same strain. That mean the elastic modulus of UHPC is larger. This is approved for the case UHPC and NSC with the same type of coarse aggregates. The UHPC without coarse aggregate contains normally quartz sand whose size is smaller than 1 mm. Its modulus of elasticity is about 48,000 MPa, lower than that of UHPC containing basalt split (approximate 58,000 MPa).

55000

70000 in CEB-FIP 1990 Model code: Concrete with quartz fine/coarse aggregates 1/3 Ec=21500 (fc/10)

Elastic modulus (MPa)

Elastic modulus (MPa)

65000

45000 experiment results: UHPC without coarse aggregate 1/3 2 Ec = 19000 (fc/10) , R = 0,8878

35000

25000 1/3 (f1,7 c/10) fc,zyl100*200 49

1,9

2,1

2,3

2,5

2,7

2,9

69

93

122

156

197

244

60000

in CEB-FIP 1990 Model Code Concrete with basalt coarse aggregates Ec=24600 (fc/10) 1/3

50000

40000

30000 1/3 (f2,0 2,1 c/10) fc,80 100*300 93

experiment results: UHPC with basalt coarse aggregates 1/3 2 Ec = 21902 (fc/10) , R = 0,849

2,2

2,3

2,4

2,5

2,6

2,7

106

122

138

156

176

197

Figure 3.13.: Relation elastic modulus vesus compressive strength.(Tue et al. (101; 70))

The relationship between the elastic modulus and compressive strength for UHPC is similar as that proposed in MC-90 (16) for NSC and HSC, regardless of the grain size. However, due to the high paste volume, the modulus of elasticity

46


of UHPC is about 12% lower than that predicted with the equation in MC-90 for UHPC (70). Figure 3.13 shows the relation of the elastic modulus with the compressive strength. The proposed equation for pedicting the elastic modulus of UHPC are given as follows (70; 101) :  r !   3 fc  for UHPC with coarse aggregate  21902 10 ! r (3.3) Ec =   3 fc  19000 for UHPC without coarse aggregate   10 An alternative equation has been developed by Graybeal is given in equation 3.4. Further detail could be found in (35). √ Ec = 3480 fc for UHPC without coarse aggregate (3.4) Poisson’s ratio: The Poisson’s ratio is defined as the ratio of the lateral strain to the longitudinal strain. In the linear range, the Poisson ratio of UHPC is 0.21. This value is similar to that of normal and high strength concrete. However, the increase of the lateral strain of UHPC after the limit of linearity is much smaller than NSC and HPCs as shown in Fig. 3.12. 3.4.3. Bi-axial behaviour of UHPC Multi-axial stress state exists in many reinforced concrete structures, for instance in composite beam using concrete dowel as shear connector (107; 40) or in the connecting element of UHPC truss (103), especially in the nodal joint element made of steel tubes filled UHPC (58; 105). Generally, the ultimate strength in compression-compression zone is higher than uni-axial compressive strength. For UHPC and NSC, the increase of strength in biaxial stress may up to 8% to 15% respectively compare to the uni-axial compressive strength. The increament is proportional with ductiliy of the concrete (38). UHPC is less ductile than conventional concrete, and its behaviour depends on used aggregate size, content and orientation of fiber. The test results of Curbach and Hampel (22) is summarized and presented in Fig. 3.14. It can be seen that, at all stress ratios, the bi-axial compressive strength of concrete with coarse aggregate is higher than that of UHPC without


47

coarse aggregates. The normalized stress-strength ratio indicated that, there is no remarkable difference in bi-axial strength increment between UHPC fine and coarse aggregate. The increment reached a value of normal strength concrete (10%) when the fiber content is 2.5 vol.%. However, it could be easily identify significant difference in stress-strain behaviour. Actually, in bi-axial compressive stress both UHPCs behave less brittle than that in uni-axial compression, which is similar to behaviour of NSC. b)

σ 2 fc

M2Q-2.5 1.10 1.07

1

2.5% vol

σ 2 fc

a)

1.07

1

0.9% vol

B4Q-2.5

1.25% vol

0.99

0.0% vol

0,5

0,5

0

0 0

0,5

σ 1 fc

1

0

0,5

B4Q-2.5 (D=8mm, 2.5%Vol.fiber, d/L:0.15/9mm)

BaQ-1,1 B4Q-1.25 Vol.-% fibres 0,38/30 mm

M2Q-2.5(D=0.5mm, 2.5%Vol.fiber, d/L:0.15/9mm)

B4Q-0.9 Vol.-% fibres 0,15/17 mm

1

σ 1 fc

B4Q-0.0 without fiber

Figure 3.14.: Comparison influence of grain size and fiber content to bi-axial strength increment, modified from Curbach and Hampel (22) 1,0

A A-reduction by effect of reinforcement B-complete loass of aggregate interlock

90

σ2 /f c [%]

80

0,9

0,8

UHPC with fibers 70

0,7

60

0,6

UHPC without fibers 50

0,5

reduction factor α c

100

B 40

0,4

30 0,0

2,0

4,0

6,0

8,0

0,3 10,0

ε1 [‰]

Figure 3.15.: Proposal reduction strength under compression-tension load, modified from (Fehling et al. (29))

48


A comparison of UHPC with different fiber contents was also performed. It is found that, the positive increment of biaxial strength is quite no meaning if the fiber contents is less than 2%. The stress-strain behaviour in the softening branch can be clearly seen in the specimen with 2.5% fiber. Consequently, Curbach (22) recommend minimum steel fiber should be from 2.5 vol. % fraction and to use coarse aggregate in UHPC in order to obtain high strength and ductily in bi-axial compression. The compressive strength of UHPC under compression-tension state decreases significantly and most linearity at small tensile strain level. The ultimate strength depends heavily on the tensile strain up to approximately 2.5 permiller. The decrease of bi-axial strength is related directly to the properties of the compositions of UHPC such as grain size, fiber content as well as transverse tensile strain, which are caused by the crack formation and distribution. Based on experiment on UHPC panel under compression-tension loading, Fehling et al. (29) proposed a strength reduction factor of 0.5 and 0.7 for UHPC without and with 1% fiber content, repectively. Figure 3.15 illustrates simple bi-linear approarch to consider the reduction of the compressive strength under compression-tension (29). 3.4.4. Flexural and direct tension behaviour of UHPC 20

20

15

UHPC with fine aggregate

25 increase in fiber length and/or content

20 15 10

15

First crack

10

Strain softening

5

10

Linear elastic domain 0 0.0

0.5

1.0

1.5

5

5

ft =17 MPa

UHPC with coarse aggregate

0

a)

Peak load

Strain hardening

30 Flexural stress-MPa

flexural tensile strength [MPa]

35

0

2

4 6 Deflection [mm]

8

10

0

b)

0

2

4

6

Deflection (mm)

8

10

Figure 3.16.: Flexural tensile stress-deflection diagram of G7-UHPC, by Tue et al. (108)

The flexural strength of UHPC is often obtained from 3 points test of notched beam according to RILEM TC 162-TDF, or 3 point bending test according to ASTM. The average value of flexural strength for UHPC is in the range of 10MPa to 30MPa, which depends on the composition and steel fiber content as well as fiber aspect ratio. The fiber cocktails of short and long fibers are a good alternative to ensure the flow ability on the one hand and to increase the flexural strengths on the other hand. In this context long fibers increase both the flexural


49

strength and the ductility after cracking, while short fibers increase primary the flexural strength (Fig. 3.16a). Typical UHPC behaviour under bending is characterized by linear elastic response up to the first cracking of the material, a strain-hardening phase up to the peak load, and softening phase after the peak load exhibits. Fig. 3.16b shows a typical load-deflection diagram of G7-UHPC with 1.0 % fiber content in three point bending test with notched beam. The uniaxial tensile strength of UHPC is approximately in range of 5 to 20 MPa with fiber content about 1.0 % to 2.0 % of volume fraction. However the behaviour of UHPC under direct tension is brittle at the ultimate limit state, characterized by crack localization and a sudden failure with poor ductility. To achieve a higher ductility, reinforcement should be added to structural members (49; 89). 3.4.5. Fracture properties of UHPC Fracture energy represents the total amount of work that must be done on a concrete specimen to achieve complete failure. It is usually determined by notched beam in three points bending or wedge splitting test (95) as show in Fig. 3.17. The applied force and the crack opening displacement (in short COD) are measured. Based on tensile stress versus COD derived from test result the fracture parameters can be determined. 15o

Fv

Fsp

3.5 t = 100 156

260

Notched = 25x5mm

300

Fsp

300

Figure 3.17.: Notched beam three points bending test(left) and Wedge splitting test (right) to determine fracture energy of concrete

Two main influencing factors to the fracture energy of UHPC are size of aggregate and steel fiber content. Xiao et al. (112) pointed out that, the fracture energy of UHPC without steel fiber vary in the range 50-120 N /m corresponding to a compressive and splitting tensile strength of 148 MPa and 8.3 MPa respectively. For UHPC containing crushed basalt coarse aggregates (2-5 mm), the the

50


fracture energy is over 1.8 to 2.2 times higher than that of UHPC without coarse aggregates. All the fracture parameters tend to increase with the mixture of coarse aggregates (112). Table 3.4 shows the test results for the fracture energy of UHPC without fibre has been obtained at Uni-Leipzig (74). Table 3.4.: Fracture parameters of UHPC for different mix designs, after Ma (74) selfcompacting fine-grained concrete

compacted finegrained concrete

UHPC with basalt grain

149.1 9.4 62.8 32.6 13.2

196.3 11.9 54.7 20.1 9.8

145.0 8.3 95.0 80.6 127.2

Cylinder comp. strength - N/mm2 Tensile strength - N/mm2 Fracture energy GF - N/m Characteristic length lch - mm Limit crack width - µm

In contrast, when steel fiber is added into UHPC, the fiber in UHPC plays an important role in producing prominent bridging stress between opened crack faces. The bridging stress between the largely opened crack surfaces is the main source of the very high fracture toughness and ductility of UHPFRC. Fracture energy of UHPC with steel fiber varies in range 5,000-25,000 N/m (12; 32; 97). The fracture parameter is not only dependent on the volume of fiber but also significantly influenced by the casting direction. Table 3.5 shows test results on the tensile behaviour and fracture energy conducted at Delft University. Fig. 3.18 illustrates the decrease of the characteristic length with the compressive strength for NSC, HSC and UHPC, respectively (32). 450

UHFB with mit Basaltsplitt UHPC basaltic split

300 250 200 150 100 50

fine-aggregated concrete Feinkornbeton

350

Feinkornbeton concrete fine-aggregated

Characteristic Length l (mm) charakteristische Längech(mm)

400

0 10

20

30

40

50

60

70

80

90 100 110 120 130 140 145 149 196

Druckfestigkeit (N/mm²) Compressive strength (MPa)

Figure 3.18.: Characteristic length versus versus compressive strength (32)

It can be seen that, generally, the fracture behaviour of UHPC without steel

3.5. Concluding remarks

51

fiber is not ideal. It depicts much brittleness even if its compressive strength is very high. The addition of steel fiber leads to great enhancement of the fracture properties impressively, which may from 100 - 1000 times higher than that for normal strength concrete.

3.5. Concluding remarks An overview of historical development and characteristic of UHPC was provided in this chapter, brief summary on the properties of UHPC can be stated as follows: UHPC can be produced from available material in the market without any special condition very high compressive and tensile strengths UHPC without fiber exhibits very brittle, the steel fiber is necessary to increasing ductility high dense cementitious matrix, very low permeability very low creep and shrinkage compare to conventional concretes, making the material suitable for precast/prestressed structures

In practical application, high strength of UHPC allows the designer to use smaller sections, resulting in the use of less material, to yield the same capacity. The properties of UHPC can be optimized when used in conjunction with steel or pre-stressing, which maximizes the use of the inherent compressive as well as tensile capabilities.

3. Characterization material properties of UHPC 52

M1Q

Axial tension M1Q

B3Q

Bending tension

Table 3.5.: Tensile fracture properties of UHPC with steel fiber, modified Fehling et al. (32) Specimens

M3Q

Mixtures

Ver.

Hor.

900

Hor.

WL

-

Ver.

-

18.0 17.9 18.1

Hor.

14543 -

18.3 20.4 24.2

Hor.

20355 -

17.6 -

Ver.

-

22.1 22.2 22.1

Hor.

15097 15097

11.1 13.3 16.2

Casting dir.

20100 19820

22.5 13.3 -

900 -

34.0 35.7 36.3

WL 9993 -

7.0 -

900

16757 17014

7.9 -

900

7days 28days

14.2 13.3 17.7

900

Fracture energy GF (N/m) 7days 28days 56days

Curring dir.

Tensile strength ft (N /mm 2 )

4. Experimental study for perfobond shear connector in UHPC 4.1. Introduction

Shear force P

The behaviour of steel-concrete composite beams in bending is achieved by means of the shear connectors, which play an important role in resisting the longitudinal slip and the separation of concrete slab and steel girder. The types and quantities of shear connectors depend on the shear force resulting from the bending moment and the vertical loading. Conventional shear connection in composite construction is often designed as headed stud, lying stud etc., and normal strength concrete is usually used for slab (47; 80; 27). In normal strength concrete, headed stud shear connector (HSSH) results in high ductile response as shown in Fig. 4.1. If the strength of the concrete surrounding stud are very high, then the deformation of the stud is restrained and shear connector can be shanked at base. The failure mode is brittle, the ductility is insufficient as required of several design codes.

Brittle Ductile H P P

0.5

Slip H (mm)

10.0

Figure 4.1.: Behaviour of headed stud shear connector in NSC, after Johnson (47)

The perfobond shear connector (PFSH) was first introduced by Leonhardt (62) in Germany. With this kind of shear connector, the interaction is developed by concrete dowel engaging with the perforated steel strip. In fabrication the steel

54

4. Experimental study for perfobond shear connector in UHPC

strip is cut and attached by welding to steel girder. The main advantages of the perfobond shear connection are listed as follows: the carry load can be transferred continuously between concrete slab and steel girder. the same material can be used for shear connector and steel beam, it does not require a higher steel grade for shear connector and special equipment for welding. with symmetric dowel profile two shear connector strips could be receive with only one cutting line and there is no material wasted. If the cut is carried out in the web of a steel I-girder, two composite beams without an upper flange can be produced. (41; 51; 105) the reduction of total cost by less labor work and faster in fabrication

Since the first time appear to now, perfobond shear connectors have been good alternative solutions for conventional headed stud shear connectors. Practical experiences and laboratory studies pointed out that, the strength of steel and concrete, the thickness of steel rib, the profile of dowel, the embedding rebar inside dowel as well as reinforcement in front layer etc. are important criteria for the load bearing capacity of the perfobond shear connectors. The Push-Out tests, presented and discussed in the following, aim to investigate the behaviour of the perfobond as well as headed stud shear connectors in UHPC, which are applied in composite beams. Its objective was to identify the applicability whether brittle shear connection behaviour could occur and to provide possible reinforcing solutions which ensure sufficiently ductile behaviour. During the testing, two types of dowel profile, reinforcing arrangement and steel fiber content that control the concrete-related failure modes were investigated. Due to limited condition, the experimental study could not cover all interesting aspects, therefore additional modelling work need be done. Based on these findings, the test data are used to validate the numerical model and the preliminary suggestions for design shear connection are established.

4.2. Experimental programs and specimens 4.2.1. Push-Out test specimens The standard Push-Out test (here after SPOT) was carried out in order to investigate the behaviour and characteristic parameters of the shear connectors. In

4.2. Experimental programs and specimens

55

fact, they were planned to use in the composite beams. The testing procedure and the evaluation results of the test were performed according to the guideline of EC4-Appendix B (27). Various test series were prepared for both type of shear connectors: headed stud and perfobond.

Flange

50

LVDT4

50

Rib (web)

LVDT2.2

LVDT3

LVDT3

LVDT1.2 350

LVDT1.1 420

LVDT1.2

200

300

Dowel LVDT1.1

LVDT2.1

50

UHPC (slab) Gap 40

80

20

LVDT3

Flange

50

80

a)

LVDT4

50

Rib (web)

LVDT2.2

LVDT2.1

UHPC (slab)

50

Gap 80

LVDT3

40

80

20

b)

LVDT3

LVDT1.2

LVDT3

350

LVDT1.1 420

LVDT1.2

200

300

Dowel LVDT1.1

Figure 4.2.: Standard Push-Off Test, Setup 1 (a) and Setup 1 (b)

Fig.4.2 depicts the detailed components of a specimen. There are three main parts include a thick steel plate, a perforated steel strip and a concrete block. The steel plate of 200mm width, 350mm height and 20/30mm thickness is presented for the flange (I section) or web (in T section) in steel girder. Its stiffness must be strong enough to ensure the transfer of shear force from flange/web to perforated steel strip and concrete dowels. The perforated strip with dimensions 65/75mm × 310mm and 10mm thickness were considered as steel rib of the perfobond connector. As depicted in the figure, each steel rib has two holes of 45mm diameter through which UHPC will flow to form the concrete dowels. The profile of dowel was designed with two variants namely closed dowel(CDW) and open dowel (ODW), as illustrated are described in Fig. 4.7. The concrete block was 300mm wide, 350mm high and 80mm thick that acts the concrete slab in composite beams. And it includes two dowels which are used to against shear force

56


from the steel rib. Generally, all specimens are symmetric with identical dimensions of concrete bock and steel parts as well as thickness of steel rib. In the specimens using headed stud shear connector, two steel ribs were replaced by eight φ16mm×60mm headed studs, which welded into the flange or web directly. 500 450 400

2

Stress [N/mm ]

350 300 250 200 150 100 50 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Strain [%]

Figure 4.3.: Typical stress-strain curve of structural steel at room temperature, modified Outinen et al. (85)

. 800

Stress (MPa)

600

400

200 Dia. 12mm Dia. 10mm Dia. 8mm Dia. 6mm

0 0

5

10

15 Strain (‰)

20

25

30

Figure 4.4.: Typical stress-strain curves of Bst500 reinforcement

In this study, structural steel grade S355 was used for both Push-Out (PO) specimens and composite beams. The mechanical properties of this steel were determined from tensile test. However, there were no test for steel plates, all test


57

data were archived from research work carried out by Outinen et al (85) and Byfield et al (13). The values of yield strength, elastic modulus and ultimate strength were evaluated at 380 MPa, 506 MPa and 202.6 GPa, respectively. The typical stress strain curve are shown in Fig. 4.3. The details of the mechanical properties are given in table 4.1. Table 4.1.: Mechanical properties of steel grade S355 and reinforcing bar Bst 500 S355

Bst 500

386 506

520.00 600.00

202,590 2,235 24

210,000 -

0.20 1.50 4.00

0.22 -

Yield strength fsy (MPa) Ultimate strength - fsu (MPa) Elastic Modulus - Es (MPa) Hardening Modulus - Esh (MPa) Elongation after fracture (%) Yield strain εsy (%) Strain hardening εsh (%) Ultimate limit strain εsu (%)

Bst500 grade reinforcement was used for all specimens. In order to obtain the essential characteristics, tension test were carried out for rebar with diameter of φ6mm, φ8mm, φ10mm and 12 as well. Average values of yield, ultimate strength and limit yield strain of reinforcing bar from φ8mm to φ12mm are 520 Mp, 600 Mpa and 0.22% respectively. The typical stress-strain curves are plotted in Fig. 4.4 and the main mechanical properties are also listed in Tab. 4.1. In the experimental framework of composite beams and Push-Out test, the UPHC G7 mix proportion was used for various test series. The details of material composition was given in previous chapter. The steel fiber content was specified with 0.5% (G7-150-0.5%) and 1% (G7-150-1.0%) in order to investigate the influence of tensile toughness of concrete on the specimen behaviour. The typical material response curve of G7-UHPC in uni-axial compression and three points bending stress states are shown in Fig. 4.5. The basic properties of G7-UHPC are given in table 4.2. Table 4.2.: Material properties of UHPC

Concrete B4Q UHPC∗ 1% fiber G7 UHPC 0.5% fiber G7 UHPC 1.0% fiber ∗

Compressive strength (MPa)

Elastic modulus (GPa)

Flexural strength (MPa)

Elastic strain (h)

Limit strain (h)

146.0 171.8 171.8

50.6 56.7 57.8

14.7 9.4 17.1

2.0 1.8 2.1

3.4 3.1 3.5

UHPC B4Q mixture is used in bending testing of the composite beams B1 to B4

58


160

20

Stress (MPa)

G7-RILEM-BeamTest

120

15

80

10

40

5 G7-Lateral strain G7-Vertical strain

0 -4.0

-3.0

-2.0

-1.0 0.0 Strain (‰)

1.0

2.0

0 0.0

2.0

4.0 6.0 Displacement (mm)

8.0

10.0

Figure 4.5.: Material responses of G7-UHPC 1% steel fiber, stress-strain diagram in compression test (left) and stress-deflection in RILEM beam test(right)

a) Formwork

c) Specimens after casting

b) Inside a specimen before casting

d) Specimen for test

Figure 4.6.: Casting Push-Out specimens

The specimens of each individual test series were prepared and cast in the vertical direction from the same batch of concrete. Numerous of concrete cylinders of φ100mm×200mm were also cast and stored alongside the specimen and tested at


59

regular intervals. At the stage of producing PO specimens, the gaps at bottom of steel ribs with dimension of 20×20mm×70mm were early created by two foam blocks. The aim is to ensure that the steel flange/web and concrete block are properly relative slip in the push out test. Further, resistant force will occur only at interface areas between concrete dowel and steel rib. Before test these holes were checked again. Fig. 4.6 depicts the form work, the rebar arrangement and the specimen ready for test. 4.2.2. Arrangement for Push-Out series Parameters investigated in the experiment program include the profile of dowel, the embedded rebar in UHPC dowel, the transverse reinforcement in cover layer, as well as the content of steel fiber in concrete. Besides, the headed stud shear connector was also examined in order to compare the conventional and the novel shear connection in UHPC. Table 4.3.: Parameter for Push-Out test program Series

Concrete

Setup

NOS∗

Rebar∗∗

1

G7-150-1.0%

S1

3

2 3 4

-

S2 S2 S2

3 3 3

RO RA RAB

ODW without rebar ODW with rebar in dowel ODW with rebar in dowel and cover

5 6 7

G7-150-1.0% -

S1 S1 S1

3 3 3

RO RA RAB

CDW without rebar CDW with rebar in dowel CDW with rebar in dowel and cover

8 9

G7-150-0.5% G7-150-1.0%

S2 S2

2 2

RB RB

CDW with rebar in cover CDW with rebar in cover

10 11

G7-150-0.5% G7-150-0.5%

S2 S2

1 1

RAB RAB

CDW with rebar in dowel and cover CDW with φ12mm rebar in dowel and φ 8mm in cover

Description Headed stud (φ16mm, Bst500)

∗

Number of specimen Rebar Bst500 and φ8mm dia. were used in all series except for series 11 RO: without rebar, RA: rebar in dowel, RB: rebar in cover, RAB: rebar in dowel and cover ∗∗

The experimental program of Push-Out test was planed in many stages, the specimen groups were divided into eleven difference series, and a total of 27 specimens were undertaken. Table 4.3 shows the details of the UHPC mixer, specimen quantity, rebar configuration, as well as the dowel profile in each test

60


50 50x4=200

350

S355

T=10mm 33

Ø45

25

50

150

75 35 40

series. Fig. 4.7 illustrates the details of dowel profiles with their dimensions and the location of reinforcement in each specimen.

40

65

a)

b)

c)

e)

f)

g)

50x4=200

T=10mm 33

25

50

Ø45 20

65

40

65

d) 50

S355

150

350

75 35 40

65

h)

Figure 4.7.: CDW (above line) and ODW (below line) shear connectors, (a & e)-without rebar, (b & f)-rebar in dowel, (c & g)-rebar in front cover, (d & h)-rebar in dowel and front cover

The group of series 2 to 7 aimed to evaluate the influence of the test setup on the specimen behaviour. Moreover the effect of reinforcing bar inside each group was also observed. In these series all specimens were produced with the same concrete containing 1.0% steel fiber content. In constrast, series 8 and 9 were cast with different UHCPs so as to investigate the effect of concrete ductility on the load-slip behaviour. The last group of series 10 and 11 intend to dertermine the effect of the rebar area on capacity of the shear connectors. 4.2.3. Standard Push-Out test setup As previously mentioned, the test setup was divided into two primary groups named S1 and S2. The setup S1 was designed to simulate steel girder with top flange (I section), while S2 deals with the steel beams without top flange (T section). The test process was carried out on Walter+Bai servo hydraulic control system with a maximum capacity of 4000 kN. The applied load was transfered to steel flange through a very thick steel plate of 100 mm to steel rib and UHPC dowel. Moreover, the loading rate was controlled according to the prescribed load path. Fig. 4.8 demonstrates the specimen in testing system.


61

Figure 4.8.: Push-Out specimen in 4000 kN load frame and controller system

Figure 4.9.: Instrumentation setup in SPOT Setup 1(left) and Setup 2 (right)

During the test progress, the applied force on the top specimen was monitored automatically via load cell of the testing system, and the relative slip between steel plate and concrete block was captured by LVDT 3 and LVDT 4. The opening crack in the concrete surface were measured by two pairs of LVDT 1.1,2 and 2.1,2. All measured data were recorded automatically by the high precision 48channels HBM data-logger system. Fig. 4.2 sketches the location of device on the specimens and Fig. 4.9 shows Push-Out test setups as well as the instrumentation.

