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Bending displacement capacity of elongated reinforced concrete columns Chin, Helen Hau Ling 2012

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BENDING DISPLACEMENT CAPACITY OF ELONGATED REINFORCED CONCRETE COLUMNS  by Helen Chin  B.A.Sc., The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2012  © Helen Chin, 2012 ii  Abstract  The bending displacement capacity of elongated wall-like gravity-load columns subjected to lateral displacements due to earthquake demands on a high-rise building is of considerable concern.  The long cross-sectional dimension makes these members much less flexible compared to square columns. Elongated gravity-load columns are popular because they can be hidden in walls and because they reduce the span of floor slabs, which means the thickness of the floor slabs can be reduced. No previous tests have been done on elongated gravity-load columns subjected to simulated earthquake loading. In the current study, five half-scale specimens including four column specimens and one wall specimen were subjected to constant axial compression and reverse cyclic lateral load to determine the displacement capacity of the members.  The cross-sectional width-to-length ratios of the four columns were 1:1 (square), 1:2, 1:4, 1:8 and the wall specimen was 1:8. The load- deformation responses of the specimens were predicted using two nonlinear programs Response2000 and VecTor2, as well as hand calculation procedures. The predictions were used to design the test setup and were compared with the test results in order to better understand the significance of the test results. The predicted load capacities of all specimens were found to be similar to the observed maximum loads; but the displacement capacities of all specimens were significantly higher than predicted. Slip of the vertical reinforcing bars from the column foundations contributed to a large part of the increased displacement capacity of the columns. Only the elongated columns with a cross-sectional width-to-length ratios of 1:4 and 1:8 and the wall specimen suffered complete collapse during the test.  iii  Table of Contents  Abstract  .............................................................................................................................  ii Table of Contents  .............................................................................................................  iii List of Tables  ....................................................................................................................  xiii List of Figures  ...................................................................................................................  xxi List of Symbols .................................................................................................................. xxxv Acknowledgements ....................................................................................................... xxxvix Chapter 1: Introduction  ..................................................................................................  1 1.1  Background  ............................................................................................................  1 1.2  Previous Studies on Reinforced Concrete Columns  ..............................................  2 1.3  Scope and Objectives of the Current Study  ...........................................................  8 1.4  Overview of Thesis  ................................................................................................  9 Chapter 2: Design of Test Specimens  .............................................................................  11 2.1  Design for Axial Load on Gravity Column  ............................................................  11 2.2  Relation of Factored Axial Compression to Axial Compression with Seismic Drift  12 2.2.1  Axial Load in High-rise Buildings  .................................................................  12 2.2.2  Typical Load Ratios Related to Seismic  ........................................................  15 2.2.3  Load Ratios According to ACI Design Standards  ..........................................  22  2.3  Design of Test Specimens  ......................................................................................  27  2.4 The Wall Specimen  .................................................................................................  31 Chapter 3: Behaviour Predictions  ..................................................................................  32  3.1 Predicting Moment-Curvature Behaviour  ...............................................................  32 iv    3.1.1 Moment-Curvature from Response2000  .........................................................  33   3.1.2 Maximum Moment and Curvature at 0.0035 Compression Strain from Response2000  .................................................................................................  35   3.1.3 Moment-Curvature from Vector2  ....................................................................  36   3.1.4 Moment and Curvature at Failure from VecTor 2  ...........................................  38   3.1.5 Moment-Curvature by Hand Calculations ........................................................  39   3.1.6 Moment and Curvature at 0.0035 Compression Strain by Code Method  .......  41   3.1.7 Comparison of Moment-Curvature Response  .................................................  43  3.2  Predicting Load-Displacement Behaviour  .............................................................  45   3.2.1 Push-Over Analysis with Response2000  .........................................................  45   3.2.2 Push-Over Analysis with VecTor2  ..................................................................  47   3.2.3 Load-Deformation by Hand Calculations  .......................................................  48   3.2.4 Comparison of Load-Deformation Responses  ................................................  55  3.3  Cyclic and Reverse Cyclic Responses  ...................................................................  57  3.4  Strains and Stresses  ................................................................................................  59   3.4.1 Strain Profiles from Response2000  .................................................................  59   3.4.2 Strain Profiles from VecTor2  ..........................................................................  60   3.4.3 Strain Profiles from Hand Calculation  ............................................................  61   3.4.4 Stress Distribution from VecTor2  ...................................................................  61  3.5  Checking for Shear Failure  ....................................................................................  64   3.5.1 Crack Pattern from Response2000  ..................................................................  64   3.5.2 Crack Pattern from VecTor2  ...........................................................................  66   3.5.3 Shear Strength Prediction with Code Equations  .............................................  67 v  Chapter 4: Specimen Construction and Test Set-up  ....................................................  71  4.1  Overview of the Specimens ....................................................................................  71  4.2  Specimen Foundations  ...........................................................................................  72  4.3  Construction of the Specimens  ...............................................................................  75  4.4  Material Properties  .................................................................................................  78  4.5  Test Setup for Column Specimens  .........................................................................  79  4.6  Instrumentation .......................................................................................................  82  4.7  Testing Protocol  .....................................................................................................  83  4.8  Actual Testing Procedure  .......................................................................................  84 Chapter 5: Test Results  ...................................................................................................  85  5.1  Lateral Load-Displacement Relation  .....................................................................  85   5.1.1  1:1 Column Specimen  ....................................................................................  85   5.1.2  1:2 Column Specimen  ....................................................................................  87   5.1.3  1:4 Column Specimen  ....................................................................................  89   5.1.4  1:8 Column Specimen  ....................................................................................  91   5.1.5  1:8 Wall Specimen  .........................................................................................  91  5.2  Strains and Curvatures at Compression Strain of Approximately 0.0035  .............  93   5.2.1  1:1 Column Specimen  ....................................................................................  93   5.2.2  1:2 Column Specimen  ....................................................................................  94   5.2.3  1:4 Column Specimen  ....................................................................................  95   5.2.4  1:8 Column Specimen  ....................................................................................  97   5.2.5  1:8 Wall Specimen  .........................................................................................  98  5.3  Failure Mode  ..........................................................................................................  99 vi    5.3.1  1:1 Column Specimen  ....................................................................................  99   5.3.2  1:2 Column Specimen  ....................................................................................  100   5.3.3  1:4 Column Specimen  ....................................................................................  101   5.3.4  1:8 Column Specimen  ....................................................................................  102   5.3.5  1:8 Wall Specimen  .........................................................................................  103  5.4  Comparing Results for All Specimens  ...................................................................  104 Chapter 6: Summary & Conclusion  ...............................................................................  108  6.1  Summary of Test Results  .......................................................................................  108  6.2  Improvements to Testing Procedures  .....................................................................  112  6.3  Further Research  ....................................................................................................  113 References   ........................................................................................................................  115 Appendices  ........................................................................................................................  118  Appendix A1  1:1 Column Specimen Test ....................................................................  119   A1.1  1:1 Column Testing .........................................................................................  120    A1.1.1  Specimen Information ..............................................................................  118    A1.1.2  Instrumentation  .......................................................................................  120    A1.1.3  Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part I) ..................  121    A1.1.4  Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II) .................  122    A1.1.5  Testing Phase 3: Reverse Cyclic Lateral Load Tests (Part III) ................  123   A1.2  1:1 Column Data  .............................................................................................  132    A1.2.1 Axial Load vs. Vertical Displacement  .....................................................  132    A1.2.2 Lateral Load Phase 1 Results  ...................................................................  134    A1.2.3 Lateral Load Phase 2 Results  ...................................................................  138 vii     A1.2.4 Lateral Load Phase 3 Results  ...................................................................  141    A1.2.5 Second Order Effects Estimation  .............................................................  142    A1.2.6 Load-Displacement Results and Prediction Comparison  ........................  142    A1.2.7 Displacement due to Bar Slip  ..................................................................  143    A1.2.8 Curvatures and Section Strain Profiles  ....................................................  146    A1.2.9  Failure Mode ............................................................................................  150  Appendix A2  1:2 Column Specimen Test ....................................................................  151   A2.1  1:2 Column Testing .........................................................................................  152    A2.1.1 Specimen Information  ..............................................................................  152    A2.1.2 Instrumentation  ........................................................................................  152    A2.1.3 Testing Phase 0: Cyclic Axial Load Tests  ...............................................  153    A2.1.4 Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part I)  ..................  156    A2.1.5 Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II)  .................  157    A2.1.6 Testing Phase 3: Reverse Cyclic Lateral Load Tests (Part III)  ................  163   A2.2  1:2 Column Data  .............................................................................................  168    A2.2.1 Axial Load vs. Vertical Displacement  .....................................................  168    A2.2.2 Lateral Load Phase 1 Results  ...................................................................  171    A2.2.3 Lateral Load Phase 2 Results  ...................................................................  177    A2.2.4 Lateral Load Phase 3 Results  ...................................................................  178    A2.2.5 Second Order Effects Estimation  .............................................................  180    A2.2.6 Load-Displacement Results and Prediction Comparison  ........................  181    A2.2.7 Curvatures and Section Strain Profiles  ....................................................  184    A2.2.8 Failure Mode  ............................................................................................  188 viii   Appendix A3  1:4 Column Specimen Test ....................................................................  190   A3.1  1:4 Column Testing .........................................................................................  191    A3.1.1 Specimen Information  ..............................................................................  191    A3.1.2 Instrumentation  ........................................................................................  191    A3.1.3 Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part I)  ..................  192    A3.1.4 Axial Load Cycles after Jacks were Repaired  .........................................  194    A3.1.5 Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II)  .................  194    A3.1.6 Testing Phase 3: Reverse Cyclic Lateral Load Tests (Part III)  ................  196    A3.1.7 Testing Phase 4: Reverse Cyclic Lateral Load Tests (Part IV)  ...............  199    A3.1.8 Axial Loading after Testing  .....................................................................  200   A3.2 1:4 Column Data  ..............................................................................................  204    A3.2.1 Lateral Load Phase 1 Results  ...................................................................  204    A3.2.2 Axial Load vs. Vertical Displacement after Jack Repair  .........................  207    A3.2.3 Lateral Load Phase 2 Results  ...................................................................  210    A3.2.4 Lateral Load Phase 3 Results  ...................................................................  213    A3.2.5 Lateral Load Phase 4 Results  ...................................................................  214    A3.2.6 Axial Loading Results after Specimen Failed  .........................................  215    A3.2.7 Second Order Effects Estimation  .............................................................  216    A3.2.8 Load-Displacement Results and Prediction Comparison  ........................  217    A3.2.9 Displacement due to Bar Slip  ..................................................................  219    A3.2.10 Curvatures and Section Strain Profiles  ..................................................  219    A3.2.11 Failure Mode  ..........................................................................................  224  Appendix A4  1:8  Column Specimen Test....................................................................  226 ix    A4.1  1:8 Column Testing .........................................................................................  227    A4.1.1 Specimen Information  ..............................................................................  227    A4.1.2 Instrumentation  ........................................................................................  227    A4.1.3 Testing: Reverse Cyclic Lateral Load Test  ..............................................  228   A4.2 1:8 Column Data ...............................................................................................  234    A4.2.1 Axial Load vs. Vertical Displacement  .....................................................  234    A4.2.2 Lateral Load Results  ................................................................................  236    A4.2.3 Second Order Effects Estimation  .............................................................  239    A4.2.4 Load-Displacement Results and Prediction Comparison  ........................  239    A4.2.5 Displacement due to Bar Slip  ..................................................................  240    A4.2.6 Curvatures and Section Strain Profiles  ....................................................  241    A4.2.7 Failure Mode  ............................................................................................  244  Appendix A5  1:8  Wall Specimen Test .........................................................................  246   A5.1  1:8 Wall Testing ..............................................................................................  247    A5.1.1 Specimen Information  ..............................................................................  247    A5.1.2 Instrumentation  ........................................................................................  248    A5.1.3 Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part I)  ..................  248    A5.1.4 Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II)  .................  250   A5.2 1:8 Wall Data  ...................................................................................................  260    A5.2.1 Axial Load vs. Vertical Displacement  .....................................................  260    A5.2.2 Lateral Load Phase 1 Results  ...................................................................  262    A5.2.3 Lateral Load Phase 2 Results  ...................................................................  266    A5.2.4 Second Order Effects Estimation  .............................................................  269 x     A5.2.5 Load-Displacement Results and Prediction Comparison  ........................  270    A5.2.6 Displacement due to Bar Slip  ..................................................................  270    A5.2.7 Curvatures and Section Strain Profiles  ....................................................  272    A5.2.8 Failure Mode  ............................................................................................  277  Appendix B  Column Load Takedown  .........................................................................  279   B1  Maximum Spam Length Equations  ...................................................................  280   B2  Live Load Reduction Equations  ........................................................................  280   B3  Column Load Resistance Equations  ..................................................................  281   B4  Tributary Areas for 5, 10, 20, 30, 40 & 50-storey Columns  ..............................  282   B5  Gravitational Loads & Relation with Seismic Drift  ..........................................  287   B6  Column Load Takedown Spreadsheets  ..............................................................  295    B6.1 Column Load Takedown Interior Columns (CSA)  .....................................  296    B6.2 Column Load Takedown Exterior Columns (CSA)  ....................................  301    B6.3 Column Load Takedown Interior Columns (ACI)  ......................................  306    B6.4 Column Load Takedown Exterior Columns (ACI)  .....................................  311  Appendix C  Specimen Drawings  .................................................................................  316   C1  Column Reinforcement Details  .........................................................................  317   C2  As-built Column Tie Locations  .........................................................................  326   C3  Test Set-up Drawings  .........................................................................................  332   C4  LVDT Mounts Drawings  ...................................................................................  340   C5  Other Design Drawings  .....................................................................................  345  Appendix D  Specimen Predictions by Hand Calculations  ...........................................  347   D1  1:1 Column Specimen  .......................................................................................  348 xi     D1.1  Column Specimen Moment-Curvature and Load-Displacement Predictions (with Concrete Cover)  .........................................................................................  349    D1.2  Column Specimen Moment-Curvature and Load-Displacement Predictions (without Concrete Cover)  ....................................................................................  353   D2  1:2 Column Specimen  .......................................................................................  357    D2.1  1:2 Column Specimen Moment-Curvature and Load-Displacement Predictions (with Concrete Cover)  .........................................................................................  358    D2.2  1:2 Column Specimen Moment-Curvature and Load-Displacement Predictions (without Concrete Cover)  ....................................................................................  362   D3  1:4 Column Specimen  .......................................................................................  366    D3.1 1:4 Column Specimen Moment-Curvature and Load-Displacement Predictions (with Concrete Cover)  .........................................................................................  367    D3.2 1:4 Column Specimen Moment-Curvature and Load-Displacement Predictions (without Concrete Cover)  ....................................................................................  371   D4  1:8 Column Specimen  .......................................................................................  375    D4.1 1:8 Column Specimen Moment-Curvature and Load-Displacement Predictions (with Concrete Cover)  .........................................................................................  376    D4.2 1:8 Column Specimen Moment-Curvature and Load-Displacement Predictions (without Concrete Cover)  ....................................................................................  380  Appendix E  The Chilean Wall Specimen  ....................................................................  384   E1  Introduction  ........................................................................................................  385   E2  Testing Procedure  ..............................................................................................  386   E3  Test Set-up  .........................................................................................................  387 xii    E4  Chilean Wall Analysis  .......................................................................................  390    E4.1 Modeling the Specimen with VecTor2  .......................................................  390    E4.2 Specimen Model Push-over Analysis with Axial Compression  .................  391    E4.3 Modeling the Chilean Wall with VecTor2  ..................................................  393    E4.4 Element Behaviour in the Wall Prototype Model  .......................................  396     E4.4.1 Edge Elements – Elements 64 & 72  ....................................................  396     E4.4.2 Second Elements – Elements 65 & 71  .................................................  398     E4.4.3 Third Elements – Elements 66 & 70  ...................................................  400   E5  Conclusion  .........................................................................................................  402   xiii  List of Tables  Chapter 1: Introduction  ..................................................................................................  1 Table 1.1  Some Parameters and Results from Previous Column Tests .............................  8 Chapter 2: Design of Test Specimen  ..............................................................................  11 Table 2.1  Maximum Clear Span Length for Varying Slab Thickness  ..............................  14 Table 2.2  Some Useful Indicators on Earthquake and Maximum Possible Axial Load Relations  ............................................................................................................  16 Table 2.3  Some Useful Indicators on Earthquake and Maximum Possible Axial Load Relations (ACI)  .................................................................................................  22 Table 2.4  Column Prototype Dimensions  .........................................................................  27 Table 2.5  Scaled Column Specimen Dimensions & Reinforcement  ................................  28 Chapter 3: Behaviour Predictions  ..................................................................................  32 Table 3.1  Maximum Moment and Curvature at 0.0035 Compression Strain from Response2000 .....................................................................................................  36 Table 3.2  Moment, Curvature and Compression Strain at Failure from VecTor2  ...........  39 Table 3.3  Maximum Moment and Curvature at 0.0035 Compression Strain from Hand Calculation  .........................................................................................................  41 Table 3.4  Moment and Curvature at 0.0035 Compression Strain from Code Calculation  42 Table 3.5  Maximum Loads and Displacements from Response2000  ...............................  46 Table 3.6  Loads and Displacements at Failure from VecTor2  .........................................  47 Table 3.7  Plastic Hinge Length of Specimens  ..................................................................  50 xiv  Table 3.8  Loads and Displacements at 0.0035 Compression Strain from Hand Approximation  ...................................................................................................  54 Table 3.9  Shear Resistances of the Specimens Predicted by Different Code Equations  ..  69 Chapter 4: Specimen Construction and Test Set-up  ....................................................  71 Table 4.1  Average As-built Tie Elevations [mm] from Top of Footing  ...........................  72 Table 4.2  As-built Average Specimen Heights  .................................................................  72 Table 4.3  Concrete Cylinder Test Results  ........................................................................  78 Chapter 5: Test Results  ...................................................................................................  85 Table 5.1  Vertical Strains for 1:1 Column Specimen when ecomp ~0.0035  ......................  93 Table 5.2  Average Curvatures for 1:1 Column Specimen when ecomp ~ 0.0035 [rad/km]  94 Table 5.3  Vertical Strains for 1:2 Column Specimen when ecomp ~0.0035  ......................  95 Table 5.4  Average Curvatures for 1:2 Column Specimen when ecomp ~ 0.0035 [rad/km]  95 Table 5.5  Vertical Strains for 1:4 Column Specimen when ecomp ~0.0035  ......................  96 Table 5.6  Average Curvatures for 1:4 Column Specimen when ecomp ~ 0.0035 [rad/km]  96 Table 5.7  Vertical Strains for 1:8 Column Specimen when ecomp ~0.0035  ......................  97 Table 5.8  Average Curvatures for 1:8 Column Specimen when ecomp ~ 0.0035 [rad/km]  97 Table 5.9  Vertical Strains for 1:8 Wall Specimen when ecomp ~0.0035  ...........................  98 Table 5.10  Average Curvatures for 1:8 Wall Specimen when ecomp ~ 0.0035 [rad/km]  ..  98 Chapter 6: Summary & Conclusion  ...............................................................................  108 Table 6.1  Predicted Maximum Loads and Displacements for all Specimens  ...................  109 Table 6.2  Measured Maximum Loads and Displacements for all Specimens  ..................  110 Table 6.3  Measured Bar Slip Displacements for all Specimens  .......................................  111 Appendix A1: 1:1 Column Specimen Test  .....................................................................  119 xv  Table A1.1  Loading Protocol on 1:1 Column Specimen ...................................................  129 Table A1.2  Estimated Compression Strains  .....................................................................  134 Table A1.3  Estimating Horizontal Displacement cause by Bar Slip  ................................  146 Table A1.4  Vertical Strains at Various Heights when Tension Strain ~0.002  .................  149 Table A1.5  Vertical Strains at Various Heights when Compression Strain ~0.0035 ........  149 Table A1.6  Vertical Strains at Various Heights when Specimen Displacement ~16mm ..   149 Table A1.7  Vertical Strains at Various Heights when Specimen Displacement ~34mm ..   149 Table A1.8  Average Curvatures of Different Sections at Various Load Points [rad/km]   150 Appendix A2: 1:2 Column Specimen Test  .....................................................................  151 Table A2.1  Loading on 1:2 Column Specimen .................................................................  