BEHAVIOUR AND DESIGN OF COMPOSITE STEEL CONCRETE nbsp; BEHAVIOUR AND DESIGN OF COMPOSITE STEEL-CONCRETE ... 3 Design of composite slab ... Composite steel-concrete slabs are widely

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  • POLITECNICO DI MILANO

    SCUOLA DI INGEGNERIA CIVILE, AMBIENTALE E TERRITORIALE

    CORSO DI LAUREA MAGISTRALE IN INGEGNERIA CIVILE-

    CIVIL ENGINEERING

    BEHAVIOUR AND DESIGN OF COMPOSITE STEEL-CONCRETE

    SLABS

    Relatore: Prof. Massimiliano Bocciarelli Relatore: Prof. Gianluca Ranzi

    Tesi di laurea magistrale di: Riccardo Luzzi Matr. 819034

    Anno Accademico 2014/2015

  • To my family,

    for its support throughout my life

  • 1

    Contents

    Figures.......................................................................................................... 4Tables ........................................................................................................... 8Abstract ........................................................................................................ 9Abstract ...................................................................................................... 10Introduction ............................................................................................... 11

    Introduction ...................................................................................................................... 11Background ....................................................................................................................... 11Objectives of the study.................................................................................................... 13Organization of the thesis ............................................................................................... 14

    1 Literature Review ............................................................................... 151.1 Introduction ............................................................................................................... 151.2 Background ................................................................................................................. 15

    1.2.1 Historical Background ....................................................................................... 181.3 Ultimate behaviour .................................................................................................... 191.4 Time-dependent behaviour ...................................................................................... 25

    2 Materials ............................................................................................. 302.1 Introduction ............................................................................................................... 302.2 Concrete ...................................................................................................................... 30

    2.2.1 Time Dependent Deformation of concrete ................................................... 302.2.2 The elastic deformation of concrete ............................................................... 312.2.3 Creep .................................................................................................................... 312.2.4 Shrinkage ............................................................................................................. 33

    2.3 Numerical methods for time analysis of concrete ................................................ 352.3.1 The superposition integral ................................................................................ 352.3.2 The effective modulus method (EMM) .......................................................... 362.3.3 The age-adjusted effective modulus method (AEMM) ................................ 362.3.4 The Step-by-step method (SSM) ...................................................................... 38

    2.4 The non-uniform shrinkage on composite slab cross-section ............................ 422.4.1 Comparison with experimental results ........................................................... 44

    2.5 Steel .............................................................................................................................. 462.5.1 Conventional, non-prestressed reinforcement .............................................. 462.5.2 Metal Sheeting .................................................................................................... 47

    3 Design of composite slab ..................................................................... 493.1 Introduction ............................................................................................................... 493.2 Limit state requirements specified by Australian draft code AS2327 ................ 50

    3.2.1 Ultimate limit state: Flexure.............................................................................. 503.2.2 Ultimate limit state: Vertical shear ................................................................... 533.2.3 Serviceability limit state: deflection ................................................................. 533.2.4 Slab deflection by simplified calculation ......................................................... 56

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    3.2.4.1 Short term deflection ................................................................................. 563.2.4.2 Creep deflection .......................................................................................... 593.2.4.3 Shrinkage deflection ................................................................................... 60

    3.3 Parametric study ......................................................................................................... 613.3.1 Considerations on the governing limit state for the design of composite slabs ............................................................................................................................... 623.3.2 Considerations on the total deflection ............................................................ 78

    4 Finite Element Model ......................................................................... 814.1 Introduction ............................................................................................................... 814.2 Euler-Bernoulli beam model and weak form ........................................................ 81

    4.2.1 Field displacements ............................................................................................ 824.2.2 Equilibrium ......................................................................................................... 84

    4.3 Nonlinear Finite element formulation .................................................................... 874.3.1 Shape Functions ................................................................................................. 87

    4.4 Nonlinear analysis using the Newton-Raphson method ..................................... 914.4.1 Overview of the Newton-Raphson Method .................................................. 91

    4.5 Cross-sectional modelling ....................................................................................... 1004.5.1 Concrete area discretization ........................................................................... 1004.5.2 Reinforcement discretization .......................................................................... 1014.5.3 Metal sheeting discretization .......................................................................... 102

    4.6 Validation of the finite element model ................................................................. 1035 Refined Design Analysis ................................................................... 105

    5.1 Introduction ............................................................................................................. 1055.2 Design of the thickness using FEA ...................................................................... 1055.3 Comparisons on deflection between FEA and code approach ........................ 107

    5.3.1 General remarks ............................................................................................... 1075.3.2 Incremental deflection ..................................................................................... 1075.3.3 Total deflection ................................................................................................ 1095.3.4 Considerations on uniform shrinkage model ............................................... 110

    6 Conclusions ....................................................................................... 1136.1 Introduction ............................................................................................................. 1136.2 Concluding remarks ................................................................................................ 1136.3 Recommendations for future work ....................................................................... 117

    References ................................................................................................ 118A1 Material Properties ........................................................................ 122

    A.1.1 Concrete ................................................................................................................ 122A.1.1.1 Strength (AS3600-2009, 3.1.1) ................................................................... 123

    A2 Additional Results Chapter 3 ....................................................... 127A2.1 Influence of the live load on total deflection ................................................... 127

    A2.1.1 Profile 1 .......................................................................................................... 127A2.1.2 Profile 2 .......................................................................................................... 128

    A2.2 Influence of the thickness of the profiled on total deflection ....................... 129A