62


4.2.4. Loading procedure Load history was set up according to the guideline of EC4 (27), the preliminary estimated ultimate strength (Pu ) was evaluated based on earlier test or experiences. And then it was used to set limit values in the load path. The loading rate was controlled either by force or by displacement, depending on the period of the test. Last [kN]

Attempt at the end of 20 mm overall displacement 10mm in total displacement

ec 0,0075 m m/s

20sec mm/s

by disp.

20s

20s

0,0 02

20s

70 kN (0.1 Pu)

0,0 02

mm/s

ec

350 kN (0.4Pu)

ec

20sec

25 cycles with 20sec to hold the upper and lower load

0,0075 m m/s ec (0,01 mm /sec)

Ultimate load (Pu)

by force

by disp.

Time [min]

Figure 4.10.: Load history for SPOT

A typical load history for SPOT is shown in Fig. 4.10. The load path is divide into three domains. Firstly, the load continuously increased up to 40% of Pu (response still lies in elastic domain) then repeated in two cycles. In the second period, the load is repeated 25 cycles with magnitude between 10% and 40% of Pu . In the last stage, the load increased continuously until the specimen fails. The purpose of repeated load is to eliminate the friction and cohesion forces between concrete and steel surfaces in order to obtain actual results of load-slip behaviour. After that, in the analysis result phase, the residual strain in test is removed.

4.3. Test results and observations 4.3.1. Resistance and slip results Based on the measured load-slip diagrams, the test results for each series were evaluated in term of the ultimate load and the slip characteristic criteria according to the guideline of EC4 (27). A summary of the test results including the

4.3. Test results and observations

63

mean value of maximum applied load, the characteristic resistance PRk , the slip capacity δuk , and the ultimate capacity of individual shear connector (PRk ,1 ) is presented in table 4.4. Table 4.4.: Summary Standard Push-Out Test results Series

Profile

Test Setup

NOSHC∗

1

H. Stud

S1

8

2 3 4

ODW -

S2 S2 S2

4 4 4

5 6 7

CDW -

S1 S1 S1

8 9

CDW -

10 11

CDW -

Rebar

Pavg kN

PRk kN

PRk ,1 kN

δuk mm

1216.74

963.88

120.49

2.24

RO RA RAB

811.29 862.61 1065.53

730.61 776.36 958.98

182.65 194.09 239.74

0.62 1.22 4.64

4 4 4

RO RA RAB

903.11 935.47 1116.30

812.80 841.92 1004.43

203.20 210.48 251.11

1.01 1.33 4.61

S2 S2

4 4

RB RB

771.98 878.35

694.78 790.51

164.1 193.99

0.88 0.98

S2 S2

4 4

RAB RAB

967.99 1005.13

871.19 904.62

217.80 226.15

2.16 3.66

∗:

Number of shear connectors RO: without rebar, RA: rebar in dowel, RB: rebar in cover, RAB: rebar in dowel and cover

As exhibited from the table, the series 4 and 7 give the best results in both term of load bearing capacity and ductility. The ultimate load and characteristic slip of each type of shear connectors are approximate 250kN and 4.6mm, respectively, nearly equivalent in both series. And then, series 1 with headed stud also provides reasonable values, but the slip capacity is still slightly less than the requirements for the ductile shear connector. For other series of 2, 3, 5, 6 and 8, 9 without extra reinforcement in dowel, their bearing capacity is lower than 20% to 30% compare to series 4 or 7. Moreover, it can be easily identified that, the slip capacity of these series are too low, which means that the specimens may fail in brittle mode. The details of the test observations, the illustration of results and a further discussions will be given in follow parts. 4.3.2. Behaviour of headed stud shear connectors in UHPC The load-slip behaviour and the crack opening of the headed stud shear connectors (here after HSSC) are presented in Fig. 4.11 and 4.12, respectively. The mean value of the characteristic stud strength (PRk ) and slip (δuk ) are 120.48 kN and 2.24 mm respectively. As can be seen from the crack opening diagram, the

64


measured maximum values are 0.05mm and 0.015mm corresponding to the compression and tension areas. The strain of concrete at maximum position equals to 0.5 h, it is also very small compared to the ultimate strain of concrete. When the stud is almost completely shanked then the strain path turns back to its initial state. By checking on the surface of concrete block after test, no crack can be observed. It can be conducted that, in the case of HSSC in UHPC the deformation on concrete surface is insignificant. 200

Specimen 1 Specimen 2 Specimen 3

1200

150

800

100

400

50

8 studs 16mm dia.

0

0

2

4 6 Relative slip (mm)

8

10

0

Figure 4.11.: Load-slip diagram of headed studs shear connectors in UHPC

−0.6 1600

−0.5

Strain on concrete surface (%o) −0.4 −0.3 −0.2 −0.1 0 0.1

0.3

Spec1. LVDT 1.1 Spec1. LVDT2 .2 Spec2. LVDT 1.1 Spec2. LVDT 2.1

1200 Applied load (kN)

0.2

800

400

LVDT1.1

LVDT2.1

0 −0.06

−0.045

−0.03 −0.015 0 Crack Openning (mm)

Figure 4.12.: Crack opening in concrete surfaces

0.015

0.03

Average shear force on a stud (kN)

Applied load (kN)

1600


a) begin loading

b) stud increases distortion

c) sliding

d) formed plastic zone and then shanked

65

Stud shanked at base

Figure 4.13.: Failure process and shanked of HSSH at footing

Fig. 4.13 demonstrates a cut away of the specimen after test. It can be seen that, the main failure caused by shearing of the stud at the base. This could be explained as follow: under horizontal load the stud deformed at the base area (a), however, the distortion in the whole body of stud seems very small, which can be neglected. This is because the concrete surrounding stud is too strong, which restricts the deformation of the stud. On other hand, the concrete bock and steel part have relative movement at contact surface, which generates shear force at the foot of stud. When the load increases, the stud continue sliding in horizontal direction (c). Then a plastic zone is formed (d). Ultimately, the stud is shanked at the base and the concrete slab entirely separated from steel girder. This failure mode is same for all specimens when the maximum slip reaches approximate 7.0 mm. If the numerous studs are added, in general, the plastic deformation is not enough to activate bearing capacity of all studs. Consequently, the increasing diameter of studs may more efficient than increase quantity. The addition transverse reinforcement in the concrete block is also not very efficient due to its contribution to improvement ductility of studs are very limited. 4.3.3. General behaviour of perfobond shear connector in UHPC In the case of perfobond shear connection (series 2 to 11), the UHPC dowel plays the main role for carring the shear force which is transferred from steel rib. At the contact surfaces between UHCP and steel strip, the major stress state is in tension and shear as shown in Fig. 4.14. Beside that, the deformation of steel

66


strip also generate a punching force into cover layer, which cause tensile strain in the front surface. The magnitude of punching force depends on the dowel profile.

Figure 4.14.: Basic mechanics of perfobond shear connector (left), stress state in concrete dowel, after Kraus and Wurzer (57)(right)

O'

O

Slip

Skew O'

O

Figure 4.15.: Deformation of the steel ribs after test

Applied load (kN)

1000

dia. 8mm, 1.0% fiber

800

300

Series 5 Series 6 Series 7 Series 9 Series 10 Series 11

250 200


600

150


400

100

200

50

0

0

2


8

Figure 4.16.: Overview behaviour of perfobond shear contectors

10

0

Average shear force on a dowel (kN)

1200


67

As can be observed from the test and results, the main reason resulting in the collapse of the specimen is failure of the concrete at the dowel and cracks formed in the concrete slab along the steel rib. At the surrounding hole area of steel rib, the distortion is relative small for CDW specimens (series 5 to 7), but it is considerable large for ODW (series 2 to 4). As shown in Fig. 4.15 the deformation of specimens with ODW alway larger than CDW. This may be due to the fact that, the acting force from steel rib into concrete cover is also greater. The density of crack on concrete appears of ODW specimens is more dense than CDW specimens. Fig. 4.16 shows the load-slip behaviour of test series 5 to 11, which have the same dowel profile. In general, it can be seen that, the ultimate strength and the response after peak value depend on the amount and the arrangement of reinforcements. In the series 4 and 7, the combination of reinforcement and high steel fiber content affects the re-distribution of the internal force inside the concrete block. Especially, when cracks grow enough large the steel fiber are activated and formed the bridges to transfer internal force between areas. This allows the specimen to maintain resistance capacity and the collapse progress occurs more slowly. The primary factors that influence the performance of perfobond shear connector are summarized as follows: strength of concrete, steel and reinforcement total amount of additional reinforcing bar and its configuration steel fibers content in concrete mixture profile of dowel and thickness of steel plate experiment setup

4.3.4. Influence of dowel profile and test setup The influence of the dowel profile and test setup can be obtained through comparison of test results of series 2 to 4 and 5 to 7. The load slip behaviour curves are demonstrated in Fig. 4.17, as exhibited the shape of correlative curves is very similar. It can be noticed that, with the same materials and reinforcement arrangement, the influence of test setup on specimen behaviour is not remarkable.

68


1200


Applied load (kN)

1000 800 600 400 200 0

0

2


8

10

Figure 4.17.: Load-Slip behaviour of CDW and ODW (1 % steel fiber)

When no reinforcement was add into the dowel or front cover, the CDW specimens give a little higher results in both term of bearing capacity and ductility. However the behaviour of these series are still classified into poor ductility group. When rebars are added, the performance is improved significantly, the pair of curves are nearly the same. As can be observed, the specimens with ODW has more cracks than CDW. It is very difficult to distinguish the effect of dowel profile. 4.3.5. Influence of fiber content to load slip-behaviour The influence of fiber content was considered by comparing the results between series 8 (0.5% fiber content) and 9 (1.0% fiber content). In fact, both series have the same rebar arrangement, test setup and shape of dowel. The load-slip and crack opening curves are plotted in Fig. 4.18 and 4.19, respectively. The ultimate strength of the specimens are identified at 771.98 kN and 878.35 kN corresponding to 0.5% and 1.0% steel fiber content in UHPC. The resistance capacity increases about 15.0%, while the chacteristic slip increased approximate 5.0%. The crack patten exhibited in Fig. 4.20 indicated that, the specimens with less fiber content (series 8) show larger amount of crack and their distribition has also higher density. The measured crack width varies from 0.1mm to 0.5mm and large cracks appear more frequently than in the specimens of series 8.


69

1200

Series 8 Series 9

Applied load (kN)

1000 800 600 1.0% steel fiber

400 0.5% steel fiber

200 0

0

2


8

10

Figure 4.18.: Influence of fiber content on load-slip behaviour series 8: 0.5% and series 9: 1% vol. steel fiber

1200

−6

−4

−2

Strain (%o ) 0

4

6

S8, Spec2:LVDT 1.1 S8, Spec2:LVDT 2.1 S9, Spec2:LVDT 1.1 S9, Spec2:LVDT 2.1


2

800 600 400 200 0 −0.6

−0.4

−0.2 0 0.2 Crack openning (mm)

0.4

0.6

Figure 4.19.: Crack opening curves of series 8 and 9

The increase of additional fiber content in concrete mixture leads to higher tensile strength of concrete and fracture energy. When the specimen is subjected to load, the primary stress state in dowel areas is in tension-shear, thus the steel fiber is activated. The long steel fiber makes the bridges between crack areas, while short steel fiber enhances the toughness of concrete. Therefore the internal force in damage regions is re-distributed. The material in neighbor critical areas is also attended to carry load. Consequently, the ultimate capacity of specimen is improved and the cracks reduces.

70


Figure 4.20.: Crack pattern of SPOT with UHPC 0.5% (left) and 1% (right) steel fiber

Figure 4.21.: Crack on the concrete surface, without reinforcement in cover (left) and with reinforcement(right)

However, as shown on the load-slip curves, the specimen with 1.0% steel fiber and without reinforcing bar in concrete dowel still exhibit very poor ductility. If more steel fiber are added, the behaviour might be better. However, if the fiber content exceeds 2.0% then workabiliy becomes a problem. The concrete is more difficult flow through holes to form dowels that affect the quality of the shear connecters. Further more, in the economic aspect, with more steel fibers the total material cost grow up very fast, but the performance improvement is not as expected. It can be noticed that, steel fiber is not the key factor to determine the load-slip behaviour of Push-Out specimen. To achieve better performance, the reinforcing must be used.


71

4.3.6. Influence of transverse reinforcement arrangement The effect of transverse reinforcement arrangement can be assessed through results of series 5, 6 and 9, whose load-slip diagrams are shown in Fig. 4.22. The curves A, B and C represent for specimens with and without added reinforcing bar, respectively. 1200

Series 5 Series 6 Series 9

Applied load (kN)

1000

C

800 B

600

II

A

400

I

200 0

0

2


8

10

Figure 4.22.: Effect of transverse reinforcement arrangement on load-slip behaviour

Comparison between case A and B, the ultimate load of case B is slightly higher than case A, with 862.16 kN and 827.09 kN, respectively. And the relative slip is the seem straight offset from 0.82mm to 1.35mm. The characteristic shapes of both load-slip curves are very similar. This indicate that, the reinforcement arranged in front surface play a minor role in improving the load bearing capacity and ductility of specimen. The transverse reinforcement in front surface helps to reduce crack opening only. On other hand, a comparison between case A and C, in which the reinforcement located thought holes (φ8 mm) indicate that, the performance of specimen is improved significantly. The increment of the ultimate load and ductility are 18% and 120% respectively. After the peak, the specimen maintain high load bearing capacity continuously. The dowel are not completely shanked until loading progress stop. The specimens without transverse reinforcement in front surface (series 5 and 6) shows very large cracks in the surface. Especially, in series 5 (curve A) the crack split the concrete into two parts separately. For remaining series, the cracks on

72


surface are relative small due to the present of transverse reinforcements (Fig. 4.21). 4.3.7. Influence of embedding reinforcement through concrete dowel 1200 UHPC: 0.5% vol. fiber content

Series 10 Series 11


Rebar ø12mm in dowel

800 600

Rebar ø8mm in dowel

400 200 0

0

2


8

10

Figure 4.23.: Influence of reinforcement thought dowel

To investigate the influence of reinforcement in UHPC dowel, series 10 and 11 were compared. These series have a reinforcement and concrete area (As /Ac ) ratio of 3.15% and 7.11% respectively. The load-slip diagrams are described in Fig. 4.23. It can be indentified that, the ultimate strenght was enhanced from 959.96 kN to 1005.13 kN (ca. 4.7 %) that is under expected compare to increase amount of reinforcement. In the desending branch of load-slip curves, load capacity of the specimens is maintainted in long period. The characteristic slip increases impressively from 2.5 mm to 3.66mm (approximate 46.4%). It can pointed out that, the ration way to improve slip capacity perfobond shear connector is addition of rebar into concrete dowel. Rather than increasing fiber content of concrete. The most disadvantage of this method is the preventing concrete flow thought out hole on steel rib. The diameter of the rebar should be optimized according to the grain size of the aggregate and the length of steel fiber.

4.4. Summary conclusions for Push-Out test

73

4.4. Summary conclusions for Push-Out test Experimental studies for various kinds of shear connections with SPOT according to EC4 (27) were carried out with eleven series, which include HSSH, PFSH with open and closed profile specimens. The conclusions from this study can be drawn as follows: Conventional headed stud shear connector in UHPC slab gives poor ductility. The stud fails in a shearing mode at base due to the restraint of very high strength concrete surround it. It is not recommended for using with UHPC. The perfobond shear connector exhibits good performance and suitable for use in UHPC composite beams in terms of load carrying and practical fabrication. Both of investigated dowel profiles give equivalent ultimate load and slip capacity. The influence of test setup is insignificant to the performance of specimens. The deformation around hole in steel rib is relative small. The open dowel shows bigger distortion than closed dowel. Strain of critical area may reach yield limit, but this needed to be confirm by FEM simulation. The capacity of shear connector depends on the compressive and tensile strength of UHPC rather than the yielding of steel rib. Perfobond shear connector in UHPC without transverse reinforcement in dowel provide very low ductility. After reached ultimate load, the capacity decreases very quick due to the collapse of dowel. And the shear connector fail in brittle mode. Transverse reinforcement in front surface contributes to prevent crack opening, whose amount should be designed according this condition. The addition of reinforcement in dowel is stronglt recommended. The embedded rebar though concrete dowel increases the ductility rather than the ultimate load. But the improvements are not enough. However, it play a major factors to enhanced the slip capacity. The increase of loadslip capacity is not proportional with additional reinforcement ratio. The diameter of embedded reinforcement must be limited, depending on the grain size of aggregate and the length of fiber. A combining of transverse reinforcement in front and embedding in dowel together, lead to significantly improvement of the performance of the connector. Especially, an optimization of fiber content, diameter of the reinforcement will give better results. Minimum content fiber should be not

74


less than 0.5% volume fraction. The appropriated fiber content about 1.0% is optimized in term of technical requirement and economic aspect. Due to lack of condition to performing test for large amount investigation, the FE modeling is necessary for further study. It should focus on influence of steel plate thickness, geometry of dowel, and effect of material strength to final behaviour.

The test data from experimental program is not enough to investigate influence of other factors such as distant between the dowels as well as their profile areas. Combining experimental study and simulation is necessary in order to better understand the local behaviour and obtain explicit formula to predict performance of shear connector.

5. Experimental investigation on the structural behaviour of steel-UHPC composite beams 5.1. Introduction In this chapter will be introduce detail of experimental study of composite beams which were carried out at University of Leipzig (Uni-Leipzig). The composite beam was made of ultra high performance concrete and high strength structural steel. Several test series were conducted to obtained overview behaviour as well as to ensure the feasibility of this new structure. The relevant such as structural behaviour of composite beams and failure mode, load bearing capacity in ultimate and serviceability limit states, load-slip response of shear connection will be mentioned .

5.2. Experimental program for composite beams 5.2.1. Aim and Objectives The experimental study aimed to evaluate the structural response of the SteelUHPC composite beams under static load. Through large scale test some aspects below could be understood: global structural behaviour of the composite beam under static load mode of failure and response on each material part (development of stressstrain) relation between applied load, bending moment and relative slip key parameters governing to global behaviour of beam local strain development in steel rib verify performance of UHPC perfobond shear connectors

The test data is also to be used on validation the numerical model.

76

5. Experimental investigation on the structural behaviour of steel-UHPC composite beams

5.2.2. Design and construction of test specimens The composite beams for testing were designed according to EC4 (27) (section 6), in fact simple plastic method was used. The connection between steel and UHPC slab was assumed as full shear connection. In the design calculation, all material and load factors were set to unity. The beams were divided into two series: series one includes 04 beams (B1 to B4), remaining series has 02 beams (B5 and B6). The steel girder I and T sections were used and UHPC was used for concrete slab. Table 5.1 gives a short description of each beams in the test series. In the case of I steel girders, shear connectors were welded to the top flange by continuous steel strip. Otherwise, for the T girder, shear connectors were formed as an extension of the web and cut directly. The spacing between two holes are 100 mm or 150 mm depending on the specific purpose of the test, and the hole is 45 mm diameter for all beams. Table 5.1.: Description of composite beams Series

Beam ID

Series 1 Series 2 -

B1 B2 B3 B4 B5 B6

Shear Connector and spacing Open dowel, 59 x 100 mm Closed dowel, 59 x 100 mm Closed dowel, 39 x 150 mm Open dowel, 39 x 150 mm Closed dowel, 79 x 100 mm Open dowel, 79 x 100 mm

Steel girder section and concrete slab I shape, 500 x 100 mm I shape, 500 x 100 mm inversed T, 500 x 100 mm inversed T, 500 x 100 mm inversed T, 400 x 100 mm inversed T, 400 x 100 mm

Table 5.2.: Transverse reinforcement arrangement in concrete slab Series

Beam ID

Reinforcement in font layer

Reinforcement embedding in dowel

Series 1 -

B1 B2 B3 B4

φ φ φ φ

8 8 8 8

Series 2 -

B5 B6

φ 8 mm @ 80 mm φ 8 mm @ 100 mm

8 8 8 8

mm mm mm mm

@ @ @ @

100 100 100 100

mm mm mm mm

mm mm mm mm

@ @ @ @

200 200 150 150

mm mm mm mm

(twice dowel) (twice dowel) (each dowel) (each dowel)

no reinforcement 8 mm @ 100 mm (each dowel)

Transverse reinforcing rebar with diameter of 8 mm were placed in two layers at top and bottom of the UHPC slab. The top layer had a spacing of 80 mm/100 mm and the bottom layer had spacing of 100 mm/150 mm respective to that of shear connectors. The longitudinal reinforcement was arranged with four φ10 mm rebar placed in both sides of the shear connectors. Table 5.2 summarizes the arrangement of the transverse reinforcement in each beam.

5.2. Experimental program for composite beams

77

Figure 5.1.: Sketch layout of Beam B1 and B2 A. S

Steel plate S355 6000mm x 355mm x 12mm, 39 holes dia. 45mm Beam 4, length 6m

Beam 3, length 6m 150

aw=8mm

3000 UHPC slab 500

500

100

60 30

30mm 320

150

Thick. 12mm

45

45

30mm

30mm

Cross section beam 3

410

12mm

385

ø8@100mm 12mm

60 60

60

4ø10mm

150

200

Cross section beam 4

Detail of dowel profiles, open dowel (left), close dowel (right)

Figure 5.2.: Sketch layout of Beam B3 and B4

S355 structural steel and Bst500 grade reinforcement were utilized to produce all composite beams, whose material properties are identical with steel of Push-Out test. Additionly, the B4Q-UHPC mixture was used to made 04 beams of series 1. And all beams of Series 2 was cast with G7-UHPC mixture. All UHPC mixtures contain coarse aggregate (2-5 mm and 5-8 mm) and steel fiber of 0.5% (G7) and 1.0% (B4Q). The primary mechanical properties of both concrete are listed in table 4.2. Further details of material compositions were given in 3.2.4, table 3.2.


78

The number of shear connector was determined based on the Push-Out tests data. Unfortunately, it is not always available due to some out of controlled reasons. Thus, in the cases of beams of series 2, the result of Push-Out test came too late. Therefore, its is not insufficient information for making right decision during design progress. The beam B5 was designed without reinforcement in dowel, which lead to less longitudinal shear resistance. However, hence several wrongs good lessons were obtained. Fig. 5.1 depicts the design layout of the composite beams B1 and B2. Both beams were 6.0m in length and 410 mm in height. Moreover the pairs of the beam are the same of cross section with I steel girder of 300×310×10×14 mm and concrete slab of 500×100 mm. The difference between two beams is only in profile of shear connector, beam B1 and B2 were designed with ODW and CDW, respectively. These beams aimed to reach full plastic moment in steel girder. More full shear connection degrees are also considered to verify load transfer capacity of dowel. A. S

Steel plate S355 8000mm x 345mm x 14mm, 79 holes dia. 45mm Beam 6

Beam 5

150

aw=8mmaw=8mm

4000 400

400

UHPC slab 100

100

100

60 30

ø8@100mm

14mm

ø8@100mm

14mm

400

Beam 5 without embedding reinforcement in close dowel

14mm

400

Beam 6 with added einforcement in open dowel

45mm

390

4ø10mm

410

60 45 45

400

Girder section

Detail of dowel profiles, open dowel (left), close dowel (right)

Figure 5.3.: Design layout of Beam B5 and B6

The sketch of beam B3 and B4 are described in Fig. 5.2, they have the same length and concrete slab section with previous beams B1 and B2. The spacing between shear connector was 150 mm which is greater than that of beam B1 and B2 (less shear connection degree). Both beams B3 and B4 were designed with T girder and are only different on bottom flange. The flange of beam B3 was 320 mm in width that expected to fail in concrete slab or shear connection. While the flange width of beam B4 was 200 mm which is expected to be fail by yielding of steel girder and crushing of concrete in compression zone. The second series include beam B5 and B6 depicted in Fig. 5.3. They were designed and built in the second stage of experimental program. The test of

5.2. Experimental program for composite beams

79

series 2 had two purposes: to evaluate potential of reducing fiber contents in UHPC and stress in concrete slab only in compression. The strain distribution over height of slab would be nearly constant. Due to the lack Push-Out test data, beam B5 was made to contain no reinforcement in concrete dowel. The reinforcement was arranged only in top cover layer of concrete slab with spacing of 80 mm. The influence of transverse reinforcement in cover layer on lateral shear resistance is also analyzed for beam B5. To build composite beams, the steel girders were fabricated in factory and transported to laboratory while the rebar and concrete work were performed in laboratory. Numerous cylinders and cubic were cast to test the mechanical properties of concrete, which were cured beside composite beams. 5.2.3. Test set-up and instrumentation Large scale experiments were arranged according to four points bending test scheme. The hinge support was installed at the North end and the South end was placed on roller support. Fig. 5.4 and 5.5 sketch the general layout of test setup of Series 1 and 2, respectively. The test was generally displacement controlled while the speed varied during testing. Each specimen was cycled in a similar fashion as the Push-Out test specimens described earlier (Fig. 4.10), i.e. at least twenty seven (27) times between 10% and a proof load of about 40% of the expected ultimate bending strength. After the last cycle completed, the load was applied continuously until the beam failure occurred or until the load dropped to a significant amount below its maximum value. There are four basic types of instrumentations utilized in the tests. Strain gages was used to capture the strain on the steel girders, the shear connectors and the concrete slab. Whereas, linear string potentiometers were used to measure deflection along span. The relative slip, strain of concrete, rotation angle at support and opening crack on the concrete surface were measured by linear variable displacement transducers (LVDT). Load cell was used to measure live loads applied to the beams. When test in progress, all measured data were recorded automatically by the 48-channels HBM measuring system. Details of instrumentation are described in Fig. 5.4 and 5.5. The loading equipment system and typical installed transducers are shown in Fig. 5.6.