165 Table A2.2  Estimated Compression Strains  .....................................................................  171 Table A2.3  Vertical Strains at Various Heights when Tension Strain ~0.002  .................  187 Table A2.4  Vertical Strains at Various Heights when Compression Strain ~0.0035  .......  187 Table A2.5  Vertical Strains at Various Heights when Specimen Displacement ~15mm ..   187 Table A2.6  Vertical Strains at Various Heights when Specimen Displacement ~20mm ..   187 Table A2.7  Average Curvatures of Different Sections at Various Load Points [rad/km]   188 Appendix A3: 1:4 Column Specimen Test  .....................................................................  190 Table A3.1  Loading on 1:4 Column Specimen .................................................................  201 Table A3.2  Estimated Compression Strains  .....................................................................  210 Table A3.3  Estimating Horizontal Displacement caused by Bar Slip  ..............................  219 Table A3.4  Vertical Strains at Various Heights when Tension Strain ~0.002  .................  222 Table A3.5  Vertical Strains at Various Heights when Compression Strain ~0.0035  .......  222 Table A3.6  Vertical Strains at Various Heights when Specimen Displacement ~11mm ..   223 xvi  Table A3.7  Vertical Strains at Various Heights when Specimen Displacement ~18mm ..   223 Table A3.8  Average Curvatures of Different Sections at Various Load Points [rad/km]   223 Appendix A4: 1:8 Column Specimen Test  .....................................................................  226 Table A4.1  Loading on 1:8 Column Specimen .................................................................  232 Table A4.2  Estimated Compression Strains  .....................................................................  236 Table A4.3  Vertical Strains at Various Heights after Application of Axial Load  ............  243 Table A4.4  Vertical Strains at Various Heights when Specimen Displacement ~1.5mm .  243 Table A4.5  Vertical Strains at Various Heights when Specimen Displacement ~5mm ....  243 Table A4.6  Vertical Strains at Various Heights when Specimen Displacement ~9.4mm .  243 Table A4.7  Average Curvatures of Different Sections at Various Load Points [rad/km] .  243 Appendix A5: 1:8 Wall Specimen Test  ..........................................................................  246 Table A5.1  Loading on 1:8 Wall Specimen .......................................................................  257 Table A5.2  Estimated Compression Strains  .....................................................................  262 Table A5.3  Estimating Horizontal Displacement caused by Bar Slip  ..............................  272 Table A5.4  Vertical Strains at Various Heights when Tension Strain ~0.002  .................  275 Table A5.5  Vertical Strains at Various Heights when Compression Strain ~0.0035  .......  275 Table A5.6  Vertical Strains at Various Heights when Specimen Displacement ~5mm  ...  276 Table A5.7  Vertical Strains at Various Heights when Specimen Displacement ~8mm ....  276 Table A5.8  Average Curvatures of Different Sections at Various Load Points [rad/km] .  276 Appendix B: Column Load Takedown  ..........................................................................  279 Table B4.1(a)  Tributary Areas for Square Columns for a 5-storey Building ....................  282 Table B4.1(b)  Tributary Areas for Square Columns for a 10-storey Building  .................  282 Table B4.1(c)  Tributary Areas for Square Columns for a 20-storey Building  .................  282 xvii  Table B4.1(d)  Tributary Areas for Square Columns for a 30-storey Building  .................  282 Table B4.1(e)  Tributary Areas for Square Columns for a 40-storey Building  .................  283 Table B4.1(f)  Tributary Areas for Square Columns for a 50-storey Building  ..................  283 Table B4.2(a)  Tributary Areas for 1:2 Elongated Columns for a 5-storey Building  ........  283 Table B4.2(b)  Tributary Areas for 1:2 Elongated Columns for a 10-storey Building .......  283 Table B4.2(c)  Tributary Areas for 1:2 Elongated Columns for a 20-storey Building .......  283 Table B4.2(d)  Tributary Areas for 1:2 Elongated Columns for a 30-storey Building .......  284 Table B4.2(e)  Tributary Areas for 1:2 Elongated Columns for a 40-storey Building .......  284 Table B4.2(f)  Tributary Areas for 1:2 Elongated Columns for a 50-storey Building .......  284 Table B4.3(a)  Tributary Areas for 1:4 Elongated Columns for a 5-storey Building .........  284 Table B4.3(b)  Tributary Areas for 1:4 Elongated Columns for a 10-storey Building .......  284 Table B4.3(c)  Tributary Areas for 1:4 Elongated Columns for a 20-storey Building .......  285 Table B4.3(d)  Tributary Areas for 1:4 Elongated Columns for a 30-storey Building .......  285 Table B4.3(e)  Tributary Areas for 1:4 Elongated Columns for a 40-storey Building .......  285 Table B4.3(f)  Tributary Areas for 1:4 Elongated Columns for a 50-storey Building .......  285 Table B4.4(a)  Tributary Areas for 1:8 Elongated Columns for a 5-storey Building .........  285 Table B4.4(b)  Tributary Areas for 1:8 Elongated Columns for a 10-storey Building .......  286 Table B4.4(c)  Tributary Areas for 1:8 Elongated Columns for a 20-storey Building .......  286 Table B4.4(d)  Tributary Areas for 1:8 Elongated Columns for a 30-storey Building .......  286 Table B4.4(e)  Tributary Areas for 1:8 Elongated Columns for a 40-storey Building .......  286 Table B4.4(f)  Tributary Areas for 1:8 Elongated Columns for a 50-storey Building .......  286 Table B5.1  Dead Load for Varying Slab Thicknesses .......................................................  287 Table B5.2(a)  Loads for Square Interior Columns with 5” (127mm) Slab Thickness ......  287 xviii  Table B5.2(b)  Loads for 1:2 Elongated Interior Columns with 5” (127mm) Slab Thickness       .......................................................................................................................  287 Table B5.2(c)  Loads for 1:4 Elongated Interior Columns with 5” (127mm) Slab Thickness       .......................................................................................................................  287 Table B5.2(d)  Loads for 1:8 Elongated Interior Columns with 5” (127mm) Slab Thickness       .......................................................................................................................  288 Table B5.3(a)  Loads for Square Exterior Columns with 5” (127mm) Slab Thickness .....  288 Table B5.3(b)  Loads for 1:2 Elongated Exterior Columns with 5” (127mm) Slab Thickness       .......................................................................................................................  288 Table B5.3(c)  Loads for 1:4 Elongated Exterior Columns with 5” (127mm) Slab Thickness       .......................................................................................................................  288 Table B5.3(d)  Loads for 1:8 Elongated Exterior Columns with 5” (127mm) Slab Thickness       .......................................................................................................................  289 Table B5.4(a)  Loads for Square Interior Columns with 6” (152.4mm) Slab Thickness ...  289 Table B5.4(b)  Loads for 1:2 Elongated Interior Columns with 6” (152.4mm) Slab Thickness       .......................................................................................................................  289 Table B5.4(c)  Loads for 1:4 Elongated Interior Columns with 6” (152.4mm) Slab Thickness       .......................................................................................................................  289 Table B5.4(d)  Loads for 1:8 Elongated Interior Columns with 6” (152.4mm) Slab Thickness       .......................................................................................................................  290 Table B5.5(a)  Loads for Square Exterior Columns with 6” (152.4mm) Slab Thickness ..  290 Table B5.5(b)  Loads for 1:2 Elongated Exterior Columns with 6” (152.4mm) Slab Thickness       .......................................................................................................................  290 xix  Table B5.5(c)  Loads for 1:4 Elongated Exterior Columns with 6” (152.4mm) Slab Thickness       .......................................................................................................................  290 Table B5.5(d)  Loads for 1:8 Elongated Exterior Columns with 6” (152.4mm) Slab Thickness       .......................................................................................................................  291 Table B5.6(a)  Loads for Square Interior Columns with 8” (203.2mm) Slab Thickness ...  291 Table B5.6(b)  Loads for 1:2 Elongated Interior Columns with 8” (203.2mm) Slab Thickness       .......................................................................................................................  291 Table B5.6(c)  Loads for 1:4 Elongated Interior Columns with 8” (203.2mm) Slab Thickness       .......................................................................................................................  291 Table B5.6(d)  Loads for 1:8 Elongated Interior Columns with 8” (203.2mm) Slab Thickness       .......................................................................................................................  292 Table B5.7(a)  Loads for Square Exterior Columns with 8” (203.2mm) Slab Thickness ..  292 Table B5.7(b)  Loads for 1:2 Elongated Exterior Columns with 8” (203.2mm) Slab Thickness       .......................................................................................................................  292 Table B5.7(c)  Loads for 1:4 Elongated Exterior Columns with 8” (203.2mm) Slab Thickness       .......................................................................................................................  292 Table B5.7(d)  Loads for 1:8 Elongated Exterior Columns with 8” (203.2mm) Slab Thickness       .......................................................................................................................  293 Table B5.8(a)  Loads for Square Interior Columns with 10” (254mm) Slab Thickness ....  293 Table B5.8(b)  Loads for 1:2 Elongated Interior Columns with 10” (254mm) Slab Thickness       .......................................................................................................................  293 Table B5.8(c)  Loads for 1:4 Elongated Interior Columns with 10” (254mm) Slab Thickness       .......................................................................................................................  293 xx  Table B5.8(d)  Loads for 1:8 Elongated Interior Columns with 10” (254mm) Slab Thickness       .......................................................................................................................  294 Table B5.9(a)  Loads for Square Exterior Columns with 10” (254mm) Slab Thickness ...  294 Table B5.9(b)  Loads for 1:2 Elongated Exterior Columns with 10” (254mm) Slab Thickness       .......................................................................................................................  294 Table B5.9(c)  Loads for 1:4 Elongated Exterior Columns with 10” (254mm) Slab Thickness       .......................................................................................................................  294 Table B5.9(d)  Loads for 1:8 Elongated Exterior Columns with 10” (254mm) Slab Thickness       .......................................................................................................................  295   xxi  List of Figures  Chapter 2: Design of Test Specimens  .............................................................................  11 Figure 2.1  Tributary Areas for Columns ............................................................................  14 Figure 2.2  Summary of D/(D+L) for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses ...............................................  18 Figure 2.3  Summary of Ps/Pf for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses ..............................................................  19 Figure 2.4  Summary of Ps/Pr0 for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses ...............................................  20 Figure 2.5  Summary of P/f’cAg for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses ...............................................  21 Figure 2.6  Summary of D/(D+L) for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) ....................................  23 Figure 2.7  Summary of Ps/Pf for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) ....................................................  24 Figure 2.8  Summary of Ps/Pr0 for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) ....................................  25 Figure 2.9  Summary of P/f’cAg for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) ....................................  26 Figure 2.10  Scaled Column Specimen Cross Sections ......................................................  29 Figure 2.11  Scaled Column Specimen Elevation Views  ..................................................  30 Figure 2.12  1:8 Wall Specimen .........................................................................................  31 xxii  Chapter 3: Behaviour Predictions  ..................................................................................  32 Figure 3.1  Specimen Cross-Section Models with Concrete Cover in Response 2000 ......  33 Figure 3.2  Specimen Cross-Section Models without Concrete Cover in Response 2000 .  34 Figure 3.3  Moment-Curvature Responses from Response2000 ........................................  35 Figure 3.4  Specimen Model in Vector2 .............................................................................  37 Figure 3.5  Moment-Curvature Responses from VecTor2 .................................................  38 Figure 3.6  Moment and Curvature Response by Hand Calculation ..................................  43 Figure 3.7  Moment-Curvature Response Comparison of Various Methods .....................  44 Figure 3.8  Load-Displacement from Response2000 .........................................................  46 Figure 3.9  Load-Displacement from VecTor2 ...................................................................  48 Figure 3.10  Curvature Along Height of Specimen ............................................................  49 Figure 3.11  Trilinear Approximation to Moment-Curvature Plots (with Concrete Cover) 51 Figure 3.12  Trilinear Approximation to Moment0Curvature Plots (no Concrete Cover) .  52 Figure 3.13  Load-Deformation from Hand Approximation ..............................................  53 Figure 3.14  Load-Displacement Response Comparison of Various Methods ...................  56 Figure 3.15  Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:1 Column Specimen........................................................................................................  57 Figure 3.16  Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:2 Column Specimen........................................................................................................  58 Figure 3.17  Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:4 Column Specimen........................................................................................................  58 Figure 3.18  Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:8 Column Specimen........................................................................................................  59 xxiii  Figure 3.19  Strain Profiles from Response 2000 ...............................................................  60 Figure 3.20  Strain Profiles from VecTor2 .........................................................................  60 Figure 3.21  Strain Profiles from Hand and Code Calculations .........................................  61 Figure 3.22  Stress Distribution of 1:1 Column from VecTor2 near Failure ......................  62 Figure 3.23  Stress Distribution of 1:2 Column from VecTor2 near Failure ......................  62 Figure 3.24  Stress Distribution of 1:4 Column from VecTor2 near Failure ......................  63 Figure 3.25  Stress Distribution of 1:8 Column from VecTor2 near Failure ......................  63 Figure 3.26  Crack Pattern from Response2000 .................................................................  65 Figure 3.27  Model Response and Failure Envelope of 1:8 Column from Response2000 .  66 Figure 3.28  Crack Pattern from VecTor2 ..........................................................................  66 Figure 3.29  Vr/Vf Ratios of the Specimens by Different Code Equations .........................  69 Chapter 4: Specimen Construction and Test Set-up  ....................................................  71 Figure 4.1  Specimen Foundations ......................................................................................  73 Figure 4.2  Force on Footing ...............................................................................................  74 Figure 4.3  Footing Check for Overturning and Sliding .....................................................  74 Figure 4.4  Foundation Formwork ......................................................................................  75 Figure 4.5  Rebar Installation ..............................................................................................  76 Figure 4.6  First Concrete Pour ...........................................................................................  77 Figure 4.7  Column Formwork ...........................................................................................  77 Figure 4.8  Defects in the Specimens ..................................................................................  78 Figure 4.9  Test Set-up for Applying Axial Load ...............................................................  80 Figure 4.10  Test Set-up for Applying Lateral Load ..........................................................  81 Figure 4.11  Horizontal Stabilizer .......................................................................................  82 xxiv  Figure 4.12  LVDT Locations .............................................................................................  83 Chapter 5: Test Results  ...................................................................................................  85 Figure 5.1  Lateral Load-Displacement Plot of 1:1 Column Specimen ..............................  86 Figure 5.2  Lateral Load-Displacement Plot of 1:2 Column Specimen ..............................  88 Figure 5.3  Lateral Load-Displacement Plot of 1:4 Column Specimen ..............................  90 Figure 5.4  Lateral Displacement-Time Plot of 1:8 Column Specimen .............................  91 Figure 5.5  Lateral Load-Displacement Plot of 1:8 Wall Specimen ...................................  92 Figure 5.6  Test Ended at Rebar Snapping and Loss of too much Cover ...........................  100 Figure 5.7  Test Ended at Rebar Buckling ..........................................................................  101 Figure 5.8  Test Ended at Specimen Splitting .....................................................................  102 Figure 5.9  Test Stopped at Specimen Splitting ..................................................................  103 Figure 5.10  Test Ended at Specimen Splitting and Ties Opening .....................................  104 Figure 5.11  Comparison of Load-Displacement Behaviour of All Specimens .................  105 Appendix A1: 1:1 Column Specimen Test  .....................................................................  119 Figure A1.1  1:1 Column Specimen Plan View ..................................................................  120 Figure A1.2  As-built LVDT Locations for 1:1 Column ....................................................  121 Figure A1.3  First Concrete Spalling after Testing Phase 2 ...............................................  123 Figure A1.4  Concrete Spalling after Target Specimen Displacement 25mm Cycle 3 ......  124 Figure A1.5  Concrete Spalling after Target Specimen Displacement 30mm Cycle 3 ......  125 Figure A1.6(a) Rebar Buckling after Jack Full Stroke Cycle 1 ..........................................  125 Figure A1.6(b) Rebar Buckling after Jack Full Stroke Cycle 1 ..........................................  126 Figure A1.7  Concrete Spall up to 4 th  Tie after Testing ......................................................  127 Figure A1.8(a)  Rebar Snap on Right Side after Testing ....................................................  127 xxv  Figure A1.8(b)  Rebar Snap on Left Side after Testing ......................................................  128 Figure A1.9  Concrete at Base Almost All Gone after Testing ..........................................  128 Figure A1.10  Actual Loading Cycles on 1:1 Column Specimen .......................................  129 Figure A1.11  1:1 Column Specimen after Testing ............................................................  131 Figure A1.12(a)  Axial Load-Displacement Plot for LVDT D8 .........................................  132 Figure A1.12(b)  Axial Load-Displacement Plot for LVDT D10 ......................................  132 Figure A1.12(c)  Axial Load-Displacement Plot for LVDT D5 .........................................  133 Figure A1.12(d)  Axial Load-Displacement Plot for LVDT D7 ........................................  133 Figure A1.12(e)  Axial Load-Displacement Plot for LVDT D4 .........................................  133 Figure A1.12(f)  Axial Load-Displacement Plot for LVDT D6 .........................................  134 Figure A1.13  Lateral Load-Displacement of 1:1 Column Specimen (Phase 1) ................  135 Figure A1.14(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 1) ..................  136 Figure A1.14(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 1) ...............  136 Figure A1.14(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 1) ..................  136 Figure A1.14(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 1) .................  137 Figure A1.14(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 1) ..................  137 Figure A1.14(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 1) ..................  137 Figure A1.15  Lateral Load-Displacement of 1:1 Column Specimen (Phase 2) ................  138 Figure A1.16(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 2) ..................  139 Figure A1.16(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 2) ...............  139 Figure A1.16(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 2) ..................  139 Figure A1.16(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 2) .................  140 Figure A1.16(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 2) ..................  140 xxvi  Figure A1.16(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 2) ..................  140 Figure A1.17  Lateral Load-Displacement of 1:1 Column Specimen (Phase 3) ................  141 Figure A1.18  Results and Prediction Comparison .............................................................  144 Figure A1.19(a)  Measured Slip at Phase 1 ........................................................................  145 Figure A1.19(b)  Measured Slip at Phase 2 ........................................................................  145 Figure A1.19(c)  Measured Slip at Phase 3 ........................................................................  145 Figure A1.20(a)  Strain Profile through Top LVDTs during Jack Pushing ........................  147 Figure A1.20(b)  Strain Profile through Top LVDTs during Jack Pulling .........................  147 Figure A1.20(c)  Strain Profile through Middle LVDTs during Jack Pushing ...................  147 Figure A1.20(d)  Strain Profile through Middle LVDTs during Jack Pulling ....................  148 Figure A1.20(e)  Strain Profile through Bottom LVDTs during Jack Pushing ..................  148 Figure A1.20(f)  Strain Profile through Bottom LVDTs during Jack Pulling ....................  148 Appendix A2: 1:2 Column Specimen Test  .....................................................................  151 Figure A2.1  1:2 Column Specimen Plan View ..................................................................  152 Figure A2.2  As-built LVDT Locations for 1:2 Column ....................................................  153 Figure A2.3  Shrinkage Crack Locations and Crack Widths ..............................................  155 Figure A2.4  Extra Threaded Rods to Reduce Slack in Set-up ...........................................  157 Figure A2.5(a)  First Tension Cracks on Specimen ............................................................  159 Figure A2.5(b)  First Tension Cracks on Front Face of Specimen .....................................  159 Figure A2.6  Concrete Cover Started Spalling at Base of Column ....................................  160 Figure A2.7  Concrete Cover Spalled Off after Large Cracks Formed along Edge ...........  160 Figure A2.8  Severe Concrete Cover Spalling after Cycling ..............................................  161 Figure A2.9  1:2 Column Specimen after Lateral Test Phase 2 ..........................................  162 xxvii  Figure A2.10  Actual Loading Cycles on 1:2 Column Specimen .......................................  164 Figure A2.11  1:2 Column Specimen after Testing ............................................................  166 Figure A2.12(a)  Axial Load-Displacement Plot for LVDT D8 .........................................  168 Figure A2.12(b)  Axial Load-Displacement Plot for LVDT D10 ......................................  169 Figure A2.12(c)  Axial Load-Displacement Plot for LVDT D5 .........................................  169 Figure A2.12(d)  Axial Load-Displacement Plot for LVDT D7 ........................................  170 Figure A2.12(e)  Axial Load-Displacement Plot for LVDT D4 .........................................  170 Figure A2.12(f)  Axial Load-Displacement Plot for LVDT D6 .........................................  171 Figure A2.13  Lateral Load-Displacement of 1:2 Column Specimen (Phase 1) ................  172 Figure A2.14  Lateral Load-Displacement after LVDT Mounts Fixed (Phase 1) ..............  173 Figure A2.15  Lateral Load-Displacement after Load Cell Zeroed at Constant Axial Load (Phase 1) ......................................................................................................  174 Figure A2.16(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 1) ..................  175 Figure A2.16(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 1) ...............  175 Figure A2.16(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 1) ..................  175 Figure A2.16(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 1) .................  176 Figure A2.16(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 1) ..................  176 Figure A2.16(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 1) ..................  176 Figure A2.17  Lateral Load-Displacement to Match Specimen Displacement in Push and Pull Directions (Phase 2) ....................................................................................  177 Figure A2.18  Lateral Load-Displacement of 1:2 Column Specimen (Phase 2) ................  178 Figure A2.19  Lateral Load-Displacement of 1:2 Column Specimen (Phase 3) ................  179 Figure A2.20  Lateral Load-Displacement for Last Cycle (Phase 3) .................................  180 xxviii  Figure A2.21  Lever Arm for Second Order Effects ..........................................................  181 Figure A2.22  Results and Prediction Comparison .............................................................  183 Figure A2.23(a)  Strain Profile through Top LVDTs during Jack Pushing ........................  185 Figure A2.23(b)  Strain Profile through Top LVDTs during Jack Pulling .........................  185 Figure A2.23(c)  Strain Profile through Middle LVDTs during Jack Pushing ...................  185 Figure A2.23(d)  Strain Profile through Middle LVDTs during Jack Pulling ....................  186 Figure A2.23(e)  Strain Profile through Bottom LVDTs during Jack Pushing ..................  186 Figure A2.23(f)  Strain Profile through Bottom LVDTs during Jack Pulling ....................  186 Appendix A3: 1:4 Column Specimen Test  .....................................................................  190 Figure A3.1  1:4 Column Specimen Plan View ..................................................................  191 Figure A3.2  As-built LVDT Locations for 1:4 Column ....................................................  192 Figure A3.3  Specimen Cracks after Phase 2 ......................................................................  195 Figure A3.4  Extra LVDTs for Bar Slip .............................................................................  196 Figure A3.5  Concrete Broke Off after +15/-30mm Cycle 1 ..............................................  197 Figure A3.6  Concrete Damage after +25/-50mm Cycle 1 (Left & Right).........................  198 Figure A3.7  Concrete Damage after +25/-50mm Cycle 1 (Front & Back on Left)...........  198 Figure A3.8  Serious Concrete Crushing and Rebar Buckling after +23/-30mm Cycle 2 ..  199 Figure A3.9  Damage on the Right Side after +23/-30mm Cycle 2 ...................................  200 Figure A3.10  Actual Loading Cycles on 1:4 Column Specimen .......................................  201 Figure A3.11  1:4 Column Specimen after Testing ............................................................  202 Figure A3.12  Lateral Load-Displacement of 1:4 Column Specimen (Phase 1) ................  204 Figure A3.13(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 1) ..................  205 Figure A3.13(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 1) ...............  205 xxix  Figure A3.13(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 1) ..................  206 Figure A3.13(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 1) .................  206 Figure A3.13(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 1) ..................  206 Figure A3.13(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 1) ..................  207 Figure A3.14(a)  Axial Load-Displacement Plot for LVDT D8 .........................................  208 Figure A3.14(b)  Axial Load-Displacement Plot for LVDT D10 ......................................  208 Figure A3.14(c)  Axial Load-Displacement Plot for LVDT D5 .........................................  208 Figure A3.14(d)  Axial Load-Displacement Plot for LVDT D7 ........................................  209 Figure A3.14(e)  Axial Load-Displacement Plot for LVDT D4 .........................................  209 Figure A3.14(f)  Axial Load-Displacement Plot for LVDT D6 .........................................  209 Figure A3.15  Lateral Load-Displacement of 1:4 Column Specimen (Phase 2) ................  210 Figure A3.16(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 2) ..................  211 Figure A3.16(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 2) ...............  