THE FACE BENDING BEHAVIOUR OF BLIND-BOLTED CONNECTIONS TO CONCRETE-FILLED HOLLOW SECTIONS Ahmed Mohamed Elamin Ahmed Elamin BEng (Hons), MSc Thesis submitted to the University of Nottingham for the degree of Doctor of Philosophy October 2013 Centre for Structural Engineering and Construction Materials, Mechanics and Structures Division Faculty of Engineering Abstract Structural Hollow Sections have superior structural performance over open sections and are currently available as circular, elliptical or rectangular sections. However, the practical use of these sections is limited due to complexities involved in their connections. The lack of access to the interior of the section makes it almost impossible to use standard bolted connections. The so-called Blind Bolts are therefore used as fasteners to alleviate these complexities by allowing for bolted rather than, the-not-so-popular, welded connections to hollow sections. Lindapter’s Hollo-Bolt is one of the Blind Bolts used for hollow sections connections. However its established use is currently restricted to transferring tensile forces and vertical shear only. Filling Square Hollow Sections (SHS) with concrete, when utilising Hollo-Bolts, was found to improve the connections’ performance in resisting moments, but there is currently no guidance available for the design of such connections. Many methods are used to model connections behaviour. The so-called component method has emerged to be the most favourite and has been adopted in the Eurocode 3. In this method, the connection is divided into basic components. Each component has a contribution to the structural behaviour of the connection. For Hollo-Bolted moment resisting connections, the behaviour of two of the components, fastener in tension and concrete- filled SHS face in bending, are not available. The application of the component method is therefore not possible. This research aims to devise a model to predict the behaviour of the concrete-filled SHS face in bending. A novel analytical model of the concrete-filled SHS face bending has been proposed in this work. The model has three parts: Initial Stiffness, Yield Force and Post-Yield Stiffness. The Initial Stiffness was formulated by theoretically substituting the face of the concrete-filled SHS with a beam element. The beam is assumed to be loaded by a rigid strip and fixed at its ends. Yield line analysis was used to investigate possible failure mechanisms and associated strengths. The model adopted the mechanism which theoretically led to the i critical yield force. The Post-Yield Stiffness was taken as a percentage of the Initial Stiffness in line with other work from the literature. An extensive full-scale experimental programme was undertaken to calibrate the aforementioned analytical model, and to examine the effects of varying parameters on the SHS face bending behaviour. Typical experiments involved one row of two bolts pulled out of concrete-filled SHS. A special dummy bolts were manufactured to the exact size and geometry of open Hollo-Bolts, and were used in the experimental programme to remove the influence of any deformation associated with the real Hollo-Bolts, and thus isolate the face bending behaviour. Non-contact video-based equipment was used to record the SHS face deformation. Three parameters were varied: the SHS face slenderness ratio, the bolts gauge to SHS width ratio and the concrete in-fill compressive strength. A finite element model was also developed to complement the experimental programme. The model was developed using the ANSYS Parametric Design Language (APDL) to allow for easy parametric analysis and knowledge transfer. Dimensions, parameters and materials properties could be easily altered in the fully parametric model script. The outcomes of the experimental programme and the finite element model were used to formulate design charts for two calibration factors: k for the is calculation of Initial Stiffness, k for the calculation of Yield Force. A chart was yf also formulated for the Post-Yield stiffness ratio. The proposed analytical model (semi-analytical after calibration) was compared with the results of experimental programme and finite element modelling. The model was found to capture the behaviour of concrete-filled SHS face bending with sufficient accuracy, lying between 90% prediction lines derived from the experimental results. This is considered sufficient for the proposed model to capture the concrete-filled SHS face bending component for connection design purposes. ii List of Contents Abstract ........................................................................................................... i List of Contents .............................................................................................. iii List of Figures .................................................................................................vii List of Tables ................................................................................................. xiii List of Notation ............................................................................................. xiv Roman symbols ........................................................................................ xiv Capital roman symbols .............................................................................. xv Greek symbols ........................................................................................... xv Abbreviations ............................................................................................... xvi Trademarks ................................................................................................... xvi Acknowledgements ..................................................................................... xvii Declaration ................................................................................................. xviii Chapter 1: Introduction ............................................................................... 1 1.1 Background .......................................................................................... 1 1.2 Research Aim and Objectives............................................................... 4 1.3 Research Methodology ........................................................................ 5 1.4 Overview of the Thesis ......................................................................... 6 Chapter 2: Literature Review ....................................................................... 8 2.1 Introduction ......................................................................................... 8 2.2 Beam-to-Column joints ........................................................................ 9 2.2.1 Joints Classification ..................................................................... 10 2.2.2 Methods of modelling Joints Behaviour ..................................... 13 2.2.3 The Component Method ............................................................. 15 2.3 SHS Joints ........................................................................................... 19 2.4 The Hollo-Bolt .................................................................................... 21 2.5 Why concrete-filled SHS? ................................................................... 23 2.6 The concrete-filled SHS face bending ................................................ 24 2.6.1 Initial Stiffness ............................................................................ 25 2.6.2 Yield Force (Resistance) .............................................................. 30 2.6.3 Post-Yield Stiffness ..................................................................... 32 2.7 Summary ............................................................................................ 32 Chapter 3: Analytical Modelling ................................................................ 34 3.1 Introduction ....................................................................................... 34 3.2 The Initial Stiffness Component ......................................................... 35 3.3 The Resistance ................................................................................... 38 3.3.1 Mechanism 1 .............................................................................. 41 3.3.2 Mechanism 2 .............................................................................. 43 iii 3.3.3 Mechanism 3 .............................................................................. 45 3.3.4 Mechanism 4 .............................................................................. 47 3.3.5 Comparison of Mechanisms ....................................................... 49 3.4 Post-yield Stiffness ............................................................................. 51 3.5 Proposed Model ................................................................................. 52 3.6 Summary ............................................................................................ 53 Chapter 4: Experimental Programme ......................................................... 54 4.1 Introduction ....................................................................................... 54 4.2 Design of Experimental Programme .................................................. 55 4.2.1 Parameters.................................................................................. 55 4.2.2 Range .......................................................................................... 56 4.2.3 Test Matrix .................................................................................. 61 4.3 Description of the Samples ................................................................ 62 4.4 Test set-up.......................................................................................... 65 4.4.1 Testing Rig and Layout ................................................................ 66 4.4.2 Actuator and Control Program ................................................... 70 4.5 Instrumentation A: The Video Gauge ................................................ 72 4.5.1 Introduction ................................................................................ 72 4.5.2 Targets Identification .................................................................. 74 4.5.3 Calibration................................................................................... 75 4.5.4 Accuracy ...................................................................................... 