80

LVDT-linear variable displacement transducer LVDT

SG-strain gages PT-Potentiometer Load cell

NORTH LVDT-1

SOUTH

LVDT-11

LVDT-2 LVDT-3

LVDT-4

475

LVDT-5

LVDT-6

LVDT-9

LVDT-8 LVDT-10

LVDT-7

LVDT-15

1100

LVDT-12 150

PT-1

1425

PT-3

PT-2

1050

750

500

150

1975

6000 85 65

35

85 65

85 65

LVDT-11 440

100

SG-8 SG-11

120

Weg-15

SG-9

20

Weg-14

Weg-13

Strain gages location to measure strain on the steel rib

520

1605

LVDT-10

SG-7

SG-10 SG-12

875

LVDT location to measure crack opening on the concrete surface

LVDT-9

SG-13 100

1050

120

1050

20

460

SG-14 SG-17

SG-15 SG-16 SG-18

Strain gages location on the cross section 1-1 (left) and 2-2 (right)

installation of strain gages and LVDT to measure strain of concrete in concrete slab at midle section

LVDT

LVDT

Figure 5.4.: Instrumentation for flexural test of composite beams Series 1

Load cell

LVDT-11

LVDT-1 LVDT-4

50

LVDT-13 150

625

LVDT-12

1275

PT-3

1900

LVDT-9

LVDT-7 LVDT-8

LVDT-6 1200

Load cell

100

750

PT-2

1200

2600

750

LVDT-10 PT-1

LVDT-5

LVDT-3

1275

750 750

3100

1250

3850 8000

100

100

LVDT-9

LVDT-11 SG-6

SG-12

SG-5

SG-11

SG-3 SG-4

30

30

SG-7 SG-8

100

SG-2

LVDT-12 100

SG-1

100

100

LVDT-10

SG-9 SG-10

Strain gage location on section 1-1 (left) and section 2-2 (right)

Figure 5.5.: Instrumentation for flexural test of composite beams Series 2

LVDT-2

625

150

5.3. Analysis of the test results and observations

81

Installation strain gages (left) to measure strain at midle section of steel girder and LVDT to measure horizontal and up slip between steel and concrete. (Series 1)

Test layout of series 1, three points bending test

measuring slip and the end of beam

Test layout of series 2, four points bending test

measuring flexural by 3 potentionalmeters

LVDT and long strain gages for measure strain of concrete

Figure 5.6.: Equipment for flexural test of composite beams Series 1-2

5.3. Analysis of the test results and observations 5.3.1. General The main results including the ultimate load, plastic moment and mode of failure are summarized in table 5.3. Total additional load including self weight of composite beams, auxiliary cylinders and steel girder were added to applied load. However, when the beam was lifted into testing placement, the effect of self weight on flexural, shear slip and initial strain could not captured. Their effects were ignored in the analysis results.


82

At the initial state, friction and cohesion forces on the contact surfaces between steel and concrete were generated. Through cycle loading these forces were eliminated, but this may generate residual strain in the final data. In the analysis results step, the residual strain was removed by offset strain technique. Then the real behaviour will be obtained, as shown in Fig. 5.7. Table 5.3.: Summary of test result of the composite beams Beam

Test Ult. load

∗:

∗

Calculation

Mode of failure

Plas. Moment

Plas. Moment

PU ,test (kN)

MRd,pl,test (kNm)

∗∗ M Rd,pl,cal

B1

724.11

911.68

976.81

B2 B3 B4

764.94 959.70 996.28

939.73 1178.99 1224.52

976.81 1658.68 1122.69

B5 B6

616.40 1285.28

955.42 1992.18

2159.37 2159.37 -

(kNm) Yielding of steel girder and crushing of concrete same as above Collapsed of shear connector Yielding of steel girder crushing of concrete Collapsed of shear connector Yielding of steel girder and crushing of concrete

total subjected load to the beam without self weight plastic moment was calculated according EC4(2004) (27)

∗∗ :

Applied load (kN)

1000

1000 load-disp. in cycling load stage

750

750

500

500 Approximated line

250

250 residual strain

0

offset strain

0

50

100 Deflection (mm)

150

200

0

0

50

100 Deflection (mm)

Figure 5.7.: Force-deflection curve before and after remove residual strain

150

200


83

5.3.2. Structural behaviour and Observations of beam B1 and B2 Load deflection behaviour The concrete slab of the beam B1 and B2 were built with the same concrete (B4Q 1% steel fiber). However, the tests of beam B1 and B2 were carried out at 14 and 21 days of concrete ages, the average compressive strength at the same time with test were 142.5 MPa and 154.8 MPa, respectively. The concrete strength and ultimate strain in beam B2 are slightly higher than that in beam B1. 1000

Beam B1 Beam B2

Applied load (kN)

800

Plasticity and crushed domain

Ultimate load

B

C

C

Yield domain

600

A

Elastic limit, 533.76 kN

400

Rebar Φ8mm in dowel

Elastic domain

200

0

0

50


P/2

100 Deflection (mm)

P/2

150

Figure 5.8.: Load-deflection behaviour of composite beam B1 and B2

Figure 5.9.: Plastic of steel girder and crushed of concrete slab

200

84


The load versus deflection (at midspan section) curves are shown in Fig. 5.8 for both beams B1 and B2. As exhibited, the general behaviour of the composite beam could be divided into three domains: elasticity, yielding and plasticity. Within the elastic region, the load-deflection relation shows linear under loading and discharge. At the elastic limit point (A), the applied load on beam B1 and B2 reached the same of 560 kN that is approximate 73 % of ultimate load, while deflections reach 35mm that equals 1/200 clear span. It can be seen that, the beam B1 and B2 show good performance in serviceability limit state. After elastic limit, the behaviour show yielding and response curve is flattened at point B and reached ultimate strength at 724.11 kN and 764.94 kN corresponding to beam B1 and B2. When applied force increased continuously, the neutral axis moved to upper part of the cross section, a below part of concrete section began to subject to tension and the height of the compressive zone reduced (Fig. 5.9). The test of beam B1 was stopped at a deflection of 132 mm and beam B2 was extended up to 200 mm. The beams collapsed completely when the concrete slab crushed and splited completely. The main failure of the beams is caused by the plastic deformation of steel girder and crushing of concrete slab. The kind of failure mode is recognized as ductility. As show in Fig. 5.8, the initial stiffness and ascending branch of Beam B1 and B2 almost overlap up to the ultimate load. It was noticed that, in this case the effect of concrete age on ultimate strength of beam is unremarkable. A comparison of the post peak branch of beam B1 and B2, indicate that, the concrete age plays an important role in controlling the increase of the strain rate in order to extend ductility of the structure. It can be observed after test that, there are no lateral cracks on the concrete slab which can be identified outside the area between loading points. The failure occurred at the middle span region only. In a similar manner, transverse cracks on the front surface of concrete did not appear in both beams. The end slip of beam B1 is very small which can be neglected. While the end slip of beam B2 is slightly higher. But it is still insufficient to cause damage on the shear connectors, the failure of shear connection was not taken place. Furthermore, the local buckling did not happen on the top flange or the web, thus failure buckling mode was excluded.


85

Moment - curvature relationship

Figure 5.10.: Moment curvature relationship of beam B1 and B2

The moment-curvature relationship was determined by the rotation angle of critical section at middle span, which curvature κ = (εtop + εbot ) /H , where εtop , εbot are strain of top and bottom fiber of section, respectively; H is total height of the composite cross section. The moment - curvature curves of beam B1 and B2 are plotted in Fig. 5.10. The diagrams show that, at low load level the force-deflection relationships are linearity until the first yield moment is reached, (M/Mu ratio approximate of 0.7). After achieving the maximum moment, the branch curve stretches continuously, and seems to be flattened. This indicate that the cross section rotates and forms plastic hinge. Development of strain in steel and concrete Fig. 5.11 presents the strain development of both beams B1 and B2, while the distribution of strain over the height of cross section is plotted in Fig. 5.12. It should be noticed that, the measured strain of concrete slab at midspan section encounters unexpected problem. Once of displacement transducer(LVDT-9) was broken and dropped during the test. Therefore the strain curve that measured at bottom concrete slab is not shown in Fig. 5.11 (left). Similarly, in Fig. 5.12, only test data at low load level was captured.


86

Applied load (kN)

1000

1000 B1-LVDT9-bot. conc. slab B1-LVDT10-top conc. slab B2-LVDT10-top conc. slab

800

Yielding domain

600 Strain in concrete slab

400

B2-LVDT10 B1-LVDT10

-6

-4

Ultimate load (Pu)

600

Elastic limit = 533.76 kN

Strain in steel girder

400 Elastic domain

B1-LVDT9

200 0

800

B1-SG10- top fl. steel beam B1-SG11- bot. fl. steel beam B2-SG10- top fl. steel beam B2-SG11- bot. fl. steel beam

-2 0 Strain (‰)

200

2

4

0

B2-SG11 B1-SG11

-2

0

2

4 6 Strain (‰)

B2-SG10 B1-SG10

8

10

Figure 5.11.: Strain development in concrete slab (left) and steel girder(right) of composite beam B1 and B2

Through a comparison of the strain at the same measured position in bottom flange, web and concrete slab, it can be seen that the shape of curves are nearly the same. The strain at bottom flange of beam B1 is slightly greater than that of beam B2, the strain in bottom flange of beam B1 achieves yield point of 2.6hcompared to 1.9 hof beam B2. The actual load at the first yield point reached 533.76 kN for both beams (approximate 0.7PU ). While bottom flange begin to yields, the strain in other part of steel girder such as web, top flange, concrete slab are still in elastic domain. In this stage, the neutral axis lies within the web as shown in Fig. 5.12, in which the strain state in upper flange and concrete slab are compressive. ultimate strain

Beam B1

ultimate strain

Beam B2

Height of cross section

400 350 300 250 200 150 0.45Pu 0.71Pu 0.90Pu 0.99Pu

100 50 0

-5

0

yield strain

5 10 Strain (‰)

15

0.44Pu 0.70Pu 0.90Pu 0.99Pu 20

-5

0

yield strain

5 10 Strain (‰)

15

20

Figure 5.12.: Strain development in cross section of composite beam B1 and B2

With the increase of the applied load, the neutral axis went to upward direction and reached new position at bottom concrete slab, corresponding to the applied load at 622.68 kN (ca. 0.84PU ). The strain in the bottom flange and a part of web were fully plastic. However, the compressive train in top fiber concrete of


87

slab was still of 2.0hwhilst the strain in bottom changed to neutral state before subjected to tension. With the neutral axis continuing go up, parts of the bottom slab were in tension. The height of compression zone reduce onto about 2/3 of slab thickness. As a result, the compressive tress and strain in the remain part of concrete slab increased very fast. The composite beam achieved its ultimate strength when the compression and tension fiber of concrete slab reached strain of 3.2hand 1.8h, respectively. The plastic hinge fully formed. The beams collapsed when concrete crushed due to strain exceed its critical values. Relative slip between concrete and steel The relative slip between the steel girder and concrete slab include longitudinal and up slip as well.Through analyzing measured data, it can seen that, the magnitude of the slip in vertical direction has very small value (ca. < 0.14 mm). The effect of up-slip is not necessary to be considered and can be ignored in the evaluation of the global behaviour. The longitudinal slip at various load level is shown in Fig. 5.13, whereas the slip for the beam B1 and B2 were displayed. According to test setup as mentioned, a pair of concentrate loaded were located at relative coordinate (±0.1) in Fig. 5.13.

Logitudinal slip (mm)

1.00 0.75 0.50

B1−0.45Pu B1−0.71Pu B1−0.90Pu B1−0.99Pu B2−0.45Pu B2−0.71Pu B2−0.90Pu B2−0.99Pu

+ - LVDT

Beam B1

Beam B2

0.25 0.00 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 Relative distance from midspan of the beam

0.4

0.5

Figure 5.13.: Longitudinal slip of beam B1 (left) and B2 (right)

As displayed in the Fig. 5.13, the longitudinal slip increases along with imposed load, but their relation is not linearity. When loading within the elastic regime( < 0.7PU ) the slip reached about 0.1 mm to 0.2 mm in both beams. The distribution of the longitudinal slip from the midspan section outward to the ends are nearly identical. This means that, the lateral shear force which transfers load from concrete slab to steel girder is uniform distributed. Based on the load-slip response in yielding and plastic domains, the slip grew up very fast and the values achieve in range of 0.15 mm to 0.3 mm. Which are

88


nearly two times of that slip developed before. Especially, the slip of beam B2 is significantly greater compared to that of beam B1. This can be explained by the older concrete age, it allows the slip continuous develop until the crushing of concrete. Along with the change in magnitude, the slip distribution also changed clearly with high magnitude around the concentrate load area and reduced to both end sides. As a result, it can be seen that, in the full shear connection, the distribution of horizontal shear force is not uniform. The shear flow depend on the increasing of the bending moment along beam. Deformation of perforated steel strip The deformation of the perforated strip in shear connectors was measured by embedding rosettes strain gages which were attached on steel rib near hole of dowel. The horizontal strain components are shown in Fig. 5.14. As exhibited, all strains in investigated locations reach maximum values of 0.7h, which is relative small compared to the yield strain of structural steel S355. Furthermore, distortions of the holes on steel rib before and after test are little difference. Consequently, the influence of the deformations of steel strip on the load carrying of shear connectors are not remarkable. The failure of shear connector should focus into concrete dowel together with related constituent components. 1000

Applied load (kN)

B1−SG1 B1−SG3 B2−SG1 800 B2−SG4

600

400

200 B1-SG1 B1-SG3 B2-SG1

0 −1.00

−0.80

B2-SG4

−0.60 −0.40 Strain (‰)

−0.20

0.00

Figure 5.14.: Lateral strain surround hole of perforated strip

In the case of other beams in which T cross section girder was used, the perforated strip was stretched from the web of steel girder. Therefore, its thickness is always greater than steel rib in the beam B1 and B2, the strain and distortion are smaller


89

too. Hence, when considering these beams, the influence of deformation of steel rib on the performance of shear connectors can also be ignored. 5.3.3. Structural behaviour and Observation of beam B3 and B4 Load - deflection behaviour Another two beams in Series 1 include B3 and B4, as early described. The bottom flange of beam B3 is 320 mm width and 30 mm thickness. While bottom flange of beam B4 was cut into 200 mm and thickness is the same beam B3. Both beams were tested at concrete ages over 28 days and the of the averaged compressive strength fck was evaluated at 155.0 MPa. Fig. 5.15 shows the diagrams of loaddeflection in middle span of the beams. 1000

C

C

Beam B3 Beam B4

Concrete crushed

Yield domain

Applied load (kN)

800

A

Elastic limit, 800.0 kN

600


400


Elastic domain P/2

200

0

0

50

100 Deflection (mm)

P/2

150

200

Figure 5.15.: Load-deflection behaviour of composite beam B3 and B4

As observed during the test, beam B3 failed when load increased. The broken progress occurred suddenly and without any prior warning phenomena. The main cause of failure was due to the collapse of the shear connectors which happened on the side of the roller support (Fig. 5.16). In middle span area (space between two concentrate points), there are no cracks before beam was collapsed. The cracks appear due to applied load after steel girder and concrete separated completely. The ultimate strength of beam is 996.28 kN and corresponding deflection is 35 mm. It can be seen that, the beam B3 behaves generally in elastic regime though out in the whole response. The measured strains in concrete slab and girder show all values are under yield limit. The failure can be classified as a brittle mode.

90


Although the shear connection degree of this beam was designed to be lower than 100%, but the failure progess of shear connectors is not expected. The discussion on the collapse of the shear connector will be mentioned late (section 5.3.3).

Middle span area, there are no cracks before beam collapsed. The cracks as appear due to alpplied load subjected slab after steel girder and concrete separated.

Failure of shear connector in right side of the beam.

Figure 5.16.: Failure of beam B3 due to collapse of shear connector in right side

For beam B4, by reducing the width of bottom flange into 200 mm (30 mm thickness), the shear connection degree increased greater than 130%. The loaddeflection shown in Fig. 5.15 indicate the general behaviour of the beam was not only limited in the elastic region but also also extended to yielding and plastic domain. The ultimate strength and corresponding deflection reach 996.28 kN and 95 mm, respectively. The fall down of the shear connectors did not occurr. When the beam is nearly collapsed, many vertical cracks appear in the middle span area. They are symbols of concrete to be crushed. In general, the beam failed in a ductile mode, which is caused by yielding apart of steel girder and crushing of concrete slab. Table 5.4.: Comparison of ultimate strength, deflection and stiffness of beams B2 with B3 and B4

Ultimate strength (kN) Deflection at peak load (mm) Force at first yield (kN) Deflection at first yield (kN)

B2

B3

Diff.

B4

Diff.

764.94 112.18 580.00 33.50

959.70 32.77 32.77

+25.46% -70.79% -

996.28 92.10 797.10 36.78

+30.31% -17.90% -

sign (-) : decreasing sign (+) : increasing

To evaluate the efficient of design in term of using material and performance behaviour, a comparison was taken and shown in Table 5.4, where represents the


91

ultimate strength, the deflection as well as the interesting values at the first yield point. The beams B1 and B2 have the same cross section area (CSA) of steel girder, their cross section areas are less than 10% compared to beam B3 and greater than 32% compared to beam B4. The reults show Tee cross section girder has significant possitive effect. In fact, beam B3 has CSA greater than 10% whereas it has 25% higher than in ultimate strength and 70% smaller in deflection. The performance might be further improved if shear connection capacity was better designed. Moreover, beam B4 with CSA less than of 30% compare to beam B1/B2, however it give impressive results with 30.31% higher in bearing capacity and 17.90% in reduced deflection. Another interesting aspect also is the initial stiffness of the beam, which may be helpful for the design in servicebility limit state (SLS). In this term, the Tee girder shows dominant strategy. Load-Strain development in concrete slab and steel beam Fig. 5.17 and Fig. 5.18 present load-strain curves and strain development respectively, which were measured at midspan sections of beam B3 and B4. In the case of beam B3, both the compressive and tensile strain in top and bottom fiber of beam are less than 2.0h. The strain in the bottom flange of steel girder achieved yield strain first, whereas concrete slab and upper part of the web are still in the elastic regime. The strain at the bottom of the concrete slab and top of the web was approximate at entire load level, therefore the relative slip between concrete slab and steel rib are unremarkable (Fig. 5.18). It can be noticed that, the shear connectors worked well until suddenly collapsed. For beam B4, the strain in bottom flange of steel girder reach limit of elastic at applied load of 600 kN, whereas strain in concrete are still in elastic. The strain in concrete began yielding then two of three steel areas were over limit values as shown in Fig. 5.18. At load lever of 0.8PU the top of web and bottom of concrete slab change from compression to tension state. The strain in both steel and concrete part increased very fast, while the load carrying capacity increased slower. The beam failed when the concrete slab crushed whose compressive strain was over 3.6hand steel girder was in plastic state. The failure mode of the beam B4 could be considered as ductile.


Applied load (kN)

92 1000

1000

800

800 concrete

600

steel

600

B3-LVDT11 B3-LVDT10

400

400 B3-LVD10 conc. B3-LVDT11 conc. B4-LVDT10 conc. B4-LVDT11 conc.

200 0

B4-LVDT11

-6

-4

B4-LVDT10

-2

0

Strain (‰)

2

0

B3-SG7

B4-SG11

B3-SG12

B3-SG7- web (above N.A) steel B3-SG12- bot. fl. steel B4-SG10- web (above N.A) steel B4-SG11- bot. fl. steel

200

4

B4-SG7

-2

0

2

4

6

8

10

Strain (‰)

Figure 5.17.: Load-strain behaviour of composite beam B3 and B4, concrete slab (left) and steel girder (right)

Figure 5.18.: Load-strain development in cross section beam B3(left) and B4 (right)

Load - slip relation The longitudinal and up slips were measured in the same manner as previous beams B1 and B2. In fact, only slip data in the left side of a beam were captured due to symmetric characteristic of the beams. Unfortunately, in actual the left and right supports are different. As a result, the failure of shear connector occurred earlier in the right side (roller support). This has happened in testing beam B3, shear connection was broken and no slip data in right side were captured. This is an expense lesson learned from this test. Fig. 5.19 shows the load-slip relationship of beam B3(left) and B4(right). Two beams B3 and B4 have lower shear connection degree compare to beam B1 and


93

B2. The slip distribution at low load level are nearly uniform, and their magnitude changed when loading grew up. The peak of the relative slip located at relative coordinate of ±0.4 and decreased to the midspan section. The maximum slip obtained is less than 0.5 mm in both beam B3 and B4. The load-slip development of beam B3 was not expresed as the same manner with Push-Out test. Comparison with characteristic slip obtained from SPOT (Series 7, tab. 4.4), the real slip of the beam are equal to 1/8 δk only. It can be seen that, the characteristic slip from Push-Out test is much more higher than the actual slip in the beam. The ductility requirement for UHPC perfobond shear connector must be examined carefully when considering the redistribution of forces between shear connectors.


1.00 0.75 0.50

B3−0.45Pu B3−0.71Pu B3−0.90Pu B3−0.99Pu

B4−0.45Pu B4−0.71Pu B4−0.90Pu B4−0.99Pu

Beam B3

Beam B4

0.25 0.00 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 Relative distance from midspan of the beam

0.5

Figure 5.19.: Diagram Load-longitudinal slip in beam B3 and B4

Contrast with beam B3, the different of slip between the shear connector of beam B4 are relative small. At high load level the slip is nearly uniform in region between the concentrate load and the support. This indicate that the acting force on shear connectors were re-distributed. The maximum slip of beam B4 was 0.4 mm which is very small compare to slip capacity which obtained from Push-Out test. However, It is not easy to predict when the failure will occur if the load continues increasing. The slip behaviour of UHPC perforbond shear connector should be further investigated. 5.3.4. Test results and observing of beam B5 Beam B5 was designed to utilized maximum compression capacity of UHPC slab. As mentioned earlier, due to the lack of Push Out test data, which are essential to evaluate the influence of reinforcement on the capacity of UHPC dowels. The beam was decided to construct without embedding reinforcement in concrete

94


dowel and increasing of 10% tranverse reinforcement in front surface. With a spacing between reinforcement of 8cm evenly along the beam. Two beams of Series 2 were cast at the same day and kept in the room conditions. After beam B5 and B6 were constructed, the test of beam B5 was performed first with a concrete age of 24 days. The compressive strength of concrete is approximated 155 MPa, which meet the requirement in specimen design . Load - deflection behaviour 1000 B5−Deflection at midspan section B5−Deflection at quartspan section. P/2

Applied load (kN)

800

P/2

8m

Rebar Φ8@80mm in front surface

600

400 Shear connector failure at 13th cycle of loading

200

0

0

20

40

60

80

100

Deflection (mm)

Figure 5.20.: Load - deflection behaviour diagrams of beam B5

The Load deflection behaviour of beam B5 is presented in Fig. 5.20 and the relation between load versus strain in middle span section was presented in Fig. 5.21. The beam exhibits very poor loading capacity. In fact, the ultimate strength is only 616.40 kN (40% of predicted ultimate capacity). The measured strain at concrete slab and steel girder vary also in range between 1.0hand 1.5hrespectively. The curves show the responses of the materials was limited in elastic region only. As can be Observed from the test, the beam had failure at 13th load cycle in pre-loading period with the collapse of shear connector as the primary reason. The beam failed as the same manner with beam beam B3. That is the progress of collapse happened suddenly without any warning phenomena. There are no transverse cracks was found on front surface of the concrete slab. The crack only appeared after specimens was broken. The failure mode of the beam is identified as brittle.


95

1000 B5−SG3− web (below N.A) steel B5−SG4− bot. fl. steel B5−SG5− bot. conc. slab B5−SG6− top conc. slab

B5-SG6 B5-SG5


B5-SG3 B5-SG4

600

400

200

0

−4

−3

−2

−1

0

1

2

Strain (%o )

Figure 5.21.: Load - strain response of beam B5

Load - slip behaviour Fig. 5.22 shows load-slip behaviour under various load levels. At low loading (0.26 PU ) the slip distribution is nearly uniform with very small magnitude that can be ignored. At higher load level (0.5PU to 1.0PU ) slip magnitude are greater in the end area and reduce evenly to midspan section. The maximum value of slip reach about 0.18 mm and their magnitude changed not too much between load levels. The shear connection system collapsed when slip is less than 0.2 mm. In general, the structural behaviour of beam B5 looks as the same fashion as beam B3.