211 Figure A3.16(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 2) ..................  211 Figure A3.16(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 2) .................  212 Figure A3.16(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 2) ..................  212 Figure A3.16(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 2) ..................  212 Figure A3.17  Lateral Load-Displacement of 1:4 Column Specimen (Phase 3) ................  213 Figure A3.18  Lateral Load-Displacement of 1:4 Column Specimen (Phase 4) ................  215 Figure A3.19(a)  Axial Load vs. Vertical Displacement after Test (LVDT D8) ................  216 Figure A3.19(b)  Axial Load vs. Vertical Displacement after Test (LVDT D10) ..............  216 Figure A3.20  Results and Prediction Comparison .............................................................  218 Figure A3.21(a)  Strain Profile through Top LVDTs during Jack Pushing ........................  220 xxx  Figure A3.21(b)  Strain Profile through Top LVDTs during Jack Pulling .........................  221 Figure A3.21(c)  Strain Profile through Middle LVDTs during Jack Pushing ...................  221 Figure A3.21(d)  Strain Profile through Middle LVDTs during Jack Pulling ....................  221 Figure A3.21(e)  Strain Profile through Bottom LVDTs during Jack Pushing ..................  222 Figure A3.21(f)  Strain Profile through Bottom LVDTs during Jack Pulling ....................  222 Appendix A4: 1:8 Column Specimen Test  .....................................................................  226 Figure A4.1  1:8 Column Specimen Plan View ..................................................................  227 Figure A4.2  LVDT Locations for 1:8 Column ..................................................................  228 Figure A4.3  Concrete Cover fell off in Front & Cracking ................................................  230 Figure A4.4  Concrete Cover fell off at Back & Cracking .................................................  230 Figure A4.5  Concrete Crushing and Rebar Buckling on Right .........................................  231 Figure A4.6  Specimen Split along its Length ....................................................................  231 Figure A4.7  1:8 Column Specimen after Testing ..............................................................  232 Figure A4.8(a)  Axial Load-Displacement Plot for LVDT D8 ...........................................  234 Figure A4.8(b)  Axial Load-Displacement Plot for LVDT D10 ........................................  234 Figure A4.8(c)  Axial Load-Displacement Plot for LVDT D5 ...........................................  235 Figure A4.8(d)  Axial Load-Displacement Plot for LVDT D7 ..........................................  235 Figure A4.8(e)  Axial Load-Displacement Plot for LVDT D4 ...........................................  235 Figure A4.8(f)  Axial Load-Displacement Plot for LVDT D6 ...........................................  236 Figure A4.9  Horizontal Displacement vs. Time Plot for 1:8 Column Specimen ..............  237 Figure A4.10(a)  Vertical Displacement vs. Time at LVDT D8 ........................................  237 Figure A4.10(b)  Vertical Displacement vs. Time at LVDT D10 ......................................  238 Figure A4.10(c)  Vertical Displacement vs. Time at LVDT D5 ........................................  238 xxxi  Figure A4.10(d)  Vertical Displacement vs. Time at LVDT D7 ........................................  238 Figure A4.10(e)  Vertical Displacement vs. Time at LVDT D4 ........................................  239 Figure A4.10(f)  Vertical Displacement vs. Time at LVDT D6 .........................................  239 Figure A4.11  Slip at LVDT D1 vs. Time ..........................................................................  240 Figure A4.12  Slip at LVDT D1 vs. Specimen Displacement ............................................  240 Figure A4.13(a)  Strain Profile through Top LVDTs during Jack Pushing ........................  242 Figure A4.13(b)  Strain Profile through Middle LVDTs during Jack Pushing ..................  242 Figure A4.13(c)  Strain Profile through Bottom LVDTs during Jack Pushing ..................  242 Appendix A5: 1:8 Wall Specimen Test  ..........................................................................  246 Figure A5.1  1:8 Wall Specimen Plan View .......................................................................  247 Figure A5.2  LVDT Locations for 1:8 Wall .......................................................................  248 Figure A5.3  First Specimen Damage Observed ................................................................  250 Figure A5.4  Cracks after Target Specimen Displacement +/-5mm Cycle 1 .....................  251 Figure A5.5  Concrete Crushing on the Right ....................................................................  252 Figure A5.6(a)  Right Side after Target Specimen Displacement 9mm Cycle 1 ................  253 Figure A5.6(b)  Left Side after Target Specimen Displacement 9mm Cycle 1 ..................  253 Figure A5.7  Right Side Cover off after Target Specimen Displacement 9mm Cycle 3 ....  254 Figure A5.8  Specimen Split after Failure ..........................................................................  255 Figure A5.9  Rebar Buckling and Ties Opening .................................................................  256 Figure A5.10  Concrete Cover gone on Both Ends ............................................................  256 Figure A5.11  Actual Loading Cycles on 1:8 Wall Specimen ............................................  257 Figure A5.12  1:8 Wall Specimen after Testing .................................................................  258 Figure A5.13(a)  Axial Load-Displacement Plot for LVDT D8 .........................................  260 xxxii  Figure A5.13(b)  Axial Load-Displacement Plot for LVDT D10 ......................................  261 Figure A5.13(c)  Axial Load-Displacement Plot for LVDT D5 .........................................  261 Figure A5.13(d)  Axial Load-Displacement Plot for LVDT D7 ........................................  261 Figure A5.13(e)  Axial Load-Displacement Plot for LVDT D4 .........................................  262 Figure A5.13(f)  Axial Load-Displacement Plot for LVDT D6 .........................................  262 Figure A5.14  Lateral Load-Displacement of 1:8 Wall Specimen (Phase 1) .....................  263 Figure A5.15(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 1) ..................  264 Figure A5.15(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 1) ...............  264 Figure A5.15(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 1) ..................  265 Figure A5.15(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 1) .................  265 Figure A5.15(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 1) ..................  265 Figure A5.15(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 1) ..................  266 Figure A5.16  Lateral Load-Displacement of 1:8 Wall Specimen (Phase 2) .....................  267 Figure A5.17(a)  Lateral Load-Vertical Displacement at LVDT D8 (Phase 2) ..................  267 Figure A5.17(b)  Lateral Load-Vertical Displacement at LVDT D10 (Phase 2) ...............  268 Figure A5.17(c)  Lateral Load-Vertical Displacement at LVDT D5 (Phase 2) ..................  268 Figure A5.17(d)  Lateral Load-Vertical Displacement at LVDT D7 (Phase 2) .................  268 Figure A5.17(e)  Lateral Load-Vertical Displacement at LVDT D4 (Phase 2) ..................  269 Figure A5.17(f)  Lateral Load-Vertical Displacement at LVDT D6 (Phase 2) ..................  269 Figure A5.18  Results and Prediction Comparison .............................................................  271 Figure A5.19(a)  Measured Slip at LVDT D1 (Left: Phase 1, Right: Phase 2) ..................  272 Figure A5.19(b)  Measured Slip at LVDT D3 (Left: Phase 1, Right: Phase 2) ..................  272 Figure A5.20(a)  Strain Profile through Top LVDTs during Jack Pushing ........................  273 xxxiii  Figure A5.20(b)  Strain Profile through Top LVDTs during Jack Pulling .........................  274 Figure A5.20(c)  Strain Profile through Middle LVDTs during Jack Pushing ...................  274 Figure A5.20(d)  Strain Profile through Middle LVDTs during Jack Pulling ....................  274 Figure A5.20(e)  Strain Profile through Bottom LVDTs during Jack Pushing ..................  275 Figure A5.20(f)  Strain Profile through Bottom LVDTs during Jack Pulling ....................  275 Appendix E: The Chilean Wall Specimen  .....................................................................  384 Figure E1.1  Chilean Wall Specimen ..................................................................................  386 Figure E2.1  Element Experiences both Tension and Compression in Earthquake ............  386 Figure E3.1  Set-up for Tension Application ......................................................................  388 Figure E3.2  Different Set-up for Different Footings .........................................................  389 Figure E3.3  Extra Rods on Chilean Wall Specimen for Applying Tension ......................  390 Figure E4.1  Chilean Wall Specimen Model in VecTor2 ...................................................  391 Figure E4.2  Load-Displacement for Chilean Wall Specimen in VecTor2 ........................  392 Figure E4.3  Crack Patterns for Chilean Wall Specimen at Failure ...................................  393 Figure E4.4  Wall Prototype Model in VecTor2 .................................................................  394 Figure E4.5  Load-Displacement of Wall Prototype Model in VecTor2 ............................  395 Figure E4.6  Crack Patterns for Wall Prototype Model in VecTor2 ..................................  395 Figure E4.7  Elements at One Wall Length from Base .......................................................  396 Figure E4.8  Lateral Load vs. Axial Load for Edge Elements ............................................  397 Figure E4.9 Element Shear Stress vs. Total Displacement for Edge Elements ..................  397 Figure E4.10  Element Shear Stress vs. Element Strains for Edge Elements .....................  398 Figure E4.11  Lateral Load vs. Axial Load for Second Elements ......................................  399 Figure E4.12  Element Shear Stress vs. Total Displacement for Second Elements ...........  399 xxxiv  Figure E4.13  Element Shear Stress vs. Element Strains for Second Elements .................  400 Figure E4.14  Lateral Load vs. Axial Load for Third Elements .........................................  400 Figure E4.15  Element Shear Stress vs. Total Displacement for Third Elements ..............  401 Figure E4.16  Element Shear Stress vs. Element Strains for Third Elements ....................  401   xxxv  List of Symbols  A area of a concrete component of the equivalent concrete area of a steel component Ab area of a single reinforcement bar Ac area of concrete (minus the area of steel embedded in the concrete) Ag gross area of a section As total area of steel reinforcement Av area of shear reinforcement bw width of section c compression strain depth; distance from extreme compression fibre to neutral axis d effective depth of a member; distance from extreme compression fibre to centroid of tension reinforcement db diameter of a reinforcement bar dv effective shear depth Ec modulus of elasticity of concrete Es modulus of elasticity of steel F force in reinforcement bar f’c specified compressive strength of concrete fs reinforcement steel stress at specified loads Fy,fy specified yield strength of non-prestressed reinforcement hw height of member l distance from the critical section to the point of contraflexure L  length along column height from point of loading (top of column) xxxvi  L1  length from point of loading to point with curvature f1 L2  length from point of loading to point with curvature f2 ld development length of reinforcement lp plastic hinge length of member Mf factored moment Nf factored axial load normal to the cross-section occurring simultaneously with Vf P axial load normal to cross-section Pc critical axial load Pf factored axial load due to gravitational loads Pr0 factored axial load resistance at zero eccentricity Pr.max maximum axial load resistance Ps axial force with seismic drift; force in steel reinforcement s shear reinforcement spacing sZ crack spacing parameter dependent on crack control characteristics of longitudinal reinforcement sZE equivalent value of sZ that allows for influence of aggregate size ub uniform bond stress Vc concrete shear resistance Vf factored shear Vs steel shear resistance w width of cross-section y distance from reference point (taken as top of section) to component yCG neutral axis of a member cross-section xxxvii  a1 ratio of average stress in rectangular compression block to the specified concrete strength b factor accounting for shear resistance of cracked concrete b1 ratio of depth of rectangular compression block to depth of the neutral axis gc density of concrete Di inelastic displacement e’c maximum strain = √f'c/2500 ecu compression strain capacity ecomp compression strain in specimen es reinforcement strain etop strain at top of section (compression side) ex longitudinal strain at mid-depth of the member due to factored loads ey steel yield strain Θ inelastic rotation at the base of a member; angle of inclination of diagonal compressive stresses to the longitudinal axis of the member l factor to account for low-density concrete m coefficient of friction r ratio of non-prestressed tension reinforcement f curvature at base of column xxxviii  f1 1 st  point in trilinear approximation of moment-curvature with a change in slope f2  2 nd  point in trilinear approximation of moment-curvature with a change in slope fc concrete resistance factor fcap curvature capacity fs steel resistance factor   xxxix  Acknowledgements  I offer my enduring gratitude to my professor, Dr. Perry Adebar, who has guided me along these years from start to completion of my research, as well as the technicians in the Structural Laboratory for helping me throughout the experiments.  Special thanks are owed to my parents, whose have supported me throughout my years of education.  1  Chapter  1: Introduction 1.1 Background In the design of a typical high-rise building in Canada, the structure is divided into components that are part of the seismic-force-resisting-system (SFRS) such as the concrete shear walls, and components that are part of the gravity-load system such as the columns that support the floor slabs. During an earthquake, both the shear walls and the gravity-load columns will be subjected to lateral displacement demands. Currently, the Canadian Concrete Design Code CSA A23.3 requires special seismic detailing in the shear walls, but not in gravity-load columns.  Moreover, it does not require engineers to do nonlinear analyses for design, which is needed to determine the inelastic displacement profiles of a building’s seismic force resisting system. (Adebar et al. 2010) The lateral displacements of a building due to an earthquake will cause a column to bend. As a result of this bending, one side of the column will be subjected to larger compression strains while the opposite side will be subjected to smaller compression strains and possibly tension strains. The bending capacity of a column will usually be controlled by the ability of the column to tolerate the larger compression strains on one side of the column. Elongated (wall-like) columns with a large cross-sectional length-to-width ratio are commonly used in high-rise buildings in Canada for architectural reasons and because the longer horizontal dimension of the column results in a shorter span of the floor slab, which allows thinner floor slabs to be used. The longer horizontal dimension of these columns makes them much less flexible in bending.  Concerns have been raised about whether elongated columns can withstand the lateral displacements demands during an earthquake. As the curvature capacity is equal to the compression strain depth divided by the 2  compression strain capacity of concrete, a longer column with a larger compression strain depth will have a smaller curvature capacity. The compression strain capacity of unconfined concrete is generally assumed to be 0.0035 according to CSA A23.3, but this may not be true for elongated columns because they are very similar to thin walls.  1.2 Previous Studies on Reinforced Concrete Columns Numerous studies have been done on reinforced concrete columns under seismic loading, but only a small portion of these have been on gravity-load columns.  This section briefly summarizes some of the previous studies that have been done to investigate the behaviour of concrete columns under repeated loadings. Table 1.1 at the end of this section summarizes the main parameters from the various studies and compares these with the columns tested as part of the current study. Wright and Sozen (1973) tested twelve reinforced concrete column specimens to a displacement larger than the yield displacement to study the behavior of reinforced concrete systems subjected to earthquake motions.  The specimens had a cross-section width-to-length ratio of 1:2 and the vertical (longitudinal) reinforcement ratio was 2.4%.  The test specimens were subjected to varying axial load from 0.071f’cAg to 0.147f’cAg, varying transverse reinforcement ratio and different reverse cyclic loading protocols.  Results show that stiffness of the specimens decreased greatly with cycling load.  Failure occurred from inclined cracks, concrete spalling, stirrup yielding and abrasive rubbing due to motion along incline cracks. Deformations were first caused by flexure and later by shear. [Ref#1 in Table 1.1] The study on the ductility of rectangular reinforced concrete columns with axial load by Gill et al. (1979) shows that the greater the level of axial load, the greater the difference 3  between predicted and measured lateral loads and moments.  The specimens were square with P/f’cAg values between 0.15 to 0.55.  A reverse cyclic lateral load was applied at mid- height of the specimens.  It was noted that there was a distinct spreading of plastic hinging action at higher levels of axial load.  Although there was an increase of plastic hinge length with ductility factor, actual plastic hinge lengths were less than predicted using Baker’s method: lp = 0.5d+√d ∙(l/d) where d is the effective depth of the member (mm) and l is the distance from the critical section to the point of contraflexure. [Ref#2 in Table 1.1] Arakawa et al. (1982) tested eighteen half-sized square column specimens under cyclic loading and axial load (0.33f’cAg) to observe the inelastic behavior of reinforced concrete columns with different rate of cyclic loading.  It was found that inelastic deformation capacity was influenced by the loading rate, level of axial load, concrete strength, shear span ratios and longitudinal steel ratio. [Ref#3 in Table 1.1] Umehara and Jirsa (1982) tested ten rectangular short columns with a fixed-fixed end subjected to an axial load between 0.16f’cAg and 0.27f’cAg and an applied cyclic deformation at the top to simulate short columns between building floors.  The width-to-length ratio of all specimens was approximately 1:1.78.  Results of the test were compared with those of square columns.  Results show that the application of axial load increases the strain gradient along the longitudinal reinforcement and causes a more rapid deterioration of strength.  Shear was the main failure mode in these specimens.  [Ref#4 in Table 1.1] Zhou et al (1985) did a study on the behavior of concrete short columns under high axial load from 0.6f’cAg to 0.9f’cAg to investigate the seismic behaviour of reinforced concrete columns under high axial compression and cyclic lateral loads.  Thirty-five scale models were tested with varying axial compression ratio, shear span ratio, and ties.  The 4  specimens were displaced under static reverse cycles and results indicate that bending strength increases with axial compression increase when axial compression ratio is less than 0.6, and decreases with axial compression increase when axial compression ratio is more than 0.6. [Ref#5 in Table 1.1] Soesianawati et al. (1986) investigated the strength and ductility of reinforced concrete columns by testing four square columns under axial compression (0.1f’cAg to 0.3f’cAg) and cyclic lateral loading applied at mid-height.  The main variable was transverse steel, which ranged from 17 to 46% of the NZS 3101:1982 recommended quantity for ductile detailing.  The specimen with a lower axial load ratio showed that flexural cracks grow faster and wider, as compared to specimens with higher axial load ratio.  The main failure mode for the specimens with more transverse steel was fracture of longitudinal bars at extreme tensile fibre, while the failure mode for specimens with low transverse steel was failure of hoop anchorage followed by buckling of longitudinal bars.  [Ref#6 in Table 1.1] Azizinamini et al. (1988) studied the effects of transverse reinforcement on column seismic performance by testing twelve full-scale column specimens subjected to constant axial load between 0.21f’cAg and 0.31f’cAg, and cyclic lateral load at mid-height.  Major variables were axial load level, type, amount and spacing of ties.  The main failure mode was concrete cover crushing at a displacement ductility ratio of two, followed by concrete cover spalling at ductility ratios of four and higher. [Ref#7 in Table 1.1] An experimental program was carried out by Watson and Park (1989) to investigate the flexural strength and ductility of reinforced concrete columns under simulated earthquake loading.  Five square and two octagonal column specimens were tested with high axial compression (0.5f’cAg to 0.7f’cAg) and a reverse cyclic lateral load applied at mid-height. 5  The main variable was the quantity of transverse reinforcement.  Specimens with lower axial load were observed to have flexural cracks at 75% of the theoretical lateral load.  For the specimens with heavy axial load, fine vertical cracks were observed, but they were far from the plastic hinge regions.  Further loading of the specimen showed spalling of concrete cover at the plastic hinge regions and resulted in a concrete crushing failure with buckling of longitudinal bars.  [Ref#8 in Table 1.1] Tanaka and Park (1990) tested eight square columns to study the effects of lateral confinement on the ductile behavior of reinforced concrete columns.  Major variables were the type of transverse reinforcement, axial load level and aspect ratio of the columns.  The specimens were loaded with constant axial load (0.1f’cAg to 0.3f’cAg) and a cyclic lateral loading at the top.  Failure mode was mainly flexural.  Later, Park and Paulay (1990) tested an extra rectangular specimen with width-to-length ratio of 1:1.5 (400 mm x 600 mm), and results indicated a flexural failure as well. [Ref#9&10 in Table 1.1] Lynn et al. (1998) evaluated the seismic performance of existing reinforced concrete building columns built before the 1970’s in terms of lateral and vertical load-resistance. Eight full-scale specimens with widely-spaced ties were loaded with constant axial compression (0.07f’cAg to 0.28f’cAg) and cyclic lateral displacements.  Failure modes include concrete crushing, buckling of longitudinal reinforcement and lap-splice, flexural bond splitting, shear and axial load collapse.  [Ref#11 in Table 1.1] Four full-scale columns were tested in double bending under uni-directional lateral load by Sezen and Moehle (2002) to identify the main for shear failure and gravity load collapse of lightly reinforced concrete columns.  Flexural cracks formed at low lateral load, and shear cracks started to form at around yield displacement.  The specimen under high 6  axial load failed in shear in a brittle manner at two times yield displacement.  Other specimens experienced concrete cover spalling and large shear cracks until three times yield displacement, when they failed from flexural, shear, bond cracks, tie opening, longitudinal bar buckling and concrete crushing. [Ref#12 in Table 1.1] Pujol (2002) studied the drift capacity of reinforced concrete columns subjected to displacement reversals by testing eight test assemblies under axial load varying from 0.08f’cAg to 0.21f’cAg and a lateral load applied at the end.  Each assembly contained two column specimens joined together by a centre stub which acted as a base for the cantilevered columns.  Major variables included tie spacing, axial load level and displacement history. His test showed that drift capacity decrease is related to the amplitude and number of loading cycles beyond yield displacement.  All specimens exhibited inclined cracks before yield, and reached their respective flexural capacity and inelastic deformations.  A large reduction in stiffness was observed when transverse strains exceeded 3%.  The specimens with smaller tie spacing were able to withstand more load cycles before stiffness reduction.  Pujol concluded the displacement cycles before reaching the drift ratio at yield do not affect the drift capacity of a reinforced concrete column.  [Ref#13 in Table 1.1] Bechtoula, Kono, Arai and Watanabe (2002) assessed the damage of reinforced concrete columns under high axial loading by testing eight half-scale and eight full-scale square columns with varying and constant axial load and reverse bilateral displacement.  The columns were designed to fail in flexure before shear.  A lateral load was applied to the top of the columns and all specimens showed ductile flexural behavior, with more damage to specimens subjected to high axial load. Spalling of concrete was limited to 0.5 times cross- sectional length for small specimens and 1.5 times cross-sectional length for large specimens. 7  High axial load increased the rate of shortening of the columns, while specimens with low axial load did not show much shortening.  [Ref#14 in Table 1.1] Sheikh and Yeh (1990) tested fifteen square columns for their behaviour under different constant axial loads and tie configurations with applied flexure and pushed to large deformations.  Results showed that the level of axial load and the amount of lateral steel have great effects on column behaviour.  Comparing results of specimens with the same tie configuration, Sheikh and Yeh found that with high axial loads, ductility of the columns was reduced for columns with an inner loop tie.  For the specimens with no cross ties, a high axial load reduced the ties’ ability to confine the concrete, and resulted in a lower moment capacity.  [Ref#15 in Table 1.1]  Negro, Mola, Molina and Magonette (2004) did a full-scale pseudo-dynamic testing of a torsionally unbalanced three-storey non-seismic reinforced concrete frame as part of the research project “Seismic Performance Assessment and Rehabilitation of existing buildings” (SPEAR).  The specimen is a simplified three-storey building with a height of 3 metres which represented old construction in southern Europe where there was no provisions for earthquake resistance.  The specimen contained eight square columns (250 mm x 250 mm) and one rectangular column with width-to-length ratio 1:3 (250 mm x 750 mm). A suite of 7 pairs of semi-artificial record modulated after historic events was applied as a bi-directional force on the structure during the test.  Maximum drift of the square columns was found to be around 70 mm while that of the rectangular column was around 60 mm at the second storey. It was also observed that the column with the highest axial load was damaged the most from extended spalling at the top of the storey. [Ref#16 in Table 1.1] 8   Table 1.1 below shows a summary of the column tests described above with a few useful parameters and results, compared to the specimens of this test. Table 1.1 – Some Parameters and Results from Previous Column Tests Ref#  L-to-W Length Tie Spac. M/VL P/f'cAg # tested Failure (Date) Ratio (mm) [mm]  Mode* 1 (1973) 2.0 305 64-147 4.25 0.07-0.15 12 FS 2 (1979) 1.0 550 62-206 1.5 0.21-0.60 4 F 3 (1982) 1.0 250 152 1.5-2.5 0.33 18 F 4 (1982) 1.8 410 89 2.22 0.16-0.27 10 S 5 (1985) 1.0 80 80 1-3 0.60-0.90 35 FS 6 (1986) 1.0 400 78-186 2.25 0.10-0.30 4 F 7 (1988) 1.0 457 102-203 1.9-2.1 0.21-0.31 12 F 8 (1989) 1.0 400 52-96 2.25 0.5000.70 7 F 9 (1990) 1.0 400/550 80-220 4.5/3 0.10-0.30 8 F 10 (1990) 1.5 600 80-160 -- 0.10 1 F 11 (1998) 1.0 457 304.8/457.2 6.5 0.07-0.28 8 4 FS, 4 S 12 (2002) 1.0 457 304.8 6.5 0.15-0.61 4 FS 13 (2002) 2.0 305 38.1-76.2 2.25 0.08-0.21 16 F 14 (2002) 1.0 250/560/ 600 40/100 2-2.6 0.30-0.60 16 F 15 (1990) 1.0 305 54-173 4.5 0.46-0.78 15 F 16 (2004) 3.0 750 250 --  1 F Current (C1) 1.0 400 150 3.0 0.31 1 F Current (C2) 2.0 550 150 2.2 0.33 1 F Current (C4) 4.0 800 150 1.5 0.31 1 F Current (C8) 8.0 1100 135 1.1 0.33 1 F Current (W8) 8.0 1100 135 1.1 0.33 1 F *Failure Mode: F(Flexural), S(Shear), FS(Flexural-Shear)  1.3 Scope and Objectives of the Current Study Very few tests have been done on gravity-load columns with high axial loads, especially elongated gravity-load columns. The objective of this study is to study the bending deformation capacity of elongated columns by testing several specimens with cross-sectional length-to-width ratios of 1:1, 1:2, 1:4 and 1:8.   9  1.4 Overview of Thesis Chapter 2 introduces the current design procedures for gravity-load columns according to CSA A23.3.  Load takedowns were done for several buildings with various numbers of storeys and slab thicknesses to find the relationship between factored axial load for gravity-load column designs (1.25 dead load + 1.5 live load) and factored axial load for earthquake design (1.0 dead load + 0.5 live load), as well as some other useful load relationship indicators for high-rise buildings.  This information was used to design the test specimens and this is presented at the end of Chapter 2. Chapter 3 presents the predictions that were done for the load-deformation response of the test specimens. These predictions were needed to determine the capacity of equipment needed for the test, as well as predicting the failure mode of the specimens to ensure that shear failure is not an issue.  Moment-curvature and load-displacement responses were predicted by two computer programs, Response2000 and VecTor2, in addition to hand calculations done using code simplified procedures.  Results were compared against each other and the largest load and displacement were used to select suitable jacks and LVDTs for the test. The predictions were also compared with the test observations in Chapter 5. Chapter 4 presents the information on the test specimens, the test set-up, material properties, instrumentation and loading protocols, while the detailed testing procedures are presented in the appendices. Chapter 5 presents a summary of the results obtained from the tests including the load-displacement relationships, and the measured strains and curvatures.  More detailed observations for each test specimen are provided in appendices. 