75 4.6 Instrumentation B: The Digital Image Correlation ............................. 76 4.7 Material Properties ............................................................................ 78 4.7.1 Structural Hollow Sections ......................................................... 78 4.7.2 Dummy Bolts............................................................................... 79 4.7.3 Concrete in-fill ............................................................................ 81 4.8 Test Procedure ................................................................................... 83 4.9 Summary ............................................................................................ 85 Chapter 5: Experimental Results ................................................................ 86 5.1 Introduction ....................................................................................... 86 5.2 Errors & Corrections........................................................................... 87 5.3 Failure Criteria .................................................................................... 88 5.4 Visual Observations ............................................................................ 90 5.5 Force-Displacement Results ............................................................... 95 5.5.1 Raw Force-Displacement Results ............................................... 95 5.5.2 Possible Sources of Variation in Repeated Tests ...................... 102 5.5.3 Normalised Force-Displacement Results .................................. 107 5.5.4 Parametric Analysis .................................................................. 114 5.6 Digital Image Correlation Results (DIC) ............................................ 120 5.7 Summary .......................................................................................... 125 iv Chapter 6: Finite Element Modelling ........................................................ 126 6.1 Introduction ..................................................................................... 126 6.2 Description of the Model ................................................................. 128 6.2.1 Element Types .......................................................................... 130 6.2.2 Concrete Failure Criteria in ANSYS ........................................... 136 6.2.3 Material Models ....................................................................... 137 6.2.4 Boundary Conditions ................................................................ 142 6.2.5 Loading and Solution ................................................................ 143 6.2.6 Model Mesh .............................................................................. 144 6.2.7 Model Illustration ..................................................................... 147 6.3 General Behaviour of the Finite Element Model ............................. 150 6.3.1 SHS Face Bending ...................................................................... 150 6.3.2 Observations ............................................................................. 151 6.3.3 Strain Distribution on SHS Face ................................................ 153 6.4 Results and Validation (force-displacement curves) ....................... 153 6.5 Parameters Variation Analysis ......................................................... 159 6.5.1 The effect of SHS slenderness .................................................. 161 6.5.2 The effect of bolt gauge ............................................................ 163 6.6 Proposed Charts for SHS 200x200 ................................................... 167 6.7 Summary .......................................................................................... 169 Chapter 7: Semi-Analytical Model ............................................................ 170 7.1 Introduction ..................................................................................... 170 7.2 Experimental Linear Data-Fit ........................................................... 171 7.3 Calibration Factor k .......................................................................... 175 7.3.1 Background ............................................................................... 176 7.3.2 Initial Stiffness calibration factor (k ) ....................................... 178 is 7.3.3 Yield Force calibration factor (k )............................................. 182 yf 7.3.4 Discussion ................................................................................. 186 7.4 Post-Yield Stiffness ........................................................................... 188 7.4.1 Effect of SHS face slenderness ratio (μ) .................................... 188 7.4.2 Effect of bolt gauge to SHS width ratio (β) ............................... 190 7.4.3 Effect of concrete in-fill compressive strength ........................ 192 7.5 Proposed Semi-Analytical Model ..................................................... 195 7.5.1 Part 1: Initial Stiffness ............................................................... 195 7.5.2 Part 2: Yield Force ..................................................................... 196 7.5.3 Part 3: Post-Yield Stiffness ratio ............................................... 