0.40 0.30

B5−0.26Pu B5−0.44Pu B5−0.82Pu B5−0.98Pu

0.20 0.10 0.00 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 Relative distance from midspan of the beam

Figure 5.22.: Longitudinal slip of beam B5

0.5


96

Fig. 5.23 presents slip development at several locations and its scaled image was plotted together. As shown in the figure, when the load is small enough. The load-slip relation exhibit linear elastic relationship. Residual strain after loading-discharge cycle is not meaningfully due to the abstention of reinforcement and low fiber contents. However, the micro crack in concrete had developed evenly after loading cycle. If a shear connector is subjected to a big enough shear force, the pre-cracked in concrete dowel could be the main factor for the collapse of the weakest shear connector. Therefore, acting force on remain shear connectors is interesting and it may exceed their resistance capacity. The falling of the next weaker shear connector will occur very fast after first the one. The composite beam will fail completely in shortly. Consequently, the capacity of the shear connection not only depend on sum of individual strength but also on the distribution shear force along beam. 1500

600 B5-LVDT 2 B5-LVDT 3 B5-LVDT 4 B5-LVDT 5 B5-LVDT 6 B5-LVDT 8 shear connector collapsed at 13th cylce of repeat loading stage

Applied load (kN)

1250 1000 750

500 shear connectors collapsed

400

500 300 B5-LVDT 2 B5-LVDT 3 B5-LVDT 5

250 0

0

1

2

3

Relative slip (mm)

4

200

0

0.1

0.2

0.3

0.4

Relative slip (mm)

Figure 5.23.: Slip development of beam B5

The results obtained from this test implies that the transverse reinforcing bar in cover layer play very limited role in increasing the strength of perfobond shear connector, even if large amount of reinforcing bar is used. Compare with corresponding Push-Out test data, the achieved characteristic slip is greater than 3 to 5 times slip in beams. Once more again, the standard Push-Out test does not reflect exactly the real behaviour of perfobond shear connection in composite beams.


97

5.3.5. Test results and observing of beam B6 Load-deflection behaviour Beam B6 was designed similar to beam B5, but ODW was used rather than CDW. Reinforcing bar φ8 mm was added to UHPC dowel as well as front layer of concrete slab. The load-deflection behaviour and failure progress are shown in Fig. 5.24 and Fig. 5.26, respectively. 1500

Beam B6−midle span section Beam B6−quarter span section

Applied load (kN)

1250 1000 Concrete slab crushed

750 Rebar Φ8mm in dowel and Φ8@100mm in front conc. surface

500

P/2

P/2

250 8m

0

0

20

40

60

80

100

Deflection (mm)

Figure 5.24.: Load - deflection diagrams of beam B6, UHPC G7 0.5 % fiber content

The beam B6 achieved a ultimate strength of 1285.28 kN and corresponding deflection in middle section was about 90 mm. As shown in Fig. 5.24, loaddeflection behaviour of the beam could be approximated as two straight lines: the first segment from starting point to ultimate load (at which the beam collapsed) and the second segment continue from peak load until beam fall down completely. The appearance of second line can be illustrated as: when concrete slab was suddenly broken, then load from hydraulic jack subjected directly to steel girder which remains the bearing capacity. The descending branch was not representative for ductility of the beams. As observer from the test, the failure of beam was caused by the crushing of concrete slab in the compression zone. Though over cross section of concrete slab, the material was subjected to compressive stress/strain only. When the stress in concrete slab exceed its strength, the fall down progress happened suddenly and generated high-strength explosive. There are many fragments thrown out surrounding area as depicted on figure 5.26. The explosive caused by UHPC has

98


low steel fiber content and stress rate increasing very fast. Investigating UHPC slab after test, many transverse cracks appear along beam. However, these crack were caused by subjected force after ultimate load was achieved. These transverse cracks did not contribute to failure of the beam. Based on the load-deflection curve, the failure mode of the beam can be considered as brittle general behaviour in elastic response. Load - Slip behaviour In the tests of beam B5 and B6, longitudinal slip were measured in both sides in order to capture all sip data and avoid loss data if the failure of shear connector occurred in one side only. In this test, the shear connection was sufficient to transfer load from concrete to steel girder, as expected. Fig. 5.25 presents the distribution of slip at several load levels. In fact, the maximum slip reach 0.35 mm only. This means that, the real slip in composite beam is very small compared to its characteristic slip obtained from SPOT. Similar to other tested beams, the slip distribution show not uniform along beam. The biggest value locate at relative coordinate ±0.3 from midspan section.


0.40 B6−0.15Pu B6−0.47Pu B6−0.80Pu B6−1.00Pu

0.30 0.20 0.10

0.00 −0.5 −0.4 −0.3 −0.2 −0.1

0.0

0.1

0.2

0.3

0.4

0.5

Relative distance from midspan of the beam

Figure 5.25.: Load - slip behaviour of beam B6

Strain development over cross section The strain development of concrete and steel girder are presented in Fig. 5.27, where the compressive and tensile strains of both steel and concrete were plotted in the left and right respectively. It can be seen that, only the strain in bottom flange and web of steel girder were in tension. All other parts include web and concrete slab were in compression.


99

Explosive when concrete slab crushed

Concrete slab after crushed (plane view) Figure 5.26.: Failure progress of composite beam B6

... and (bottom view)


100

The strain in bottom flange (SG4) achieved 1.8h corresponding to peak that load, which nearly equals to the nominal yield strain limit of S355 steel. Consider web, the strain in bottom was steel in elastic whereas it reached 2.2h in the top (SG1) and began yielding. On other hand, the maximum strain in bottom and top surfaces of concrete slab were 2.2h and 3.7h respective, which lie in fracture plastic zone of concrete. It can be noticed that, the strain in concrete slab exceed that corresponding to the ultimate strength and lead to concrete crushed before the steel girder enter into plastic regime. 1500 concrete slab crushed


B6-SG4 B6-SG1

1000

B6-SG6

B6-SG2

B6-SG3

B6-SG5

750 500

B6-SG1

B6-SG6 B6-SG1

250

B6-SG2

B6-SG5

B6-SG3

B6-SG2

B6-SG4

B6-SG3

B6-SG5

B6-SG4

0

-4

-3

B6-SG6

-2

-1 Strain ( ‰ )

0

1

2

Figure 5.27.: Load-Strain at middle span section of beam B6

Height of cross section (mm)

concrete slab crushed in compression zone

ultimate compressive strain

400 350 300

Yield strain area in compression zone of the web

250 200

0.47Pu 0.73Pu 0.90Pu 1.00Pu

150 100 50 0 -5.0

yield strain limit

-2.5

0.47Pu 0.78Pu 0.90Pu 1.00Pu

yield strain limit

0.0 Strain (‰)

2.5

yield strain limit

5.0

-5.0

-2.5

yield strain limit

0.0 Strain (‰)

2.5

5.0

Figure 5.28.: Strain development in middle span section (left) and one third section (right) of beam B6

The strain distribution over cross section at midspan and one third span section are illustrated in Fig. 5.28. According to the figures shown above, the neutral

5.4. Shear flow distribution in composite beam

101

Height over slab (mm)

axis always lie below horizontal central axis of cross section (150 mm from bottom up), and its position changes insignificantly during of loading. A comparison of the different strain at top of the web and bottom of the slab at ultimate limit state, it can be seen that, one third span is greater than midspan due to the fact that the longitudinal slip at this section is higher. 100 75

Ac,ap

50

Ac,fp

25 0 0.0

1.0

2.0

3.0

Strain (%o )

4.0

0

30

60

90

120 150 180

Stress (MPa)

Figure 5.29.: Stress-strain over slab thickness

5.4. Shear flow distribution in composite beam 5.4.1. Load-slip behaviour in composite beam versus Push-Out test In general, the characteristic load-slip curve derived from Push-Out test was often used to design shear connection of a composite beam. In this section, the comparison on load-slip of composite beam and Push-Out test was conducted in order to obtain correlation between characteristic slips. Two selected load-slip curves of beam B3 (shear connector failed) and SPOT Series 7 are demonstrated in Fig.5.30. The ratio P /PU is presented in ordinate axis, while the peak slip of the beam (at ±0.4) and relative slip of SPOT are exhibited on abscissa. As shown in figure the shear connection of the beam failed when the slip reached 0.4 mm only, the load slip curve show the shear connector behaves very high linear elastic. The yielding and plastic phase did not present clearly in the curve. In contrast, the slip of SPOT reached 4.2 mm and characteristic curve shows completely response state include elastic, yielding as well as plastic regions. The difference between ultimate slip and characteristic slip is approximately 4.0 mm which is significantly large. Similarly, consider beam B5 that failed by shear connection system. The ultimate and characteristic slips of the beam B5 and SPOT Series 8 respectively are illustrated in Fig. 5.31. According to the figures, the ultimate slip of beam B5 only reached 0.2 mm, while characteristic slip has about 4 times greater. The behaviour exhibits the same manner with beam B3.

102

5. Experimental investigation on the structural behaviour of steel-UHPC composite beams 1.2

Loading ratio P/Pu

PU 1 PRK

shear connetor in composite beam collapsed

Ultimate load

Beam B3−LVDT 4 SPOT series 7

0.8 0.6

~4mm

0.4

Ultimate slip when shear connector broken Characteristic slip from SPOT

0.2 0

0

1

2


5

6

Figure 5.30.: Comparison load slip behaviour of shear connector in composite beam and push out test 1.2 1 Loading ratio P/Pmax

Beam B5−LVDT 5 SPOT serires 8

PU PRk

0.8 0.6 ~4 times

0.4 ultimate slip from beam test

Characteristic slip from SPOT

0.2 0 0.0

0.5

1.0 Relative slip (mm)

1.5

2.0

Figure 5.31.: Comparison load slip behaviour of shear connector in composite beam and push out test

The above comparison reveal that, the standard Push-Out test according to EC4 (27) gives results better predictions of the behaviour of connectors in beams. The same problem occurred on headed stud shear connector also early indicated by some authors such as Johnson and Anderson (48) and Ernst (25).

5.4. Shear flow distribution in composite beam

103

5.4.2. Distribution of longitudinal shear forces Through previous discussion on load-slip results, for bending of single span composite beams subjected concentrate loads the slip distribution is nearly uniform at low load level. With the increase of load, their distribution and location of peak slip are changed to highly non uniform. Based on experimental results, It can be seen that, the shear connection degree is a major factor influencing to the distribution of slip. The summarized peak slip location versus shear connection degrees of beam B1 to B6 is plotted in Fig. 5.32 and listed in Table 5.5. Table 5.5.: Peak slip location versus actual shear connection degree Beam Peak slip location (x/L) Degree of shear connection∗ (%) ∗

B1

B2

B3

B4

B5

B6

0.08 119.88

0.08 125.54

0.38 87.62

0.38 121.33

0.4 90.26

0.32 100.00

Shear resistance was calculated with active shear connectors only


1.00

B2

0.75 0.50

B3 B1

0.25

B6

B1−0.99Pu B2−0.99Pu B3−0.99Pu B4−0.99Pu B5−0.98Pu B6−1.00Pu

B4 B5

0.00 0.0

0.1

0.2

0.3

0.4

0.5

Relative distance from midspan section to the right end Figure 5.32.: Slip distribution versus degree shear connection concentrate load

uniform load

longtitudinal shear force according elastic theory longtitudinal shear force according plastic theory

longtitudinal shear force according elastic theory longtitudinal shear force according plastic theory

Figure 5.33.: Longitudinal shear force in composite beams

104


The shear connection degrees is defined as follow: β=

min(Rsh ,Rc ) .100% Nfc

(5.1)

where: Rsh is resistance of shear connectors, Rc is resistance of concrete slab and Nfc is actual longitudinal shear force as well. As shown in the figure, for both beam B1 and B2 with full shear connection (DSC ca. 120%), the peak slip locates at relative distance ±0.1(x/L). Beam B3 and B4 with lower shear connection degree corresponding to 87.62% and 121.33%, the peak slip located at ±0.38(x/L), which is more far way from center than beam B2 and B2. Especiall beam B5 with very low shear resistance capacity, peak slip continute move to outside that nearer support. Based on analysis of load-slip it can be noticed that, in the case of full shear connection the longitudinal shear force regime may distribute as shown in Fig. 5.33. The peak could be move to the end of beam when shear connection degree reduced. The collapse progress is to occur on a shear connector near support first, and then a next series of weaker shear connectors will fail due to the domino effect. In the case of uniform load, experimental work on composite beams were conducted by Chapman and Balakrishnan (19), and recent numerical work was performed by Queiroz et al. (86). They have pointed out that, the shear flow has also highly non uniform distribution. A typical shear flow curve is illustrated in Fig. 5.33.

5.5. Summary conclusions Based on the experiment results, the following conclusions can be drawn: The performance of composite beam is significantly improved when normal strength concrete is replaced by UHPC. Perfobond shear connectors with both dowel profiles give good performance in term of load transfer and shear resistance. In practical fabrication open dowel is more advantageous than closed dowel in term of reinforcing installation and casting of concrete. The basic behaviour of composite beam made of UHPC is similar with composite beam made of NSC with three primary domains: elastic, yielding and plastic domains. In the case of full shear connection the simple rigid plastic can be used to predict ultimate plastic moment.

5.5. Summary conclusions

105

The shear perfobond shear connectors with variant shape can transfer the shear forces from concrete slab to steel the girder effectively. Actual slip in the composite beam is much smaller than its characteristic slip obtained from standard push out test. Consequently, the partial shear connection is not recommended. Distribution of longitudinal shear force is not uniform in both cases of concentrate and uniform load. Therefore the design of shear connection must take into account this effect. Embedded reinforcing bar in UHPC dowel play most important role in improving the ductility as well as the strength of shear connection system. In contrast, the transverse reinforcement in front surface only play minor role in enhancing the ductility of shear connectors. However they are necessary to prevent tensile force which causes crack on the concrete surface. The composite beam with Tee steel girder can provide 30% to 50% higher bearing capacity than I section with the same cross section area. The influence of long-tem cycling load (fatige load), types of shear connectors and stability of UHPC composite beam are subjects left for further study.

106


6. Material models for Finite Element Modelling 6.1. General Steel concrete composite beams are made of three material with different characteristics, namely concrete, structural steel and reinforcing bars. Steel and rebar can be considered as homogeneous materials whose properties are generally well defined. Concrete is, on the other hand, heterogeneous material made of many constituents. Its mechanical properties scatter more widely and can not be defined easily. Let consider load-slip diagram of push out test and load-deformation of composite beam, which were shown in Fig. 4.16 and Fig. 5.8 respectively. It can be easily identified that, the behaviour of these structures are highly nonlinear response. It can be roughly divided into three range: un-cracked elastic stage, crack propagation and the plastic (yielding or crushing). The nonlinear response is caused by two major effects, namely cracking of concrete in tension (such as UHPC dowel region), and yielding of the steel girder/reinforcement or crushing of concrete in compression zone of slab. Moreover, nonlinearities also arise from interaction of parts of structures, such as bond-slip between reinforcing bar and concrete, aggregate interlock at cracks, dowel action of reinforcing steel crossing a crack and interface between steel and the concrete surfaces, .etc. The time-dependent effects also contribute to nonlinear behaviour. Furthermore, the stress-strain relation of concrete is not only nonlinear, but also different in compression and in tension and the mechanical properties are dependent on concrete age at loading and on environmental conditions. The material properties of steel and concrete are also greatly different (59). From structural engineering point of view, it is difficult to understand the complete mechanics of a structural response of composite beam as well shear connector from experiments alone. Within this study, numerical analysis has become increasingly important in obtaining an improved understanding on structural behaviour such as load transfer from concrete slab to steel girder, distribution of longitudinal shear force, stress field in dowel region etc. With the advent of high speed computers and special tool for simulation, the nonlinearity of material

108

6. Material models for Finite Element Modelling

should be taken into account, in order to describe nonlinear response of structures under external load. Some numerical investigation will be conducted with variant of model parameters. The first part of this chapter will short introduce the material models for structural steel and reinforcement. Then next will focus microplane model M4 for concrete. The uni-axial compression and bending of three points notched beam will be modeled and analyzed in order to evaluate influence of each parameter on numerical results. A procedure for adjusting key parameters of microplane M4 for UHPC was proposed.

6.2. Material models for structural steel and reinforcement Structural steel is generally a homogeneous material, therefore the specification of single stress-strain relation is usually sufficient to defined the material properties needed in analysis. In this study, structural steel is modelled as an elastic-plastic material incorporating strain hardening. Figure 6.1 shows the stress strain diagram for steel in tension. Specifically, the relationship is linearly elastic up to yielding (fsy ), linear hardening occurs up to the ultimate tensile (fsu ) stress and the stress remains constant until the tensile failure strain is reached. For all practical purposes the steel also exhibits the same way in compression.

Figure 6.1.: Bilinear Elasto-plastic material model for structural steel

For the modelling of reinforcing bar, the elastic-plastic material model for structural steel is used with small modification in yield plateau portion. Hwak and

6.3. Microplane M4 material model for concrete

109

Filippou (59), Chen et al. (20) pointed out that, since steel reinforcement have been used in concrete construction as form of rebar or wire, it is not necessary to introduce the complexities of three-dimensional constitutive model for steel. In this study, the simulation work would be concentrated to Push-Out and composite beams tests. In fact Push-Out tests requires considering the local behaviour caused by larger deformation at dowel region. Whereas composite beams modelling demands to take into account the global response and local longitudinal slips. To utilize the computational efficiencies and achieve reasonable results, all most structural models will be discretized by 3D solid element (brick element). The reinforcement in Push-Out test will be idealized by 3D solid element, whilst in the composite beam the one dimensional stress-strain for reinforcing bar is used. The deformed reinforcement Bst 500 grade was used for all specimens of composite beams and Push-Out tests. Its mechanical properties are given in table 4.1. According to the design of the beams, most of reinforcing bars were arranged in front surfaces, which lie in compression fiber of UHCP slab. Therefore the bond interaction effect between reinforcing steel and surrounding concrete is omitted and perfect bonding is assumed in the analysis.

6.3. Microplane M4 material model for concrete 6.3.1. Aspects of concrete material model Many constitutive models for describing the mechanical behaviour of concrete are currently in use in the analysis of reinforcement concrete structures. These can divided into two main approaches: namely, the phenomenological and the micromechanics-based models. The former had been inspired by the classical macroscopic theories of plasticity and damage, and attempts to account for general tri-axial states of stress and strain. However, they have generally proven to be inadequate in providing unified constitutive relation that accurately reflect experimental data for arbitrary deformation histories. To overcome these lacks, Bazant and Oh (9) introduced an alternative micro structural approach, which referred as ’microplane model’, based on slip theory of plasticity. Over three decades, Bazant and his co-work have presented a series of progressively improved version of the microplane models. In particular, the M4 formulation of the microplane model has been proven to yield predictions that are in good agreement with experiment data. It had been integrated

110


into many commercial finite element (FE) code such as ATENA (18) and open source FE code as OOFEM. Further more, many worldwide researchers implemented microplane M4 model in special FE softwares such as DYNA3D, ADINA, ABAQUS, LIMFES etc. to solve their specific problems. Many successfully applications were reported in literature such as Bhattachary (10), Baky (6), Liu and Foster (65; 66; 67), Heger et al. (105). In numerical study of this work, the microplane M4 constitutive material model was used for concrete material. Moreover, to avoid mesh sensitivity, the crack band approach was also employed (8; 17). The microplane model M4 integrated in the ATENA software is according to Bazant’s formulation (7), whose basic formula will be summarized in the next part. Full details concerning the underlying hypothesis, basis relation of microplane M4 and advantage as well as disadvantage in practical applications can be found in Bazant et al. (7; 15; 11), Babua et al. (5). Through out numerical simulation framework, the finite element code-ATENA (18) was employed to carried out finite element analysis. The program offers a wide range of options regarding element types, material behaviour and numerical solution controls etc. The preparation of the input data (pre-processing) and evaluation of the numerical results (post-processing) are performed using the commercial program GID (24). These utilized advanced graphic user interfaces features, auto-meshing as well as sophisticated post-processor and graphics presentation to speed up the analyses. 6.3.2. Microplane M4 material model in ATENA With the constitutive law of the microplane model M4, the macro stress on the microplane is explicity determined from the stress-strain relationships, that have been developed for a generic microplane. The micro stress are then combined using principle work to get macro stress at a point. The micro stresses are split into normal and tangential on each microplane. With the normal components further split into deviatoric and volumetric components. Figure 6.2 shows the steps involved for extracting the macro-stresses at a point from the macro-strains. The presented volume of material is viewed at the microstructural level, and is considered as three dimensional element defined by set of microplane of different arranged in regular patten. Figure 6.2 depicts a typical representation, which includes a set of microplane 28 equally and distributed on surface of hemisphere. These planes represent the damage or weak planes at the microstructural lever or plane of microcrack.


Kinematic constraint

Macro strain tensor ε ij

Equilibrium

Macro stress tensor σ ij

Material law

Micro strain εV , ε N , ε D , ε L , ε M

111

Micro stress σV , σ N , σ D , σ L , σ M

adjustment

Figure 6.2.: Calculation macro stress scheme in microplane model

z n ε

ε

z

εN εM

εK

y

σ x

y

x

Figure 6.3.: Strain component on a micro plane

The orientation of a microplane is characterized by the unit normal n of components ni (indices i and j refer to the components in Cartesian co-ordinates xi ). In the formulation with kinematic constraint, which makes it possible to describe softening in a stable manner, the strain vector εN on the microplane is the projection of the macroscopic strain tensor εij . So the components of this vector are εNi = εij nj . The normal strain on the microplane can be expressed as follow: εN = Nij εij ; Nij = ni nj

(6.1)

where repeated indices imply summation over i = 1, 2, 3. To better control the triaxial behaviour of the concrete, the normal strain εN was split into two vector: volumetric strain εV , and the deviatoric strain εD , i.e: εN = εV + εD . The volumetric component characterizes the hydro static

112


behaviour of the concrete and is defined as: εD = εN − εV ; εV = εkk /3

(6.2)

where εV = volumetric strain (mean strain), same for all the microplanes. Defining εS = spreading strain (or lateral strain) = mean normal strain in the lateral directions lying in the microplane, the volume change may be written as 3(εN − εD ) = εN + 2εS , which clarifies the physical meaning. εD =

2 (εN − εS ) 3

(6.3)

To characterize the shear strains on the microplane (εT ), it is further decomposed into two components with respect to perpendicular direction m and l in the plane, the shear strain components may be written as follows: εM = Mij εij , εL = Lij εij

(6.4)

in which Mij = (mi nj + mj ni )/2 and Lij = (li nj + lj ni )/2. The magnitude of εT is given by: p (6.5) εT = εL 2 + εM 2 In the macroscopic level, the behaviour of concrete is considered to arise from micro crack initiated at the microscopic level. The concept of boundary was introduced to taken account the microscopic behaviour after cracking, and simulate the softening behaviour of concrete. Figure 6.4 illustrate micro stress boundary for the normal (a), deviatoric (b), volumetric(c) and shear(d) stress respectively (7). Within the boundaries, the response is incrementally elastic, although the elastic moduli may undergo progressive degradation as a result of damage. Exceeding the boundary stress is never allowed. Travel along the boundary is permitted only if the strain increment is of the same sign as the stress; otherwise, elastic unloading occurs. In the increment constitutive equation could be written as rate form follows: σ˙ V = EV ε˙V ; σ˙ D = ED ε˙D ; σ˙ M = ET ε˙M ; σ˙ L = ET ε˙L

(6.6)

where EV , ED , ET are microplane elastic moduli whose relationship to the macroscopic Young’s modulus and Poisson’s ratio as follows: EV = E /(1 − 2ν); ED = 5E /[(2 + 3µ)(1 + ν)]; and ET = µED

(6.7)

Here, µ is parameter that characterizes the effect of damage, which is best chosen with µ = 1.


113

b σD /E

b σN /E

εN

εD

a) Normal boundary σvb /E b) Deviatoric boundary σTb /ET

εv

σN/ET c) Volumetric boundary

d) Shear boundary

Figure 6.4.: Microplane boundary

Along the boundaries the various microstress-microstrain relation are (Bazant et al. (7)):

b σV =

b σD =

  fV+ (+εV ) = 

EV k1 c13

if σV ≥ 0

2

[1 + (c14 /k1 ) < εV −k1 c13 >] εV  −  fV (−εV ) = −Ek1 k3 exp − k1 k4   fD+ (+εD ) =   −  fD (−εD ) =

Ek1 c5 2

1 + [< εD − c5 c6 k1 > /(k1 c1 8c7 )] Ek1 c8 2

1 + [< −εD − c8 c9 k1 > /(k1 c7 )]

b σN = fN (εN ) = Ek1 c1 exp −

b σT = fT (−εN ) =

(6.8) if σV < 0

< εN − c1 c2 k1 > k1 c3 + < −c4 σV /EV >

o ET k1 k2 c10 < −σN + σN > o ET k1 k2 + c10 < −σN + σN >

if σD ≥ 0 (6.9) if σD < 0

(6.10)

(6.11)

114


The macro volumetric stress is calculated as the minimum of the previous value and average of the microscopic normal stress over unit hemisphere expressed as:

Z σV =

σN d Ω π

(6.12)

Ω

The static equivalent of stress between macroscopic and microscopic lever can be enforced by using principle work written for whole surface Ω of a unit hemisphere. The macroscopic stress tensor is expressed as (7):

3 σij = σV δij + 2π

Z

σD

δij Nij − 3

+ σL Lij + σM Mij d Ω

(6.13)

Ω

The integration in Equation (6.13), is performed numerically by an optimal Gaussian integration formula for spherical surface using a finite number of integration points on the surface of the hemisphere, which may be expressed in the form: Z f (x )d Ω = wα f (xα ) (6.14) Ω

Equation (6.13 is rewritten as: σij ≈ σV δij + 6

NX =m N =1

δij + σL Lij + σM Mij wN σD Nij − 3 N

(6.15)

Applicable aspects of Microplane M4 to UHPC The microplane M4 model contains many material parameters, which are dimensionless. Among of them, four adjustable parameters k1 , k2 , k3 and k4 as well as the initial modulus of elasticity, which are sufficient to specify the peak uniaxial compressive stress, its corresponding strain and the volumetric boundary and the plastic limit of the concrete under high confinement. The k2 , k3 and k4 are mainly related to very confinement level or hydro static pressure, therefore less importance in uni-axial compression and flexural. The other 17 constant coefficients have been chosen such that the intrinsic relationships give a relatively good agreement with a broad range of experimental data. In brief, the

6.4. Parameter study of Microplane

115

coefficients c1 , c2 , c3 , c4 , c13 and c14 control uniaxial tension strength; coefficients c5 , c6 , c7 , c8 and c9 control uniaxial compression strength; coefficients c10 , c11 and c12 control the shear strength; and coefficients c15 , c16 and c17 control the damage and unloading behaviour of the concrete (15). The value of model parameters in original M4 model were determined based on the calibration against standard experimental tests. However, the set of test data ware used for calibration are normal concrete, which compressive strength not exceed 50 MPa. Therefore, their mechanical properties are significant different with UHPC. Consequently, to utilized M4 model, it is essential to re-adjustment only few key parameters to get agreement with data set obtained from experiment of UHPC. In applicable point of view, the main disadvantage of M4 model is the model has too many parameters. Most of them do not have a simple physical interpretation, and therefore it is difficult to determine their values from experiments. However, the outcome of numerical analysis and reliability of these results always depend on the input parameter. The output can only be reliable only if the input parameter can be determine with sufficient accuracy. In the next part, inverse analysis procedure is used, where the output results will be compared to real properties, in order to derive a suitable input parameters. Due to the lack of test data, the inverse analysis only performed for uni-axial and RILEM bending specimens. These tests were carried out along with POT and composite beams as in experimental study.