10  The last chapter, Chapter 6 gives a brief summary of the findings and lists a few improvements and suggestions which could be applied to future testing. As briefly mentioned above, the appendices of this thesis include more details of the information summarized in the chapters, such as the raw data from analyses and the design calculations. Appendix A contains an in-depth description of the testing procedure and results, plots from data, and photos during the test for each specimen.  Appendix B contains equations and tables showing the various load relationships obtained from the load takedowns, as well as sample load takedown spreadsheets of high-rise buildings analyzed according to the National Building Code of Canada 2005 (NBCC05).  Appendix C includes design drawings for the specimens, test set-up and instrumentation supports.  Appendix D contains hand calculation spreadsheets for the moment-curvature and load-displacement responses for all the specimens with and without concrete cover.  Appendix E contains summary of work done and data for a planned wall test that was modified in the end to be similar to the column tests. 11  Chapter  2: Design of Test Specimens According to the current Canadian concrete design code (CSA A23.3 2004) and the National Building Code of Canada (NBCC 2005), the design of columns is based on the maximum possible axial load due to gravity loads during the life of the structure, defined as 1.25 dead load plus 1.5 live load.  However, the axial load during an earthquake will be significantly less than the maximum during the life of the structure, defined by 1.0 dead load plus 0.5 live load. This chapter discusses the relationship between earthquake forces and gravity forces in columns.  Several high-rise building models are analyzed to estimate the axial load acting on a column during an earthquake and the maximum possible axial loads.  Several other parameters are also found for describing column behavior.  2.1 Design for Axial Load on Gravity Column In the current Canadian concrete design code (CSA A23.3 2004), reinforced concrete columns are designed in two parts: longitudinal steel, which takes the axial loads, and ties, which are used to confine the concrete and help with shear forces. Clause 10.10 is used for Canada’s column design.  A column is designed for adequate factored resistance for factored axial load and moments.  The factored load resistance (Pr0) is found by considering the resistances of the concrete and steel in the columns separately.  Pr0 = a1fcf’cAc + fsfyAs  (Eqn 10-10) [Cl.10.10.4] For tied columns, which are how most high-rise columns are designed nowadays, the maximum column axial resistance is taken as 80% of the axial resistance. 12   Pr,max = 0.8Pr0  (Eqn 10-9) [Cl.10.10.4] The amount of ties in a column is calculated based on clause 7.6.5, by calculating the maximum allowable tie spacing as the smallest of: • 16 times the diameter of the smallest longitudinal bar or the smallest bar in a bundle • 48 times the tie diameter • Least dimension of the column • 300mm in compression members containing bundled bars  2.2 Relation of Factored Axial Compression to Axial Compression with Seismic Drift In order to determine the loading for the test specimens, which is needed for the design of the specimens themselves, the relation between axial loads and seismic loads in typical high-rise buildings was first determined.  2.2.1 Axial Load in High-rise Buildings  For gravity-load columns, the main consideration of loading is dead load and live load.  Dead load includes any load that will stay with the structure over time, such as the weight of the slabs, beams, columns and partition walls.  Live load refers mainly to occupancy loads.  It is a variable load which includes people and furniture. Dead load includes self-weight of the structure, using a concrete density of 24 kN/m 3 , and superimposed partition loads of 0.5 kPa.  The dead load per unit area is calculated by multiplying the slab thickness with the density of concrete.  Extra dead load on each floor includes the weight of the columns, calculated by multiplying the volume of the column with 13  the density of concrete.  Table B5.1 in Appendix B5 shows the dead load for the different slab thicknesses per square area. Buildings of various heights between 5 and 50 storeys were considered, with slab thickness between 5” (127 mm) and 10” (254 mm). The maximum exterior span is approximately 27 times the thickness of the slab and the maximum interior span is approximately 30 times the thickness of the slab according to CSA A23.3.  Equations used are in Appendix B1. Slabs with thickness of 5”(127 mm), 6”(152.4 mm), 8”(203.2 mm) and 10”(254 mm) were considered as the typical slab thicknesses used in high rise buildings. The maximum clear spans allowable are shown in Table 2.1. The maximum tributary area of an interior column is the product of the two column dimensions plus the clear spans.  Corner columns are considered as the most critical case for exterior columns due to their heavier dead loads compared to edge columns.  Tributary area for a corner column is the product of the two column dimensions plus half of the clear spans (Figure 2.1).  Since the columns go through the slabs and do not take live load, their areas should be deducted from the tributary areas explained above to get the actual tributary areas. However, for simplicity, the areas of the columns were included in this calculation. The dimensions of a column are dependent on the load it takes, therefore, trial and error was used to determine the column size for buildings of different heights.  The factored load at the bottom floor of the building was compared to the axial resistance capacity of the columns to determine the column size, assuming a reinforcement ratio of 1%. The height of each storey was taken to be 9 ft (2.743 m) and the strength of the column concrete, f’c was assumed to be 30 MPa. 14  Tabulated results of the column sizes and tributary areas for buildings with heights 5, 10, 20, 30, 40 and 50 storeys are presented in Tables B4.1(a) to B4.4(f) in Appendix B4. Live load includes all occupancy loads and non-permanent loads.  According to the National Building Code of Canada 2005, a live load of 2.4 kPa is chosen for residential high- rise buildings.  The live load reduction factor is applied where applicable according to Cl.4.1.5.9 in Part 4 of the NBCC05.  Live load only depends on the tributary area.  Live load reduction equations are presented in Appendix B2. Table 2.1 – Maximum clear span length for varying slab thickness Slab Thickness [mm] Interior Clear Span [mm] Exterior Clear Span [mm] 127 3810 3464 152.4 4572 4156 203.2 6096 5542 254 7620 6927   Figure 2.1 - Tributary Areas for Columns 15  2.2.2 Typical Load Ratios Related to Seismic A few relationships between the dead and live loads of high rise buildings were found to estimate the range of axial loads a building experiences.  The D/(D+L) ratio, where D is the total unfactored dead load and L is the total unfactored live load) shows the dead load as a fraction of the total axial load.  Next the relation between the factored axial load due to gravity (Pf = 1.25D + 1.5L) and the axial force with seismic drift (Ps = 1.0D + 0.5L) were determined from the D/(D+L) ratio to relate the maximum possible axial load for the lifetime of the structure to the axial load caused by an earthquake.  Assuming the axial load due to gravity is the maximum axial load in the columns (Pr,max) as specified by A23.3, the ratio of Ps/Pf will equal the ratio of Ps/Pr,max. However, for design purposes, the maximum axial load in the column is limited at 80% of the factored maximum axial load resistance of the column, Pr0.  Thus, the ratio Ps/Pr0 = 0.8Ps/Pr,max.  Lastly, the amount of axial load in a column is usually represented by the P/f’cAg ratio, where P is the axial load, f’c is the 28-day concrete strength and Ag is the gross area of the column section. Table 2.2 below summarizes the few useful indicators mentioned.  Figures 2.2 to Figure 2.5 show the plots of the indicators with respect to different storey numbers and slab thickness.  The P/f’cAg ratio range of the test specimens are indicated in Figure 2.5 with the values for normal high-rise buildings.  The axial load, P, in the test specimens is 1500 kN, with concrete strength, f’c, of 30 MPa at 28-days and gross area ranging from 151 250 mm 2  to 160 000 mm 2 .  The design of the specimens is discussed in more detail in the next section. Appendix B5 includes detailed data on the dead and live loads, and the ratios of the gravity loads of all the buildings analyzed.  Appendix B6 includes samples of column load takedown spreadsheets. 16  Table 2.2 – Some Useful Indicators on Earthquake and Maximum Possible Axial Load Relations Indicator (Ratio) 5 Storeys 20 Storeys 50 Storeys  Min. [%] Max. [%] Min. [%] Max. [%] Min. [%] Max. [%] D/(D+L) 68.5 83.3 76.4 88.1 80.5 90.9 Ps/Pf 63.4 71.0 67.2 73.5 69.5 75.0 When Prmax = Pf Ps/Prmax 63.4 71.0 67.2 73.5 69.5 75.0 Ps/Pr0 50.7 56.8 52.6 58.8 55.6 60.0 Ps/f’cAg 1.8 40.2 7.0 46.4 17.1 50.5  The plots for D/D+L, Ps/Pf and Ps/Pr0 show similar trends in the values of the ratios as storey height increases.  The values for a 5-inch slab 5-storey building square and 1:2 exterior columns can be observed to be much higher than the expected values on the trend. This is due to the fact that a minimum column dimension of 250 mm has been used in all column load takedown.  This minimum size column contributes to a higher dead load relative to live load for buildings with less storeys and smaller slabs.  Moreover, the plots show an obvious drop for 5-storey buildings.  This is caused by the live load reduction factor not being applied to the roof.  Compared to the 10, 20, 30, 40 and 50-storey buildings, the area of the roof influences the total live load more in a 5-storey building.  The increase in live load/dead load ratio at this storey level reduces the values of the D/D+L, Ps/Pf and Ps/Pr0 ratios. For the P/f’cAg plot, it can be seen that the values for P/f’cAg increases linearly for thin slabs, and especially in exterior columns, while they do not have an obvious trend for thicker slabs.  Column dimensions are designed to resist the gravity loads with dimension increments of 25 mm.  With thin slabs, columns with minimum dimensions are sufficient to withstand the load for all storeys, thus the P/f’cAg values vary linearly with a constant area. 17  With thick slabs, columns with different sizes are designed for buildings with different storeys, thus the values of P and Ag change, causing the values of P/f’cAg to increase or decrease.   18   Figure 2.2 - Summary of D/(D+L) for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses 19   Figure 2.3 - Summary of Ps/Pf for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses 20   Figure 2.4 - Summary of Ps/Pr0 for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses 21   Figure 2.5 - Summary of P/f’cAg for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses 22  2.2.3 Load Ratios According to ACI Design Standards A similar analysis is done on the relationship between the factored axial compression due to gravity loads and factored axial compression due to seismic loads using the ACI Design Standards (ASCE7 2005).   The factored axial compression due to gravity loads during the life of the structure is defined as 1.2 dead load plus 1.6 live load, and the axial compression due to earthquakes is defined as 1.2 dead load plus 0.5 live load. According to ASCE7 Standards, the live load on offices is taken as 2.4 kPa whereas it is taken as 1.92 kPa in residential areas.  A live load of 2.4 kPa is used in this analysis to be consistent with the 2.4 kPa live load used in the analysis following NBCC05 standards.  A live load reduction factor is applied to tributary areas larger than 37.2 m 2 . For simplicity, the columns in the test building were not redesigned, thus the same columns are used in both the CSA and ACI column load takedowns although the loads are different.  The following tables show the same indicators as in Section 2.2.2, with some changes to some parameters due to differences in standards. Table 2.3 – Some Useful Indicators on Earthquake and Maximum Possible Axial Load Relations (ACI) Indicator (Ratio) 5 Storeys 20 Storeys 50 Storeys  Min. [%] Max. [%] Min. [%] Max. [%] Min. [%] Max. [%] D/(D+L) 67.9 85.2 80.4 89.9 84.0 92.3 Ps/Pf 73.4 87.1 83.0 91.0 86.0 93.1 When Prmax=Pf Ps/fPn 73.4 87.1 83.0 91.0 86.0 93.1 Ps/fP0 58.7 87.1 66.4 72.8 68.8 74.5 Ps/f’cAg 2.1 46.9 8.1 54.5 20.1 59.5 where P0 = 0.85f’cAc + fyAs and fPn = f0.8P0 for tied columns Figures 2.6 to 2.9 below show the plots of the indicators with respect to different storey numbers and slab thickness. 23   Figure 2.6 - Summary of D/(D+L) for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) 24   Figure 2.7 - Summary of Ps/Pf for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) 25   Figure 2.8 - Summary of Ps/fP0 for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thicknesses (ACI) 26   Figure 2.9 - Summary of P/f’cAg for Square and Elongated Columns for Buildings with Different Storey Heights and Slab Thickness (ACI) 27  2.3 Design of Test Specimens Original prototypes are designed to reflect real columns used in high-rise buildings. These prototypes are scaled down by a factor of two in each direction to produce designs for the test specimens.  Jacks with a capacity of 800 kN each are available for this test, thus, the starting load is the maximum axial load on the specimens, taken as 1500 kN with two jacks. Scaling up by a factor of 2 in each direction, the axial load to be applied on the prototypes is 6000 kN. Column prototypes are designed with width-to-length ratios of 1:1, 1:2, 1:4 and 1:8. All columns have approximately the same cross-sectional areas.  From the results of the load takedowns in the previous section, and assuming a concrete strength (f’c) of 30 MPa, Ps/f’cAg ratios range from 20% to 45%.  Using a Ps of 6000 kN, the area of the column prototypes was approximated to be 615,400 mm 2 . The different specimen prototypes were designed for gravity loads assuming slenderness is not an issue, ie. short column design.  The areas of the prototypes range from 605,000 mm 2  to 640,000 mm 2  and they are summarized in Table 2.4 below. Table 2.4 – Column Prototype Dimensions Column 1:1 1:2 1:4 1:8 Col. Width [mm] 800 550 400 275 Col. Length [mm]  800 1100 1600 2200 Area [mm 2 ] 640,000 605,000 640,000 605,000  The height of the prototypes is 2.74 metres, which is the typical height of a storey. The cover of the columns is 40 mm to the principal reinforcement as per CSA A23.3.  The prototypes were scaled down by a factor of 2 in each direction to obtain the dimensions of the specimens, as shown in Table 2.5 below.  The areas of the specimens range from 151,250 28  mm 2  to 160,000 mm 2 .  Assuming a reinforcement ratio (r) of approximately 1%, 8-15M bars were chosen as the longitudinal reinforcement of the reinforcement, providing a steel area (As) or 1600 mm 2 . 10M bars were used as ties in all column specimens.  Minimum tie spacing was determined according to Clause 7.6.5.2 of CSA A23.3. Figure 2.10 shows the cross-sections of the specimens and Figure 2.11 shows the elevation view of the columns. Table 2.5 – Scaled Column Specimen Dimensions & Reinforcement Column 1:1 1:2 1:4 1:8 Long. Reinforcement 8-15M 8-15M 8-15M 8-15M Ties 10M@150 10M @150 10M @150 10M @135 Col. Width [mm] 400 275 200 137.5 Col. Length [mm]  400 550 800 1100 Reinf. Ratio [%] 1.0 1.06 1.0 1.06 29   Figure 2.10 – Scaled Column Specimen Cross Sections  The tie spacing of the 1:8 column specimen is 345 mm, which is larger than the maximum longitudinal reinforcement spacing of 250 mm, scaled from the 500 mm allowable spacing in CSA A23.3. However, the 1:8 column specimen has dimensions of 1100 mm (44”) x 137.5 mm (5.5”), which can still represent an actual column used in buildings, therefore at this point, it is uncertain if the specimen will behave like a half-scaled model or an actual column.  30   Figure 2.11 – Scaled Column Specimen Elevation Views 31  2.4 The Wall Specimen In addition to the four column specimens mentioned above, an extra wall specimen was designed based on the 1:8 column specimen.  The initial reason for designing this extra specimen was because of the Chilean Earthquake which occurred in February 2010 in the coast of the Maule Region, Chile.  Observations show that most buildings collapsed because of failures of columns and walls on the ground level.  These Chilean walls are very similar to the 1:8 column specimen in this test, with long and slender cross-sections.  However, the transverse reinforcement of these walls is very different from the standard specified in the Canadian Concrete Design Code. The 1:8 Wall specimen has a cross-section identical to the 1:8 column specimen, same longitudinal bars but different tie arrangements.  There were no cross-ties throughout the column, but instead, hoops are formed by two G-shaped ties placed alternatively (Figure 2.12).  Figure 2.12 – 1:8 Wall Specimen     32  Chapter  3: Behaviour Predictions One goal of this test is to determine the bending moment and displacement capacities of elongated columns.  Before the test is conducted, the specimens are modeled with different computer programs to predict the moment-curvature behaviour due to the different cross- sections.  Hand calculated moment-curvature responses based on parabolic strain distributions are also used to approximate the maximum displacements by integration of the moment of the curvature along the height.  However, there is a chance that the specimens may fail in shear instead of bending.  Crack patterns and strain profiles from Response2000 and VecTor2, as well as shear calculations according to the CSA and ACI code equations are used to ensure that failure of the specimens will be caused by concrete crushing in bending and not by shear.  The 1:8 wall specimen is expected to have similar behaviour to the 1:8 column specimen, with the difference being the arrangement of ties.  Therefore, only the 1:8 column specimen was modeled in this section and the results were used for both the column and wall specimen for comparison to actual data.  3.1 Predicting Moment-Curvature Behaviour  The moment-curvature responses of the specimens were determined according to the specimens’ cross-sectional properties in two computer programs: Response2000 and VecTor2.  Response 2000 is a sectional analysis program that calculates the strength and ductility of a reinforced concrete cross-section subjected to shear, moment and axial load (Response). VecTor2 is a non-linear finite element analysis program for 2-dimensional reinforced concrete membrane structures subjected to quasi-static load conditions.  The formulation of the program is based on the Modified Compression Field Theory and the 33  Disturbed Stress Field Model, using a total-load iterative procedure based on a secant stiffness formulation (VecTor). The moment-curvature responses of the specimens were also determined by hand by assuming a parabolic strain distribution over the compression depth of the specimens.  3.1.1 Moment-Curvature from Response2000 The cross-sections of the specimens were modeled in Response2000 with concrete compression strength (f’c) of 35 MPa, steel yield strength (fy) of 450 MPa, and steel modulus of elasticity (Es) of 200 000 MPa.  Two models were analyzed for each specimen, one with concrete cover to predict the bahaviour before concrete spalling, and one without concrete cover for the response after concrete spalling (Figure 3.1 and 3.2).  The longitudinal steel rebars were modeled as 15M bars with an area of 200 mm 2  per bar, and the ties were 10M bars with area 100 mm 2  each. The program automatically calculates the area, moment of inertia, neutral axis depth and the sectional modulus for each cross-section.  Figure 3.1 – Specimen Cross-Section Models with Concrete Cover in Response2000  34   Figure 3.2 – Specimen Cross-Section Models without Concrete Cover in Response2000  The maximum moment demands of the columns were predicted using the sectional response function in Response2000.  Sectional response involves solving for cross-sectional properties of the columns, such as the moment-curvature response, strain diagrams, longitudinal concrete and reinforcement stresses, compression block depth and internal forces at different moment values. The moment-curvature diagram of the cross-section was obtained automatically from Response and shown in Figure 3.3 below. 35   Figure 3.3 – Moment-Curvature Responses from Response2000  3.1.2 Maximum Moment and Curvature at 0.0035 Compression Strain from Response2000 The moment capacities of the specimens were obtained as the maximum moment from the moment-curvature plots.  However, the moment-curvature analysis in Response2000 does not terminate when the compression strain in the section reaches -0.0035 and beyond, whereas in the Concrete Design Code CSA A23.3 it is suggested to assume the maximum compression strain as -0.0035.  Table 3.1 below lists the points of maximum moment and curvature at a compression strain of -0.0035 for all four specimens.   36  Table 3.1 – Maximum Moment and Curvature at 0.0035 Compression Strain from Response2000  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Max. Moment [kNm] 309.3 396.8 599.3 808.6 Curvature @0.0035 Strain [rad/km] 21.2 14.5 10.5 7.3 WITHOUT CONCRETE COVER Max. Moment [kNm] 285.1 370.8 573.1 782.6 Curvature @0.0035 Strain [rad/km] 21.5 14.7 10.5 7.3  3.1.3 Moment-Curvature from VecTor2 The specimens were modeled as-is in VecTor2, because VecTor2 is a non-linear finite analysis program which uses different analysis methods compared to Response2000. The models were built as a 1570 mm column with a 350 mm footing.  A lateral load acts at a point 1370 mm from the top of the footing, spread over a vertical length of approximately 200 mm, and an axial load of 1500 kN was applied at the top of the specimen.  The specimens were modeled in terms of nodes and rectangular elements, the reinforcing bars as truss elements, and the applied loads were modeled as distributed point loads on the nodes (Figure 3.4). Push-over analysis was done on the specimens with concrete compression strength (f’c) of 35 MPa, steel yield strength (fy) of 450 MPa, and steel modulus of elasticity (Es) of 200 000 MPa.  A load-deformation plot was provided by VecTor2 for each specimen. Moment values at the base of the specimens were found by multiplying the loads at each load stage with the height of the specimen above the footing.  The compression and tension strains at the base of the specimen were found by reading off the vertical strain values of the two edge elements at the base layer.  The difference of these strain values divided by the length of 37  the cross section gives the curvature of the specimens.  The moment-curvature response is then plotted by the obtained moment and curvature values (Figure 3.5).   Figure 3.4 – Specimen Model in VecTor2 38   Figure 3.5 – Moment-Curvature Responses from VecTor2  3.1.4 Moment and Curvature at Failure from VecTor2 The moment values obtained from Response2000 dropped after the peaks were reached, but the analyses in VecTor2 kept going with a slight increase in moment and a huge increase in curvature when the specimens fail.  Since the moment did not drop until failure, the moment and curvature values at point of failure were recorded.  Table 3.2 below shows the moment, curvature and compression strain values at failure obtained from VecTor2 for all four specimens.   39  Table 3.2 – Moment, Curvature and Compression Strain at Failure from VecTor2  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Moment @failure [kNm] 268.4 362.1 547.5 738.8 Curvature @failure[rad/km] 17.8 12.2 7.00 4.75 Comp. Strain @failure [mm/m] -3.73 -3.90 -3.26 -2.98 WITHOUT CONCRETE COVER Max. Moment [kNm] 238.2 330.8 519.0 698.2 Max. Curvature [rad/km] 14.3 10.8 6.89 5.37 Comp. Strain @failure [mm/m] -2.65 -3.12 -2.99 -3.33  3.1.5 Moment-Curvature by Hand Calculations The moment-curvature behavior of the specimens were also predicted by hand calculations with the help of a spreadsheet (Appendix D).  Assuming a parabolic strain distribution, the concrete compression block factors were found by the following equations.  a1 = [(etop/e'c) - (etop/e'c)2/3]/b1 … (3.1)  b1 = [4-(etop/e'c)] / [6-2*(etop/e'c)] … (3.2) where etop = strain at top of section (compression side)    e’c = max strain = √f'c/2500 A concrete compression stress of 35 MPa is used, with a steel yield strength of 450MPa and a steel modulus of elasticity of 200 000 MPa.  The concrete modulus of elasticity is found according to CSA A23.3-04 Cl.8.6.2.2.  Ec = (3300*√f'c+6900)(gc/2300) 1.5 … (3.3) where  gc = concrete density = 24 kN/m 3  40  The neutral axis of the cross-section was found by  yCG = SAy / SA … (3.4) where   A = area of a concrete component of the equivalent concrete area of a                  steel component    y = distance from reference point (taken as top of section) to       component The first point on the moment-curvature graph was found by assuming the compression strain depth, c, equals to the cross-section length of the specimen.  A top strain was guessed, which was used to find the compression block factors.  Using the compression block factors, the compression force in the concrete was found by  Pc = a1f'cb1cw … (3.5) where  w = width of the cross-section The strain profile was assumed to be linear across the length of the cross-section, and the strains at each steel layer were found by proportioning.  The stress at each steel layer was found by  fs = max(Eses, fy) or min (-Eses, -fy) … (3.6)  The force in each steel layer was then calculated from the stress.  Ps = fsAs          for tension … (3.7)  Ps = As (fs - a1f'c)          for compression … (3.8)  The total force on the cross section, P, is the sum of the compression force from the concrete, compression and tension forces from the steel.  Iteration was done on the value of the top strain until equilibrium of forces was reached, ie. when P equals the applied load of 41  -1500 kN.  After equilibrium of forces was reached, the moment was found by the sum of the forces multiply by the moment arms.  The moment arm is the distance between the centroid of the steel or concrete component to the neutral axis of the cross-section.  The curvature was found by dividing the difference between the top strain and the strain at the bottom-most steel layer over the length from the top of the cross-section to the bottom-most steel layer.  The maximum top strain was assumed to be -0.0035 according to the concrete code. Twenty top strains between the first point on the moment-curvature graph and -0.0035 at equal intervals were used to plot the moment-curvature graph as shown in Figure 3.6 below. Table 3.3 shows the maximum moments and curvatures at a top strain of -0.0035 by hand calculation. Table 3.3 – Maximum Moment and Curvature at 0.0035 Compression Strain from Hand Calculation  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Max. Moment [kNm] 310.7 401.4 605.8 826.8 Curvature @-0.0035 Strain [rad/km] 23.3 15.7 11.3 8.0 WITHOUT CONCRETE COVER Max. Moment [kNm] 285.7 375.6 581.3 800.8 Curvature @-0.0035 Strain [rad/km] 23.7 16.0 11.4 8.0  3.1.6 Moment and Curvature at 0.0035 Compression Strain by Code Method The Canadian concrete code CSA A23.3 specifies a simplified method to calculate the maximum moment and curvatures by assuming a maximum top strain of -0.0035.  The concrete compression block factors can be found by the simplified equations according to Cl.10.1.7. 42   a1 = 0.85 – 0.0015f’c ≤ 0.67 … (3.9)  b1 = 0.97 – 0.0025f’c ≤ 0.67 … (3.10) The forces in the concrete and steel were found by the same method as described in section 3.1.5.  The value of the compression strain depth was iterated until equilibrium of forces was reached.  The moment was obtained by the sum of the forces multiplied by the moment arm.  The curvature capacity can be predicted using the depth of the compressive stress distribution, c, and the height of the cross-section, lw:  fcap = 0.0035/c          for compression … (3.11)  Table 3.4 shows the moments and curvatures at 0.0035 compression strain by code calculation. Table 3.4 – Moment and Curvature at 0.0035 Compression Strain from Code Calculation  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Moment @0.0035 Strain [kNm] 296.2 378.8 574.9 780.9 Curvature @0.0035 Strain [rad/km] 22.1 15.0 10.7 7.6 WITHOUT CONCRETE COVER Moment @0.0035 Strain [kNm] 274.2 353.9 549.3 755.6 Curvature @0.0035 Strain [rad/km] 22.1 15.3 10.9 7.7  43   Figure 3.6 – Moment and Curvature Response by Hand Calculation  3.1.7 Comparison of Moment-Curvature Response The moment-curvature response of the specimens depends on the assumed concrete and steel stresses and strain behavior and the cross-section properties. Moment-curvature relationships from Response2000, VecTor2 and hand calculations were obtained as discussed in section 3.1.  Figure 3.7 shows the moment-curvature predictions obtained from various methods plotted together.  Results are observed to be similar. 44   Figure 3.7 – Moment-Curvature Response Comparison of Various Methods 45  3.2 Predicting Load-Displacement Behaviour The displacement capacities of the specimens are estimated by using the member response solver in Response2000, load-deformation plot in VecTor2 and linear moment- curvature approximation by hand.  3.2.1 Push-Over Analysis with Response2000 A push-over analysis was done with Response2000, taking into account the cross- section geometry, the reinforcement layout, as well as the height of the specimens.  Three models were analyzed for each specimen.  The first two models were used to predict the behavior of the specimens, using f’c equals 35 MPa and fy equals 450 MPa, with and without concrete cover.  The third model was used to choose a jack for the test, using f’c equals 35 MPa and fy equals 600 MPa, with concrete cover.  Figure 3.8 shows the load-deformation plots of the first two models and Table 3.5 shows the maximum loads and displacements obtained by the three models.  The analyses terminated after the load peaked and dropped to approximately 95% of the peak load. 46  Table 3.5 – Maximum Loads and Displacements from Response2000  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Fy = 450 MPa Max. Load [kN] 225.8 289.7 437.5 590.2 Max. Displacement [mm] 8.5 6.0 4.4 3.6 etop at Max. Moment [mm/m] -2.75 -2.67 -2.57 -2.67 WITHOUT CONCRETE COVER Fy = 450 MPa Max. Load [kN] 208.1 270.6 418.3 571.1 Max. Displacement [mm] 8.7 6.1 4.5 3.5 etop at Max. Moment [mm/m] -2.67 -2.55 -2.64 -2.51 Fy = 600 MPa Max. Load [kN] 241.5 304.8 463.4 627.6 Max. Displacement [mm] 10.1 7.1 5.4 4.4 etop at Max. Moment [mm/m] -2.86 -2.73 -2.85 -2.95   Figure 3.8 – Load-Displacement from Response2000 47  3.2.2 Push-Over Analysis with VecTor2 The load-deformation plots can be obtained directly from Vector2 using the same models in section 3.1.3.  Two load cases were considered in the model, gravity loading and reverse cyclic loading due to a lateral load applied at 1370 mm from the top of the footing.  A constant load of 1500 kN acted on the top of the specimen distributed evenly on the top nodes.  The FormWorks model was then run in VecTor2, and the results viewed in Augustus, the post-processor of VecTor2.  Figure 3.9 below shows the load-displacement plots of the specimens.  Table 3.6 shows the loads and displacements at failure obtained from VecTor2.  