196 7.5.4 How to use the proposed charts .............................................. 197 7.6 Statistical Analysis ............................................................................ 201 7.7 Prediction of Yield Force in the proposed model ............................ 209 7.8 Proposed Semi-Analytical Model limitations ................................... 214 v 7.9 Summary .......................................................................................... 215 Chapter 8: Conclusions and Recommendations ........................................ 216 8.1 Introduction ..................................................................................... 216 8.2 Observations and Conclusions ......................................................... 218 8.3 Contribution of this work ................................................................. 222 8.4 Application of the proposed Semi-Analytical model ....................... 223 8.5 Recommendations for Future Work ................................................ 224 References ..................................................................................................... 228 vi List of Figures Figure ‎1.1 Typical beam-to-hollow section column connections ........................... 2 Figure ‎1.2 Some of the Blind Bolts .......................................................................... 3 Figure ‎2.1 Joint configurations ............................................................................... 9 Figure ‎2.2 Typical joint M-φ behaviour ................................................................ 10 Figure ‎2.3 Joints classification by stiffness ........................................................... 11 Figure ‎2.4 Joints classification by strength ........................................................... 12 Figure ‎2.5 Comparison of joints ductility .............................................................. 12 Figure ‎2.6 Basic components in bolted end-plate connection (SCI/BCSA, 2005) . 16 Figure ‎2.7 Actual and idealised bi-linear behaviour of a component................... 17 Figure ‎2.8 Bi-linear components in-series / in-parallel (Kurobane et al., 2004) ... 17 Figure ‎2.9 Typical open section-to-SHS column connections ............................... 20 Figure ‎2.10 3-Part Hollo-Bolt (Lindapter, 2013c) .................................................... 21 Figure ‎2.11 5-Part Hollo-Bolt (Lindapter, 2013c) .................................................... 22 Figure ‎2.12 Hollo-Bolt Installation steps (Lindapter, 2013b) .................................. 22 Figure ‎2.13 Hollo-Bolt with and without concrete (Tizani and Ridley-Ellis, 2003) . 24 Figure ‎2.14 Bi-linear idealisation of the component .............................................. 25 Figure ‎2.15 Comparison of Initial Stiffness of SHS face bending ............................ 28 Figure ‎2.16 Web/face loaded by equivalent strip (Simões da Silva et al, 2004) .... 29 Figure ‎2.17 Equivalent fixed beam loaded by rigid strip ........................................ 29 Figure ‎2.18 Assumed failure pattern of SHS face (SCI/BCSA, 2002) ....................... 31 Figure ‎3.1 Web/face loaded by equivalent strip (Simões da Silva et al, 2004) .... 36 Figure ‎3.2 Typical hexagon nut layout (BSI, 2012)................................................ 36 Figure ‎3.3 Assumed load transfer mechanism from Hollo-Bolts to SHS face ....... 37 Figure ‎3.4 Possible failure mechanisms (using yield line analysis) ....................... 39 Figure ‎3.5 Mechanism 1 yield-lines pattern ......................................................... 41 Figure ‎3.6 Mechanism 2 yield-lines pattern ......................................................... 43 Figure ‎3.7 Mechanism 3 yield-lines pattern ......................................................... 46 Figure ‎3.8 Mechanism 4 yield-lines pattern ......................................................... 47 Figure ‎3.9 Yield force theoretically calculated for SHS 200x200x10 .................... 50 Figure ‎3.10 Yield force theoretically calculated for SHS 300x300x10 .................... 50 Figure ‎3.11 Yield force theoretically calculated for SHS 200x200x5 ...................... 51 vii Figure ‎3.12 Proposed Bi-Linear analytical model ................................................... 52 Figure ‎4.1 Minimum Gauge and Edge distances .................................................. 58 Figure ‎4.2 Illustration of minimum SHS width requirement ................................ 60 Figure ‎4.3 Test ID description ............................................................................... 62 Figure ‎4.4 Typical SHS sample layout ................................................................... 65 Figure ‎4.5 Dummy Bolt ......................................................................................... 66 Figure ‎4.6 Test layout CAD drawing (Elevation) ................................................... 68 Figure ‎4.7 Test layout CAD drawing (Plan) ........................................................... 69 Figure ‎4.8 Testing rig ............................................................................................ 70 Figure ‎4.9 Zoom-in of Test lay-out (Push-out) ...................................................... 