6.4. Parameter study of Microplane 6.4.1. Setting up virtual test In oder to model the experimental observed behaviour of concrete, FE modelling based approach is used for the investigation. Tests on compressive cylinder specimen can give compressive strength and elastic modulus, whilst from bending test can be obtained flexural strength, and stress-crack opening behaviour, hence other fracture parameters can also be determined. The uni-axial compression test on cylinder with 150 mm diameter and 300 mm high cylinder was created, while for RILEM beam a 550mm long with cross section 150 × 150mm and 25 × 5mm notched gap was modeled for three point flexural experiment. Fig. 6.6 depicts 3D-solid finite element mesh, support and loading configuration of virtual tests.

116


P

P

150 Cylinder ø150x300mm notched = 25x5mm

25

150

550

25

Stress (MPa)

Figure 6.5.: FE simulation RILEM (left) bending test and uni-axial compression (right) 160

20

120

15

80

10

40 0 -4.0

5

B4Q-axial strain B4Q-Lateral strain G7-Lateral strain G7-Vertical strain

-3.0

-2.0

-1.0 Strain (‰)

G7-RILEM-BeamTest B4Q-RILEM-BeamTest

0.0

1.0

2.0

0 0.0

2.0

4.0

6.0

8.0

10.0

Displacement (mm)

Figure 6.6.: Typical stress-strain of uni-axial compression test (left) and bending stressdisplacement diagram of RILEM three points bending test (right)

The full cylinder model consists of 1936 nodes and 1620 isoparametric solid elements; each element has eight nodes with 2 × 2 × 2 Gaussian points. Fully restrained ends are considered for the cylinder to represent the boundary conditions with dominant friction. Similarly, model for RILEM beam was created with 640 nodes and 412 brick elements. The element size of both models are around 15 to 35mm that aimed to reduce overall computing time of numerical investigation1 . In addition, the element size in this specimens modelling is corresponding to size of element in Push-Out specimens and composite beams. The crack band parameter obtained from material level examination to be used in structural modelling.

1A

analysis with 100 load steps will take approximate 16 minutes and 70 minute for cylinder and Rilem beam model respectively.


117

6.4.2. Input parameter and sensitivity analysis A several model parameters were selected for numerical investigation, the first group include elastic modulus (E ) and and k1 . The second group involves c1 , c3 , c4 , c5 , c7 , as well c8 . These parameters may affect directly the analysis result of concrete under compression and tension. Other parameters include c10 , c11 , c12 influenceing the shear resistance were investigated along with PushOut model. They are associated to local response of concrete dowel in Push-Out test and composite beam structures. Table 6.1.: Boundaries for the microplane model parameters Parameter

Range of value Min

Max

Increment

E (MPa) ν k1

57,000 0.2 1.14e-4

70,000

1500

4.5e-4

0.35E-4

c1 c3 c4 c5 c7 c8 c10 c11 c12

0.1 10 30.0 1.0 20.0 4.0 0.2 0.1 5000.00

0.9 80.0 250.0 4.0 200.0 20.0 1.4 0.7 11000

0.1 10.0 30.0 0.5 20.0 2.0 0.2 0.1 1000.0

In the current analysis, the default value of set of parameter in ATENA was considered as basic origin. For each parameter its value to be arranged in limited range. The bounds of these parameters were set to values shown in Table 6.1. An auxiliary tool was developed and it calls ATENACONSOLE program for finite element analysis, extracting results after processing and then modifying/generating input data file for new analysis as well. All processes with auxiliary tool were carried out fully automatically. For an investigation of the influence of individual parameter such as elastic modulus, only its value was changed. All other parameter are keep constant with their default values. 6.4.3. UHPC experimental data Experimental data were collected from specimen tests within research program on UHPC which carried out by Uni-Leipzig and Uni-Kassel.(105; 107; 30). Fig. 6.6 shows stress-strain curves (left) according to compression test of G7 and B4Q.

118


As exhibit on the figure, the general behaviour uni-axial of both kinds of UHPC are very similar, the steel fiber is not significant effect on compressive behaviour. Compressive strength and strain at peak were approximate 150MPa and 3.3h respectively. In addition, from these diagrams it can be recognized easily that, the stress-strain curve does not exhibit softening branch (branch after ultimate strength). Typical flexural stress versus deflection of G7 and B4Q UHPC are shown in Fig. 6.6 (right), the flexural strength of 17 MPa of G7 compare to 14MPa of B4Q UHPC. Two mixer of UHPC G7 and B4Q with the same fiber contents of 1% does not show too much difference in flexural strength. The significant difference of UHCP compare to NSC/HSC exhibit in softening branch. In fact that, the B4Q using only one type of steel fiber, which is longer than G7. That affects directly the post peak behaviour of flexural specimen. While G7 using cocktail steel fiber with length of 6 and 13mm, it gave higher tensile strenght but less ductile in post peak stage. The flexural test data for G7 mixer with 0.5% fiber content are not available. The material matrix, and especially steel fiber play the major role in improving the ductile properties of concrete. Hence, the fracture energy is improved as well. With the application of higher toughness concrete into composite beam to enhance ductility of UHPC dowel when carrying and transfer shear force from concrete slab to steel girder can be obtained. 6.4.4. Results of M4 model parameters investigation and discussion Parameter: elastic modulus Fig. 6.7 shows the influence of elastic modulus on compression and bending behaviour. As exhibited from the compression test, any change of elastic modulus cause a vertical scaling transformation of all response of stress and strain curve. However, the lateral strain is not affected in this case due to the fact that the specimens dose not confined. The elastic modulus derived from numerical model Eout are alway less than input value Ein , however the ratio Ein /Eout nearly constant. Observing on bending test, the elastic modulus seem to influence on ultimate flexural strength (fct ). But any change of Ein does not affect the overall flexural behaviour. Thus, to reach target value Eout that equals to test value Etest , the input value ∗ of elastic modulus Ein should be modified as follows: Eout = Etest ∗ Ein /Eout , and corresponding the new value of compressive strength determined as: fc∗ =


119

∗ fc,out ∗ Ein /Eout . In the same manner, this rule can be applied for flexural strength. 20 G7-RILEM-Exper. G7-Sim-E0 G7-Sim-E1 G7-Sim-E3 G7-Sim-E5 G7-Sim-E6

160 G7−Expr.−Lateral strain G7−Expr.−Vertical strain G7−Sim.−E0−Lateral strain G7−Sim.−E0−Vertical strain G7−Sim.−E2−Lateral strain G7−Sim.−E2−Vertical strain G7−Sim.−E4−Lateral strain G7−Sim.−E4−Vertical strain G7−Sim.−E5−Lateral strain G7−Sim.−E5−Vertical strain

120

12

Stress (MPa)

Stress (MPa)

16

8

80

40

4 0 0.0

2.0

4.0

6.0

8.0

0 −4.0

10.0

−3.0

−2.0

Displacement (mm)

−1.0 0.0 Strain (%o)

1.0

2.0

Figure 6.7.: Effect of changing elastic modulus to flexural and compression specimens

Parameter: k1 The influence of parameter k1 is presented in Fig. 6.8. For the cylinder test, a change of k1 causes radial scaling of stress-strain curve with respect to the origin. 0 If this parameter change from k1 to some other value k1 , all stress-strain are 0 multiply by the ratio k1 /k1 . With default value of k1 = 1.5 and adjusted elastic ∗ , the peak stress value and accompanied strain are still less than modulus Eout actual values, given by test. 20

12 8

80

40

4 0 0.0

G7−Expr.−Lateral strain G7−Expr.−Vertical strain G7−Sim.−K1−0−Lat. G7−Sim.−K1−0−Ver. G7−Sim.−K1−2−Lat. G7−Sim.−K1−2−Ver. G7−Sim.−K1−4−Lat. G7−Sim.−K1−4−Ver. G7−Sim.−K1−6−Lat. G7−Sim.−K1−6−Ver. G7−Sim.−K1−8−Lat. G7−Sim.−K1−8−Ver.

120 Stress (MPa)

Stress (MPa)

16

160 G7−RILEM−Exper. G7−Sim.−K1−0 G7−Sim.−K1−1 G7−Sim.−K1−3 G7−Sim.−K1−5 G7−Sim.−K1−6

2.0


8.0

10.0

0 −4.0

−3.0

−2.0

−1.0 0.0 Strain (%o)

1.0

2.0

Figure 6.8.: Effect of k1 parameter

In the bending test, parameter k1 not only influences the flexural strength, but also the deflection behaviour after peak. An increasing of k1 leads to increase ductility and fracture energy of material in tension as well. This is very important characteristic, in fact, which contributes to the spread tensile force to neighbor

120


regions of concrete dowel in composite beams. The capacity and ductility of structures are improved too. At material level, the stress-strain curves generated by numerical simulations are in good agreement with test curves, the combining adjustment for parameters E and k1 should be applied. However, stress-deflection in bending test is more complicate, therefore requires to combine with other parameters. Parameter: c1 and c3 The investigation results of the parameter c1 are described in Fig. 6.9. In fact, parameter c1 controls peak value of flexural stress and post peak behaviour as well. The sigfinicant changing appear when c1 reach value of 0.5 (default c1 = 0.2). And if value of c1 greater than 0.7 then difference does not occur. On other hand, a modify of c1 does not affect the stress-strain curve of compressive cylinder test. 20

12 8

80

40

4 0 0.0

G7−Expr.−Lateral strain G7−Expr.−Vertical strain G7−Sim.−C1−0−Lat. G7−Sim.−C1−0−Ver. G7−Sim.−C1−2−Lat. G7−Sim.−C1−2−Ver. G7−Sim.−C1−4−Lat. G7−Sim.−C1−4−Ver. G7−Sim.−C1−7−Lat. G7−Sim.−C1−7−Ver.

120 Stress (MPa)

Stress (MPa)

16

160 G7−RILEM−Exper. G7−Sim.−C1−0 G7−Sim.−C1−1 G7−Sim.−C1−3 G7−Sim.−C1−5 G7−Sim.−C1−7

2.0


8.0

0 −4.0

10.0

−3.0

−2.0

−1.0 0.0 Strain (%o)

1.0

2.0

1.0

2.0

Figure 6.9.: Influence of parameter c1 160

20

12 8

80

40

4 0 0.0


120 Stress (MPa)

Stress (MPa)

16

G7−RILEM−Exper. G7−Sim.−C3−0 G7−Sim.−C3−1 G7−Sim.−C3−2 G7−Sim.−C3−5 G7−Sim.−C3−6

2.0


8.0

Figure 6.10.: Influence of parameter c3

10.0

0 −4.0

−3.0

−2.0

−1.0 Strain (%o)

0.0


121

In contrast to c1 , parameter c3 controls directly peak and post peak of bending 0 behaviour. The increment of fct is not linear proportional with ratio c3 /c3 , therefore it is very difficult to establish explicite formula for control flexural strength and the ductility of behaviour as well. For uni-axial compression stress state, similarly with c1 , parameter c3 has almost no influence. Parameter: c5 , c7 and c8 The group of these parameters have no influence on flexural strength, they affect uni-axial compression stress state. According to Caner et al. (15), parameter c5 control volumetric expansion in compressive uni-axial stress test. A changing of parameter c5 leads to radial scaling of both stress and strain with respect to the origin, whose role is similar to parameter k1 . 160

20

12 8

80

40

4 0 0.0

G7−Expr.−Lateral strain G7−Expr.−Vertical strain G7−Sim.−C5−0−Lat. G7−Sim.−C5−0−Ver. G7−Sim.−C5−2−Lat. G7−Sim.−C5−2−Ver. G7−Sim.−C5−4−Lat. G7−Sim.−C5−4−Ver. G7−Sim.−C5−5−Lat. G7−Sim.−C5−5−Ver. G7−Sim.−C5−6−Lat. G7−Sim.−C5−6−Ver.

120 Stress (MPa)

Stress (MPa)

16


2.0


8.0

0 −4.0

10.0

−3.0

−2.0

−1.0

0.0

1.0

2.0

0.0

1.0

2.0

Strain (%o)


20

12 8

80

40

4 0 0.0


120 Stress (MPa)

Stress (MPa)

16


2.0


8.0

10.0

0 −4.0

−3.0

−2.0

−1.0 Strain (%o)

Figure 6.12.: Influence of parameter c7

Parameter c7 controls steepness of post peak branch in uni-axial compressive stress test. In the case of UHPC which softening branch after peak stress is

122


omitted, the parameter c7 is helpful to control this branch by using less than or equal default value. Parameter c8 should not be changed in practical application. 160

20

12 8

80

40

4 0 0.0

G7−Expr.−Lateral strain G7−Expr.−Vertical strain G7−Sim.−C8−0−Lateral strain G7−Sim.−C8−0−Vertical strain G7−Sim.−C8−2−Lateral strain G7−Sim.−C8−2−Vertical strain G7−Sim.−C8−4−Lateral strain G7−Sim.−C8−4−Vertical strain G7−Sim.−C8−6−Lateral strain G7−Sim.−C8−6−Vertical strain G7−Sim.−C8−8−Lateral strain G7−Sim.−C8−8−Vertical strain

120 Stress (MPa)

Stress (MPa)

16


2.0


8.0

0 −4.0

10.0

−3.0

−2.0

−1.0 Strain (%o)

0.0

1.0

2.0

−1.0 0.0 Strain (%o)

1.0

2.0


12 8

80

40

4 0 0.0


120 Stress (MPa)

Stress (MPa)

16

160 G7−RILEM−Exper. G7−Sim.−C12−0 G7−Sim.−C12−1 G7−Sim.−C12−3 G7−Sim.−C12−4 G7−Sim.−C12−6

2.0


8.0

10.0

0 −4.0

−3.0

−2.0

Figure 6.14.: Influence of parameters c4 , c10 , c11 and c12

Parameter c4 gives results which does not affects to compression and bending. It should be used as default value of program. Further examinations were also performed with parameters c10 , c11 and c12 as well. The group of these parameters only effect the stress state in trial axial compression test or tension-shear stress state. As can be seen in Fig. 6.14, no significant difference appears on the uni-axial and bending test. The numerical study of Push Out test in this work had pointed out that, the parameter c10 is very sensitive in bi-axial tension-shear stress state, while the influence of two parameters c11 and c12 is not remarkable. It will be mentioned again in the part modelling of Push-Out test chapter 7.

6.5. Proposed set of parameter for UHPC

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6.5. Proposed set of parameter for UHPC 6.5.1. Adjustment strategy for model parameters As describe earlier, the model parameters can be divided into three groups, which affect to uni-axial compression and bending test independently. The first group includes E and k1 , second group involves c1 and c3 , the remain group contain c4 , c5 , c7 and c8 . It can easily seen that, to control compressive strength, only two parameter E and k1 are sufficient. In addition, by the combining with parameter c1 and c3 the behaviour in tension and compression can be completed controlled. All other parameters in the third group can be ignored and kept their default values. The procedure for the adjustment of the model parameter can be arranged as the following steps: prefer value of parameter c1 , which ensure sufficient required ductility choose a value of elastic modulus E to output equals to test value. calculate new peak of compressive stress and then re-calculate parameter k1 to obtain required compressive strength. try with c3 to derive the best value until the flexural strength reach real value in the experiment.

6.5.2. Result of compression and bending modelling with M4 160

20

G7-Expr.-Lateral strain G7-Expr.-Vertical strain G7-Sim.-Trial-1-Lat. G7-Sim.-Trial-1-Ver.

G7-Experiment. G7-Simumation

120 Stress (MPa)

Stress (MPa)

15

10

40

5

0 0.0

80

2.0


8.0

10.0

0 -4.0

-3.0

-2.0

-1.0 Strain (‰)

0.0

1.0

2.0

Figure 6.15.: Stress-displacement and Stress-strain response of G7-UHPC (1% vol. steel fiber) with Microplane M4 material model adjusted parameters

124


160

20

B4Q-Expr.-Lateral strain B4Q-Expr.-Vertical strain B4Q-Sim.-Trial-1-Lat. B4Q-Sim.-Trial-1-Ver.

B4Q−Experiment. B4Q−Simulation−1

120 Stress (MPa)

Stress (MPa)

15

10

40

5

0 0.0

80

2.0

4.0

6.0

8.0

10.0

0 -4.0

-3.0

-2.0

Displacement (mm)

-1.0 Strain (‰)

0.0

1.0

2.0

Figure 6.16.: Stress-displacement and Stress-strain response of B4Q-UHPC (1% vol. steel fiber) with Microplane M4

Table 6.2.: Value of M4 model parameters for UHPC G7 and B4Q Concrete UHPC G7 ∗ UHPC B4Q∗ ∗

Parameter E (MPa)

k1

c1

c3

66131.9 59300.0

2.75E-04 2.80E-04

0.70 0.70

14.0 10.0

: UHPC with 1% steel fiber

With the guideline mentioned above, numerous attempts were performed. The simulation results of the cylinder and RILEM beam are presented in Fig. 6.15 and Fig. 6.16. The details of the adjusted parameters are listed in table 6.2. The stress-axial strain curve and peak value of uni-axial compression show excellent agreement with experiments, while stress- lateral strain is reasonable. Thus, it causes Poisson’s ratio little smaller actual value and varies in range 0.19 to 0.21. Observing stress-deflection curves of bending behaviour, the flexural strengths reach actual value of experiment. However, the slope of softening branch in modelling show steeper than experiment, the area limited curve and abscissa are equivalent. Generally, it is really difficult to control simulation results that best fit with multi targets simultaneously. There are many reasons to explain for the answers. In this work, the numerical results at material level are found to be reasonable and can be applied for structural analysis level.

6.6. Concluding remarks In this chapter, material models for structural steel, reinforcing bar and UHPC as well were presented. The microplane M4 model theory was summarized and

6.6. Concluding remarks

125

discussed in term of applicable to UHPC. The experimental uni-axial compressive stress and bending tests were conducted with M4 model. The input values of the material parameters for various kinds of UHPC were derived and validated by inverse analysis. The main conclusions that can be drawn as: Elastic-perfectly plastic material model is suitable to present for reinforcement and structural steel. Microplane model M4 with many advantage can be used for UHPC. This material model includes more than twenty parameters, however only few parameters are required change to describe the behaviour of UHPC. The set of input parameters including elastic modulus, k1 , c1 and c3 are identified for G-7 and B4Q UHPC used in this work. The application of microplane model M4 in modelling of the Push-Out test requires further examinations on c10 , c11 as well as c12 , which affect directly the tension-shear behaviour. The structural model should be validated with available experimental data.

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7. Finite Element Modelling 7.1. Introduction Previous studies on the bearing behaviour of steel-concrete composite with perfobond dowels were mainly focused on experimental investigations with limited quantity. In the Push-Out tests, both the yielding of embedded reinforcing bars in UHPC dowels and the local damage of concrete interspersing the holes have been found. Moreover, the stress field in front cover is interesting to explain the contribution of transverse reinforcement in restricting the crack opening in the concrete surface. As a simple mechanical model, the concrete interspersing the holes may be considered as a dowel loaded in shear and extreme local compression (62; 110). However, the general validity of this model has not yet been sufficiently validated. For the composite beams, the experimental study gave very meaningful information on ultimate bending capacity, failure mode and load slip distribution. The strain development in specified section and local damage of concrete in the slab have been observed during test. Among of beam tests, two of them were failed due to the collapse of the shear connectors, which occurred at very early as expected. Furthermore, the result indicate that, the load-slip behaviour of shear connector in composite beam are significantly different from the characteristic load-slip curve derived from Push-Out test. Consequently, the distribution of the longitudinal shear force on each perforbon connector must be made clear. Thus this is useful for enhancing the accuracy of the predicted bearing capacity of composite beams. The chapter focus on the numerical modelling of Push-Out test and composite beams, by using the powerful ATENA software (18) (version 3.3.1). Fully three dimensional model with material nonlinearity was taken into account to evaluate not only global behaviour but also local deformation. The chapter was divided into two parts: firstly, a finite element model for Push-Out test is developed, in order to predict the ultimate bearing capacity and explain the local damage of concrete zone as well as the yielding of steel. The second part focuses on

128

7. Finite Element Modelling

the development a 3D model for composite beams, with accounts for complexity geometry and nonlinear behaviour of materials. The finite element analysis attempts to following aims: evaluate global structural behaviour of composite beams with slab made of UHPC, various profiles of steel girder and types of shear connector were considered with the same properties of UHPC slab. predict the ultimate load, performance of each steel profile and failure mode as well. determine the distribution of longitudinal shear force and the influence of the degree of shear connection on the bearing capacity.

In addition, this section also discussed several issues relating to computations such as, element mesh density, convergence, load control etc.

7.2. Modelling of Push Out Test 7.2.1. Finite element model Geometry of push-out specimens Finite element model for SPOT was developed according to the experimental study, with most primary details and dimensions are the same testing specimens. Some cosmetic details were ignored to reduce the potential risks in finite element mesh. Consequently, this is also contributes to improved accuracy of the model. Contact surfaces

Steel rib

UHPC dowel Slip force

Steel rib

UHPC slab 20mm gap for reaction free

Steel flange Open dowel

Figure 7.1.: Geometry of push-out test specimens

Closed dowel

7.2. Modelling of Push Out Test

129

The symmetry of the specimen was taken into account to reduce computational effort, therefore only a half of the specimens was modeled. Figure 7.1 shows a half of the typical Push-Out test specimen, which was used in numerical investigation. In the finite element model, the trapezoidal steel rip was replaced by rectangular plate with the same thickness. The data input preparation and presentation analysis results were performed with ATENA/GID program. A special tool, named Tool4Atena was developed to assist the preparation of the data file, to call ATENA solver module and to extract results. Finite element mesh and kinematic conditions Applied force steel flange

reinf. bar in dowel

UHPC dowel UHPC slab

front layer

a half of model y

Support in bottom surface

z

x

1200



hole 20x20mm

800

reinf. bar in front layer

Interface between steel and concrete surfaces

600 400 200 0

0

2


8

10

steel perforated rib

Figure 7.2.: Finite Element model of Push-Out specimen

The Push-Out model was constructed with three solid blocks corresponding to steel, concrete slab and reinforcement parts. The last two blocks were glued and

130


meshed together, the nodes on the contact surfaces were merged completely. The main aim is to ensuring that, the bond between UHPC and the reinforcement are perfectly without any relative slip. Remaining steel part was meshed separately with concrete and reinforcing bars. The interface between steel and concrete is processed in later. The most important aspect for the Push-Out model is kinematic condition must be satisfied . Which can be shortly described as follow: the perfobond rib can move in downward direction relatively with concrete slab under push-down load. the reaction force against moving down only appear at above half of concrete dowel. the interaction in normal direction of steel rib surface must be taken into account due to the deformation of the concrete block.

As shown in Fig. 7.2, the FE model of Push-Out specimen was created with full three dimensional, which uses two types of elements from the ATENA element library. The concrete slab, steel flange, perforated rib and reinforcing bar were modeled using CCIsoBrick8 3D three-dimensional solid elements. There are two different idealizations which satisfy kinematic condition as stated above. The consideration was based on economy of computation time, ease of data definition as well as the agreement with test data. The first approach is to use constrain degree of freedom technique, which mergers the same displacement value in a degrees of freedom. In fact, the coincident nodes at contact surfaces between steel and concrete are constrained with appropriated translation DOFs depending on their positions. The second approach is to use gap element to represent the interface surfaces. This method allows the transfer of force from concrete to steel and the friction force is also considered. A comparison was carried out for several analytical cases. For local damage investigation purposes, the coupling DOFs approach has more advantage. It was adopted for Push-Out simulation, while interface approach was used for analysis of the composite beams. Figure 7.3 shows the position of the DOFs to be constrained, where coincident nodes on a half above of dowel were merged completely with three DOFs Ux, Uy and Uz. While at coincident concrete and steel rib surfaces nodes were coupled either in X or Z direction. In addition those nodes at corner were couple in both X and Z DOFs. The merging of nodes replaces all the nodes that lie at the same coordinate location with only one node, and the lowest number of all the nodes merged is retained.