Table 3.6 – Loads and Displacements at Failure from VecTor2  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Load at Failure [kN] 195.9 264.3 399.6 539.3 Displacement at Failure [mm] 4.34 3.26 2.56 2.22 WITHOUT CONCRETE COVER Load at Failure [kN] 173.9 241.5 378.8 509.6 Displacement at Failure [mm] 5.55 3.83 2.67 2.74  48   Figure 3.9 – Load-Displacement from VecTor2  3.2.3 Load-Deformation by Hand Calculations  A numerical trilinear model was fitted to the moment-curvature plots obtained in section 3.1.5.  The elastic displacement of each specimen at a particular loading is obtained by the sum of the moment of curvature about the point of loading along the height of the column (Figure 3.10). 49   Figure 3.10 – Curvature Along Height of Specimen  If f < f1,  D = fL 2 /3 … (3.12) If f2 ≥ f≥ f1,  D = f1L1 2 /3+f1(L 2 -L1 2 )/2+(f-f1)(L-L1)(2L+L1)/6 … (3.13) If f≥ f2,  D = f1L1 2 /3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2 -(L1+L2) 2 ]/2+(f-f2)(L-L1- L2)(2L+L1+L2)/6  … (3.14) where  f = curvature at base of column    f1 = 1 st  point in trilinear approximation of moment-curvature with a         change in slope f2 = 2 nd  point in trilinear approximation of moment-curvature with a 50          change in slope    L = length along column height from point of loading (top of column)    L1 = length from point of loading to point with curvature f1    L2 = length from point of loading to point with curvature f2  Figure 3.11 and Figure 3.12 show the trilinear approximations of the moment- curvature plots.  Inelastic displacement was found by assuming a plastic hinge length equals to half the cross-sectional length of the specimens.  This assumption may not be valid for the longer columns, especially the 1:8 specimen.  The curvature at a compression strain of 0.0035 is defined to be the curvature capacity, fcap, of the specimen.  The inelastic rotation at the base is calculated as  Θ = (fcap – f2)lp … (3.15) where  lp = plastic hinge length From the rotation, the inelastic displacement was found by  Di = Ѳi(hw-0.5lp) … (3.16) where  hw = height of column specimen (from top of footing)  Table 3.7 shows the plastic hinge length used for the calculations.  Figure 3.13 shows the load-deformation curves of the specimens.  Table 3.7 – Plastic Hinge Length of Specimens  1:1 Column 1:2 Column 1:4 Column 1:8 Column Plastic Hinge Length, lp [mm] 200 275 400 550 51   Figure 3.11 – Trilinear Approximation to Moment-Curvature Plots (with Concrete Cover) 52   Figure 3.12 – Trilinear Approximation to Moment-Curvature Plots (no Concrete Cover) 53   Figure 3.13 – Load-Deformation from Hand Approximation Aside from displacement due to a lateral force at the top, past research shows that rebar slip at the base of the columns during cracking may lead to significant additional displacement, up to the same displacement due to cross-sectional properties. According to Sezen and Setzler (2008), the reinforcement bar is modeled by assuming linear elastic behaviour and a uniform bond stress ub over the development length ld of the bar. By using equilibrium, the force in the bar  F = fsAb = ubpdbld … (3.17)  From which the development length, ld, can be obtained by substituting the area of the   bar 54   ld = 0.25fsdb/ub …(3.18) where  ub = uniform bond stress = 1.0√f’c    db = diameter of longitudinal bars    fs = steel stress, taken as the yield stress  Stress at the end of the bar is zero, and increases linearly to fs at where the load is applied.  Integrating the strains over the length, the slip can be found by  slip = eyld/2 … (3.19) where  ey = steel yield strain Slip refers to the amount of pull-out of the longitudinal bars.  To find the displacement at the top of the specimens caused by slip, the rotation at the base of the columns due to slip was obtained by dividing the slip over the tension arm (d-c).  The additional displacement at the top of the specimen equals the rotation caused by slip multiplied by the height of the column. The following table shows the displacement predictions of the specimens by hand approximation. Table 3.8 – Loads and Displacements at 0.0035 Compression Strain from Hand Approximation  1:1 Column 1:2 Column 1:4 Column 1:8 Column WITH CONCRETE COVER Load at -0.0035 Strain [kN] 226.8 293.0 442.2 603.5 Elastic Displacement [mm] 6.4 4.7 3.3 2.4 Inelastic Displacement [mm] 2.9 2.4 2.6 2.3 WITHOUT CONCRETE COVER Load at -0.0035 Strain [kN] 208.5 274.1 424.3 584.5 Elastic Displacement [mm] 6.8 7.2 5.9 4.7 Inelastic Displacement [mm] 2.8 2.4 2.5 2.3 DISPLACEMENT DUE TO SLIP [mm] 1.76 1.34 0.90 0.67 55  3.2.4 Comparison of Load-Deformation Responses The load-displacement plots from all three methods were compared and it was noted that the displacements obtained from VecTor2 were relatively lower.  This was mainly caused by an unevenly distribution in the steel stress, whereas the steel stresses were assumed to vary linearly along the profile in Response2000 and hand calculations. Figure 3.14 shows the load-displacement predictions obtained from various methods plotted together. 56   Figure 3.14 – Load-Displacement Response Comparison of Various Methods 57  3.3 Cyclic and Reverse Cyclic Responses Cyclic and reverse cyclic push-over analyses were further done in VecTor2 to more accurately predict the behavior of the specimens.  The maximum loads obtained from section 3.2.2 were used as references to determine the loading stages in the cyclic analyses.  Each specimen was loaded in approximately ten steps, with three cycles at each load increment, until failure.  Cyclic models were loaded the same way as monotonic models.  However, in the reverse cyclic models, extra truss bars were added linking both edges of the specimens at load level to ensure that concrete does not fail at the loading zone when the specimens are pushed the reverse side. Results from the cyclic and reverse cyclic analyses were compared with those from monotonic analyses.  Results are shown in Figures 3.15 to 3.18 below.  Figure 3.15 – Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:1 Column Specimen 58    Figure 3.16– Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:2 Column Specimen  Figure 3.17 – Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:4 Column Specimen 59   Figure 3.18 – Monotonic, Cyclic and Reverse Cyclic Push-Over Analyses for 1:8 Column Specimen  3.4 Strains and Stresses 3.4.1 Strain Profiles from Response2000 Top and bottom strain values at different loading stage can be obtained from Response2000.  Response2000 assumes a linear strain distribution along the cross-section length.  Figure 3.19 shows the strain profiles of the specimens at maximum moment and at top strain equals -0.0035 for the models with concrete cover. 60   Figure 3.19 – Strain Profiles from Response2000 3.4.2 Strain Profiles from VecTor2 Strain profiles were obtained from VecTor2 by cutting a section through the first layer of elements above the footing.  Figure 3.20 shows the strain profiles of the specimens approximately at failure.  Figure 3.20 – Strain Profiles from VecTor2 61  3.4.3 Strain Profiles from Hand Calculation Hand calculations assumed a maximum top strain of -0.0035 and that the strain varies linearly through the cross-section length.  Iterations were done to get the compression strain depth, c, of each specimen until equilibrium of axial forces was reached, and the linear strain profile was obtained by proportioning.  Figure 3.21 shows the strain profiles calculated by hand and code methods.  Figure 3.21 – Strain Profiles from Hand and Code Calculations 3.4.4 Stress Distribution fromVecTor2 Stress distributions can be obtained from VecTor2 at various stages during loading. Stresses are largest at the base of the columns as shown in the following diagrams. 62   Figure 3.22 – Stress Distribution of 1:1 Column from VecTor2 near Failure  Figure 3.23 – Stress Distribution of 1:2 Column from VecTor2 near Failure 63   Figure 3.24 – Stress Distribution of 1:4 Column from VecTor2 near Failure  Figure 3.25 – Stress Distribution of 1:8 Column from VecTor2 near Failure 64  The stress distribution diagrams of all four specimens show the axial stress on the compression side reaching concrete strength before the tension side reaches steel yield strength.  This shows that the predicted failure mode of the specimens is flexural failure by concrete crushing.  3.5 Checking for Shear Failure The specimens are designed to fail with concrete crushing during bending failure. However, the long and narrow specimens look more like squat walls than columns. Therefore there is a concern that shear failure may occur, especially in the specimen with a width-to-length ratio of 1:8. Three different tools were used to check whether shear plays an important part in the failure of the specimens, including Response2000, VecTor2 and code equations.  3.5.1 Crack Pattern from Response2000 Solving for member response is the only way in Response to predict shear behaviour of the members.  This is the same as the push-over analysis used to solve for the load- deformation behaviour in the previous sections.  Figure 3.26 shows the crack patterns of the different specimens at maximum lateral load. 65   Figure 3.26 – Crack Pattern from Response2000 Large cracks concentrated at the base of the specimens on the tension face indicate that moment failure is the major failure mode.  Shear cracks can be seen in the longer specimens, but they are relatively small compared to the flexural cracks.  Figure 3.27 further indicates that the long specimen will fail by flexure.  It can be seen that the model response (indicated in red) touched the failure envelope (indicated with blue) on the right side, which is the moment envelope instead of the shear envelope at the top of the plot. 66   Figure 3.27 – Model Response and Failure Envelope of 1:8 Column from Response2000 3.5.2 Crack Pattern from VecTor2 The cracking patterns of the four specimens were also obtained from VecTor2 near failure.  Similar to Response2000, they show more flexural cracks compared to shear cracks, even for the longest specimen (Figure 3.28).  Figure 3.28 – Crack Pattern from VecTor2 67  3.5.3 Shear Strength Prediction with Code Equations Hand calculations are done to predict shear resistance of the four test specimens according to the Canadian concrete design code CSA A23.3-04.  The general method specified in clause 11.3.6.4 is used as the main method of prediction.  The simplified method in clause 11.3.6.3 and shear equations from the ACI code are further used to check the creditability of the results obtained from the CSA general method. The factored shear resistance of a member is determined according to CSA A23.3-04 Cl.11.3.3:  Vr = Vc + Vs ≤ 0.25fcf’cbwdv … (3.20)  The concrete and steel shear resistances can be found by the following two equations respectively:  Vc = fclb√f’cbwdv … (3.21)  Vs = fsAvfydv cotθ/s … (3.22) In the CSA general method, the values of b and θ are determined from the strain at mid-depth of the cross section, which is given in the code to be: ex = Mf/dv + Vf + 0.5Nf 2EsAs  … (3.23) The moment and shear at a distance dv from the base of the column is used for the Mf and Vf values.  These forces are calculated from the maximum moment and shear forces obtained from Response2000 as the best estimates unless further analysis results are available.  68  The values of b and θ are found by    where sze = 300 if the section satisfies the minimum transverse reinforcement         requirement … (3.24)  θ = 29 + 7000ex … (3.25)  Table 3.9 below shows the shear resistance of the different columns obtained by the CSA general method and their comparison with the resistances obtained from several other methods from the ACI code. The ratio of the shear resistance to the maximum shear demand serves as a factor of safety indicator at this load stage. It shows how much shear capacity is left in the member when it is loaded up to the shear force at maximum moment.  The shear resistances calculated do not represent the actual shear resistances of the columns because the method to calculate mid-depth longitudinal strain is an iterative process. Figure 3.29 shows a plot of the Vr/Vf ratios. b = 0.40 x 1300 1+1500ex 1000+sze 69  Table 3.9 – Shear Resistances of the Specimens Predicted by Different Code Equations Column 1:1 1:2 1:4 1:8 Vr - CSA General Method [kN] 562.9 592.0 849.8 1120.9 Vr/Vf  2.48 2.02 1.92 1.86 Vr - CSA Simplified Method [kN] 338.8 375.19 561.1 780.6 Vr/Vf 1.49 1.28 1.27 1.29 Vr - Lower Bound ACI 11-4 [kN] 395.8 421.4 574.7 745.1 Vr/Vf 1.75 1.44 1.34 1.26 Vr - Upper Bound ACI 11-7 [kN] 415.1 424.4 594.8 758.7 Vr/Vf 1.83 1.45 1.34 1.26 Vr - Upper Bound ACI 11-12 [kN] 827.6 844.4 1025.8 1194.8 Vr/Vf 3.65 2.88 2.32 1.98 Vr - Upper Bound Limit ACI [kN] 844.5 839.7 1043.5 1204.2 Vr/Vf 3.72 2.87 2.36 1.99   Figure 3.29– Vr/Vf Ratios of the Specimens by Different Code Equations  Due to the amount of longitudinal and transverse reinforcement designed for bending and shear, failure by bending is expected.  The specimen has a reinforcement ratio of approximately 1%.  This is larger than the minimum amount of reinforcement required as 70  specified in the Concrete Code.  However, the specimen is long, which increases the spacing of the longitudinal reinforcement in the long direction.  At the same time, the long cross- section increases the stiffness of the section, and it is expected to be weak against turning. The transverse reinforcement amount is also bumped up from the actual amount required for shear resistance. The results from Response2000, VecTor2 and code equations confirm that shear failure should not be a problem in the test.  71  Chapter  4: Specimen Construction and Test Set-up The specimens were constructed and cured in the Structural Laboratory.  A reverse cyclic load test was performed on the four column specimens under a constant axial compression while the wall specimen was tested with cycles of tension and compression together with a cyclic lateral load.  4.1 Overview of the Specimens As mentioned in Chapter 2, the column specimens were designed with different width-to-length ratios of 1:1, 1:2, 1:4 and 1:8 and a reinforcement ratio of approximately 1%. The wall specimen has width-to-length ratio of 1:8, with the same dimensions as the 1:8 column specimen. The height of the specimens was taken to be the half-storey height of 1.37 m.  An extra 200 mm is added at the top, which section is heavily reinforced with horizontal and vertical ties. This extra piece of a more rigid concrete at the top serves to connect the specimen to the horizontal jack and loading beam. The actual positions of the first three ties from the base of each specimen were measured after the rebar cage is tied.  In addition, the actual heights of the specimens were measured after concrete pour.  The average as-built tie elevations are shown in Table 4.1 below.  Drawings of actual as-built tie elevation and spacing for the first four ties from the base are included in Appendix C2.  The as-built specimen heights are shown in Table 4.2. Foundation design is discussed in the next section.   72  Table 4.1 – Average As-built Tie Elevations [mm] from Top of Footing  1:1 Col 1:2 Col 1:4 Col 1:8 Col Wall 1st Tie 136 150 157 138 142 2nd Tie 285 300 300 277 282 3rd Tie 450 455 458 422 407 4th Tie 600 613 612 554 547  Table 4.2 – As-built Average Specimen Heights  1:1 Col 1:2 Col 1:4 Col 1:8 Col Wall Footing Height [mm] 363 360 358 363 356 Column Height [mm] 1573 1577 1570 1572 1575 Total Height [mm] 1936 1937 1928 1935 1931  Due to space conflict in the installation of the horizontal jack to the strong wall, the actual elevation of lateral load application is slightly higher than the designed height of 1.74 m from the base of the column specimens.  The load was applied at a height of 1758 mm from the floor (ie. approximately 1400 mm from the top of the footings). The specimens were grouted at the top to a total height of 1950 mm so that the specimens are of the same height during testing and so that a smooth surface can be obtained to more evenly distribute the applied axial load.  4.2 Specimen Foundations  The column specimens were built on foundations which connected the specimen to the floor of the laboratory with Dywidag rods.  In order to simulate a column element with a fixed base, the foundations were much more heavily reinforced in both directions and a stronger concrete of strength 50 MPa was used.  The foundations of all specimens were designed to be 350 mm in height.  Actual foundation height was measured to be around 360 mm.  Foundations for the 1:1 and 1:2 73  column specimens were 810 mm x 810 mm in area and those for the other longer specimens were 1420 mm x 810 mm in area.  Figure 4.1 shows the plan views of the two different foundations.  Figure 4.1 – Specimen Foundations  The foundations were tied down to the ground with 2” (50.8 mm) Dywidag bars to prevent, or minimize, movement in the foundations during testing.   A factor of safety was included in the foundation design by calculating the maximum shear demand using an assumed concrete strength of 40 MPa and steel yield strength of 600 MPa.  Widths and lengths of the foundations were at least 100 mm longer each way from the centre of the anchorage holes. The bending moment and shear diagrams of the footings are obtained and they are designed as deep beams.  Forces are mostly transferred according to the strut-and-tie model. The compression force in the concrete is taken up by the reinforcement in tension and the reaction force from the ground (Figure 4.2). 74   Figure 4.2 – Forces on Footing Slip and overturning checks are done to ensure that the tie-down bars have sufficient strength to resist foundation failure, so that failure will occur in the column portion.  Friction at the base of the column is calculated by multiplying the reaction force due to weight and axial load by a coefficient of friction, m, taken to be 0.5.  The friction force at the base helps prevent sliding of the columns by resisting the applied lateral force (Figure 4.3).  Figure 4.3 – Footing Check for Overturning and Sliding 75  The longitudinal reinforcement bars in the columns are extended into the foundation and hooked at the base to prevent the use of splices.  Two extra column ties are added inside the footing to hold the longitudinal bars in place.  4.3 Construction of the Specimens  The construction of the specimens was done in the Structural Laboratory.  Formwork for the specimens was made with 0.5” plywood boards and 2”x4” wooden beams.  The specimens were poured in two phases, the foundation phase and the column phase.  The formwork for the foundations was constructed before the first pour, and the formwork for the columns were constructed after the first pour.  The 2”x4” beams were used as studs at the side of the foundation formwork and beams along the frame, and were nailed firmly to a piece of plywood at the base to prevent the formwork from falling apart when pressure was exerted during concrete pouring.  2” PVC pipes are used to create holes through the foundation for inserting tying Dywidag bars. Figure 4.4 shows the formwork for both foundations.  Figure 4.4 – Foundation Formwork 76   Foundation formwork construction started on 20 th  July, 2010 and was finished on 29 th  July, 2010.  Rebar cages for both the foundations and columns were tied together on 4 th  and 5 th  August, 2010 (Figure 4.5).  Figure 4.5 – Rebar Installation  The first concrete pour occurred on 6 th  August, 2010. Concrete with strength 50 MPa was produced by Ocean Construction Supplies and delivered on site.  The concrete was vibrated and the surface flattened except for the area connecting the foundation to the column (Figure 4.6).  The formwork for the columns was built after first pour.  2”x4” studs were nailed onto plywood boards to form four walls around the columns, which were secured by 2”x4” collars all around at several points along the height.  The column formwork was then nailed onto the foundation formwork to prevent movement during concrete pour (Figure 4.7).  Concrete for the columns was poured on 13 th  August, 2010.  Concrete with strength 30 MPa was used.  The specimens were vibrated and flattened at the top.  They were allowed to cure for around one week before the forms were stripped. 77   Figure 4.6 – First Concrete Pour  After the formwork was removed, it was discovered that the concrete did not cover the whole volume behind the column formwork (Figure 4.8).  This was due to insufficient vibration during pouring.   High strength cement paste was used to repair the specimens.   Figure 4.7 –Column Formwork 78   Figure 4.8 – Defects in the Specimens  4.4 Material Properties Eighteen concrete cylinders were casted on 13 th  August, 2010 during the second pour. Twelve of these cylinders were moist cured starting from 17 th  August, 2010, while the other six were dry cured.  On 29 th  September, 2010, two of the moist cured cylinders were tested and the results are shown in Table 4.3 below.  The rate of loading was 0.24 MPa/sec. Before the actual tests were performed, the rest of the cylinders were all tested and the results are also shown in Table 4.3.  The rate of loading was 0.24 MPa/sec. Table 4.3 – Concrete Cylinder Test Results. Test# Date of Test Age [days] Moist/Field Cured Peak Load [kN] Strength [MPa] Avg. Strength [MPa] 1 2010-Sep-29 48 Moist 265.7 33.8 31.9 2 2010-Sep-29 48 Moist 235.9 30.0 3 2011-Apr-05 232 Moist 289.4 36.9 39.3 4 2011-Apr-05 232 Moist 327.3 41.7 7 2011-Jun-14 274 Moist 309.7 39.4 38.0 8 2011-Jun-14 274 Moist 262.2 33.4 9 2011-Jun-14 274 Moist 323.4 41.2 79  5 2011-Apr-05 232 Field 271.4 34.6 32.2 6 2011-Apr-05 232 Field 233.0 29.7 10 2011-Jun-14 274 Field 270.4 34.4 32.7 11 2011-Jun-14 274 Field 242.9 30.9   Average concrete strength was found to be 36.4 MPa for moist cured and 32.45 MPa for field cured.  Average of the two is 34.4 MPa.  The strength of 35 MPa used in the predictions is reasonable.  All reinforcement are of Grade 400 MPa with a typical yield strength between 430 to 470 MPa (for predictions, a steel yield strength of 450 MPa was used). No tests on actual steel yield strength was done because the reinforcement was not expected to yield in the tests, therefore the actual strength of the reinforcement is unknown.  4.5 Test Setup for Column Specimens A reverse cyclic lateral test with a constant axial load was to be done on the specimens to test for their behavior under lateral displacement loading.  The axial load was to simulate dead and live loads on top storeys acting on the gravity-load column.  Two vertical jacks with capacities 785 kN each controlled by hydraulic pressure were used to keep the axial constant at 1500 kN.  These two jacks were spaced 6 feet (1830 mm) apart and connected to the floor by Dywidag rods. Axial load was applied onto the specimen by means of a loading cruciform, as shown in Figure 4.9 below. The loading cruciform consisted of an I-beam with a HSS bolted to the bottom flange by four 1-inch bolts.  The vertical jacks were connected to the I-beam at the ends.  The HSS helped to spread the axial load more evenly over the top of the specimen, which was grouted to provide a flat surface. 80   Figure 4.9 – Test Set-up for Applying Axial Load The horizontal jack for applying the lateral load was mounted onto the strong wall by a 2” steel plate at a height of 1758 mm above the ground (measured to the centreline of the jack setup) , and connected to the specimen by two 4”x8” HSS with Dywidag rods tied on both sides (Figure 4.10).  During set-up, a safety chain was used to hold the horizontal jack onto the strong wall before it was connected to the specimen.  The chain was loosened during the test. To minimize second order effects, the ‘lever arm’ for the vertical load was extended as much as possible.  This was done by connecting the vertical jacks directly onto the loading 81  cruciform and leaving the area below the jacks empty with only the Dywidag rods to allow rotation.  Figure 4.10 – Test Set-up for Applying Lateral Load Since some of the specimens are long and narrow, they may tend to displace out of plane when a horizontal force is applied to the long direction.  Out-of-plane movement was prevented by means of a horizontal stabilizer mounted on the strong wall perpendicular to the long side of the specimen. The stabilizer consists of two 4”x8” HSS beams connected to the strong wall at a height of 2103 mm from the floor by Dywidag bars on a plate and connected to the HSS on the loading cruciform by using one threaded rod through the HSS secured onto two plates at 82  the side (Figure 4.11).  A piece of plastic with a smooth surface was placed in between the plates and the HSS to allow horizontal movement of the loading HSS against the stabilizer during pushing.   Figure 4.11 – Horizontal Stabilizer  4.6 Instrumentation Failure by concrete spalling due to bending was expected near the base of the column, therefore vertical linear variable differential transformers (LVDT) are mainly located on both sides of the column near the base.  Three vertical LVDTs were installed on each end of the column specimens approximately at the mid-point in between the second, third, fourth and 83  fifth ties.  Two horizontal LVDTs were installed slightly below the horizontal load beam (approximately 1210 mm) to measure the exact lateral displacement of the specimens. Figure 4.12 shows the nominal LVDT locations for the specimens.  Actual LVDT locations for each specimen are presented in Appendix A. The displacement of the lateral jack was also monitored, with an additional load cell to measure the force.  Data were being recorded every second during the test.  Figure 4.12 – LVDT Locations  4.7 Testing Protocol The predicted results showed a very small displacement capacity for the specimens, thus a small increase in displacement may produce a huge increase in moment at the base of 84  the specimen.  To start the test, the specimen would be cycled with 1 mm displacement in each of the push and pull directions.  Based on the response of the load-deformation curve measured from the load cell and horizontal LVDTs, the cyclic displacement would be increased by 1 or 2 mm.  Each displacement would be cycled three times until the specimen reached approximately the yielding load, before cycling each displacement once until the specimen failed, or showed obvious signs of failure behavior (such a severe buckling of the rebars). Applied displacement is controlled by the displacement of the lateral jack.  However, the actual displacement of the specimen will be smaller than that of the jack because of slack in the test set-up.  Load-displacement relation of the specimen would be plotted during the test to obtain the actual displacement of the specimen.  This displacement value would be used to determine the next displacement increment of the lateral jack.  4.8 Actual Testing Procedure The actual testing of each specimen differs because the loading sequence was determined for each specimen during the test.  Detailed information and data for each specimen are included in Appendix A.  A brief summary of data analysis is presented in the next chapter. 85  Chapter  5: Test Results The main goal of this study is to determine the bending displacement and moment capacities of elongated columns.  This chapter presents and explains briefly the results obtained from the tests in terms of several plots and tables.  More detailed plots, data and discussion can be found in Appendix A.  5.1 Lateral Load-Displacement Relation The maximum lateral load gives the bending moment capacity of the columns at the base, and the maximum specimen displacement is the bending displacement capacity.  The load-displacement envelope of each test was plotted against the predicted load-displacement responses below.  5.1.1 1:1 Column Specimen The 1:1 column specimen was the fourth to test. Starting this specimen the cycles were increased by setting a target specimen displacement and matching the jack displacements in both the push and pull directions to obtain the closest specimen displacement to the target displacement.  The data from the first cycle of each increase in target specimen were used to plot the envelope of the load-displacement plots, and all other cycles were plotted as dots on the same graph (Figure 5.1). 86   Figure 5.1 – Lateral Load-Displacement Envelope of 1:1 Column Specimen   Second order effects were induced when the axial load was not applied vertically downwards due to a lateral displacement.  The force at each data point caused by second order effects was found by the horizontal component of the axial force, proportioned by a lever arm equaled to the height from the floor to the top swivel of the vertical jack and the measured horizontal displacement.  A more detailed discussion in calculating second order effects is in Appendix A2 section A2.2.5. The stiffness of the specimen was found to be very similar to the predicted response in the pull direction, and slightly more flexible in the push direction.  This specimen has the 87  most similar stiffness compared to the initial prediction by using just the column height in the specimen model fixed at the top of the footing.  The load capacity of the specimen was slightly larger than predicted in the pull direction, but it was much more flexible than predictions in both ways.  It is believed that the specimen was able to displace further, but due to limitations on the stroke range of the jack and LVDTs, larger displacement cycles were not tested. The specimen showed similar load-displacement behaviour in both the push and pull directions.  The sudden increase of load at both ends of the plot was suspected to be caused by the jack pulling on part of the test set-up.  The test set-up was designed to be able to allow specimen displacement of approximately 50 mm based on the predicted maximum displacement of 25 mm.  However, the test beams might not be perfectly centred during set- up, resulting in part of the load acting on the test set-up when the specimen displacement approached 50 mm.  5.1.2 1:2 Column Specimen The 1:2 column specimen was the first to test, therefore a lot of cycles were done to observe the relation between jack and specimen displacements during the test.  The specimen was cycled a few times for smaller displacements and it was observed that the first cycle usually gave the largest load at that displacement level.  Therefore, the load and displacement of the first cycle at each displacement level were used to plot the envelope of the load- displacement relation, presented in Figure 5.2 below. All other cycles were plotted as dots on the same graph. 88   Figure 5.2 – Lateral Load-Displacement Envelope of 1:2 Column Specimen  Second order effects were calculated the same way as the other specimens.  After deduction of second order effects, the load capacity for this specimen is almost the same as predicted.  The specimen stiffness was found to be much less than the initial predicted stiffness, but very similar to the revised predicted stiffness, which was modeled as a column fixed at the base with a height of the column plus footing.  This may be caused by the many load cycles done on the specimen, which weakened the specimen compared to one pushover analysis in the models; the slip on the tension side rebar which gave rise to larger lateral 89  displacements; the patched up concrete at certain areas of the specimen due to inadequate vibration during casting; and/or movement at the base of the footing which was not measured during the test. The maximum load capacity when the specimen was pushed is slightly larger than that when the specimen was pulled.  