70 Figure ‎4.10 A screen snap-shot of actuator control program ................................ 72 Figure ‎4.11 A screen snap-shot of actuator control program during test .............. 72 Figure ‎4.12 Video Gauge Components ................................................................... 75 Figure ‎4.13 Video Gauge calibration ...................................................................... 76 Figure ‎4.14 CAD drawing and testing process of mechanical pieces ..................... 79 Figure ‎4.15 Handling SHS 300x300 samples ........................................................... 84 Figure ‎5.1 Accuracy and Precision ........................................................................ 87 Figure ‎5.2 Dummy-bolt push-out of SHS hole ...................................................... 89 Figure ‎5.3 Experiment b200t8g100C40-1 failure .................................................. 90 Figure ‎5.4 Different SHS face bending behaviour ................................................. 91 Figure ‎5.5 Sample b200t8g80C40-2 after the concrete-infill was exposed.......... 92 Figure ‎5.6 Concrete attachment to dummy-bolts in sample b200t8g60C40-3 .... 93 Figure ‎5.7 Strain distribution on SHS face ............................................................ 94 Figure ‎5.8 Force-Displacement relationship of b200t8g80C20-1&2 (raw) ........... 96 Figure ‎5.9 Force-Displacement relationship of b200t8g80C50-1,2&3 (raw)........ 96 Figure ‎5.10 Force-Displacement relationship of b200t8g80C80-1&2 (raw) ........... 97 Figure ‎5.11 Force-Displacement relationship of b200t8g60C40-1,2&3 (raw)........ 97 Figure ‎5.12 Force-Displacement relationship of b200t8g80C40-1,2,3&4 (raw)..... 98 Figure ‎5.13 Force-Displacement relationship of b200t8g100C40-1&2 (raw)......... 98 Figure ‎5.14 Force-Displacement relationship of b200t10g80C40-1&2 (raw)......... 99 Figure ‎5.15 Force-Displacement relationship of b200t6.3g80C40-1&2 (raw)........ 99 Figure ‎5.16 Force-Displacement relationship of b200t5g80C40-1&2 (raw) ......... 100 Figure ‎5.17 Force-Displacement relationship of b300t12g120C40-1&2 (raw)..... 100 viii Figure ‎5.18 Force-Displacement relationship of b300t16g120C40-1&2 (raw)..... 101 Figure ‎5.19 Proper and improper dummy bolts alignment .................................. 103 Figure ‎5.20 The weld-seam in tested face of Sample b200t8g100C40-2 ............. 104 Figure ‎5.21 Updated Test ID description .............................................................. 107 Figure ‎5.22 b200t8g80C20-1&2 Normalised F-D relationships ............................ 108 Figure ‎5.23 b200t8g80C50-2&3 Normalised F-D relationships ............................ 108 Figure ‎5.24 b200t8g80C80-1&2 Normalised F-D relationships ............................ 109 Figure ‎5.25 b200t8g60C40-2&3 Normalised F-D relationships ............................ 109 Figure ‎5.26 b200t8g80C40-3&4 Normalised F-D relationships ............................ 110 Figure ‎5.27 b200t8g100C40-1&2 Normalised F-D relationships .......................... 110 Figure ‎5.28 b200t10g80C40-1&2 Normalised F-D relationships .......................... 111 Figure ‎5.29 b200t6.3g80C40-1&2 Normalised F-D relationships ......................... 111 Figure ‎5.30 b200t5g80C40-1&2 Normalised F-D relationships ............................ 112 Figure ‎5.31 b300t12.5g120C40-1&2 Normalised F-D relationships ..................... 112 Figure ‎5.32 b300t16g120C40-1&2 Normalised F-D relationships ........................ 113 Figure ‎5.33 The effect of bolt gauge on SHS face bending ................................... 115 Figure ‎5.34 The effect of bolt gauge on SHS face bending (zoom-in) .................. 115 Figure ‎5.35 The effect of SHS face slenderness on SHS face bending .................. 117 Figure ‎5.36 The effect of SHS face slenderness on face bending (zoom-in)......... 117 Figure ‎5.37 The effect concrete strength on SHS face bending ........................... 118 Figure ‎5.38 Speckle pattern disturbed in b200t8g80C40-DIC .............................. 121 Figure ‎5.39 Strain development on SHS face captured using DIC ........................ 122 Figure ‎5.40 SHS face deformation across a section-line passing over bolts ......... 123 Figure ‎5.41 SHS face deformation across a section-line passing over one bolt ... 124 Figure ‎6.1 Numerical model Flowchart .............................................................. 129 Figure ‎6.2 SOLID185 Geometry (ANSYS, 2010c) ................................................. 131 Figure ‎6.3 SOLID65 Geometry (ANSYS, 2010c) ................................................... 132 Figure ‎6.4 CONTA173 Geometry ((ANSYS, 2010c) .............................................. 134 Figure ‎6.5 TARGE170 Geometry (ANSYS, 2010c) ................................................ 135 Figure ‎6.6 Stress-Strain relationship for different concrete grades ................... 142 Figure ‎6.7 Finite element model Boundary Conditions ...................................... 143 Figure ‎6.8 The direction of applied displacement in the finite element model . 144 Figure ‎6.9 Meshed dummy bolts ........................................................................ 145 Figure ‎6.10 Mesh sensitivity analysis.................................................................... 146 ix