131

Loading and Boundary conditions Because only of a half of the specimen was modeled, the appropriated boundary condition should be applied to the surfaces at the symmetric planes. In fact, the restrain condition in X direction is assigned to all nodes on the symmetric plane. And then, all nodes of bottom surface were restrained in Y direction. Finally, the intersection lines of front and bottom surface were restrained for both Ux and Uy DOFs. Fig. 7.3 shows a typical boundary condition of a Push Out model. enforced disp Uy = 10mm

Uy = 10mm

Coupling dofs: Ux,z Coupling dof: Uz

full connection Ux,y,z

full connection Ux,y,z

Coupling dof: Uz

Coupling dofs: Ux,z Coupling dof: Uz Coupling dof: Uz

Ux Uz

Ux,z

Res. Ux

Res. Ux

Uz Ux,z

a) y

Res. Ux Restraint Uy x

b)

a)

b)

a) Constraint DOFs in concrete dowel and perforated steel strip b) Constraint DOFs in interface surfaces between steel and concrete

Figure 7.3.: Loading, boundary conditions and constrain DOFs at contact surfaces between steel and concrete

As in actual tests, the prescribed displacement was applied at the top of the steel flange, all nodes have a uniform displacement in down ward direction. The loading rate was increased very slowly by dividing into more than 250 sub steps. In the elastic domain, the load steps was divided thinly scattered, otherwise in the inelastic domain (yielding or plastic/crushed) load step was specified very fine. Numerical experience indicates that, the control with difference load steps

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save more computational time and achieved better convergence during solving equilibrium equation system. To improve convergence in each load step, linear search algorithm was turned on and a maximum of 50 iterations was allowed. To obtain the load-slip response, the applied load can be calculated through by sum of vertical reaction forces at bottom of the concrete slab. And the slip was measured as relative displacement between the nodes on the steel flange and that on the concrete slab, which are the same position in real test. Material behaviour specifications The nonlinear material corresponding to each part of specimens were taken into account. In fact the steel flange and rib as well as reinforcing bars were modelled as an isotropic bilinear elastic-plastic perfectly material. The microplane model M4 was used for describing the behaviour of all concrete parts. The parameters of M4 model were determined based on calibration of cylinder and RILEM beam test as discussed in chapter 6. 7.2.2. Experimental validation finite element model The proposed numerical model for Push-Out test was validated through a comparison with experiments. The first group includes series 3 and 4 with open dowel, and the second group consists series 6 and 7 with closed dowel. The reinforcing bar arrangement are the same for both groups, however these groups are different in test setup. The details of specimen design and test setup of each series was given in table 4.3. As observed from the test results, the load-slip behaviour of POT exhibits highly nonlinear behaviour in pre. and post peak branch. The nonlinearity came from many sources such as material, interaction on contact surface and the geometry which are not accurate due to production. Among of them, the nonlinear behaviour of concrete material plays an important role, and it is a critical factor influencing to the predicted strength and behaviour of Push-Out specimen. With material parameters of concrete obtained from material level calibration the load slip behaviour from FE analysis show similar with that observed in experiment. However the predicted ultimate load is often approximate 20% to 35% higher than the test reults and the slip coressponding to peak load is also significantly disparate with test. Thus, it is worth mentioning that the calibrated parameter of model M4 give insufficient accuracy. The reason is quite easy to understand: there are many differences between real specimen and numerical


133

model. Not all physical process occured in the real specimen could be taken into account in simulation. Furthermore, the accuracy of constitutive material models for concrete is not alway sufficient. The trial analyses indicate that, the principle stress state of local damage area is in tension-shear. In general, the response of Push-Out models are very sensitive to parameter c10 in M4 model. A changing of c10 leads to radial scaling of applied force and slip. Furthermore, parameter c1 slightly affects the peak load and slope in softening branch. In order, to achieve sufficient agreement with experimental data, parameter c1 and c10 must be adjusted. The trial analysis was performed until the simulation results converge to experimental data. The convergence was achieved only after a few analysis trials. Hence, adjusted input parameter of model M4 will be used thought all Push-Out simulations. The comparison between FE simulation and experiment on ultimate load and characteristic slip are shown in Table 7.1. It can be seen that, the ultimate load predicted from FE simulation is approximately 2.75% to 8.3% higher than experimental results. However, estimated chracteristc slips have large diverge with test data, the difference vary around 30% to 40.0% depending on the embedded rebar arrangement. Table 7.1.: Comparison of ultimate capacity predicted by ATENA with experimental values Ultimate capacity Specimens

Exper.

Predicted

Pu (kN)

Characteristic slip

Diff.

Exper.

%

Predicted

δ (mm)

Diff. %

ODW-3 (series 3) ODW-4 (series 4)

862.61 1065.53

833.31 1154.17

3.40 8.32

1.22 4.64

2.46 4.32

6.70

CDW-6 (series 6) CDW-7 (series 7)

935.47 1116.30

874.31 1146.78

6.54 2.73

1.33 4.61

0.73 2.82

44.83 39.2

Fig. 7.4 (series 2 and 4) and Fig. 7.5 (series 5 and 7) depict the comparisons between the FE model results and the experimental data for load-slip curves respectively. As shown in the figures, the numerical solutions exhibit very good convergence in softening branch, allowing to describe full behaviour of Push-Out model until collapse occurred. This show critical advantage of microplane model to other fracture-plastic based models in simulating highly nonlinearity problem of structural concrete.

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1400 Series 3−experiment Series 4−experiment Series 3−modelling Series 4−modelling

Applied load (kN)

1200 1000 800 600 400 200 0 0.0

2.0

4.0 6.0 Relative slip (mm)

8.0

10.0

Figure 7.4.: Comparison load-slip response of experimental and FE analysis for Push-Out series 3 and 4 (open dowel)

1400 Series 6−experiment Series 7−experiment Series 6−Modelling Series 7−Modelling

Applied load (kN)

1200 1000 800 600 400 200 0 0.0

2.0

4.0 6.0 Relative slip (mm)

8.0

10.0

Figure 7.5.: Comparison load-slip response of experimental and FE analysis for Push-Out series 6 and 7 (closed dowel)

It can be seen from above figures that, with full embedded rebars in dowel and front layer, the deformation show poorer ductility compared to the experiment. While in the case of without rebars in cover the deformation/slip obtained from numerical modelling is alway higher than the experiment results. This means that, the effect of reinforcement is sufficiently taken into account, on the other hand, material model of concrete produced larger strain than actual response. From concrete material model point of view, the problem may caused by the


135

limitation of current microplane model M4 in describing the tensile-shear stress state, which need further study. Generally, the result of numerical modelling show reasonable agreement with measured load-slip response for both types of open and closed dowel. The simulation of the specimens with embedded rebars in dowel and front cover is more accurate than that without reinforcement. According to recommendations achieved from test, the numerical study will focuses on the specimens with full rebars. Hence, FE modelling will be used to predict the strength of perfobond shear connectors in UHPC slab. In addition a parametric study is carried out. The numerical investigation will concentrate on the effect of design parameter on the ultimate load capacity, the generated results may be helpful for predicting the ultimate capacity of perfobond shear connector. 7.2.3. Local behaviour Push-Out specimens General In order to illustrate finite element analysis for local behaviour, the investigation will focuses on Push-Out test series 4 and 7, where reinforcements were embedded in both dowel and cover. As mentioned in preceding chapter, these cases may be most favorite for practical application. The numerical results regarding the deformation and displacement field at peak load are plotted in Figs. 7.6 and 7.7, respectively. Observed from distortion and the displacement fields of concrete block and reinforcement, the FE results show similar manner as that taken from experiments. At local damage region of concrete dowel in both sides of the steel rib, the displacement vector has exceptional magnitude compared to other regions. The direction of displacement vector trends to be downward and outward to free sides. These illustrate for integrated forces act as shear in concrete dowel, punching and tension in front cover. The measured effective width of damage region is approximate five times the thickness of steel rib, while the strain outside is relative small. This may be a noticeable improvement on the shear transfer band width. The distortion on both ODW and CWL explains the fact of the appear of punching forces as a result of the deformation of perforated holes. And the punching force causes a local damage area which locates in the head of the dowel. Generally, the local damaged area (due to punching force) of ODW is often larger than that with closed dowel, whose size of damaged area is approximately 1.2 times diameter of the concrete dowel. Thus, the transverse reinforcing bars in cover layer are necessary to resist the cracking on concrete surface. In practical

136


applications, if the spacing between shear connector is greater than four times of the dowel diameter then the transverse reinforcement within that span may be neglected. Tension-shear area

Tensile force on concrete surface

dowel rebars

Vhi

Punching in front surface

Thi

P hi

Punching force

Thi Vhi

Tlo lo

Shear force lo

Tlo Vlo

Vlo a) Deformation

b) Displacement field

Figure 7.6.: Local deformation of the series 4 - Open dowel with test setup 2

Tension-shear area

Tensile force on concrete surface

dowel rebars

Vhi

Punching in front surface

P hi

Thi Punching force

Thi Vhi

Tlo

Shear force lo

Vlo a) Deformation

Vlo

Tlo

b) Displacement field

Figure 7.7.: Local deformation of the series 7 - Closed dowel with test setup 1

Local stress distribution in steel rib The analysis of the local behaviour of the steel rib can be explored by focusing on the stress distribution over steel flanges and ribs. Fig. 7.8 illustrates the engineering principal stress distribution at peak load and average stress development at some critical points for ODW and CDW shear connectors. It can be seen that, the distribution of critical regions of open and closed perforated holes are slightly different. With OWD high tension areas of the steel rib concentrate in welding edge and around holes (point A and B), and the compressive areas locate on the edge between two holes (point C). In contrary, in the case of CDW the high


137

critical tensile stress concentrates on the perimeter of the holes (point E), this area may be broken if the push down force increase continually. The magnitude and scope of the tensile stress in two holes are significantly different. Point E is higher approximate 40% than that of point E1. 400

tensile stress

ODW−Point A ODW−Point B

B

Stress (MPa)

compressive stress

300

C

ODW−Point C

200 100 0

A

−100 0.0

2.0

4.0

6.0

8.0

10.0

8.0

10.0

Relative slip (mm)

400

tensile stress

ODW−Point D

D

ODW−Point F ODW−Point G

G E

Stress (MPa)

compressive stress

ODW−Point E

300 200 100 0

F G1 E1

−100 0.0

2.0

D1

4.0

6.0

Relative slip (mm)

Figure 7.8.: Local stress distrubution in the steel rib

Observing the stress development diagrams in Fig. 7.8. One can see that the peak tensile stress of critical area in open hole reaches 270 MPa while in closed holes achieves 200 MPa only. Comparing representative domains (B vs D, A vs F), the stress of open dowel are approximate 15% to 25% higher than that for close dowels. The stress result obtained from FE simulation of series 3 to 4 and series 6 to 7 shows that the stress/strain in steel rib are alway less than the yield strength limit.The steel exhibits elastic behaviour, which agrees with obsevation from tests. A comparison of Figs. 7.4 and 7.5 to 7.8 indicates that stress increament in steel rib is slower than the resistance load. This can be explained by strength of steel rib is higher.

138


Local damage of concrete blocks 10.0

K

tensile areas

J

compressive areas

I1 J1

Strain − εyy (%o )

I

I1

7.5

punching

I

5.0

K

2.5

ODW−Point I ODW−Point J

0.0

ODW−Point I1 ODW−Point J1

−2.5

ODW−Point K

J

−5.0 J1

−7.5 −10.0 0.0

2.0

4.0

6.0

8.0

10.0

Relative slip (mm)

a) Open dowel 10.0 N

7.5

tensile areas

5.0

M

L1 M1

compressive areas

Strain − εyy (%o )

L

punching

N

L1

L

2.5

CDW−Point L CDW−Point M

0.0

CDW−Point L1 CDW−Point M1

−2.5 −7.5

−10.0 0.0

b) Closed dowel

CDW−Point N

M

−5.0

M1

2.0

4.0

6.0

8.0

10.0

Relative slip (mm)

Figure 7.9.: Local strain distribution in concrete block

The local damage investigation of concrete is carried out via examination of the local strain distribution on critical regions. Fig. 7.9 shows strain yy in a half of concrete slab at peak load, and the strain development diagrams of the typical points are also plotted in the same figures. It can be seen that, generally, the strain distribution of CDW and OWL exhibits very similar. The tensile strain region locates on the upper part of the dowel (Point I, I1 and L, L1), while the compressive domain take places almost part of dowels and its below areas (Point J, J1 and M, M1). In initial stage the damage regions is relative small and it is expanded proportional with resistant load of the dowel. After the resistance reaches peak load, the tension area are full plastic and while compression zone expands continuously. This area plays a main role in carrying external force until full crushed, exhibited in softening branch of the characteristic load slip curve. Observing point K and N where the punching force


139

concentrates to the front cover. For ODW the tensile stress at position along with both dowels are nearly the same in term of magnitude and influencing area. This is contrast to CWD with point N give exceptional magnitude compare to the remaining corresponding location. The development of strain versus slip at the critical points are shown in Fig. 7.9. It can be seen the strain increase very fast after specimen is begin loaded. The tensile strain curves reach ultimate limit value of concrete earlier than compressive strain curves. A comparison of the strain-slip diagram (Fig.7.9) to stress-slip diagram (Fig. 7.8) shows the failure of concrete dowel occurs early before the yield of the steel rib. The current design of dowel profile where the steel rib is greater than the cross section of concrete dowel, the failure mode of shear connector are controlled by plastic/crushing of concrete rather than the yield of steel. Shearing cone of concrete dowel Fig. 7.10 shows the local strain distribution on the cross section of concrete dowel. As can seen from horizontal section (Fig. 7.10b), the vertical strain is in compression state at center while far away in tension. The change of strain state results in the shear force at both sides of the steel rib that forms the punching cone as showing in Fig. 7.10c. The dimension of this cone depends on the strain state when external force is imposed. With embedded rebar of φ8mm diameter in the concrete dowel, the simulation result at peak load indicates the width of shear area is about 3 times thickness of steel rib at the top perforated hole and expands to 5 to 7 times of rib thickness at the bottom. For reinforcement, the stress distribution is demonstrated in Fig. 7.10a, the stress suddenly change from compression to tension at shear surface of the shearing cone. The compressive stress in mid strip area reach 265 MPa and 200 MPa for open and closed dowel respectively while the tensile stress reach nearly 10 MPa only. After peak load the stress in reinforcing bar increases continuously if external load still imposed, and rebars may be full yielded at center area. This point out that, the amount of rebar at center should be more than out side regions. To evaluated the effectiveness of the dowel action in shear connector, the effective width is defined by the size of highly concentrated zone in both sides of the steel rib. Observing on numerical solution when concrete dowel are full plastic, the effective width of stress strain was approximate 7 times of thickness for reinforcing bars of φ8mm and 9 to 12 times for φ14mm and φ16mm respectively. Consequently, to improve the shear resistance of shear connector, the effective

140


width of concrete should be expanded. It is ideal if the diameter of rebars in dowel and their length is not necessary equal to width of slab. The transverse reinforcement in front cover with smaller diameter should be sufficiently long to resist crack opening on the surface due to dowel action and shrinkage of concrete.

Figure 7.10.: Stress concentration distribution in rebars of Series 4 (ODW) and 7 (CDW)

Figure 7.11.: Simplified shearing cone assumption

For practical calculation resistance of plain concrete dowel, the shearing cone is simplified as a wedge as shown in Fig. 7.11, the width of top and bottom cone are t and 5t respectively.


141

7.2.4. Proposed model for prediction ultimate capacity of perforbond shear connector Parameter study In order to obtain model for predicting the ultimate capacity of perfobond shear connector made of UHPC, various numerical analyses were conducted, classified as three main groups: PFB-RE, PFB-TH and PFB-YS using the variables of the amount and yield strength of the reinforcing bars in dowel; thickness and yield strength of steel rib. In all numerical analysis some assumptions were made as follows: concrete is B4Q with parameters derived from analysis of series 7 Bst500 reinforcement with fy = 500 MPa used for all models to simplify the statistic analysis, the shear capacity of ODW and CDW are considered as the same only analytical models for CDW were considered.

The simulation results for the shear resistance of each group are listed in Tab. 7.3, and they are combined with full sets of experimental results given in Tab. 7.2 for linear regression analysis. Due to the lack of test results to validate the numerical model, the variation of concrete properties and geometry parameters should be performed in the further work. Prediction model of shear capacity As mentioned in chapter 4, the experimental study pointed out that the bearing capacity of PSC depends on concrete dowel and rebar in dowel as well as transverse reinforcement in front cover. The numerical simulation indicates that the deformation and yielding of the steel rib also contribute too. The simple prediction equation of bearing capacity of the PSC can be assumed that: Pu = β1 Pdw + β2 Pr + β3 Pfr + β4 Pa

(7.1)

Where: Pdw , Pr , Pfr and Pa are resistant capacity of concrete dowel, rebar in dowel, reinforcing bars in cover as well as steel rib respectively. And βi is weighting factor of the each contribution, which are to be determined by linear regression analysis.

142


Pdw is determined based on simplified shearing cone assumption as shown on Fig. 7.11, it can be notice that, only shear surface on the both side of steel rib are taken into account. p The area of each shear surface equals to Ash,dw = bo ×d , with bo = φ and d = 4t 2 + φ2 , where t is thickness of steel rib and φ is diameter of perforated holes. The shearing capacity of plain concrete dowel become:

p p Pdw = 2ndw φ 4t 2 + φ2 fc

(7.2)

and the remaining components are determined as follows: Pr = Ar fy,r

Pfr = Arf fy,r

Pa = ndw tφfy,a

(7.3)

Where: ndw is number of dowel in the connector, fc is cylinder compressive strength of concrete in MPa, bo and d are critical perimeter and depth of the shearing cone in mm, t is thickness of steel rib in mm, Ar , Arf are total area of transverse reinforcement in concrete dowel and front cover respectively in mm 2 , fy,r and fy,a are corresponding to the yield strength of reinforcement and structural steel in MPa. Substitute eq. 7.3 into eq. 7.1, the prediction capacity equation of the perfobond shear connector can be rewritten: p Pu = 2β1 ndw bo d fc + β2 Ar fy,r + β3 Arf fy,r + β4 ndw tφfy,a (7.4) Using multiple linear regressions with least squares procedure with all data given in Tab. 7.2 and 7.3, the β1 , β2 , β3 and β4 factors were determined as: 2β1 = 3.4579

β2 = 1.1259

β3 = 0.4054

β4 = 0.2296

(7.5)

Equation 7.4 becomes: Pu = 3.4579ndw bo d

p

fck + 1.1259Ar fy,r + 0.4054Arf fy,r + 0.2296tφfy,a (7.6)

It worth be to mention that, the scope of equation 7.6 is very limited due to the limitation of available data. The variation of concrete properties and geometry parameter should be further studied. To verify the accuracy of the equation 7.6, all experimental data are compared and listed in Tab. 7.4. The predictions show good agreement with tests and simulation for a steel fiber volume of 1.0%. For specimens contains 0.5% steel fiber, the prediction results give lower values with error varying from 20% to 30% compared to test results.

∗

Open dowel setup 2 Rebar in dowel

Open dowel setup 2 Rebar in dowel and front cover

Closed dowel set up 1 without any rebar

Closed dowel set up 1 Rebar in dowel

Closed dowel set up 1 Rebar in dowel

Closed dowel set up 2 Rebar in fron cover

Closed dowel set up 2 Rebar in fron cover

Closed dowel set up 2 Closed dowel set up 2

4 5 6

7 8 9

10 11 12

13 14 15

16 17 18

19 20

21 22

23 24

10 11

9

8

7

6

5

4

3

2

Series

10.0 10.0

10.0 10.0

10.0 10.0

10.0 10.0 10.0

10.0 10.0 10.0

10.0 10.0 10.0

10.0 10.0 10.0

10.0 10.0 10.0

10.0 10.0 10.0

t(mm)

Thick.

Cross section area of dowel: Adw = 1590.4 (mm 2 )

Open dowel setup 2 without any rebar

Description

1 2 3

Spec.

380 380

380 380

380 380

380 380 380

380 380 380

380 380 380

380 380 380

380 380 380

380 380 380

Yield strength fy(N /mm 2 )

Steel rib

Table 7.2.: Push-Out test and modelling data for linear regression analysis

201.1 113.1

0.0 0.0

0.0 0.0

201.1 201.1 201.1

201.1 201.1 201.1

0.0 0.0 0.0

201.1 201.1 201.1

201.1 201.1 201.1

0.0 0.0 0.0

Ar ,dw (mm 2 )

Dowel

502.7 502.7

502.7 502.7

502.7 502.7

502.7 502.7 502.7

0.0 0.0 0.0

0.0 0.0 0.0

502.7 502.7 502.7

0.0 0.0 0.0

0.0 0.0 0.0

Front cover Ar ,cov (mm 2 )

Reinforcement in

0.5 0.5

1.0 1.0

0.5 0.5

1.0 1.0 1.0

1.0 1.0 1.0

1.0 1.0 1.0

1.0 1.0 1.0

1.0 1.0 1.0

1.0 1.0 1.0

fb (%)

cont.

Fiber

967.99 1005.13

894.53 862.16

814.62 729.34

1113.50 1081.77 1066.10

935.47 979.87 927.87

903.01 827.09 865.25

1075.38 1068.52 1113.50

935.47 979.87 927.87

903.01 827.09 865.25

Pu,1 (kN )

strength

Ultimate

7.2. Modelling of Push Out Test 143

7. Finite Element Modelling 144

Open dowel setup 2 with full rebars. Amount rebars in dowel varying

14

13

12

Series

fb (%)

1186.70 1238.24 1277.96 1340.12

Pu,1 (kN )

strength

Front cover Ar ,cov (mm 2 )

1.0 1.0 1.0 1.0

1125.57 1203.35 1219.80

Ultimate

Ar ,dw (mm 2 )

502.7 502.7 502.7 502.7

1.0 1.0 1.0

1089.63 1126.17 1146.78 1208.97

cont.

Yield strength fy(N /mm 2 )

314.2 452.4 615.8 804.2

502.7 502.7 502.7

1.0 1.0 1.0 1.0

Fiber

t(mm)

380 380 380 380

201.1 201.1 201.1

502.7 502.7 502.7 502.7

Reinforcement in

10.0 10.0 10.0 10.0

380 380 380

201.1 201.1 201.1 201.1

Dowel

8.0 12.0 14.0

235 275 380 460

Thick.

10.0 10.0 10.0 10.0

Steel rib

Table 7.3.: Push-Out test and modelling data for linear regression analysis (con’t)

25 26 27 28 Open dowel setup 2 with full rebars. Rib thickness change

Description

29 30 31 Open dowel setup 2 with full rebars. Different in yield strength of steel

Spec.

32 33 34 35

- Each Push-Out specimen consists four dowels - Each front side consists eight φ 8mm rebars - Cross section area of rebars(Ar ,dw − mm 2 ): φ8mm: 201.1; φ10mm: 78.5; φ12mm: 113.1; φ14mm: 153.9; φ16mm: 201.1


145

Table 7.4.: Verification prediction model with experimental and simulation data Steel rib Spec.

Reinforcement in

Thick.

Yield

Dowel

Front

t(mm)

strength (N /mm 2 )

(mm 2 )

cover (mm 2 )

1 2 3

10.0 10.0 10.0

380 380 380

0.0 0.0 0.0

4 5 6

10.0 10.0 10.0

380 380 380

7 8 9

10.0 10.0 10.0

10 11 12

Ult. strength

Diff. Pu,test Pu,pred

Expt.

Pred.

Pu,test (kN )

Pu,pred. (kN )

0.0 0.0 0.0

903.01 827.09 865.25

849.86 849.86 849.86

1.06 0.97 1.02

201.1 201.1 201.1

0.0 0.0 0.0

935.47 979.87 927.87

963.05 963.05 963.05

0.97 1.02 0.96

380 380 380

201.1 201.1 201.1

502.7 502.7 502.7

1075.38 1068.52 1113.50

1064.94 1064.94 1064.94

1.01 1.00 1.05

10.0 10.0 10.0

380 380 380

0.0 0.0 0.0

0.0 0.0 0.0

903.01 827.09 865.25

849.86 849.86 849.86

1.06 0.97 1.02

13 14 15

10.0 10.0 10.0

380 380 380

201.1 201.1 201.1

0.0 0.0 0.0

935.47 979.87 927.87

963.05 963.05 963.05

0.97 1.02 0.96

16 17 18

10.0 10.0 10.0

380 380 380

201.1 201.1 201.1

502.7 502.7 502.7

1113.50 1081.77 1066.10

1064.94 1064.94 1064.94

1.05 1.02 1.00

19 20

10.0 10.0

380 380

0.0 0.0

502.7 502.7

814.62 729.34

951.76 951.76

0.86 0.77

21 22

10.0 10.0

380 380

0.0 0.0

502.7 502.7

894.53 862.16

951.76 951.76

0.94 0.91

23 24

10.0 10.0

380 380

201.1 113.1

502.7 502.7

967.99 1005.13

1064.94 1206.43

0.91 0.83

25 26 27 28

10.0 10.0 10.0 10.0

380 380 380 380

314.2 452.4 615.8 804.2

502.7 502.7 502.7 502.7

1186.70 1238.24 1277.96 1340.12

1126.61 1206.43 1298.39 1404.50

1.05 1.03 0.98 0.95

29 30 31

8.0 12.0 14.0

380 380 380

201.1 201.1 201.1

502.7 502.7 502.7

1125.57 1203.35 1219.80

1302.19 1097.69 1130.44

1.09 1.10 1.08

32 33 34 35

10.0 10.0 10.0 10.0

235 275 380 460

201.1 201.1 201.1 201.1

502.7 502.7 502.7 502.7

1089.63 1126.17 1146.78 1208.97

1005.02 1021.55 1064.94 1098.00

1.08 1.10 1.08 1.10

Pu,test of specimens from 25 to 35 obtained from parameter study

146


7.3. Modelling of composite beam 7.3.1. Finite element model Geometry of composite beam The geometry for the finite element model of the composite beams was the same in the experimental program, as mentioned in Chapter 5. The beam is 6.0m long with a clear span of 5.7m between two supports. The cross section was either I or inverted Tee steel girders with 500mm × 100mm UHPC slab. The reinforcement in concrete slab and the distribution of shear connector were arranged as in the experiments. Fig. 7.12 demonstrates the layout of the model of composite beams. To take advantage of symmetric geometry and reduce the computation cost, only one half of the beam span was modeled.