This is mostly due to the slack in the horizontal test setup.  During the pull phase, gaps in between plates were widened while rods and bolts were lengthened, thus a smaller force was needed to produce the same displacement.  5.1.3 1:4 Column Specimen The 1:4 specimen was second to test.  Due to the large flexibility observed in the previous 1:2 column test, fewer cycles were done on this specimen.  A few cycles at different displacements were done in the elastic and inelastic ranges, and the test ended after five repeated cycles in the inelastic range.  The first cycles of all displacements were plotted as the envelope and the repeated cycles were plotted as dots in the load-displacement graph in Figure 5.3. 90   Figure 5.3 – Lateral Load-Displacement Envelope of 1:4 Column Specimen  Second order effects were calculated the same way as the other specimens.  After deduction of second order effects, the load capacity for this specimen is almost the same as predicted in the pull direction and slightly larger than predicted in the push direction.  The specimen stiffness was found to be similar to the revised prediction. Similar to the other specimens, this specimen is also much more flexible than predicted.  The load-displacement behaviour in the push and pull directions are very similar.  The last data point in the pull direction was estimated using the behaviour of the jack specimen because the horizontal LVDT went out of range in the middle of the cycle. 91  5.1.4 1:8 Column Specimen An error occurred in the horizontal jack feedback and load cell data acquisition during the testing of the 1:8 column specimen.  As the result, the jack displaced considerably within a span of a few seconds and the specimen failed.  No jack displacement and load cell data were available.  Figure 5.4 below shows the displacement-time plot for this specimen. The test was stopped after approximately four seconds from the start of lateral loading.  Figure 5.4 – Lateral Displacement–Time Plot of 1:8 Column Specimen  5.1.5 1:8 Wall Specimen The 1:8 wall specimen was the last to test.  Due to technical difficulties in the testing of the 1:8 column, data from this specimen serves as a reference for both the 1:8 column and 1:8 wall specimen.  From experience gained from the previous tests, this specimen was tested by setting different target specimen displacements, with three cycles per displacement, and 92  the jack displacement was adjusted to obtain the nearest possible specimen displacement to the target.  The envelope of the load-displacement behaviour from the first cycle of each target displacement and the data from the rest of the cycles are plotted in Figure 5.5 below.  Figure 5.5 – Lateral Load-Displacement Envelope of 1:8 Wall Specimen  Second order effects were calculated the same way as the other specimens.  Due to the long length of this specimen, the horizontal displacements are much smaller compared to the other specimens, so are the forces caused by second order effects.  The load capacity for this specimen is slightly less than predicted.  This is mainly caused by the many cycles loaded on the specimen which weakened it gradually.  As expected from observing the other specimens, this specimen is also much more flexible than predicted. 93  The stiffness in the push direction is less than that of the pull direction.  Looking at the detailed load-displacement plots from each phase (Appendix A5), there were signs of obvious residual displacements after each cycle in Phase 1.  Since the test was done by pushing the specimen first, the specimen was first weaken in the push direction (mostly on the right side of the specimen according to the LVDT plots), and a larger force was needed to pull the specimen to the same displacement in the other direction.  5.2 Strains and Curvatures at Compression Strain of Approximately 0.0035 The vertical strains of the specimen on the two edges were found by the displacement measured from the LVDTs divide by the height from the top of the footing to the LVDT location.  5.2.1 1:1 Column Specimen Table 5.1 below shows the strains at both ends of the specimen when compression strain was approximately 0.0035.  The strain value at different heights for both pushing and pulling are taken from different times during the test in pairs based on the compression strain reading on the LVDT reading the compression side of the specimen. Table 5.1 – Vertical Strains for 1:1 Column Specimen when ecomp ~0.0035  Height = 524 mm Height = 371 mm Height = 222.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0031 0.0035 -0.0039 0.0038 -0.0028 0.0036 Pulling 0.0036 -0.0036 0.0037 -0.0035 0.0036 -0.0033 Note: Positive strain is compression and negative strain is tension.  94  The curvature at each height was also calculated by adding the compression and tension strain values and dividing it by the length of the specimen.  Curvatures averaged along the measured heights are presented in Table 5.2 below. Table 5.2 – Average Curvatures for 1:1 Column Specimen when ecomp ~0.0035 [rad/km]  Height = 222.5 mm Height = 371 mm Height = 524 mm Pushing 15.97 19.12 16.48 Pulling 17.13 18.02 18.00  Comparing the average curvatures to the sectional curvatures at the base of the column obtained from predictions, •  Hand prediction at compression strain = 0.0035: 23.3 rad/km •  Response Prediction at maximum load (strain = 0.0035): 21.2 rad/km •  Vector Prediction at maximum load (strain = 0.0037): 17.8 rad/km It is concluded that the estimated curvatures are most similar to the predicted values from VecTor2, but still in an acceptable range compared to the other two predictions.  It is expected that the average curvature along the height will decrease as height increases, but calculated curvatures in the above table show an increase in curvature at height = 371 mm.  5.2.2 1:2 Column Specimen Table 5.3 below shows the strains at both ends of the specimen when compression strain was approximately 0.0035.  The strain value at different heights for both pushing and pulling are taken from different times during the test in pairs based on the compression strain reading on the LVDT reading the compression side of the specimen.   95  Table 5.3 – Vertical Strains for 1:2 Column Specimen when ecomp ~0.0035  Height = 519 mm Height = 368.5 mm Height = 221 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00327 0.00360 -0.00216 0.00330 -0.00051 0.00352 Pulling 0.00360 -0.00351 0.00369 -0.00351 0.00382 -0.00459 Note: Positive strain is compression and negative strain is tension. The curvature at each height was also calculated by adding the compression and tension strain values and dividing it by the length of the specimen.  Curvatures averaged along the measured heights are presented in Table 5.4 below. Table 5.4 – Average Curvatures for 1:2 Column Specimen when ecomp ~0.0035 [rad/km]  Height = 221 mm Height = 368.5 mm Height = 519 mm Pushing 7.34 9.92 11.21 Pulling 12.79 11.89 11.57  Comparing the average curvatures to the sectional curvatures at the base of the column obtained from predictions, •  Hand prediction at compression strain = 0.0035: 15.7 rad/km •  Response Prediction at maximum load (strain = 0.0035): 14.5 rad/km •  Vector Prediction at maximum load (strain = 0.0039): 12.2 rad/km It is concluded that the estimated curvatures are most similar to the predicted values from VecTor2, but smaller than the other predictions.  Similar to the 1:1 column specimen, this specimen shows an increase in average curvature with an increase in height.  5.2.3 1:4 Column Specimen Table 5.5 below shows the strains at both ends of the specimen when compression strain was approximately 0.0035.  The strain value at different heights for both pushing and 96  pulling are taken from different times during the test in pairs based on the compression strain reading on the LVDT reading the compression side of the specimen. Table 5.5 – Vertical Strains for 1:4 Column Specimen when ecomp ~0.0035  Height = 525 mm Height = 372 mm Height = 226.5 mm  Left Side Right Side Left Side Left Side Right Side Left Side Pushing -0.00138 0.00333 -0.00104 0.00350 -0.00038 0.00360 Pulling 0.00339 -0.00229 0.00351 -0.00210 0.00338 0.00020 Note: Positive strain is compression and negative strain is tension. The curvature at each height was also calculated by adding the compression and tension strain values and dividing it by the length of the specimen.  Curvatures averaged along the measured heights are presented in Table 5.6 below. Table 5.6 –Average Curvatures for 1:4 Column Specimen when ecomp ~0.0035 [rad/km]  Height = 226.5 mm Height = 372 mm Height = 525 mm Pushing 4.55 5.69 5.90 Pulling 3.97 7.02 7.10  Comparing the average curvatures to the sectional curvatures at the base of the column obtained from predictions, •  Hand prediction at compression strain = 0.0035: 11.3 rad/km •  Response Prediction at maximum load (strain = 0.0035): 10.5 rad/km •  Vector Prediction at maximum load (strain = 0.00326): 7.0 rad/km It is concluded that the estimated curvatures are mostly smaller than predicted, but most similar to the predicted values from VecTor2.  Similar to the two specimens previously, this specimen also shows an increase in average curvature with an increase in height.    97  5.2.4 1:8 Column Specimen Only data from the first push cycle is available for this specimen.  Table 5.7 below shows the strains at both ends of the specimen when compression strain was approximately 0.0035.  Since only four sets of data are available the strains are taken from the data point most nearest to 0.0035 compression strain. The strain value at different heights for both pushing and pulling are taken from different times during the test in pairs based on the compression strain reading on the LVDT reading the compression side of the specimen. Table 5.7– Vertical Strains for 1:8 Column Specimen when ecomp ~0.0035  Height = 470 mm Height = 335 mm Height = 200 mm  Left Side Right Side Left Side Left Side Right Side Left Side Pushing -0.00144 0.00318 -0.00148 0.00404 -0.00047 0.00306 Note: Positive strain is compression and negative strain is tension. The curvature at each height was also calculated by adding the compression and tension strain values and dividing it by the length of the specimen.  Curvatures averaged along the measured heights are presented in Table 5.8 below. Table 5.8 – Curvatures for 1:8 Column Specimen when ecomp ~0.0035 [rad/km]  Height = 200 mm Height = 335 mm Height = 470 mm Pushing 7.08 5.02 2.00  Comparing the average curvatures to the sectional curvatures at the base of the column obtained from predictions, •  Hand prediction at compression strain = 0.0035: 8.0 rad/km •  Response Prediction at maximum load (strain = 0.0035): 7.3 rad/km •  Vector Prediction at maximum load (strain = 0.00326): 4.75 rad/km It is concluded that the estimated curvatures are in an acceptable range compared to the predicted values.  The average curvatures for this specimen decrease with an increase in 98  height, which matches with expectation since most of the damage of the specimen occurred near the base.  5.2.5 1:8 Wall Specimen Table 5.9 below shows the strains at both ends of the specimen when compression strain was approximately 0.0035.  The strain value at different heights for both pushing and pulling are taken from different times during the test in pairs based on the compression strain reading on the LVDT reading the compression side of the specimen. Table 5.9 – Vertical Strains for 1:8 Wall Specimen when ecomp ~0.0035  Height = 471 mm Height = 334 mm Height = 196 mm  Left Side Right Side Left Side Left Side Right Side Left Side Pushing -0.0019 0.0035 -0.0021 0.0042 -0.00003 0.0040 Pulling 0.0036 -0.0031 0.0039 -0.0030 0.0037 -0.0012 Note: Positive strain is compression and negative strain is tension. The curvature at each height was also calculated by adding the compression and tension strain values and dividing it by the length of the specimen.  Curvatures averaged along the measured heights are presented in Table 5.10 below. Table 5.10 – Curvatures for 1:8 Wall Specimen when ecomp ~0.0035 [rad/km]  Height = 196 mm Height = 334 mm Height = 471 mm Pushing 3.67 2.46 4.89 Pulling 4.49 6.21 6.09  Comparing the average curvatures to the sectional curvatures at the base of the column obtained from predictions, •  Hand prediction at compression strain = 0.0035: 8.0 rad/km •  Response Prediction at maximum load (strain = 0.0035): 7.3 rad/km •  Vector Prediction at maximum load (strain = 0.00326): 4.75 rad/km 99  It is concluded that the estimated curvatures are similar to the predicted values from VecTor2, but much less compared to the other two predictions.  Similar to the 1:1, 1:2 and 1:4 column specimens, this specimen shows an increase in curvature at the tallest measured height.  5.3 Failure Mode 5.3.1 1:1 Column Specimen The horizontal jack and LVDTs went out of stroke at approximately 50 mm specimen displacement, therefore the specimen was cycled repeatedly with full stoke until it failed.  It is believed the specimen would be able to go to further displacements if the instrumentation did not go out of stroke. No obvious damage was observed in the specimen until a displacement of 25 mm. Concrete cover fell off on both edges and the edge rebars began to buckle. The test ended after a few of the edge rebars snapped between the first and second ties (Figure 5.6).  Most of the concrete at the base was gone after testing. 100   Figure 5.6 – Test Ended at Rebar Snapping and Loss of too much Cover  5.3.2 1:2 Column Specimen The specimen did not actually collapse.  Tension cracks were first observed at a specimen displacement of around 13 mm.  Vertical cracks near the edge followed which led to concrete cover spalling off.  The test ended when the outermost longitudinal rebar was observed to buckle between the first and second ties (Figure 5.7).  Very minimal shear cracks were present. 101   Figure 5.7 – Test Ended at Rebar Buckling  5.3.3 1:4 Column Specimen Concrete cover spalled slowly on both ends starting at a displacement of around 11 mm.  A large chunk of concrete fell off on the front and back faces of the left side at a displacement of around 18 mm. Repeated cycles at smaller displacements caused the edge rebars to buckle between the first three ties.  A large crack propagated between the first and third ties and the test was stopped when the specimen split across the length (Figure 5.8). 102   Figure 5.8 – Test Ended at Specimen Splitting  5.3.4 1:8 Column Specimen The failure for this specimen happened within the span of a few seconds.   Cracks were formed going from the left side diagonally down towards the right side where the concrete crushed severely.  Rebar buckling followed soon afterwards and the specimen failed in a bang by splitting across its length. The split is only visible from the middle to the right side of the specimen, where a large crack was seen towards the left side. 103   Figure 5.9 – Test Stopped at Specimen Splitting  5.3.5 1:8 Wall Specimen Tension cracks at tie location on both edges and vertical cracks on the front and back faces along inner longitudinal bars were observed at a displacement of around 5 mm.  Further cycling caused the concrete cover to spall, rebars buckled and ties opening up in the front and back due to the lack of cross ties.  The specimen failed with a clear failure plane across the length, splitting the specimen into two. The specimen split soon after the third and fourth ties opened up.  Without cross ties, the interior longitudinal bars were not able to withstand the axial load pulling down while the specimen was moving horizontally, thus they buckled, pushing the ties outward and losing the concrete they held. 104   Figure 5.10 – Test Ended at Specimen Splitting and Ties Opening  5.4 Comparing Results for All Specimens The measured data from all the specimens were plotted on the same graph together with their respective predicted responses to observe the relation of their load-displacement behaviour caused by different cross-section width-to-length ratios of the specimens (Figure 5.11).  The peak data points of all cycles were plotted for the four specimens (1:8 column omitted due to loss in load information).  The predictions plotted in solid lines consider column models with a height of 1370 mm fixed at the base from initial design parameters. The revised predictions plotted in dotted lines consider column models with a height of 1760 mm (actual column plus footing height of 1410 mm + 350 mm) fixed at the base. 105   Figure 5.11 – Comparison of Load-Displacement Behaviour of All Specimens 106   Overall the shapes of the plots from measured data are similar to the predicted responses.  Aside from the 1:1 column specimen, all the other specimens have stiffnesses more similar to the revised predicted responses than the initial predicted responses.  This may be due to the fact that the assumptions used in the predictions, such as the plastic hinge length and yield point are based on numerous tests done on square columns, but there are not enough past researches for elongated columns tested for bending.  The load capacity of the columns are very similar to initially predicted values, except for the 1:1 column specimen where the maximum load was much higher in the pull direction. As discussed previously, this is suspected to be caused by loading on the test set-up due to movement limitations.  The only thing that is very different comparing the measured data to the predicted response is the displacement capacities.  The actual specimens are all observed to be much flexible than predicted.  Displacement capacities for hand calculations were done at a compression strain of 0.0035.  Displacement capacities from Response2000 and VecTor2 were obtained at points slightly after the loads reached maximum, where the compression strains were also near 0.0035.  However, in the tests, it was shown that the compression strains of the specimens went much further past 0.0035.  The specimens were able to withstand displacements up to double in the longer specimens and triple in the shorter specimens.  It is concluded that the reason for the large displacement capacities was due to the presence of cross ties.  Even after the cover spalled off on the sides and the edge rebars started buckling, the two interior longitudinal rebars were held together by the cross ties and the ‘core’ of the specimen could act as another smaller column itself.  This is supported by 107  the observation that the 1:8 wall specimen failed very quickly after the ties opened up because there were no cross ties to help hold the centre concrete together.  108  Chapter  6: Summary & Conclusions 6.1 Summary of Test Results  No previous tests have been done on the bending displacement capacity (strong-axis direction) of elongated wall-like gravity-load columns even though such columns are widely used nowadays in high-rise buildings because they can easily be hidden inside walls and result in thinner floor slabs.   The main goal of the current study was to determine the behaviour of elongated columns with different cross-sectional width-to-length ratios under constant axial compression and reverse cyclic lateral displacement. A set of four column specimens were designed based on an axial compression of 1500 kN, which is the maximum compression that can be applied using the available hydraulic jacks in the laboratory. From the column-load take down analysis that was done, it was determined that the axial compression load in gravity-load columns under earthquake load factors (1.0 dead load + 0.5 live load) varies from 7 to 46% of fc’Ag in typical 20-storey buildings and varies from 17 to 50% of fc’Ag in typical 50-storey buildings. Thus the specimens were designed so that an axial compression force of 1500 kN was equal to 33% of fc’Ag. The four column specimens have approximately the same cross-sectional area, but their cross-sectional width-to-length ratios were 1:1, 1:2, 1:4 to 1:8.  A fifth specimen was identical to the 1:8 column specimen except for the arrangement of ties was similar to a wall rather than a column (no cross ties). Before conducting the tests, the four different column specimens were modeled and analyzed to predict their moment-curvature and load-displacement response with a constant axial load and varying lateral load applied at the top of the specimens.  The wall specimen was assumed to behave similarly to the 1:8 column specimen, thus only four models were 109  made for the columns.   Three different methods were used to predict the behaviour and bending moment and displacement capacities of the specimens: Response2000, VecTor2 and hand calculations.  The bending moment and displacement capacities of the specimens were taken as the point when the maximum compression strain at the base of the columns reached 0.0035, which is the compression strain capacity of unconfined concrete according to the Canadian concrete design code.  The predicted maximum loads and displacement capacities are shown in Table 6.1 below.  Additional displacements from bar slip were calculated according to the Sezen and Setzler (2008) model and are also shown in the table.  Table 6.1 – Predicted Maximum Loads and Displacements for All Specimens Maximum Lateral Loads [kN]  1:1 Col. 1:2 Col. 1:4 Col. 1:8 Col. Response2000 225.8 289.7 437.5 590.2 VecTor2 195.9 264.3 399.6 539.3 Hand Calcs. 226.8 293.0 442.2 603.5 Maximum Lateral Displacements [mm] Response2000 8.5 6.0 4.4 3.6 VecTor2 4.3 3.3 2.6 2.2 Hand Calcs. * 9.3 7.1 5.9 4.7 Add. Disp. Due to Bar Slip 1.8 1.3 0.9 0.7 * Maximum displacement for hand calculations includes both elastic and inelastic displacements; but no slip.    Table 6.2 below shows the measured maximum load and displacement capacities of the specimens.  The results of the tests showed that all the specimens had more displacement capacity than predicted.  One reason is because the specimens were able to withstand compression strains much larger than 0.0035, resulting in a larger displacement capacity. 110  The load capacities were all within a reasonable range of the predicted values.  The hand calculation method and Response2000 gave similar strength predictions, while VecTor2 gave generally a 10% lower prediction of strength than the other methods. All the measured strengths were within the range of 92% to 126% of the predicted strengths. It is important to note that the 1:1and 1:2 columns did not actually ‘fail’ during the tests. They were only severely damaged by repeated cycling with large displacements.  The maximum loads shown in Table 6.2 are the measured loads before the correction (reduction) to account for second order effects (overturning moment resisted by the vertical jacks acting at an angle because of the lateral displacement).  Because of the technical problem that occurred during the testing of the 1:8 column specimen, the 1:8 wall specimen results are shown.  Table 6.2 – Measured Maximum Loads and Displacements for all Specimens  1:1 Col. 1:2 Col. 1:4 Col. 1:8 Wall Max. Load [kN] 246.7 306.5 485.3 553.8 Max. Displacement [mm] 48.6 39.8 19.2 11.3 Max. Drift (%)* 4.00 3.28 1.58 0.93 * Based on an average height above the footing of 1214 mm.  Displacements due to bar slip were measured during the test, but the lowest LVDTs mostly broke off from the specimen due to concrete cover falling off at large displacements. The following table shows the displacements due to bar slip for each specimen at the last point of bar slip measurement and the respective horizontal displacement at the same time. Exact slip calculations for the 1:2 column specimen are not available because the LVDT measuring horizontal displacement was bent during the cycles that slip was measured. Slip 111  measurements for the 1:2 and 1:4 column specimens were not very accurate because they were measured by clipping a dial gauge on the reinforcing bars after concrete cover fell off and by gluing an LVDT to the surface of the specimen.  Slip for the other two specimens (1:1 column and 1:8 wall) were measured much more accurately by installing extra LVDTs on the side of the specimen before the test. Based on the more accurate measurements on the last two specimens, the vertical bar slip contributed between 24 and 29% of the horizontal displacement of the columns.  Table 6.3 – Measured Bar Slip Displacements for all Specimens  1:1 Col. 1:2 Col. 1:4 Col. 1:8 Wall Total Horizontal Displ. [mm]* -38.8 ~+24 +19.5 +11.3 Horz. Displ. due to Bar Slip [mm]* -9.2 ~+13 +10.3 +3.3 % Horz. Displ. due to Bar Slip 24% ~56% 53% 29% * Note: Positive displacement values are from pushing half-cycles, while negative displacement values are from pulling half-cycles.  Aside from the 1:1 column specimen, all the other specimens have measured stiffnesses more similar to the revised prediction than the initial prediction.  The initial prediction was based on a fixed-base column with a height of 1370 mm (the actual distance above the footing), while the revised prediction uses a height of 1760 mm above the fixed- base. This longer height is the distance from the point of load application to the bottom of the footing, i.e., the strong floor.  The reason for difference between the 1:1 column and the other columns may be due to the fact that the assumptions used in the predictions, such as the plastic hinge length and yield point are based on numerous tests done on square (1:1) columns and not elongated columns. 112  The specimens were able to withstand displacements up to double the predicted displacement in the longer specimens and triple the predicted displacements in the shorter specimens.  One reason for the larger displacement capacities was the presence of cross ties. Even after the cover spalled off on the sides and the edge reinforcing bars started buckling, the two interior longitudinal reinforcing bars were held together by the cross ties and the ‘core’ of the specimen could act as a smaller column that was able to support the gravity loads.  This is supported by the observation that the 1:8 wall specimen failed very quickly after the ties opened up because there were no cross ties to help hold the centre concrete together.  6.2 Improvements to Testing Procedures There are no previous elongated column tests, therefore there are no references on how such tests should be done.  A custom-designed test frame was constructed for the five specimens according to the predicted maximum load and displacements, but actual testing showed that there are ways that the test set-up and testing procedure can be improved if similar tests are to be done in the future. 1. Predictions showed that the largest displacement the specimens could reach was 25 mm.  However, actual testing shows that the displacement capacity of the most slender columns is well beyond 25 mm.  The stabilizer system was designed to allow a lateral movement of approximately +/-25 mm.  This allowance needs to be increased if similar tests are done. 2. Dywidag bars were used to tie the specimens to the ground.  Although the bars were prestressed manually before the nuts were tightened, they could be easily loosened by 113  hammering.  Therefore the specimen might have moved relative to the ground while it was pushed. This displacement, which was not measured during the test, might have contributed to the measured load.  Improvements can be done by monitoring base movement and/or using threaded rods instead of Dywidag bars for tie-down. 3. Due to the alignment of holes on the strong wall and the ground, the mounting plate for the horizontal jack was only connected to the wall by two rods at the top and bottom.  Although this set-up worked fine for the test and the concern is minimum, it would be better to have at least a 4-hole support to minimize plate deflection. 4. More specimens should be constructed so that results can be compared between specimens with the same configurations and spares are available if accidents happen to any specimen. 5. LVDTs with longer ranges should be installed due to the large displacements the specimens could go to.  It would be helpful to have two LVDTs (a long one and a short one) measuring data at the more important locations for comparison, such as for the horizontal displacement on both sides of the specimen.  6.3 Further Research This test only involves one specimen for each of the four columns with different cross-sectional width-to-length ratio, and data from the 1:8 column specimen are mostly not available.  Further tests can be done with multiple specimens of the same cross-sectional width-to-length ratios so that the behaviour can be checked and compared.  The behaviour of the specimens are controlled by a lot of factors: the cross-sectional dimensions, tie 114  arrangement, actual strength of concrete due to how the specimens are casted, movement and load in the test set-up, the strength in tying down the specimens to create a fixed base, and many others.  Currently it is assumed in this test that the difference in behaviour among the four specimens is mainly caused by their different cross-sectional width-to-length ratios, but the behaviour of the 1:8 wall specimen could also be caused by its different tie arrangement. Further tests can confirm this assumption or suggest otherwise.   Moreover, further research can be done to improve the methods of predicting behaviour for elongated columns based on the results of the tests.  As shown in this experiment, all the specimens exhibited a much more flexible behaviour compared to predictions.  115  References  Adebar, P. et al. 2010, Safety of Gravity-load Columns in Shear Wall Buildings Designed to Canadian Standard CSA A23.3. Canadian Journal of Civil Engineering, Vol. 37: 1451- 1461. Arai, Yusaku; Hakim, Bechtoula; Kono, Susumu; Watanabe, Fumio 2002, Damage Assessment of Reinforced Concrete Columns Under High Axial Loading.  Personal Contact, September 2002. Arakawa, Takashi; Arai, Yasuyuki; Egashira, Keiichi; and Fujita, Yutaka 1982, Effects of the Rate of Cyclic Loading on the Load-Carrying Capacity and Inelastic Behavior of Reinforced Concrete Columns.  Transactions of the Japan Concrete Institute, Vol. 4, 1982, pp. 485-492. Azizinamini, Atorod; Johal, Lakhpal S.; Hanson, Norman W.; Musser, Donald W.; and Corley, William G. 1988, Effects of Transverse Reinforcement on Seismic Performance of Columns – A Partial Parametric Investigation.  Project No. CR-9617, Construction Technology Laboratories, Skokie, Illinois, Sept. 1988. Canadian Standards Association 2004, A23.3-04 Design of Concrete Structures Standard. Concrete Design Handbook Third Edition. January 2006. Gill, Wayne Douglas; Park, R.; and Priestley, M.J.N. 1979, Ductility of Rectangular Reinforced Concrete Columns With Axial Load.  Report 79-1, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, February 1979, 136 pages. 116  Lynn, A., Moehle, J.P., Mahin, S.A., Holmes, W.T. 1996, Seismic Evaluation of Existing Reinforced Concrete Building Columns. Earthquake Spectra, Nov. 1996, 715-739. National Research Council Canada 2005, National Building Code of Canada 2005 Volume 1, Division B, Part 4. Negro, Paolo; Mola, Elena; Molina, Javier; Magonette, Georges E. 2004, Full-scale PSD Testing of a Torsionally Unbalanced Three-Storey Non-Seismic RC Frame. In Proceedings of the 13 th  World Conference on Earthquake Engineering, Vancouver, BC, 1- 6 August 2004. Paper No. 968. Park, R.; and Paulay, T. 1990, Use of Interlocking Spirals for Transverse Reinforcement in Bridge Columns.  Strength and Ductility of Concrete Substructures of Bridges, RRU (Road Research Unit) Bulletin 84, Vol. 1, 1990, pp. 77-92. Pujol, S. 2002, Drift Capacity of Reinforced Concrete Columns Subjected to Displacement Reversals.  Thesis, Purdue University, August 2002. Response2000. Welcome to Response-2000. 2010. <http://www.ecf.utoronto.ca/~bentz/r2k.htm> Sezen H. 2002, Seismic Behavior and Modeling of Reinforced Concrete Building Columns. Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Berkeley, December 2002. Sezen, H. and Setzier, Eric J. 2008, Reinforcement Slip in Reinforced Concrete Columns. ACI Structural Journal, Vol. 105, No.3 May-June 2008. MS No. S-2006-180.R1. Title No. 105-S27. 117  Sheikh, Shamim A.; Yeh, Ching-Chung 1990, Tied Concrete Columns Under Axial Load and Flexure.  ASCE Journal of Structural Engineering, Vol.116, No. 10, October 1990. ASCE, ISSN 0733-9445/90/0010-2780. Paper No. 25170. Soesianawati, M.T.; Park, R; and Priestley, M.J.N. 1986, Limited Ductility Design of Reinforced Concrete Columns.  Report 86-10, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, March 1986, 208 pages. Tanaka, H.; and Park, R. 1990, Effect of Lateral Confining Reinforcement on the Ductile Behavior of Reinforced Concrete Columns.  Report 90-2, Department of Civil Engineering, University of Canterbury, June 1990, 458 pages Umehara, H.; and Jirsa, J.O. 1982, Shear Strength and Deterioration of Short Reinforced Concrete Columns Under Cyclic Deformations.  PMFSEL Report No. 82-3, Department of Civil Engineering, University of Texas at Austin, Austin Texas, July 1982, 256 pages. Vector Analysis Group. General Information on VecTor2 Program. 2010. <http://www.ecf.utoronto.ca/cgi-bin/cgiwrap/vector/yabb2/YaBB.pl?num=1250699551> Watson, Soesianawati; and Park, R. 1989, Design of Reinforced Concrete Frames of Limited Ductility.  Report 89-4, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, January 1989, 232 pages. Wight, J.K.; and Sozen, M.A. 1973, Shear Strength Decay in Reinforced Concrete Columns Subjected to Large Deflection Reversals. Structural Research Series No. 403, Civil Engineering Studies, University of Illinois, Urbana-Champaign, Ill., Aug 1973, 290 pages. Zhou, Xiaozhen; Higashi, Yoichi; Jiang, Weishan; and Shimizu, Yasushi 1985, Behavior of Reinforced Concrete Column Under High Axial Load.  Transactions of the Japan Concrete Institute, Vol. 7, 1985, pp. 385-392. 118         APPENDICES  119        APPENDIX A1 1:1 COLUMN SPECIMEN TEST   120  A1.1 1:1 COLUMN TESTING  The 1:1 column specimen was the fourth specimen to be tested.  It was tested separately on three different days (divided into 3 phases in this appendix) and the details are presented below.  A1.1.1 Specimen Information The 1:1 column specimen is a square specimen with a width of 400 mm, length of 400 mm and a height of 1570 mm from the top of the footing. It was casted on September 13, 2010 and tested from June 15 to June 20, 2012, with a concrete age of 646 days during the first test phase.  Figure A1.1 – 1:1 Column Specimen Plan View  A1.1.2 Instrumentation The following diagram shows the actual as-built locations of the LVDTs from the side view of the specimen.  Measurements from the LVDTs were recorded every second. 121   Figure A1.2 – As-Built LVDT Locations for 1:1 Column  A1.1.3 Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part 1)  Phase 1 testing was done on June 15, 2012, and includes testing in the elastic range of the load-displacement behavior. Target specimen displacements of +/- 1, 2, 3, 4 and 5 mm were set and the jack displacement was guessed to match the measured displacement to the target displacement.  Three cycles were done per displacement and the jack displacement was adjusted each cycle based on the measured specimen of the previous cycle.  The horizontal load is applied at a height of approximately 1410 mm from the top of the footing, together with a constant axial load of 1570 kN.  Two LVDTs at 1209 mm on the 122  left and 1204 mm on the right from the top of footing were used to measure the horizontal displacement of the specimen. The displacement measured by the right LVDT was used as a rough reference for adjusting the jack displacement after every cycle.  Jack displacements of +/2 mm (where positive is jack pushing and negative is jack pulling) was used as a starting point to get an approximate value of the slack in the system. The amount of slack decreases as a percentage of total displacement as the displacements increase. Similar to the other specimens, the slack in the pull direction was much greater compared to the push direction. A jack displacement of +2.5/-4 mm was needed to achieve the first target specimen displacement of +/-1 mm. Using trial and error with a reasonable jack displacement increment for each cycle, a jack displacement of up to +9.3/-17.1 mm was needed for the last cycle of testing in Phase 1, with a target specimen displacement of +/-5 mm.  The period loading for all cycles in this phase was 120 seconds.  No serious damage in the specimen was observed after this test phase.  However tension cracks were observed, mostly on the left side and front of the specimen along the tie locations.  A1.1.4 Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II)  The second phase of testing was done on June 19, 2012, and includes cycling the specimen 3 times each to target specimen displacements of +/- 7, 9, 13, 17 and 21 mm.  Same as the previous phase, the starting jack displacement was guessed to be +11.5/-20 mm for target specimen displacement +/-7 mm, and adjusted very cycle to match each target specimen displacement as much as possible. The specimen was getting into the elastic range 123  of its load-displacement behavior after the +/-11 mm cycles.  The period of loading was 120 seconds for the whole phase.  There was no severe damage after this phase except for a bit of concrete cover spalling in the corners (Figure A1.3).  Figure A1.3 – First Concrete Spalling after Testing Phase 2  A1.1.5 Testing Phase 3: Reverse Cyclic Lateral Load Tests (Part III)  The last phase of testing was done one day after the previous phase.  The specimen was cycled to considerable target displacements of +/- 25, 30, 35 and 40 mm.  However, it showed no signs of failing any time soon after the third cycle of target specimen displacement of +/-40mm, where the jack displacement had already reached +52.5mm in the push direction and -64 mm in the pull direction.  Due to the range limit of the jack displacement being 76 mm and the horizontal LVDTs being approximately 50 mm, a few last 124  cycles were done with the jack cycling at full stroke.  The test ended when the specimen was observed to show severe buckling and rebar snapping, which occurred after the fourth cycle of full jack displacement, with a specimen displacement of approximately +/-49 mm.  More concrete cover fell off fist after the third cycle of target specimen displacement of  +/-25 mm, up to the second tie, with the right side more severe than the left (Figure A1.4). The whole cover below the second tie was completely gone after the third cycle of target specimen displacement of +/-30 mm (Figure A1.5).  After the third cycle of target specimen displacement +/-40 mm, the edge longitudinal rebars were fully exposed and the concrete spalled up to the third tie at the corners. The edge bars started to buckle slightly after the first cycle of full range jack displacement (Figure A1.6 (a) & (b)).  Concrete kept spalling and the bars buckled further until after the third cycle.  Figure A1.4 –Concrete Spalling after Target Specimen Displacement 25mm Cycle 3 125   Figure A1.5 –Concrete Spalling after Target Specimen Displacement 30mm Cycle 3   Figure A1.6 (a) – Rebar Buckling after Jack Full Stroke Cycle 1  126   Figure A1.6 (b) – Rebar Buckling after Jack Full Stroke Cycle 1   A few ‘pop’ sounds were heard during the fourth cycle of full jack displacement. After the test ended, it was found that two rebars (middle and front) on the right side and one rebar on the left side (middle) had snapped between the first and second ties (Figure A1.8 (a) & (b)).  The specimen still appeared to be very stable although most of the concrete near the base was gone (Figure A1.9) and all the edge rebars buckled. 127   Figure A1.7 – Concrete Spall up to 4th Tie after Testing  Figure A1.8 (a) – Rebar Snap on Right Side after Testing 128   Figure A1.8 (b) – Rebar Snap on Left Side after Testing  Figure A1.9 – Concrete at Base Almost All Gone after Testing 129  The following diagram and Table A1.1 show the full loading sequence of the 1:1 column specimen. Figure A1.11 shows the specimen after testing. Figure A1.10 – Actual Loading Cycles on 1:1 Column Specimen  Table A1.1 – Loading on 1:1 Column Specimen Date Jack Displ Specimen Displ # of Cycles Max Load  [mm] [mm]  [kN] 2012-06-15 +/-2 +0.77/-0.56 1 +46.07/-38.05  +3/-4 +1.27/-1.03 1 +69.59/-67.05  +2.5/-4 +1.04/-1.01 1 +59.63/-66.74  +3.5/-5.5 +1.51/-1.33 1 +80.42/-82.90  +4/-6.5 +1.68/-1.51 1 +90.15/-86.85  +4.5/-7.5 +1.94/-1.76 1 +102.66/-98.10  +6/-10 +2.74/-2.41 1 +127.29/-123.87  +6.2/-10.5 +2.88/-2.53 1 +130.75/-127.02  +6.5/-11.5 +3.05/-2.76 1 +134.85/-134.21  +8/-13 +4/-3.22 1 +158.57/-148.27  +8/-15 +4.1/-3.87 2 +158.15/-163.7  +9.2/-17 +4.95/-4.67 1 +173.77/178.98  +9.3/-17.1 +5.06/-4.68 2 +175.98/-174.84 2012-06-19 +11.5/-20 +6.67/-6.76 1 +209.20/-201.90  +12/-20 +6.94/-6.69 1 +212.69/-195.93  +12.5/-20 +7.41/-6.80 1 +219.34/-197.68 130   +14.5/-22.5 +8.86/-7.94 1 +237.21/-215.81  +15/-23.7 +9/42-8.62 1 +240.21/-222.16  +14.8/-23.5 +9.27/-8.61 1 +235.15/-217.79  +18/-28.5 +11.79/-11.14 1 +260.81/-245.11  +20/-30 +13.56/-12.31 2 +264.99/-249.33  +24/-35.5 +16.30/-16.27 1 +266.06/-272.10  +24.8/-35.5 +17.12/-16.61 1 +265.29/-261.42  +24.8/-35.3 +17.27/-16.83 1 +262.29/-252.30  +29/-40 +20.93/-20.42 1 +271.00/-260.92  +29/-39.5 +20.88/-20.49 1 +263.93/-252.37  +29/-39 +20.94/-20.33 1 +260.09/-247.01 2012-06-20 +33/-43 +23.34/-23.46 1 +271.07/-257.50  +34/-44 +23.84/-24.44 1 +268.87/-254.12  +35/-44.5 +24.94/-24.92 1 +268.07/-254.80  +40/-50 +29.30/-29.23 1 +278.60/-276.20  +40.5/-50 +29.83/-29.31 2 +268.98/-274.23  +46/-55.5 +34.78/-33.02 1 +290.49/-289.28  +46.2/-56.2 +34.97/-33.87 1 +284.79/-285.48  +46.4/-57 +35.48/-34.55 1 +282.13/-292.20  +52/-63 +39.97/-38.81 1 +301.29/-315.88  +52.5/-64 +39.93/-39.77 1 +297.83/-311.59  +54.5/-64 +40.45/-39.55 1 +294.22/-301.10  +62/-76 +48.63/-49.03 4 +325.96/-321.28  131    Figure A1.11 (a) to (d) –1:1 Column Specimen after Testing  132  A1.2 1:1 COLUMN DATA A1.2.1 Axial Load vs. Vertical Displacement  No axial load cycles were done on this specimen, but the data from the first application of axial load before lateral testing were plotted to check the axial strains at all the LVDT positions.  By matching an approximate linear line to the axial load-displacement plots (shown as a green dotted line in Figures 1.12 (a) to (f)), the axial strains were calculated by the differences in displacements over the heights which the LVDTs measured.  The calculated strains are presented in Table A1.2.  Figure A1.12(a) – Axial Load-Displacement Plot for LVDT D8  Figure A1.12 (b) – Axial Load-Displacement Plot for LVDT D10 133   Figure A1.12(c) – Axial Load-Displacement Plot for LVDT D5  Figure A1.12(d) – Axial Load-Displacement Plot for LVDT D7  Figure A1.12(e) – Axial Load-Displacement Plot for LVDT D4 134    Figure A1.12(f) – Axial Load-Displacement Plot for LVDT D6  Table A1.2 – Estimated Compression Strains LVDT D8 D10 D5 D7 D4 D6 Location Left Top Right Top Left Mid. Right Mid. Left Bot. Right Bot. Strain 0.00073 0.00032 0.00059 0.00046 0.00071 0.0032   From the strain values, it can be seen that the strains on the left side of the specimen (D8, D5 and D4) are much larger than those on the right side (D10, D7, D6).  Also, the strains near the front half of the specimen (D4, D8, D7) are larger compared to the ones near the back half of the specimen.  This may be caused by more cracks near the front of the specimen and on the left side within the LVDT measuring ranges.  No cracks were visible before the application of axial load.  The first sign of cracking was observed after the cycles for target specimen displacement +/-2 mm.  A1.2.2 Lateral Load Phase 1 Results Phase 1 of the test was done on June 15, 2012 and includes three cycles each for target specimen displacements of +/-1, 2, 3, 5 and 5 mm.  The lateral load-displacement relation is plotted in Figure A1.13. 135    Figure A1.13 – Lateral Load-Displacement of 1:1 Column Specimen (Phase 1)  The left and right LVDTs had very similar readings.  The plot is also very symmetrical in the push and pull directions, with a slightly larger load needed to pull the specimen to the same displacement as push.  The specimen is just reaching the start of its inelastic behavior near the end of this test phase. The following plots (Figures A1.14 (a) to (f)) show the lateral load – vertical displacement relation measured from each of the vertical LVDTs.  The shape of the plots is consistent with the lateral load-displacement plot from the horizontal LVDTs on both sides, and the vertical displacement ranges are similar on both sides of the specimen for LVDTs at the same height. 136   Figure A1.14(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 1)  Figure A1.14(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 1)  Figure A1.14(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 1) 137   Figure A1.14(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 1)  Figure A1.14(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 1)  Figure A1.14(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 1)  138  A1.2.3 Lateral Load Phase 2 Results Phase 2 of the lateral load test was done on June 19, 2012 and includes 3 cycles each of target specimen displacements of +/-7, +/9, +/-13, +/-17 and +/-21 mm.  The lateral load- displacement plot (Figure A1.15) continues to show consistent behavior in both the push and pull directions. The load peaks at around 250 kN in the push direction and around 280 kN in the pull direction.  Lateral LVDTs exhibit a similar behavior and the plots are shown in Figures A1.16 (a) to (f).  Figure A1.15 – Lateral Load-Displacement of 1:1 Column Specimen (Phase 2) 139   Figure A1.16(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 2)  Figure A1.16(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 2)  Figure A1.16(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 2) 140   Figure A1.16(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 2)  Figure A1.16(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 2)  Figure A1.16(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 2)  141  A1.2.4 Lateral Load Phase 3 Results The last phase of testing was done on June 20, 2012 and includes 3 cycles each of target specimen displacements of +/-25, +/-30, +/-35, +/-40 mm and four cycles of full jack displacement, with a specimen displacement of approximately +/-49 mm.   The horizontal LVDTs went out of range in the pull direction after the first cycle of full jack displacement. The load-displacement plot is shown in Figure A1.17 below.  Most of the vertical LVDTS were already out of range starting the +/-35mm target specimen displacement cycles.  Figure A1.17 – Lateral Load-Displacement of 1:1 Column Specimen (Phase 3)   In the later cycles, it is observed that the load started increasing a bit again.  This may be due to the lateral force acting on part of the test frame instead of the specimen itself.  The test frame was designed to allow a maximum lateral movement of approximately +/-50 mm 142  based on the largest predicted displacement of 25 mm.  However, since the actual specimens were behaving much more flexibly than predicted, and due to the fact that the test frame might not be exactly centred when installed, the HSS beam on the test frame moving with the specimen might be hitting on the stabilizers at the side at large displacements.  A1.2.5 Second Order Effects Estimation The load-displacement envelope of the test was plotted by finding the maximum load and specimen displacement obtained from the first cycle of each target specimen displacement in both the push and pull cycles.  Using the method as described in Section A2.2.5, the load used to overcome second order effects was calculated for all cycle peak points and the load-displacement curve after second order effects are deducted was plotted in the following section.  A1.2.6 Load-Displacement Results and Prediction Comparison The lateral load-displacement envelope of the 1:1 column specimen, including the envelopes after second order effects were deducted, were plotted against the predicted load- displacement curves from Response2000 in Figure A1.18.  The original Response2000 prediction modeled the specimen with the design column-only height of 1370 mm, while the revised prediction modeled the specimen with the actual column plus footing height of 1760 mm.  The peak points of all the cycles in the test are shown as light blue dots. It was noted that the maximum load reached during the test was much higher than the expected.  This was explained in Section A1.2.4 that part of the measured load was pushing against the test frame.  Therefore, if we consider the last point before the sudden increase in 143  force at the end of the plot as the maximum load, then the maximum load on the push side is very similar to the predicted, and is approximately 60 kN higher than predicted in the pull direction.   The specimen was much more flexible than predicted, and even though the rebar had snapped at the fourth cycle of full jack displacement, it did not seem that the specimen will fail if it was pushed further than full stroke.  A1.2.7 Displacement due to Bar Slip Two extra LVDTs were placed in the front face of the specimen on both sides approximately 70 mm from the edges of the specimen and 50 mm above the top of footing to measure bar slip.  The LVDTs fell out with the spalled concrete at the larger displacements. The last slip displacement in the push direction was measured to be 1.56 mm at the first cycle of target specimen displacement of +/-35 mm, and the last slip displacement in the pull direction was measured to be 1.86 mm at the first cycle of target specimen displacement of +/-40 mm, which translate to horizontal displacements at the top of approximately 8.4 mm (or 24% of total measured displacement) and 9.2 mm (or 23.6% of total measured displacement) respectively. Figures A1.19 (a), (b) & (c) show the horizontal load-lateral displacement plots for the slip LVDTs (out of range data are omitted) and Table A1.3 shows the slip at a few larger specimen target displacements, using the last cycle of each displacement. 144   Figure A1.18 – Results and Prediction Comparison 145   Figure A1.19(a) – Measured Slip at Phase 1  Figure A1.19(b) – Measured Slip at Phase 2  Figure A1.19(c) – Measured Slip at Phase 3  146  Table A1.3 – Estimating Horizontal Displacement caused by Bar Slip Target Displ [mm] Measured Displ [mm] Measured Slip [mm] Translated Horz Displ [mm] % of Measured Displ +25 +24.94 1.17 6.35 25.5% -25 -24.92 1.14 5.74 23.0% +30 +30.07 1.33 7.49 24.9% -30 -29.19 1.37 7.27 24.9% +35 +34.78 1.56 8.42 24.4% -35 -34.55 1.67 8.91 25.8% -40 -38.81 -1.86 9.16 23.6%  A1.2.8 Curvatures and Section Strain Profiles  Sections were taken across where the LVDTs were located to determine the curvatures and strain profiles in the specimen during the push and pull phases.  Curvatures and strains were calculated (Tables A1.4 to A1.7) and plotted (Figures A1.20 (a) to (f)) at the following points during the test: 1.  When tension strain equaled to or was approximately 0.002 on the tension side (indicated with a blue line in the figures) 2.  When compression strain equaled to or was approximately 0.0035 on the compression side (indicated with a red line in the figures) 3.  When specimen displacement was approximately 16 mm (indicated with an orange line in the figures) 4.  When specimen displacement was approximately 34 mm (indicated with a green line in the figures) The strains were assumed to vary linearly across the section.  The measured displacements were approximately 20 mm from the edge of the specimen for all LVDTs.  The plots below show the strain profiles along the specimen length only (and not the distance between the 147  LVDTs).  The top side of the graph is the left side of the specimen and the bottom side of the graph is the right side of the specimen.  Figure A1.20(a) – Strain Profile through Top LVDTs during Jack Pushing  Figure A1.20(b) – Strain Profile through Top LVDTs during Jack Pulling  Figure A1.20(c) – Strain Profile through Middle LVDTs during Jack Pushing 148   Figure A1.20(d) – Strain Profile through Middle LVDTs during Jack Pulling  Figure A1.20(e) – Strain Profile through Bottom LVDTs during Jack Pushing  Figure A1.20(f) – Strain Profile through Bottom LVDTs during Jack Pulling  149  Table A1.4 – Vertical Strains at Various Heights when Tension Strain ~0.002  Height = 524 mm Height = 371 mm Height = 222.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0022 0.0026 -0.0024 0.0030 -0.0021 0.0030 Pulling 0.0028 -0.0023 0.0027 -0.0024 0.0031 -0.0026 Note: Positive strain is compression and negative strain is tension.  Table A1.5 – Vertical Strains at Various Heights when Compression Strain ~0.0035  Height = 524 mm Height = 371 mm Height = 222.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0031 0.0035 -0.0039 0.0038 -0.0028 0.0036 Pulling 0.0036 -0.0036 0.0037 -0.0035 0.0036 -0.0033 Note: Positive strain is compression and negative strain is tension.  Table A1.6 – Vertical Strains at Various Heights when Specimen Displacement ~ 16mm  Height = 524 mm Height = 371 mm Height = 222.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0041 0.0039 -0.0050 0.0042 -0.0062 0.0058 Pulling 0.0042 -0.0050 0.0045 -0.0048 0.0061 -0.0078 Note: Positive strain is compression and negative strain is tension.  Table A1.7 – Vertical Strains at Various Heights when Specimen Displacement ~34mm  Height = 524 mm Height = 371 mm Height = 222.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0129 0.0115 -0.0155 0.0127 -0.0193 0.0225 Pulling 0.0084 -0.0099 0.0110 -0.0134 0.0170 -0.0159 Note: Positive strain is compression and negative strain is tension.  The curvature at each section was calculated by the difference between the tension and compression strains measured at the LVDTs divided by the length between the LVDTs on both sides (in the case of this specimen, 400 mm + 2 x 20 mm = 440 mm).  Curvatures are tabulated in Table A1.8 below.  150  Table A1.8 – Average Curvatures of Different Sections at Various Load Points [rad/km] Load Stage At Bot. LVDT At Mid. LVDT At Top LVDT Pushing Tens. strain > 0.002 12.61 12.84 11.97 Comp. strain > 0.0035 15.97 19.12 16.48 Displacement ~ 16 mm 30.06 23.00 20.04 Displacement ~ 34 mm 104.41 70.47 60.98 Pulling Tens. strain > 0.002 14.34 12.45 12.71 Comp. strain > 0.0035 17.13 18.02 18.00 Displacement ~ 16 mm 34.74 23.39 22.86 Displacement ~ 34 mm 82.46 60.89 45.67  Comparing the measured curvatures to the sectional curvature at the base of the specimen obtained from predictions:  Hand prediction at compression strain = 0.0035: 23.3 rad/km  Response Prediction at maximum load (strain = 0.0035): 21.2 rad/km  Vector Prediction at maximum load (strain = 0.0037): 17.8 rad/km It is concluded that the estimated curvatures are most similar to the predicted values from VecTor2, but still in an acceptable range compared to the other two predictions.  A1.2.9 Failure Mode Not much damage was observed on the surface of the specimen until after the displacement reached approximately +/-21mm when the concrete at the bottom corners first broke off.  Further concrete cover spalled off and progressed up until the fourth tie.  The edge longitudinal rebars were exposed and started buckling.  A lot of slip was observed during large displacement cycles. The main failure mode at the end was rebar buckling and snapping due to too many cycles.  Since the specimen is square, concrete at the base broke off symmetrically in all four sides at approximately 45-degree angles. 151        APPENDIX A2 1:2 COLUMN SPECIMEN TEST   152  A2.1 1:2 COLUMN TESTING  The 1:2 column specimen was the first specimen to be tested.  It was tested separately on four different days (divided into 4 phases in this appendix) and the details are presented below.  A2.1.1 Specimen Information The 1:2 column specimen has a width of 275 mm, length of 550 mm and a height of 1570 mm from the top of the footing. It was casted on September 13, 2010 and tested from January 27 to February 10, 2012, with a concrete age of 503 days during the first test phase.  Figure A2.1 – 1:2 Column Specimen Plan View  A2.1.2 Instrumentation The following diagram shows the actual as-built locations of the LVDTs from the side view of the specimen.  Measurements from the LVDTs were recorded every second. 153   Figure A2.2 – As-built LVDT Locations for 1:2 Column  A2.1.3 Testing Phase 0: Cyclic Axial Load Tests Before the actual testing, the specimen was first loaded with cyclic axial load without any horizontal load to ensure that the instruments were working properly.  The specimen was subjected to 3 cycles of axial load of 0-500 kN, 0-750 kN, 0-1000 kN, 0-1250 kN and 1 cycle of 0-1500 kN on January 13, 2012.  After testing, the loading frame on top of the specimen was found to have slightly deformed, thus the test was paused.  The test frame was further strengthened by adding stiffeners at the mid-point of the I-beam and an extra steel plate inside the HSS.  On January 27, 2012, two more cycles of cyclic axial load to 1500 kN were applied before the lateral load was added. 154  During the axial load cycles, it was discovered that the strains measured on each of the LVDTs were not constant under pure axial load.  It was expected to have uniform strain throughout the specimen under the applied axial load.  After careful examination of the specimen, it was found that the uneven strains were cause by the existence of shrinkage cracks all over the specimen, with more on the right side of the specimen.  The closing of the shrinkage cracks produced a higher strain reading on the right side of the specimen than the left. Deducting the strains caused by crack closing, the axial compression strain on the specimen appeared to be uniform.  Figure A2.3 shows the crack location and approximate crack widths of the shrinkage cracks.  155   Figure A2.3 – Shrinkage Crack Locations and Crack Widths 156  A2.1.4 Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part I) On the same day of the last two cycles of axial load, reverse cyclic lateral loads were applied on the specimen with a lateral load approximately 1410 mm from the top of the footing, while holding the specimen down with a constant axial load of 1500 kN. The amplitudes of the cycles were controlled by the lateral jack displacement.  The two horizontal LVDTs at the top measured the specimen displacement at 1210 mm on the left and 1215 mm on the right from the top of the footing. In the first part of the lateral tests, the specimen was cycled 3 times with jack displacements of +/- 1 mm, +/- 2 mm, +/- 3 mm, +/-4 mm, +/- 5 mm, +/- 6 mm, +/- 7 mm and +/- 8 mm (positive indicates jack is pushing and negative is pulling) and an axial load of 1500 kN.  The period for each load cycle was 60 seconds for displacement of 1 mm to 5 mm, and 90 seconds for all other jack displacements.  The first day of testing ended here so that data could be analyzed to ensure measurements are reasonable before continuing. Load-displacement graphs were plotted for the load value measured from the load cell against the jack and specimen displacements.  It was noted that the specimen displacement was smaller on the right side while the jack was pushing compared to the left and vice versa during jack pulling.  It was discovered that the horizontal LVDT mounts, which were partly sitting on the ground, were preventing the horizontal LVDTs from measuring the exact specimen specimens because the ground was preventing the mounts from rotating freely. This problem was fixed by cutting approximately half an inch on the bottom of the mounts, so they were only anchored to the footing and not resting on the ground. On January 31, 2012, one cycle of +/-5 mm jack displacement and two cycles of +/-8 mm jack displacement were loaded laterally onto the specimen.  Data were again analyzed 157  after these cycles and compared to results from the previous cycles.  The specimen displacement was smaller than the jack displacement due to deformation in the specimen and slack in the test frame.  A greater slack was observed while the lateral jack was pulling due to elongations and gaps opening up due to tension.  Extra threaded rods were added and tightened around the specimen to reduce the slack in the horizontal set-up before the next test phase (Figure A2.4).  Figure A2.4 – Extra Threaded Rods to Reduce Slack in Set-up  A2.1.5 Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II) On January 31, 2012, the specimen was first cycled with +/-8 mm jack displacement to observe the difference in specimen displacement caused by the tightened rods.  It could be seen that the actual specimen displacements had increased, which means the displacement due to slack had decreased.  Next, the load cell was zeroed by moving the horizontal jack after the axial load was constant at 1500 kN.  This ensured that the lateral load was zero at the start of the lateral test.  A half cycle with +8 mm jack displacement was performed, 158  followed by half cycles of -9 mm, -10 mm, -11 mm and two half cycles of -12 mm jack displacements in order to determine the jack displacement needed to produce equal specimen displacement in the push and pull directions.  It was found that the specimen displacements measured from the horizontal LVDTs were similar in the push and pull phases at +8/-12 mm jack displacement. Further reverse lateral loads were cycled for jack displacements +10/14 mm, +11/-16 mm, +12/-17 mm, +13/-19 mm, +14/-21 mm, +15/-22 mm, +17/-25 mm and +19/-28 mm, three cycles for each displacement.  It was observed that the horizontal LVDTs were out of range due to the large specimen displacements.  Both horizontal LVDTs were adjusted so that each of them read either the displacement caused by jack pushing or pulling.  Further test cycles were done with jack displacements of +19/-28 mm, +21/-32 mm, +23/-35 mm, +25/- 38 mm, +27/-41 mm and +29/-44 mm, one cycle for each displacement. Tension cracks were first observed on the left side of the specimen near the second tie after the second half cycle of -12 mm jack displacement (Figure A2.5 (a) & (b)). Signs of concrete cover starting to spall were first observed on the right side of the specimen after the third cycle of +13/-19 mm jack displacement.  Tension cracks were also observed along the edge of the patched up concrete. Lots of vertical cracks could be seen after the third cycle of +17/-25 mm jack displacement, indicating that the concrete cover would come off soon. After the cycle of +21/-32 mm jack displacement, concrete on the right side of the specimen had spalled up to a height at the third tie (Figure A2.6 & A2.7).  Spalling on the left side was also very obvious.  More concrete spalled over after more cycles and tension cracks became visible at the base of the column specimen (Figure A2.8). 