A. S

Beam length 6.0m/8.0m 150

3000/4000 500

500

400

100

60 30

150

12mm

10mm

300

Cross section B1 &2

ø8@100mm 14mm

45mm

30mm 200

Cross section B3&4

45

410

14mm

385

60

60

150

60

400

Cross section B5&6

45

Figure 7.12.: Geometry of composite beam for FE modelling

Finite element type and meshing In the same manner with modelling of Push-Out test, the finite element software ATENA version 3.3 (18) was used in the present study to investigate the global as well as local behaviour of composite beams subjected to four points bending load. A three-dimensional (3D) FE model has been developed to account for geometric and material nonlinear behaviour of composite beams. A typical FE

7.3. Modelling of composite beam

147

discretization of a composite beam used in the present study is shown in Fig. 7.13.

Figure 7.13.: Finite Element mesh of a composite beam model Coincident node to be merged

contact inside dowel gap element 3D concrete element 3D gap element

Common node

3D steel element

a) Interface surface (3D layer)

b) Node to node connection

Figure 7.14.: Interface between steel and concrete surface

The finite element types used in the model are as follows: eight node Hexahedra (CCIsoBrick8 3D) for the steel girder, perfobond shear connectors as well as concrete slab; multi linear 3D truss element (CCIsoTruss2 3D for the reinforcing bars; interface element (CCIsoGap8 3D) for interactions at surfaces between steel and concrete. In the model, the bond between concrete and reinforcement was considered as perfectly. Additional friction and cohesion force at interface surfaces were also neglected. A minimum value of tension stiffness in tangent

148


and normal direction were assigned to avoid occurring singularity during solving equilibrium equation system (18). In the ATENA element library, the interface element has a family of hexahedra element with six or eight nodes. The two primary opposite surfaces were coupled with the surfaces of steel and concrete respectively. The thickness of contact layer was neglected. Fig. 7.14 illustrates the interface elements and its connection. In order to generate all data for analysis and post processing phases, the model was created in the GID environment and export to ATENA data file. Then the Tool4Atena was used to generate interface data before solving. Material modelling of the composite beam models The material model for composite beam analysis are derived from Push-Out test modelling. Compare to the Push-Out model, only difference in material model for reinforcing bars i.e., one dimensional (1D) multi linear hardening was used. Controlling numerical solution For simple supported composite beams analysis, the pair of concentrate load was subjected to the beams via loading plates with enough stiffness to transfer load into concrete slab (Fig. 7.13). In this model, the load was only placed on center line in transverse direction of the plate, not on overall surface. The plate will rotate together with cross section of the beam. The aim of this technique to avoid locking of loading plate, which will caused too early local damage and results in incorrect of global response. To control convergence of solution, external load was replaced by an equivalent prescribed displacement, which increases very slow and is controlled to ensure convergence of solution on each load step. The applied force is calculated by summing up all vertical reaction components. For solving nonlinear equation, full Newton-Raphson was used and linear search algorithm also turn on to accelerated convergence. In the convergence criteria, L2 norm was considered for displacement, residual and energy error. The finite element mesh was controlled enough small to ensure convergence of solution. If the density of mesh increases will result in huge of unknowns in system equations which very difficult convergence in solve nonlinear equation and take too much computation time. In this work, with a half of model, the total amount of the calculation time for 250 load steps and preparing data for post processing takes approximate 27 hours on the 2 × 2.6 GHz duo core computer.


149

Failure criterion To evaluation the failure of composite beam, the criterion as follow will be applied in the analysis: failure of steel beam when strain reach yield limit of materials. In this case at the critical section, the mean value of strain of a part is equal or greater than 0.18%. the collapse of composite beams caused by crushing of concrete in compression zone when compressive strain lies in the limit area of lower and upper boundaries corresponding to 0.3% and 0.35%. the failure of shear connectors occur when stiffness of beam is too high while amount of shear connector is less than required. The shear capacity of the total dowels is lesser than longitudinal shear force. For NSC composite beams, the second condition often occur, however for UHPC composite beam, potentials of both reasons may occur.

In the numerical analysis of composite beam the first two criteria were used as major checking conditions, while the shear failure of connector only plays a minor role. 7.3.2. Validation of the FE model Load - deflection To validate the FE model, a comparison of FE analysis result versus experimental data are best illustration. Fig. 7.15 shows the typical deformed shape of the beam B1 and the corresponding FE simulations. Table 7.5 describes the details of the beams are being compared with FE analysis. The degree of shear connection for each beam is defined as the ratio of resistance of shear connection and less than the element capacity of steel beam or UHPC slab. More detailed values also presented in this table. Table 7.6 shows all analyzed results and experimental data of the composite beams with ultimate strength and deflection at mid span. A comparison of load - defection diagram at one of quarter and mid span is presented in Fig. 7.16 and 7.17. It can be seen that the initial stiffness of the composite beams predicted by the FE model are the same as that of the experimental. In the yielding plastic zones, the response demonstrates very good agreement with test, the peak loads in simulation come earlier compared with the experiment.

150


Figure 7.15.: Deformed shape of the beam B1 and FE simulation

Table 7.5.: Description of composite beams for experimental and modelling Beam

B1 B2 B3 B4

Specimen ID

B6M-I-ODW-100 B6M-I-CDW-100 B6M-T-CDW-150 B6M-T-ODW-150

Steel

Dowel(Dia. 45mm)

Deg. of shear

girder

Quan.

Shape

Spacing

connection

I I invT invT

59 59 39 39

ODW CDW CDW ODW

100 100 150 150

126.54 153.88 95.86 111.80

The pair of ultimate load obtained by present simulation and experiment data were 748.73 kN and 756.8 kN for beam B1, 763.77 kN and 764.39 kN for beam B2, 952.86 kN and 929.96kN for beam B3 as well as 972.75kN and 877.08kN for beam B4. The difference on ultimate strength of beam B1 to B3 in range of 1.0% to 2.4% and the beam B4 is higher up to 9.8%. The simulation indicates that, the simulation for the ultimate loads are better than for deformation. The loaddeflection curves also pointed out that, the composite beam B1 and B2 were failed by yielding of steel profile while failure mode of beam B3 governed by collapse of shear connections, the behaviour show elastic only. In the numerical model, all beams exhibited the same failure mode as experiment.


151

Table 7.6.: Ultimate load and deflection results for the experimental and numerical analyses Beam

B1 B2 B3 B4

Applied load (kN)

∗:

Deflection∗ (mm)

Ultimate load (kN) Exper.

Simulation

Exper.

Simulation

748.81 761.18 952.86 996.54

756.19 763.56 929.96 877.08

100.41 110.01 32.77 92.29

78.49 84.52 30.25 45.54

yielding of steel yielding of steel shear connection yielding + crushing

Deflection at ultimate load

1000

1000

800

800

600

600

400

400 B1-Def. at 1/4 span (test) B1-Def. at 1/2 span (test) B1-Def. at 1/4 span (sim.) B1-Def. at 1/2 span (sim.)

200 0

Failure mode

0

25

50

75

100

125

B2-Def. at 1/4 span (test) B2-Def. at 1/2 span (test) B2-Def. at 1/4 span (sim.) B2-Def. at 1/2 span (sim.)

200

150

0

0

25

Deflection (mm)

50

75

100

125

150

Deflection (mm)

Applied load (kN)

Figure 7.16.: Comparison test and modelling results of beam B1 and B2, force - deflection 1200

1200

1000

1000

800

800

600

600

400

400 B3-Def. at 1/4 span (test) B3-Def. at 1/2 span (test) B3-Def. at 1/4 span (sim.) B3-Def. at 1/2 span (sim.)

200 0

0

20

40

60

Deflection (mm)

80

B4-Def. at 1/4 span (test) B4-Def. at 1/2 span (test) B4-Def. at 1/4 span (sim.) B4-Def. at 1/2 span (sim.)

200 100

0

0

20

40

60

80

100

Deflection (mm)

Figure 7.17.: Comparison test and modelling results of beam B3 and B4, force - deflection

From comparison simulation results and test data in both term force and deformation. It can be seen that, the proposed finite element model has sufficient accuracy and reliability for numerical investigation of composite beams. It is able to predict ultimate load accurately as well as the failure mode.

152


Strain in concrete slab and steel girder

Applied load (kN)

In order, to illustrate the capacity of numerical model for the local behaviour, the load - strain in the steel girder and UHPC slab of middle span are shown. Fig. 7.18 to Fig. 7.21 present load-strain response in concrete slab and steel girder of beam B1 to B4 respecitvely. It can be seen that, the strain development show very good agreement with test data, which is similar to the load-deflection curves. 1000

1000

800

800

600

600

400

400 B1-bot. flange (test) B1-top falnge (test) B1-bot. flange (sim) B1-top falnge (sim)

200 0 -1.5

0.0

1.5 3.0 4.5 6.0 Strain of steel girder(‰)

7.5

200

9.0

0 -4.0

B1-bot. slab (test) B1-top slab (test) B1-bot. slab (sim.) B1-top slab (sim.)

-3.0 -2.0 -1.0 0.0 1.0 Strain of concrete slab(‰)

2.0

Applied load (kN)

Figure 7.18.: Comparison test and modelling results of beam B1, force-strain 1000

1000

800

800

600

600

400


200 0 -1.5

0.0

1.5 3.0 4.5 6.0 Strain of steel girder(‰)

7.5

200

9.0

0 -4.0

B2-top slab (test) B2-bot. slab (sim.) B2-top slab (sim.)

-3.0 -2.0 -1.0 0.0 1.0 Strain of concrete slab(‰)

2.0

Figure 7.19.: Comparison test and modelling results of beam B2, force-strain

Observing in Fig. 7.18 and Fig. 7.19, in the initial stiffness region the load increase almost linearly with the strain. The bottom flange reach yield limit (a = 1.8h) at load 550 kN, at this load level the strain of concrete slab still lie in elastic domain. Under increasing of applied the load, the strain in steel flange develops continuously and becomes plastic. When the ultimate strength is archived at around 750 kN, the strain in UHPC slab approach closer limit of compressive strain. Comparison on strain of concrete slab and steel girder, when


153

Applied load (kN)

compressive strain achieve 3.2h the tensile train of steel is over 9.0h. The steel girder enters into plastic range prior to the crushing of concrete. The failure mode was identified as the yielding of the steel girder, as observed in the test. 1200

1200

1000

1000

800

800

600

600

400


200 0 -1.0

-0.5

0.0 0.5 1.0 1.5 2.0 Strain of steel girder (‰)

200 2.5

0 -3.0


-2.5 -2.0 -1.5 -1.0 -0.5 Strain of concrete slab (‰)

0.0

Applied load (kN)

Figure 7.20.: Comparison test and modelling results of beam B3, force-strain 1200

1200

1000

1000

800

800

600

600

400


200 0 -1.5

0.0

1.5 3.0 4.5 6.0 7.5 Strain of steel girder (‰)

200 9.0

0 -4.0


-3.0 -2.0 -1.0 0.0 1.0 Strain of concrete slab (‰)

2.0

Figure 7.21.: Comparison test and modelling results of beam B4, force-strain

As can be seen from strain behaviour of the beam B3, in general the load-strain relation is almost linear in the whole domain. The strain obtained from steel approach closer to the test data while the strain shows opposite image in the top surface, which is greater than measured value. The beam failed when both material are under critical values. The falling of beam B3 was recognized due to collapse of shear connection. The beam B4 with bottom flange was cut to be smaller than beam B3, The aim is to fail in plastic mode. As can seen from Fig. 7.21, strain increment show very good agreement with test data in both tension and compression fiber of the cross section. The strain at bottom flange reaches firstly yield limit at 780 kN and increases continuously. After peak load (PU = 877.08), a bottom fiber of

154


concrete slab became in tension and compression height was reduced. The failure mode of the beam was identified due to plastic and crushing of concrete. Local slip along beam In addition, to further demonstrate capacity of numerical model in local analysis, the slip between steel and concrete surfaces are plotted in Fig. 7.22 for beam B1 and B2 respectively. It can be noticed that, the distribution of slip is not uniform along the span of the beam. With low level load (488kN), the slip is increases slowly from the left end forward inside span, the peak value of load-slip behaviour locates at section X/L =0.35 and decreases forward to mid span section. 0.5

0.5

B2−Slip at load=480.39 kN (sim)

B1−Slip at load=487.11 kN (sim)

B2−Slip at Load=754.22 kN (sim)

B1−Slip at Load=488.98kN (test) B1−Slip at Load=748.56kN (test)

0.3 0.2 0.1

Relative slip (mm)

Relative slip (mm)

B1−Slip at Load=759.03 kN (sim)

0.4

0.4

B2−Slip at Load=486.68 kN (test) B2−Slip at Load=754.13 kN (test)

0.3 0.2 0.1

0.0 0.0 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 Relative position (from the left end to midspan section) Relative position (from the left end to midspan section)

Figure 7.22.: Comparison local slip of beam B1 (left) and B2 (right)

At the ultimate load level, load - slip increases very fast from left end into span and reach a maximum value at position X/L = 0.4. and decreasing from 0.4 to mid span section. This behaviour is very similar with result presented by Queiroz et al. (86) for case of composite beam under concentrate load. The large slip behaviour which occurs near mid span section is due to the influence of plastics deformation in around area leads to increasing slip at interface of steel and concrete. The figure also indicates that, the tendency of the simulation results is maintained along the experiment data. The proposed numerical model can predict slip distribution with high accuracy.


155

7.3.3. Local stress distribution in steel girder and shear connectors Fig. 7.24 shows the stress distribution in steel girders after the composite beams reaches the peak load. Generally, under bending load the bottom fiber of steel girder is in tension while the top fiber is in compression. The strain in top and bottom fiber of steel girder are presented in Fig. 7.18 to 7.21. B1

B2

B3

B4

Figure 7.23.: Stress distribution in girder, beam B1 to B4

The stress distribution in steel rib depends on the shape of perforated holes on steel plate and also influenced by curvature in bending. It can be seen from Fig. 7.25 that, for the closed dowel, the compression zone is formed in both lowest and highest point on perimeter of the holes. Whereas the tension area is located on both sides of the horizontal center line. For ODW shear connector, the critical tension zone located in the left and right edges of the holes while the compression area concentrate at lowest points of the holes.

156


Comparison with stress distribution which was obtained from Push-Out test (Fig. 7.8), the location of tension and compression zones are significantly different nearly opposite. The main reason is the steel rib in Push-Out test is not affected by the bending curvature which can reduce stress in steel rib. In practical design of perfobond shear connector, if the yielding of steel must be considered, the location of stress field in perforated strip should be based on the global analysis.

Figure 7.24.: Stress distribution in steel rib

Stress σxx (MPa)

300 200

B1−Tension zone σxx at Load lever=0.76 Pu

Tension zone

0

−200

300

B1−Tension zone σxx at Load lever=0.99 Pu

100

−100

400

B1−Tension zone σxx at Load lever =0.40 Pu

compression zone B1−Compression zone σxx at Load lever =0.40 Pu B1−Compression zone σxx at Load lever=0.76 Pu B1−Compression zone σxx at Load lever=0.99 Pu

−300 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 Relative position (from the left end to midspan section)

Stress σxx (MPa)

400

B2−Tension zone σxx at Load lever =0.40 Pu B2−Tension zone σxx at Load lever=0.76 Pu B2−Tension zone σxx at Load lever=0.99 Pu

200

B2−Compression zone σxx at Load lever =0.40 Pu B2−Compression zone σxx at Load lever=0.76 Pu

100

B2−Compression zone σxx at Load lever=0.99 Pu

0

−100 −200 −300 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 Relative position (from the left end to midspan section)

Figure 7.25.: Longgitudinal stress in steel rib of shear connector, beam B1 and B2

Fig. 7.25 shows the magnitude of stress in longitudinal direction along steel ribs represented for CDW and ODW. The maximum tensile stress in ODW is about 300 MPa and compressive stress reach 220 MPa which is lower than the tensile strength. The stresses concentrate highly in the middle span area and then reduce to the supports directions, the distribution stress show correlation with measured slip distribution along the beam. Contrast with ODW, in CDW the compressive stress is dominant compared with tensile stress. It achieved a maximum value at section X/L=0.1 with 200 MPa, which equals to the stress in ODW. The distribution also exhibits the same manner with ODW. Through comparing stress distribution of typical dowel profile, it can be seen that the stress in OWD is higher than CDW around 30 %. It mean thats the

7.4. Summary conclusion

157

design of CDW give higher stress than ODW. With long span composite beam that requires high logitudinal shear resistance, if the cross section of concrete dowel is increased, then CDW profile should be chosen and changed from circle to elliptical shape. 7.3.4. Shear flow on concrete dowel It is worth noting that, the reliability of the stress value in concrete obtained from the numerical computation is insufficient for analysis the shear flow distribution longitudinal beam. This problem need further improvement in the analytical model as well as constitutive model of UHPC.

7.4. Summary conclusion In this chapter full three dimensional finite element models for Push-Out test and composite beams were successfully developed, taking into account the complexity of geometry and nonlinearity of materials. The numerical models were validated with test data. Generally, the global as well as local behaviour predicted by the numerical models show good agreement with experiments. The numerical model give reasonable results in comparison with the measured load and deformation. Based on measured results as well as parameter study, a predictive model for ultimate bearing capacity of perfobond shear connector was proposed which covered on almost popular cases. The numerical study illustrate that it is helpful combining of FE modelling and experiment for better understanding the real behaviour of complex structures. On the meanwhile, the numerical study indicates there are still some disadvantage with the numerical model as stated belows: The Microplane model M4 model for concrete available in library of ATENA program (Version 3.3) is not able to accurately describe the highly tensile/flexural behaviour of concrete, especially, for UHPC with high ductility. The modelling of RILEM beam with G7N, G7N3 and G9 concrete mixer with this model were not successful. The model parameters of model M4 can not be obtained directly from test data. The parameter study with varying of material properties such as elastic modulus, compressive and tensile strength as well as the fracture energy can not carried out directly on structural models. When a parameter changes, the model should be re-validated.

158


Analysis structural concrete using mircoplane model with software ANTENA occur some convergence problem, which increases running times. In this work, the limitation of computer system on computation capacity does not allow more investigations. The improvement on constitutive model of concrete model is necessary in order to get better result as well as performance for the numerical modelling.

8. Conclusions and Future Perspective UHPC is very promising new materials that are expected to find more applications in the near future. With UHPC the structures can be thiner, slender with daring new shapes and capable of carrying more heavy load as well as more durable in extreme conditions. In this study the behaviour of composite beam made of UHPC with innovation continuous shear connector has been investigated. The research described in this thesis comprise of two phases: phase I was an experimental investigation into the behaviour of Push-Out specimens and composite beams. In phase II, numerical simulation was conducted to model the behaviour. Furthermore a modelling approach based on Finite Element Code ATENA has been established to access the local behaviour. The work undertaken in this thesis has identified a number of areas which needs further research. It may be seen as “answers” to the questions raised in Section 1.3. Recommendations for further study are also given at the end of this chapter.

8.1. Conclusion 8.1.1. Ultra high performance concrete 1. UHPC exhibits very high compressive strengths, which may reach 150MPa in normal curing condition and greater than 200 MPa if curing treatment is applied. This material also shows high brittle behaviour, in stressed compression it could be explosive when crushed. 2. The tensile strength of UHPC is significantly higher than that of normal concrete. The addition of steel fiber into concrete mixture improves remarkable the tensile strength. Long fiber controls peak tensile stress while short fiber controls the post peak behaviour. The cocktail fiber is more effective. Flexural strength can be reach 7.0 MPa to 25.0 MPa depend on volume of fiber content.

160

8. Conclusions and Future Perspective

3. UHPC shows outstanding workability. The slum flow varies from 65cm to 90cm. The rheological properties of fresh UHPC are influenced by the concrete mixer design, mixing method as well as superplasticity. The set time of UHPC is significantly delayed compared with normal concrete; final set does not occur until 12 to 24 hours after casting. When setting is initiated, UHPC gains its compressive strength very fast. 4. Due to large amount of cement used, the shrinkage of UHPC must be taken into account for use. 5. The durability of UHPC are significantly better than that of normal concrete. 6. The fracture of UHPC is influenced by the fiber content and the casting direction as well as coarse aggregate. The fracture energy varies in range of 5,000 to 20,000 N/m. 7. UHPC is a promising substitute for normal concrete and HPC in composite structures. 8. The high material cost is a restriction for the application of UHPC in practical engineering. The finding of appropriated structural solutions for UHPC is still challenging for researchers and engineers as well. 8.1.2. Composite beam members made of UHPC under static load 1. UHPC enhances the performance of composite beam The use of UHPC in composite beam lead to increased stiffness due to high elastic modulus. The deflection of beam under service condition is much smaller comparison to conventional composite beams with NSC. The ultimate strength is also higher allowing carry to more heavy load under critical conditions. The high compressive strength of UHPC placed in compression zone optimize the load distribution in the section. Thus increase significantly the load bearing capacity of composite member. The size of member can be reduced. Faster in strength development, higher in workability and not requirement special curing condition lead to save more time, labor work, energy as well as the time to market.

2. The Steel-UHPC composite beams exhibit the same manner with conventional composite member with NSC

8.1. Conclusion

161

The structural behaviour of composite beam made of UHPC is similar to traditional composite beam in the three aspects: elastic, yielding and plastic domains. In case of full shear connection, the simple rigid plastic can be used to predict ultimate plastic moment. The continuous shear connection is able to effecting transfer the load in composite beam with both Tee and I girders. The longitudinal shear distribution is not uniform, the design for strength of shear connector must taken into account weakest connectors. Composite section with Tee girder can provided 30% to 50% higher bearing capacity and stiffness than I section with the same cross section area of steel.

8.1.3. Perfobond based shear connectors in UHPC 1. The ductility of headed stud shear connector is significant in UHPC slab due to the deformation is restrained by very high strength concrete surrounding it. The connector is often failed by shanked mode at the base. This may reduce its fatigue strength under dynamic load. The stud connector is not recommended to use in composite beam made of UHPC. 2. The perfobond shear connector exhibits good performance in shear load transfer as well as the ductility. However, all the test data showed the characteristic slip δuk is still smaller than 6.0mm as requireed for ductile connector. Thus these connector can be only considered as non-ductile one in design. 3. The Perfobond connector without transverse reinforcement displays very poor ductility. Thus it is not recommended in application. The embedded rebar in dowel play a critical role for improving ductility of the connector. 4. Failure of connector is often caused by crushing of concrete and plastic of reinforcement rather than yielding of steel. Therefore the ratio of cross section area of concrete dowel to steel rib should be adjusted to obtain appropriate load distribution between materials. 5. Shear capacity of open and closed dowel are not differ much. But from practical application point of view, the open dowel is much easier for setting reinforcement and the flowing of concrete through holes in the steel rib.

162


8.1.4. Modelling of composite beams 1. Microplane model M4 for concrete is helpful for modelling the behaviour of UHPC under complex stress states. The model parameters must be calibrated with test data prior using to describes for UHPC. The parameter adjustment to fit with curves of bending test is very difficult task, especially in the case of UHPC contain high volume fiber contents. Currently, there are no general rule for adjustment. 2. The Microplane M4 which integrated in material library of the ATENA software is not sufficient strong to simulate exactly tensile-shear stress state which occurs in concrete dowels. The better constitutive material model is necessary. 3. The full three-dimensional finite element models were developed using software ATENA to successful analysis Push-Out specimens and composite beams, which taken into account complex geometry and high nonlinearity behaviour of materials. The numerical simulation shows reasonable results compare with test data. 4. Numerical studies was conducted to assess local damage Perfobond shear connector, the result pointed that, the shear connection has a remarkably influence on the stiffness and ultimate strength of the composite beam. With low degree (or partial) of shear connection the composite system is weaker than and reduce ultimate capacity. However, if increasing shear connection lead to considerably higher ductility. The strength of beam also increase up to 20%. 5. The beam with open shear connector has higher ductility than closed shear connector, although the individual shear capacity of this type is lower.

8.2. Recommendations for further research 1. Further tests needed to be conducted on UHPC shear connectors with different volumetric percentages of steel fibers to further evaluate the ability of steel fibers for enhancing the slip capacity. 2. Studies should be performed for higher ratio cross section area of concrete dowel to the area of steel rib. Moreover tests with different perforated rib thicknesses are also necessary to obtain their effect on the strength of shear connectors.

8.2. Recommendations for further research

163

3. The fatigue strength of the composite beam as well as the shear connectors should be further studied. This is very important for structures under dynamic loads such as bridge. 4. Material model of concrete need to be improved to better describe the influence of fiber content on the post peak behaviour in the bending test. Additional, the improvement is also necessary to enhance the precision of results in local damage response of shear connectors, especially in tensileshear region. 5. The general rule of identification model parameters should be further investigate, in order to obtain best results for the numerical modeling.

164


A. Appendices: Concrete mix proportional A.1. List of tables for constituent materials UHPC-B4Q 1% steel fiber UHPC-G7 1% steel fiber UHPC-G7 0.5% steel fiber

166

A. Appendices: Concrete mix proportional

B. Appendices: Standard Push-Out Test B.1. Experimental results of Standard Push-Out test Series 1: Headed stud (φ16mm, Bst500), test setup S1 Series 2: ODW without rebar, test setup S2 Series 3: ODW with rebar in core, test setup S2 Series 4: ODW with rebar in core and cover, test setup S2 Series 5: CDW without rebar, test setup S1 Series 6: CDW with rebar in core, test setup S1 Series 7: CDW with rebar in core and cover, test setup S1 Series 8: CDW with rebar in cover, 0.5% steel fiber, test setup S1 Series 9: CDW with rebar in cover, 1.0% steel fiber, test setup S1 Series 10: CDW with φ8mm rebar in core and cover, 0.5% steel fiber, test setup S1 Series 11: CDW with φ12mm rebar in core and cover, 0.5% steel fiber, test setup S1

B.2. List of drawings and charts Push-Out test setup Push-Out rebars arangement Chart of Load-slip and crack openning

168

Figure B.1.: Push-Out test setup S1 and S2

B. Appendices: Standard Push-Out Test

B.2. List of drawings and charts

Figure B.2.: Rebars arrangement of Push-Out specimens

169

170


1600

S1−1 LVDT−3 S1−1 LVDT−4

1200

Applied load (kN)

Applied load (kN)

1600

800 400 0

0

2

4

6

8

1200

S1−1−LVDT 1.1 S1−1−LVDT 1.2 S1−1−LVDT 2.1 S1−1−LVDT 2.2

800 400 0 −0.06 −0.045 −0.03 −0.015

10

Slip (mm)

0

0.015

0.03

Crack Openning (mm)

(a) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0

0

2

4

6

8

1200


800 400 0 −0.06 −0.045 −0.03 −0.015

10

Slip (mm)

0

0.015

0.03

Crack Openning (mm)

(b) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0

0

2

4

6

8

10

Slip (mm)

1200


800 400 0 −0.06 −0.045 −0.03 −0.015

0

0.015

0.03

Crack Openning (mm)

(c) Figure B.3.: Push-Out test reults: Load-Slip and Crack opening, Series 1-Headed stud shear connector, specimen-1(a), specimen-2(b), specimen-3(c)


1600

S2−LVDT−3+4

1200

Applied load (kN)

Applied load (kN)

1600

171

800 400 0

0

2

4

6

Slip (mm)

8

10

S3−LVDT−3+4

1200 800 400 0

0

2

4

6

8

10

Slip (mm)

Figure B.4.: Push-Out test reults: Load-Slip, Series 2-ODW without rebar (left), Series 3-ODW with rebar in core(right)

172


1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0

0

2

4

6

8

1200


800 400 0 −0.06 −0.045 −0.03 −0.015

10

Slip (mm)

0

0.015

0.03

Crack Openning (mm)

(a) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0

0

2

4

6

8

1200


800 400 0 −0.06 −0.045 −0.03 −0.015

10

Slip (mm)

0

0.015

0.03

Crack Openning (mm)

(b) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0

0

2

4

6

8

10

Slip (mm)

1200


800 400 0 −0.06 −0.045 −0.03 −0.015

0

0.015

0.03

Crack Openning (mm)

(c) Figure B.5.: Push-Out test reults: Load-Slip and Crack opening, Series 4-Open dowel with rebar in core and front cover, specimen-1(a), specimen-2(b), specimen-3(c)


1600


1200

Applied load (kN)

Applied load (kN)

1600

173

800 400 0 0.0

2.0

4.0

6.0

8.0

1200 800 400 0 −0.6

10.0


Slip (mm)

−0.45

−0.3

−0.15

0

0.15

Crack Openning (mm)

(a) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0 0.0

2.0

4.0

6.0

8.0

1200 800 400 0 −0.6

10.0


Slip (mm)

−0.45

−0.3

−0.15

0

0.15

Crack Openning (mm)

(b) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800 400 0 0.0

2.0

4.0

6.0

8.0

10.0

Slip (mm)


1200 800 400 0 −0.6

−0.45

−0.3

−0.15

0

0.15

Crack Openning (mm)

(c) Figure B.6.: Push-Out test reults: Load-Slip and Crack opening, Series 5-CDW without Reinforcement, specimen-1(a), specimen-2(b), specimen-3(c)

174


1600



1200

Applied load (kN)

Applied load (kN)

1600

800 400 0 0.0

2.0

4.0

6.0

8.0

1200 800 400 0 −1.0

10.0

−0.8

−0.6

−0.4

−0.2

0.0

0.2

Crack Openning (mm)

Slip (mm)

(a) 1600



1200

Applied load (kN)

Applied load (kN)

1600

800 400 0 0.0

2.0

4.0

6.0

8.0

1200 800 400 0 −1.0

10.0

−0.8

−0.6

−0.4

−0.2

0.0

0.2

Crack Openning (mm)

Slip (mm)

(b) 1600


1200

Applied load (kN)

Applied load (kN)

1600

800

400

0 0.0

2.0

4.0 6.0 Slip (mm)

8.0

10.0


1200

800

400

0 −1.0

−0.8

−0.6 −0.4 −0.2 0.0 Crack Openning (mm)

0.2

(c) Figure B.7.: Push-Out test reults: Load-Slip and Crack opening, Series 6-CDW with rebar in core, specimen-1(a), specimen-2(b), specimen-3(c)


1600

1600 1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

175

2.0

4.0

6.0

8.0

1200 800 400 0 −0.4

10.0

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(a) 1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

1200 800 400 0 −0.4

10.0

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(b) 1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

10.0

1200 800 400 0 −0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(c) Figure B.8.: Push-Out test reults: Load-Slip and Crack opening, Series 7-Open dowel with rebar in core and front cover, specimen-1(a), specimen-2(b), specimen-3(c)

176


1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

1200 800 400 0 −0.4

10.0

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(a) 1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

10.0

1200 800 400 0 −0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(b) Figure B.9.: Push-Out test reults: Load-Slip and Crack opening, Series 8-CDW with rebar in cover-UHPC 0.5% steel fiber, specimen-1(a), specimen-2(b)


1600

1600 1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

177

2.0

4.0

6.0

8.0

1200 800 400 0 −0.4

10.0

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(a) 1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

10.0

1200 800 400 0 −0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(b) Figure B.10.: Push-Out test reults: Load-Slip and Crack opening, Series 9- CDW with rebar in cover-UHPC 1.0% steel fiber, specimen-1(a), specimen-2(b)

178


1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

1200 800 400 0 −0.4

10.0

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(a) 1600

1200 800 400 0 0.0



Applied load (kN)

Applied load (kN)

1600

2.0

4.0

6.0

8.0

10.0

1200 800 400 0 −0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

Crack Openning (mm)

Slip (mm)

(b) Figure B.11.: Push-Out test reults: Load-Slip and Crack opening, Series 10-11- CDW with rebar in core and front cover-UHPC 1.0% steel fiber, φ8mm-(a), φ12mm-(b)

C. Appendices: Bending test of composite beam C.1. Design of steel-concrete composite beams for bending test Beam B1 - I girder, slab: 500 x 100 mm, Open dowel shear connector: 59 x 100 mm Beam B2 - I girder, slab: 500 x 100 mm, Closed dowel shear connector: 59 x 100 mm Beam B3 - T girder, slab: 500 x 100 mm, Closed dowel shear connector: 39 x 100 mm Beam B4 - T girder, slab: 500 x 100 mm, Open dowel shear connector: 39 x 100 mm Beam B5 - T girder, slab: 400 x 100 mm, Closed dowel shear connector: 79 x 100 mm Beam B6 - T girder, slab: 400 x 100 mm, Open dowel shear connector: 79 x 100 mm

C.2. List of drawings and charts Instrumentations for test setup Experimental results

180

C. Appendices: Bending test of composite beam

Figure C.1.: Design of the composite beam B1

C.2. List of drawings and charts


181

182





183


100 Steel plate: PL 345x14....x8000mm/S355

4,000

Stegform 2: FL 400 x 45....8000 mm/S355

79 perforated holes, Ø45mm@100mm

aw=10mm

3,100

14

400

4,000 (Full length 8000 mm)

Stegform 3: FL 120 x 10...200mm/S355

Longitudial rebars 4Ø10, Bst 500

UHPC-Slab

750

Loading plate

Reinforcing bars Ø8, Bst 500 e=80 mm

S. A.

Versuchsträger SPP1182 Serie - 2, Beam B5 7.01.2009 / Vinh

Beam B5-composite Slab, UHPC G7-0.5% steel fiber

11

Universität Leipzig Institut für Massivbau und Baustofftechnologie

S. A.


Composite Beam B5, Tee girder 390 x 400 x 45 x 14 length 8000mm, steel grade S355

120

400

100

75

100

14

390

10

200 200

Detail A

100

FL 120x200x10

aw=10mm

49

Beam B5-composite section

410

150

10

75

Detail A

400

345

Beam B5-Girder section

100 265 45

145 200 45

Ø 45

390 410

42 326 22 100 310 42

5 Ø4

184

30

120

Steel Plate: FL 345x14....x8000mm/S355

4,000 (Full length 8000 mm)

4,000

Stegform 2: FL 400 x45....8000 mm/S355

79 Aussparungen, Ø45mm, alle 100mm

aw=10mm

400

3,100

14

400

100

Stegform 3: FL 120 x 10...200mm/S355

Longitudial rebars 4Ø10, Bst 500

UHPC-Slab

750

Loading plate

Reinforcing bars Ø8, Bst 500 e=100 mm

Rebar in dowel Ø8, Bst 500 e=100 mm

Versuchsträger SPP1182 Serie - 2, Beam B6 7.01.2009 / Vinh

Beam B6-composite Slab, UHPC G7-0.5% steel fiber

11


S. A.

S. A.


75

14

49

Beam B6-composite section

410

10

150

100

200

Detail A

45

75

FL 120x200x10

aw=10mm

390

38 330 22

Detail A

400

345

Beam B6-Girder section

100 265 45

145 200 45

Ø 45

390 100 310 42

185 C.2. List of drawings and charts

410

C. Appendices: Bending test of composite beam 186

Weg-1

NORTH

Weg-2

Weg-4

DMS-2

Weg-3

DMS-1

1

Weg-6

Weg-7

2

DMS-4

DBG-1

Weg-5

DMS-3

open shear connector

Weg-8

DMS-5

3

Beam1 : Beam with top flange, dowel spacing 100mm, Drawing: I nstr umentation setup

Pmax_Test = 800 kN Pmax_Cyl = 1100 kN HEB(IPB)360

Weg-9

Weg-10,11

DBG-3

DMS-14

DMS-13

DMS-12

DMS-16 DMS-6

DMS-10

DMS-7

SECTION 2-2

DMS-17

DMS-15

DMS-8 DMS-9

DMS-11

SECTION 1-1

SOUTH

Figure C.7.: Experimental setup of the composite beam B1


Weg-1

NORTH

Weg-2

DMS-1

Weg-4 Weg-5

DMS-3

Weg-3

DMS-2

2

Weg-6

DBG-1

1

closed shear connector

DMS-5

SL_L4

Weg-7

Pmax_Cyl = 1100 kN

DMS-4

3

Beam2 : Beam with top flange, dowel spacing 100mm, Drawing: I nstr umentation setup

HEB(IPB)360

Weg-9

Weg-10

Weg-11 DBG-3

Weg-12

Weg-13

Weg-8

DMS-14

DMS-13

DMS-12

DMS-16 DMS-6

DMS-10

DMS-7

SECTION 2-2

DMS-17

DMS-15

DMS-8 DMS-9

DMS-11

SECTION 1-1

Weg-14

SOUTH

Weg-15



Weg-1 Weg-3

DMS-2

Weg-4

DMS-3

Weg-6

DMS-6

Weg-7

Weg-8

Pmax_Test = 800 kN

DMS-5

3

Pmax_Test = 800 kN Pmax_Cyl = 1100 kN

Weg-15

Weg-11 Weg-10

DBG-3

Weg-12

Weg-9

DMS-7

DMS-17

DMS-14

DMS-13

SECTION 2-2

DMS-18

DMS-16

DMS-15

DMS-8

Centroid Y

DMS-11

DMS-9 DMS-10 DMS-12

SECTION 1-1

Ce ntroid Y

Weg-16


Weg-5

DBG-1

DMS-4

2

Weg-14

NORTH

Weg-2

DMS-1

1

closed shear connector

Beam3 : Beam without top flange, dowel spacing 150mm Drawing: I nstr umentation setup

Weg-13


Weg-2

Weg-14

Weg-3

DMS-2

Weg-4

DMS-3

Weg-6

DBG-1

Weg-5

2

DMS-4

Weg-7

DMS-5

3

Weg-8

Weg-11 Weg-10

DBG-3

Initila load (cylinder+Tranvese beam+Longitudinal beam+ = 285+2*(130)+245 kgf = 793kg=7.93 kN

Weg-9

DMS-6

DMS-12

SECTION 2-2

DMS-17

DMS-15

DMS-14

DMS-16

DMS-13

Centroid Y

DMS-7

DMS-10

DMS-8 DMS-9

DMS-11

SECTION 1-1

Ce ntroid Y

Weg-13


Weg-1

DMS-1

1

open shear connector

Beam4 : Beam without top flange, dowel spacing 150mm Drawing: I nstr umentation setup

(Final setup on test beam)

Weg-15

Weg-12


Weg-13

Weg-1

150

50

625

Weg-4

1,900

1,200

2,600

DBG-3

Weg-6

300

Weg-11 Weg-12

Weg-7

D MS-8

100

D MS-7

DBG-2

100

Pmax = 800kN

1,275

1,200

Loading plate Mortar

D MS-9

D MS-10

D MS-11

D MS-12

Weg-8

1,250

100 W eg-11

W eg-12

SECTION 2-2

750

750

600

100 100

S. A.

Weg-9 Weg-10

D MS-6

D MS-5

750

Last update 12-07-2009

All DMS in longitudinal direction

W eg-10

W eg-9

100

DBG-1

7,700

8,000

D MS-1

D MS-2

D MS-3

D MS-4

SECTION 1-1

30

100 100 30

100 310

410

Pmax = 800kN


Weg-5

3,850

3,100

Versuchsträger SPP1182 Serie - 2, Instruments setup for Beam B5 and B6 7.01.2009 / Vinh

Weg-3

150

Figure C.11.: Experimental setup of the composite beam B5 and B6

Weg-2


1000

1000

Beam B1−Quarterspan Beam B1−Midspan

800

Applied load (kN)

Applied load (kN)

191

600 400 200 0 0.0

50.0

100.0

150.0

600 400 200 0 0.00

200.0

Beam B1−Rot.

800

0.01

0.02

0.03

0.04

0.05

0.06

Rotation (rad)

Deflection (mm)

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(a)

600 400 200

Beam B1−SG−6 Beam B1−SG−8 Beam B1−SG−10 Beam B1−SG−11

600 400 200 0 −6.0

0 −2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Long. strain in girder, Sect. 1−1, εxx (%o )

Beam B1−SG−7 Beam B1−SG−9 −4.5 −3.0 −1.5 0.0 Ver. strain in girder, Sect. 1−1, εyy (%o )

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)

600 400 200


0 −0.5 0.0 0.5 1.0 1.5 2.0 Long. strain in girder, Sect. 2−2, εxx (%o )

600 400 200

Beam B1−SG−13 Beam B1−SG−15 0 −0.4 −0.3 −0.2 −0.1 0.0 0.1 Ver. strain in girder, Sect. 2−2, εyy (%o )

(c) Figure C.12.: Beam B1, Load-deflection and Load-rotation (a), strain in girder section 1-1 (b) and strain in girder section 2-2 (c)

192


Applied load (kN)

1000

Beam B1−LVDT−7 Beam B1−LVDT−9 Beam B1−LVDT−10 Beam B1−LVDT−11

800 600 400 200 0

−4.0 −2.0 0.0 2.0 4.0 Long. strain in concrete slab, Sect. 1−1 and 2−2, εxx (%

(a) 1000

Beam B1−SG−1 Beam B1−SG−3

800

Applied load (kN)

Applied load (kN)

1000

600 400 200 0 −0.4

−0.3 −0.2 −0.1 0.0 Long. strain in steel rib, εxx (%o )

800 600 400

0 −0.1

0.1

Beam B1−SG−2 Beam B1−SG−4 Beam B1−SG−5

200

0.0 0.1 0.2 0.3 Ver. strain in steel rib, εyy (%o )

0.4

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)

600 400 Beam B1−LVDT−1 Beam B1−LVDT−4 Beam B1−LVDT−6 Beam B1−LVDT−8

200 0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Longitudinal slip of concrete slab (mm)

Beam B1−LVDT−2 Beam B1−LVDT−3 Beam B1−LVDT−5

600 400 200 0 −0.10

−0.05

0.00

0.05

0.10

Up slip of concrete slab (mm)

(c) Figure C.13.: Beam B1, Load-strain in concrete slab (a), strain in steel rib (b) and slip (c)


1000

1000


800

Applied load (kN)

Applied load (kN)

193

600 400 200 0 0.0

50.0

100.0

150.0

200.0

Beam B2−Rot.

800 600 400 200 0 0.00

250.0

0.01

0.03

0.04

0.06

0.07

0.09

Rotation (rad)

Deflection (mm)

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(a)

600 400 200


600 400 200 0 −6.0

0 −2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Long. strain in girder, Sect. 1−1, εxx (%o )

Beam B2−SG−7 Beam B2−SG−9 −4.5 −3.0 −1.5 0.0 Ver. strain in girder, Sect. 1−1, εyy (%o )

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)

600 400 200


0 −1.0 0.0 1.0 2.0 3.0 4.0 Long. strain in girder, Sect. 2−2, εxx (%o )

600 400 200


0 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 Ver. strain in girder, Sect. 2−2, εyy (%o )


194


Applied load (kN)

1000 800 600 400 200


0 −5.0 −4.0 −3.0 −2.0 −1.0 0.0 Long. strain in concrete slab, Sect. 1−1 and 2−2, εxx (%

(a) 1000


800

Applied load (kN)

Applied load (kN)

1000

600 400 200 0 −0.4

−0.3 −0.2 −0.1 0.0 Long. strain in steel rib, εxx (%o )

800 600 400

0 −0.1

0.1


200

0.0 0.1 0.2 0.3 Ver. strain in steel rib, εyy (%o )

0.4

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)


200 0 0.00

0.05

0.10

0.15

0.20

0.25

0.30



600 400 200 0 −0.10

−0.05

0.00

0.05

0.10



195

1000

1000

800

800

Applied load (kN)

Applied load (kN)


600 400 200 0 0.0

Beam B3−Quarterspan Beam B3−Midspan 20.0

40.0

60.0

80.0

Beam B3−Rot.

600 400 200 0 0.00

100.0

0.01

0.03

0.04

0.06

Rotation (rad)

Deflection (mm)

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(a)

600 400 200


600 400 200

Beam B3−SG−8 Beam B3−SG−10 0 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 Ver. strain in girder, Sect. 1−1, εyy (%o )

0 −1.00 −0.50 0.00 0.50 1.00 1.50 2.00 Long. strain in girder, Sect. 1−1, εxx (%o )

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)

600 400 200


0 −1.0 0.0 1.0 2.0 3.0 Long. strain in girder, Sect. 2−2, εxx (%o )

600 400 200


0 −0.6

−0.4 −0.2 0.0 0.2 0.4 0.6 Ver. strain in girder, Sect. 2−2, εyy (%o )


196


Applied load (kN)

1000 800 600 400 200


0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 Long. strain in concrete slab, Sect. 1−1 and 2−2, εxx (%

(a) 1000


800

Applied load (kN)

Applied load (kN)

1000

600 400 200 0 −1.0

−0.8 −0.6 −0.4 −0.2 Long. strain in steel rib, εxx (%o )

800 600 400

0 0.0

0.0


200

0.2 0.4 0.6 Ver. strain in steel rib, εyy (%o )

0.8

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)


200 0 0.00

0.10

0.20

0.30

0.40

0.50



600 400 200 0 −0.05

0.00

0.05

0.10

0.15



197

1000

1000

800

800

Applied load (kN)

Applied load (kN)


600 400 200 0 0.0


50.0

75.0

100.0

Beam B4−Rot.

600 400 200 0 −0.03

125.0

−0.01

0.00

0.01

0.03

Rotation (rad)

Deflection (mm)

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(a)

600 400 200


600 400 200

Beam B4−SG−6 Beam B4−SG−8 0 −6.0 −4.0 −2.0 0.0 2.0 Ver. strain in girder, Sect. 1−1, εyy (%o )

0 −4.0 0.0 4.0 8.0 12.0 16.0 20.0 Long. strain in girder, Sect. 1−1, εxx (%o )

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)

600 400 200


0 −1.0 0.0 1.0 2.0 3.0 Long. strain in girder, Sect. 2−2, εxx (%o )

600 400 200


0 −1.0

−0.8 −0.5 −0.3 0.0 0.3 0.5 Ver. strain in girder, Sect. 2−2, εyy (%o )


198


Applied load (kN)

1000 800 600 400 200


0 −6.0 −4.5 −3.0 −1.5 0.0 1.5 3.0 Long. strain in concrete slab, Sect. 1−1 and 2−2, εxx (%

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(a)

600 400 200


0 −1.0

−0.8 −0.6 −0.4 −0.2 0.0 Long. strain in steel rib, εxx (%o )

600 400 200 0 0.0

0.2

Beam B4−SG−2 Beam B4−SG−5 0.2 0.4 0.6 Ver. strain in steel rib, εyy (%o )

0.8

1000

1000

800

800

Applied load (kN)

Applied load (kN)

(b)


200 0 0.00

0.10

0.20

0.30

0.40



600 400 200 0 −0.10 −0.05

0.00

0.05

0.10

0.15

0.20




1500

1500


Beam B5−SG−3−bottom web Beam B5−SG−4−bottom flange Beam B5−SG−5−bottom slab Beam B5−SG−6−top slab



199

1000 750 500

1000 750 500 250

250 0 0.0

20.0

40.0

60.0

80.0

0 −4.0 −3.0 −2.0 −1.0 0.0 1.0 2.0 Long. strain in girder, Sect. 1−1, εxx (%o )

100.0

Deflection (mm)

1500

1500

1250


Applied load (kN)

Figure C.20.: Beam B5, Load-deflection (left), strain in girder and concrete slab at section 1-1 (right)

1000 750 500 250 0 0.0

40.0

60.0

80.0

1000 750 500 250


Beam B6−Rot.

0 −0.01

100.0

0.00

0.01

0.02

0.03

Rotation (rad)

Deflection (mm)

1500

1500

1250


Applied load (kN)

(a)

1000 750 500 250


1000 750 500 250

0 −3.0 −2.0 −1.0 0.0 1.0 2.0 Long. strain in girder, Sect. 1−1, εxx (%o )

Beam B6−SG−5 Beam B6−SG−6 0 −4.0 −3.0 −2.0 −1.0 0.0 Long. strain in concrete slab, Sect. 1−1, εxx (%o )

(b) Figure C.21.: Beam B6, Load-deflection and Load-rotation (a), strain in girder and concrete slab section 1-1 (b)


1500

1500

1250


Applied load (kN)

200

1000 750 500 250


1000 750 500 250

Beam B6−SG−11 Beam B6−SG−12 0 −4.0 −3.0 −2.0 −1.0 0.0 Long. strain in concrete slab, Sect. 2−2, εxx (%o )

0 −3.0 −2.0 −1.0 0.0 1.0 2.0 Long. strain in girder, Sect. 2−2, εxx (%o )

1500

1500

1250


Applied load (kN)

(a)

1000 750 500


250 0 0.00

0.10

0.20

0.30

1000 750 500 Beam B6−LVDT−2 Beam B6−LVDT−3 Beam B6−LVDT−5

250

0.40

Longitudinal slip of concrete slab−left side (mm)

0 0.00

0.10

0.20

0.30

0.40

Longitudinal slip of concrete slab−right side (mm)

(b) Figure C.22.: Beam B6, strain in girder and concrete slab section 2-2 (a), Load-longitudinal slip along left and right side of the beam (b)

D. Appendices: Tool for ATENA

STRUCTURE s

PHYSICAL MODEL

GID – PRE_PROCESSING , export data to ATENA

ATENA - PROCESSING

0

2

1 GID POST_ PROCESSING

PLOT CHART

TOOLs FOR ATENA

REPORT DATABASE BINARY DATA 3 CALIBRATION MATERIAL MODEL M4 Based on Test data or Code Figure D.1.: Structure of the program

PLOT CHART by GNUPLOT

202

D. Appendices: Tool for ATENA

START

SAMPLE MODEL (cubic or cylinder specimen test)

PHYSICAL MODEL FOR COMPUTER With MicroPlane M4

TESTING SPECIMENT

TEST DATA (DI SP., STRAI N)

GID – PRE_PROCESSING

ATENA DATA FILE With model parameter

c1, 2,…21, k 1,2,3,4

Run with trial parameter to 1 loop generate Set of data for next step CHECK i