159    Figure A2.5 – (a) First Tension Cracks on Left Side of Specimen (b) First Tension Cracks on Front Face of Specimen  160   Figure A2.6 – Concrete Cover Started Spalling at Base of Column   Figure A2.7 – Concrete Cover Spalled Off after Large Cracks Formed along Edge  161    Figure A2.8 – Severe Concrete Cover Spalling after Cycling 162  The specimen was dusted on February 02, 2012 to remove spalled concrete and more photos were taken of the damages, as shown in Figure A2.9 below.   163   Figure A2.9 (a) to (d) – 1:2 Column Specimen after Lateral Test Phase 2  A2.1.6 Testing Phase 3: Reverse Cyclic Lateral Load Tests (Part III)  At this point, the specimen was expected to fail soon due to the concrete cover being almost completely off at the base.  On February 10, 2012, the specimen was further cycled to jack displacements of +29/-44 mm, +30/-45 mm, +31/-46 mm and +32/-47 mm.  An extra dial gauge was installed during this test phase to measure the rebar slip at the bottom left side of the specimen. Two readings were taken at jack displacements of  +31/-46  mm and +32/- 47 mm and the measured slip were 0.1” (2.54 mm) and 0.11” (2.79 mm) respectively.  These slips were translated to horizontal specimen displacements of approximately 12~13 mm at where the horizontal LVDTs are located using the method described in section 3.2.3.  The specimen displayed no signs of failure except further concrete spalling after these cycles.  A last cycle was done where the specimen was pushed until it showed obvious signs 164  of rebar buckling at the base between the first and second ties.  The jack displacement reached a maximum of +50 mm before the test ended. The following diagram and Table A2.1 show the full loading sequence of the 1:2 column specimen. Figure A2.11 shows the specimen after testing.  Figure A2.10 – Actual Loading Cycles on 1:2 Column Specimen   165  Table A2.1 – Loading on 1:2 Column Specimen Date Jack Displ Specimen Displ # of Cycles Max Load  [mm] [mm]  [kN] 2012-01-28 +/-1 +0.48/-0.35 3 +20.87/-27.90  +/-2 +1.14/-0.69 3 +52.98/-49.60  +/-3 +1,74/-1.04 3 +80.96/-67.84  +/-4 +2.34/-1.37 3 +108.59/-83.35  +/-5 +2.97/-1.74 3 +138.05/-98.33  +/-6 +3.50/-2.13 3 +162.86/-110.83  +/-7 +4.07/-2.57 3 +188.98/-124.29  +/-8 +4.53/-2.88 3 +210.56/-134.70 2012-01-30 +/-5 +2.09/-1.49 1 +134.85/-84.15  +/-8 +3.95/-2.64 2 +227.25/-129.68 2012-01-31 +/-8 +4.53/-2.84 2 +213.38/-137.47  +8/-9 +4.52/-3.17 1 +218.88/-150.52  -10 -3.61 1 -160.71  -11 -4.00 1 -170.97  -12 -4.29 2 -183.02  +10/-14 +6.14/-5.38 3 +255.40/-201.60  +11/-16 +6.51/-6.43 3 +259.39/-219.32  +12/-17 +7.43/-6.82 3 +275.59/-223.91  +13/-19 +8.15/-7.83 3 +283.79/-237.10  +14/-21 +9.17/-8.84 3 +292.92/-250.37  +15/-22 +9.92/-9.29 3 +299.34/-250.90  +17/-25 +11.39/-10.97 3 +310.86/-265.30  +19/-28 +12.55/-12.19 4 +320.21/-275.49  +21/-32 +13.70/-12.33 1 +319.07/-289.59  +23/-35 +15.34/-14.19 1 +323.32/-290.01  +25/-38 +17.15/-16.75 1 +323.28/-293.16  +27/-41 +18.67/-18.47 1 +317.17/-297.31  +29/-44 +20.27/-21.08 1 +316.03/-293.47 2012-02-10 +29/-44 +19.74/-27.48 1 +294.51/-277.96  +30/-45 -26.06 1 +283.34/-269.90  +31/-46 -27.24 1 +280.49/-268.27  +32/-47 -28.21 1 +270.11/-262.87  +50 +39.81 1 +300.82   166    167   Figure A2.11 (a) to (d) –1:2 Column Specimen after Testing  168  A2.2 1:2 COLUMN DATA A2.2.1 Axial Load vs. Vertical Displacement Cyclic axial loads were first applied to the specimen to determine the axial compression strains.  The following plots (Figures A2.12(a) to (f)) show the axial load – vertical displacement relation measured from each of the LVDTs. The closing of the shrinkage cracks at the beginning produced a gentler slope at the beginning of the plot, and the strains picked up after the cracks were closed.  The concrete strain omitting crack-closing was estimated by the slope of a linear line matched to the second half of the plot, shown by a green line below.  The estimated compression strains are fairly uniform (Table A2.2).   Figure A2.12(a) – Axial Load-Displacement Plot for LVDT D8  169    Figure A2.12(b) – Axial Load-Displacement Plot for LVDT D10    Figure A2.12(c) – Axial Load-Displacement Plot for LVDT D5   170    Figure A2.12(d) – Axial Load-Displacement Plot for LVDT D7    Figure A2.12(e) – Axial Load-Displacement Plot for LVDT D4  171    Figure A2.12(f) – Axial Load-Displacement Plot for LVDT D6  Table A2.2 – Estimated Compression Strains LVDT D8 D10 D5 D7 D4 D6 Location Left Top Right Top Left Mid. Right Mid. Left Bot. Right Bot. Strain 0.00048 0.00056 0.00052 0.00064 0.00053 0.00065  A2.2.2 Lateral Load Phase 1 Results Phase 1 of the lateral load test was done on January 27 and 30, 2012.  It included cycling the specimen with horizontal jack displacements of +/-1 mm to +/-8 mm, with 1 mm increments and 3 cycles for each load.  The lateral load-displacement relation is plotted in Figure A2.13. 172    Figure A2.13 – Lateral Load-Displacement of 1:2 Column Specimen (Phase 1)  It is observed that the left side of the displaced quicker when the jack started pushing and slowed down when the stroke reached maximum, while the right side of the specimen behaved differently.  The cause of this behavior difference was found to be due to the inability for the LVDT mounts to rotate freely because they were partly supported off the floor. After the LVDT mounts were fixed, a cycle of +/-5 mm and +/-8 mm were applied on the specimen and the difference between the measured values from the left and right LVDTs had reduced (Figure A2.14). 173    Figure A2.14 – Lateral Load-Displacement after LVDT Mounts Fixed (Phase 1)  As shown on the above plot, there is a small “kink” at a load of approximately 20 kN.  This was caused by zeroing the load cell before the test started, so after the axial load was applied, the horizontal set up was actually in a tension of approximately 20 kN. When the jack started pushing, the tension force on the load cell eased off, and the “kink” at 20 kN was caused by the transition from the tension force to compression force.  This “kink” was moved to the zero load point by zeroing the load cell after application of axial load.  An extra cycle of +/-8 mm lateral load was applied after this change and results are plotted below (Figure A2.12). 174   Figure A2.15 – Lateral Load-Displacement after Load Cell Zeroed at Constant Axial Load (Phase 1)  The following plots (Figures A2.16 (a) to (f)) show the lateral load – vertical displacement relation measured from each of the vertical LVDTs.  Comparing the plots for D8 and D10 (top LVDTs), D5 and D7 (middle LVDTs), D4 and D6 (bottom LVDTs), it was observed that they exhibit consistent behavior in both the push and pull directions. 175   Figure A2.16(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 1)  Figure A2.16(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 1)  Figure A2.16(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 1) 176   Figure A2.16(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 1)  Figure A2.16(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 1)  Figure A2.16(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 1)  177  A2.2.3 Lateral Load Phase 2 Results Phase 2 of the lateral load test was done on January 31, 2012.  It included a few half cycles of jack displacement 8 mm to 12 mm to match the push and pull displacements of the specimen, followed by a series of cycles in the inelastic range of the specimen.  The lateral load – lateral displacement relation was plotted in Figure A2.17 for the specimen displacement matching portion and Figure A2.18 for the rest of phase 2.  Figure A2.17 – Lateral Load-Displacement to Match Specimen Displacement in Push and Pull Directions (Phase 2) 178   Figure A2.18 – Lateral Load-Displacement of 1:2 Column Specimen* (Phase 2) * Note: The LVDTs went out of range at large displacements, therefore the left LVDT (D9) was only measuring displacements in the pull direction while the right LVDT (D11) was only measuring push displacements at later cycles  A2.2.4 Lateral Load Phase 3 Results Phase 3 of the lateral load test was done on February 10, 2012.  It included a few more cycles in the inelastic range and a last cycle where the specimen was pushed until buckling of the rebar was observed above the footing.  The lateral load – lateral displacement relation in the inelastic range was plotted in Figure A2.19.  The left LVDT went out of range on the push side at large displacements, and the right LVDT was damaged during the test, thus, only data from the pull phases are available. 179   Figure A2.19 – Lateral Load-Displacement of 1:2 Column Specimen (Phase 3)  Results from the last push cycle are plotted in Figure A2.20 below.  The jack was stopped and retracted back to zero when buckling was observed on the outmost longitudinal rebar between the first and second ties. 180   Figure A2.20 – Lateral Load-Displacement for Last Cycle (Phase 3)  A2.2.5 Second Order Effects Estimation The load-displacement envelope of the test was plotted by finding the maximum load and specimen displacement obtained from each jack displacement (usually the first cycle if the same displacement was cycled multiple times) in both the push and pull cycles. Since the axial load was held constant while the specimen was cycled horizontally, part of the applied lateral load was used to overcome the extra lateral force produced by the axial load when it was not applied vertically.  The horizontal load was applied on the specimen, which was part-way to the top of the test set-up.  It was observed that the vertical jacks rotated very near the ground while the specimen was pushed, thus the lever arm for the second order effects was taken from the ground to the jack swivel on the side connected to the top loading frame (Figure A2.21). 181   Figure A2.21 – Lever Arm for Second Order Effects The force used to overcome second order effects was computed by the horizontal component of the axial load.  The displacement measured at the horizontal LVDT was projected linearly to get a proportioned displacement at the top jack swivel.  This displacement was used to estimate the force with the following equation. Second Order Force [kN] = Axial Load [kN] * cos [tan -1 ( Lever Arm [mm] )] Displacement [mm]  A2.2.6 Load-Displacement Results and Prediction Comparison The lateral load-displacement envelope of the 1:2 column specimen, including the envelopes after second order effects were deducted, were plotted against the predicted load- displacement curves from Response2000 in Figure A2.22 below.  The original Response2000 182  prediction modeled the specimen with the design column-only height of 1370 mm, while the revised prediction modeled the specimen with the actual column plus footing height of 1760 mm.  The peak points of all the cycles in the test are shown as light blue dots. It was noted that the maximum load on the specimen is very similar to the predicted load capacity.  However, the stiffness of the actual specimen is much less than the predicted. The main reason for the more flexible response was expected to be the repeated cyclic loads applied on the specimen.  Only one push was modeled in the predictions, but more than 60 cycles were applied during the test.  Continuously cycling the specimen weakened the concrete thus giving a more flexible response.  Another reason is the defects in the specimen due to patching the concrete where vibration was not adequate.  These patches created a weak zone in the concrete which was less stiff compared to the rest of the structure.  A third reason is due to rebar pull-out.  The models in the predictions consider little or no pull-out of the rebars, whereas in reality pull-out can contribute a large portion to the total displacement. Measured rebar slip in the cycles near the end proved that slip contributed to as much as 12- 13 mm horizontal displacement at total displacements of 22-24 mm.   183   Figure A2.22 – Results and Prediction Comparison 184  A2.2.7 Curvatures and Section Strain Profiles  Sections were taken across where the LVDTs were located to determine the curvatures and strain profiles in the specimen during the push and pull phases.  Curvatures and strains were calculated (Tables A2.3 to A2.6) and plotted (Figures A2.23 (a) to (f)) at the following points during the test: 1.  When tension strain equaled to or was just greater than 0.002 on the tension side (indicated with a blue line in the figures) 2.  When compression strain equaled to or was just greater than 0.0035 on the compression side (indicated with a red line in the figures) 3.  When specimen displacement was approximately 15 mm (indicated with an orange line in the figures) 4.  When specimen displacement was approximately 20 mm (indicated with a green line in the figures) The strains were assumed to vary linearly across the section.  The measured displacements were approximately 20 mm from the edge of the specimen.  The plots below show the strain profiles along the specimen length only (and not the distance between the LVDTs).  The top side of the graph is the left side of the specimen and the bottom side of the graph is the right side of the specimen. 185   Figure A2.23(a) – Strain Profile through Top LVDTs during Jack Pushing  Figure A2.23(b) – Strain Profile through Top LVDTs during Jack Pulling  Figure A2.23(c) – Strain Profile through Middle LVDTs during Jack Pushing 186   Figure A2.23(d) – Strain Profile through Middle LVDTs during Jack Pulling  Figure A2.23(e) – Strain Profile through Bottom LVDTs during Jack Pushing  Figure A2.23(f) – Strain Profile through Bottom LVDTs during Jack Pulling 187  Table A2.3 – Vertical Strains at Various Heights when Tension Strain ~0.002  Height = 519 mm Height = 368.5 mm Height = 221 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0201 0.00293 -0.00216 0.00330 -0.00229 0.00401 Pulling 0.00294 -0.00249 0.00269 -0.00239 0.00295 -0.00224 Note: Positive strain is compression and negative strain is tension.  Table A2.4 – Vertical Strains at Various Heights when Compression Strain ~0.0035  Height = 519 mm Height = 368.5 mm Height = 221 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00327 0.00360 -0.00216 0.00330 -0.00051 0.00352 Pulling 0.00360 -0.00351 0.00369 -0.00351 0.00382 -0.00459 Note: Positive strain is compression and negative strain is tension.  Table A2.5 – Vertical Strains at Various Heights when Specimen Displacement ~ 15mm  Height = 519 mm Height = 368.5 mm Height = 221 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00795 0.00637 -0.00825 0.00724 -0.01065 0.00954 Pulling 0.00593 -0.00811 0.00639 -0.00653 0.00876 -0.00938 Note: Positive strain is compression and negative strain is tension.  Table A2.6 – Vertical Strains at Various Heights when Specimen Displ ~20mm  Height = 519 mm Height = 368.5 mm Height = 221 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.01120 0.00819 -0.01226 0.00988 -0.01361 0.01283 Pulling 0.00808 -0.01286 0.00893 -0.00986 0.01303 -0.02573 Note: Positive strain is compression and negative strain is tension.  The curvature at each section was calculated by the difference between the tension and compression strains measured at the LVDTs divided by the length between the LVDTs on both sides (in the case of this specimen, 550 mm + 2 x 20 mm = 590 mm).  Curvatures are tabulated in Table A2.7 below.  188  Table A2.7 – Average Curvatures of Different Sections at Various Load Points [rad/km] Load Stage At Bot. LVDT At Mid. LVDT At Top LVDT Pushing 1. Tens. strain > 0.002 11.44 9.92 8.98 2. Comp. strain > 0.0035 7.34 9.92 11.21 3. Displacement ~ 15 mm 20.67 15.64 14.87 4. Displacement ~ 20 mm 47.99 40.23 35.13 Pulling 1. Tens. strain > 0.002 9.44 9.23 8.41 2. Comp. strain > 0.0035 12.79 11.89 11.57 3. Displacement ~ 15 mm 19.03 13.66 13.53 4. Displacement ~ 20 mm 70.53 34.18 38.20  Comparing the measured curvatures to the sectional curvatures at the base of the specimen obtained from predictions:  Hand prediction at compression strain = 0.0035: 15.7 rad/km  Response Prediction at maximum load (strain = 0.0035): 14.5 rad/km  Vector Prediction at maximum load (strain = 0.0039): 12.2 rad/km It is concluded that the estimated curvatures are most similar to the predicted values from VecTor2, but smaller than the other predictions.  A2.2.8 Failure Mode  Severe concrete spalling was observed throughout the test, with the cover near the base completely off at large displacements.  Rebar slip caused by tension was obvious in the later cycles.  The specimen did not collapse, but the rebars on the compression side buckled between the first and second ties.   Tension cracks were observed on the tension side on top of the footing, although not very visible to the eye after the concrete cover fell off.  Very minimal shear cracks were present. 189   It is concluded that the specimen failed by concrete crushing, followed by rebar pull- out and buckling. 190        APPENDIX A3 1:4 COLUMN SPECIMEN TEST   191  A3.1 1:4 COLUMN TESTING  The 1:4 column specimen was the second specimen to be tested.  It was tested separately on four different days (divided into 4 phases in this appendix) and the details are presented below.  A3.1.1 Specimen Information  1:4 column specimen has a width of 200 mm, length of 400 mm and a height of 1570 mm from the top of the footing. It was casted on September 13, 2010 and tested from March 8 to May 4, 2012, with a concrete age of 544 days during the first test phase.   The test was paused in after Phase 1 testing for jack service.  Figure A3.1 – 1:4 Column Specimen Plan View  A3.1.2 Instrumentation The following diagram shows the actual as-built locations of the LVDTs from the side view of the specimen.  Measurements from the LVDTs were recorded every second. 192   Figure A3.2 – As-Built LVDT Locations for 1:4 Column  A3.1.3 Testing Phase 1: Lateral Reverse Cyclic Axial Load Tests (Part I) On March 8, 2012, the specimen was cycled horizontal with jack displacements +/-2 mm, +/-4 mm, +/-6 mm and +/-8 mm (where positive is jack pushing to the right and negative is jack pulling to the left).  These displacements were chosen based on the elastic portion results from the 1:2 column test and Response2000 prediction comparison between the 1:2 and 1:4 column specimens. 193  The test setup was basically the same as the one used in the 1:2 column test, except that the two threaded rods for the horizontal frame was replaced by four longer Dywidag rods due to a longer specimen length. The specimen was first loaded axially before the lateral test.  Due to defects in the vertical jacks, the maximum axial load allowable was approximately 1400 kN, 100 kN less from the desired 1500 kN.  The axial load was held constant at 1400 kN during the horizontal test.  Period of loading is 90 seconds. Measured data showed that pushing the specimen to +/-6 mm and +/-8 mm jack displacement had loaded past the elastic portion of the specimen load-displacement relation. There was very little difference between the jack and specimen displacements during the push phase.  On the other hand, an obvious difference in value between the jack and specimen displacements was observed in the pull phase.  It was concluded that the lost in displacement was caused by slack in the extra ‘spacer’ added in between the jack and specimen due to a different dimension compared to the first specimen, as well as the elongation and loosening of the Dywidag rods and nuts clamping the horizontal loading frame to the specimen.  The four Dywidag rods were replaced with two 2” coarse threaded steel rods after the first phase of the test.  On further loading, it was discovered the axial load could not go higher than around 1300 kN.  The lack in axial load was later found to be the result of the hydraulic seals in the vertical jacks wearing away.  The test was put on hold while the jacks were sent to repair.  194  A3.1.4 Axial Load Cycles after Jacks were Repaired After the jacks were repaired, three cycles of axial load up to 1570 kN were performed on the specimen on April 25, 2012 to ensure the desired axial load could be reached.  The axial load was increased from the original designed 1500 kN to the capacity of the system, 3000 psi, which equals to 1570 kN tension in the jacks in order to simulate as much gravitational load on the specimen as possible.  A3.1.5 Testing Phase 2: Lateral Reverse Cyclic Axial Load Tests (Part II)  From Phase 1, it was found that a large slack in the system resulted in a large difference between the jack and specimen displacement in the pull half-cycles.  After the Dywidag rods were replaced with coarse threaded rods, 5 half-cycles in the pull direction only were performed.  The jack was exercised to lateral displacements of -2, -6, -10, -13 and -15 mm. Period of loading was 45 seconds.  After Phase 2 of testing, visible cracks were noted and shows in Figure A3.3 below. These cracks were caused mostly by cycling of the specimen during Phases 1 and 2.  The cracks from Phase 1 of testing affected the results of the axial load testing after jack repair, which will be discussed in Section A3.2.2.  195    Figure A3.3 – Specimen Cracks after Phase 2 196  A3.1.6 Testing Phase 3: Lateral Reverse Cyclic Axial Load Tests (Part III) Before the next phase of testing, two extra LVDTs were added to the base of the specimen on both sides in front to measure bar slip.  These LVDTs were mounted onto aluminum plates which were glued onto the specimen with epoxy, shown in Figure A3.4 below.  Figure A3.4 – Extra LVDTs for Bar Slip  On May 2, 2012, the specimen was cycled two times to jack displacements of +15/- 30 mm and +25/-50 mm.  Period of loading was 90 seconds.  After the first load cycle, it was observed that the concrete cover began to spall off on the left back corner (Figure 3.5 (a)), and both corners on the right at the bottom had concrete breaking off (Figure 3.5 (b)).  After the second load cycle, the concrete cover on the left side 197  had spalled up to the third tie, and on the right side up to the second tie (Figure 3.6).  Large portions of the specimen on the front and back faces were also damaged near the left side (Figure 3.7).   Figure A3.5 (a) & (b) – Concrete Broke off after +15/-30mm Cycle 1 198   Figure A3.6 – Concrete Damage after +25/-50mm Cycle 1 (Left & Right)  Figure A3.7 – Concrete Damage after +25/-50mm Cycle 1 (Front & Back on Left) 199  A3.1.7 Testing Phase 4: Lateral Reverse Cyclic Axial Load Tests (Part IV) The last phase of testing was done on May 4, 2012.  The cycles were slowed down by changing the loading period from 90 seconds to 120 seconds.  The specimen was first cycled to +21/-25 and +23/-30 mm jack displacements, two cycles for each displacement.  Since these two displacement values were less than the last displacement in the previous phase, there was no further serious damage in the specimen.  Concrete continued to fall off and the rebars began to show some obvious buckling.  After the end of the second +23/-30 mm cycle, the concrete around the edge longitudinal bars between the second the third ties were mostly gone on the left side (Figure A3.8). Concrete crushing was most serious between the first and second ties on the right side (Figure A3.9).  Figure A3.8 - Serious Concrete Crushing and Rebar Buckling after +23/-30 mm Cycle 2  200   Figure A3.9 – Damage on the Right Side after +23/-30 mm Cycle 2  An extra cycle of +23/-30 mm jack displacement was done afterwards.  The specimen failed during the push half-cycle and the test was emergency-stopped.  The failure was caused by a large crack horizontally through the specimen between the first and third ties which split the specimen.  A3.1.8 Axial Loading after Testing After the specimen failed, the hydraulic system was reset and the specimen was loaded up slowly in the axial direction to see how much axial load it can withstand.  The loading was stopped when the interior longitudinal rebars showed heavy buckling. 201  The following diagram and Table A3.1 show the full loading sequence of the 1:2 column specimen. Figure A3.11 shows the specimen after testing.  Figure A3.10 – Actual Loading Cycles on 1:4 Column Specimen Table A3.1 – Loading on 1:4 Column Specimen Date Jack Displ Specimen Displ # of Cycles Max Load  [mm] [mm]  [kN] 2012-03-08 +/-2 +0.93/-0.27 1 +108.36/-47.93  +/-4 +2.33/-0.26 1 +199.16/-80.62  +/-6 +3.85/-0.44 1 +265.37/-114.97  +/-8 +5.44/-0.71 1 +311.47/-155.03 2012-04-26 -2 0.16 1 -44.24  -6 -0.61 1 129.19  -10 -1.76 1 -215.31  -13 -2.81 1 -272.55  -15 -3.53 1 -304.6 2012-05-02 +15/-30 +10.83/-11.51 1 +451.27/-461.99  +25/-50 +18.84/-30.19 1 +503.91/-495.01 2012-05-04 +21/-25 +15.95/-13.47 1 +313.79/-229.42  +21/-25 +16.02/-13.38 1 +296.84/-233.79  +23/-30 +17.74/-17.20 1 +309.38/-239.26  +23/-30 +17.58/-18.73 1 +291.90/-210.37  +23 +19.20 1 +239.68 202    203   Figure A3.11 (a) to (d) –1:4 Column Specimen after Testing  204  A3.2 1:4 COLUMN DATA A3.2.1 Lateral Load Phase 1 Results The maximum axial load the jacks could reach during first phase of testing was around 1400 kN.   One cycle each of jack displacement +/-2, +/-4 +/-6 and +/-8 mm were applied to the specimen and the load-displacement graph is plotted in Figure 3.12.   Figure A3.12 – Lateral Load-Displacement of 1:4 Column Specimen (Phase 1) It is observed that the slack on the pulling half-cycles are very great compared to the push half-cycles.  This is mainly due to the use of Dywidag rods to clamp the specimen in place instead of threaded rods.  The large slack may also be cause by the extra “spacer” inserted between the load cell and the horizontal loading beam due to an increase in distance between the specimen and jack compared to the 1:2 column specimen last tested. 205  Figures A3.13 (a) to (f) below show the vertical displacement vs. horizontal load measured by all the vertical LVDTs.  It can be seen that something is happening to the right side of the specimen which caused a residual displacement after each cycle is performed. However, the shape of the envelopes of these plots are similar, as well as the displacement range they covered.  Figure A3.13(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 1)  Figure A3.13(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 1) 206   Figure A3.13(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 1)  Figure A3.13(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 1)  Figure A3.13(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 1) 207   Figure A3.13(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 1)  A3.2.2 Axial Load vs. Vertical Displacement after Jack Repair  After the jacks were back from repair, three axial load cycles up to 1570 kN were performed on the specimen to check if the peak pressure of 3000 psi (=1570 kN tension for the jacks) could be reached.  Due to the cracking in the specimen caused by the first lateral load phase, the axial displacements measured were not linear.  The specimen first showed a gentler slope in the axial load vs. axial displacement plots with the closing of the cracks, then the strains picked up afterwards.  The estimated axial strains at each LVDTs were plotted as a green straight line in Figures A3.14 (a) to (f) by matching against the second portion of the plots with the steeper slope. As a comparison, the data from the application of 1400 kN axial load in the first phase testing were plotted on the same graphs.  The values of the estimated strains are shown in Table 3.2.   The strain values are fairly similar on both side of the specimen at the same LVDT levels. 208    Figure A3.14(a) – Axial Load-Displacement Plot for LVDT D8   Figure A3.14(b) – Axial Load-Displacement Plot for LVDT D10   Figure A3.14(c) – Axial Load-Displacement Plot for LVDT D5 209    Figure A3.14(d) – Axial Load-Displacement Plot for LVDT D7   Figure A3.14(e) – Axial Load-Displacement Plot for LVDT D4   Figure A3.14(f) – Axial Load-Displacement Plot for LVDT D6  210  Table A3.2 – Estimated Compression Strains LVDT D8 D10 D5 D7 D4 D6 Location Left Top Right Top Left Mid. Right Mid. Left Bot. Right Bot. Strain 0.00078 0.00082 0.00094 0.00091 0.00101 0.00132  A3.2.3 Lateral Load Phase 2 Results The second phase of lateral testing involved five half-cycles of pulling to jack displacements of -2, -6, -10, -13 and -15 mm.  After the Dywidag rods were changed to coarse threaded rods, the slack has been reduced by a bit and the specimen displacements in the pull direction were matching up better with the push displacements recorded during phase 1.  Figure 3.15 shows the lateral load-displacement plot and Figures 3.16 (a) to (f) show the plots from the vertical LVDTs.  It can be seen that the left side of the specimen was showing a similar behaviour as the right side of the specimen in Phase 1.   Figure A3.15 – Lateral Load-Displacement of 1:4 Column Specimen (Phase 2) 211   Figure A3.16(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 2)  Figure A3.16(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 2)  Figure A3.16(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 2) 212   Figure A3.16(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 2)  Figure A3.16(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 2)  Figure A3.16(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 2)  213  A3.2.4 Lateral Load Phase 3 Results Phase 3 of lateral testing involved one cycle each of jack displacement +15/-30 mm and +25/-50 mm.  Since the available horizontal LVDT might not be long enough to measure the expected displacements, both horizontal LVDTs were adjusted so that each of them would measure one side of the specimen.  LVDT D11 (right side of specimen) would measure displacements during the push half-cycles and LVDT D9 (left side of specimen) would measure displacements during the pull half-cycles. Figure 3.17 below shows the load-displacement plot during this phase.   Figure A3.17 – Lateral Load-Displacement of 1:4 Column Specimen (Phase 3)  The left LVDT went out of range during the second loading cycle, thus data was lost for all displacement points beyond approximately 18 mm.  The specimen displacement in this portion was estimated by the shape of the jack load-displacement curve up to the maximum 214  displacement and then joining the maximum displacement to the last out-of-range specimen displacement.  The estimated specimen displacement is represented by a dotted yellow line in the above plot.  The extra LVDTs for measuring rebar slip fell off during the second push half-cycle on the right and during the second pull half-cycle on the left.  Information on slip is presented in Section A3.2.9.  A3.2.5 Lateral Load Phase 4 Results In the last phase, the specimen was subjected to two cycles of jack displacement +21/-25 mm and three cycles of jack displacement +23/-30 mm.  In the push half-cycle of jack displacement +23/-30 mm, the specimen failed by a crack across the length, splitting the specimen and buckling most of the edge rebars on both sides.   The period in this phase was slowed down, but since the specimen was severely damaged on all four sides, there was a lot of noise in the collected data. The load-displacement plot for the last phase is shown in Figure 3.18. 215    Figure A3.18 – Lateral Load-Displacement of 1:4 Column Specimen (Phase 4)  A3.2.6 Axial Loading Results after Specimen Failed The specimen was further tested for axial load capacity after it failed.  Since most of the lower LVDTs had already gone out of range, only the data from the top vertical LVDTs were plotted.  From the plots, it can be seen that the specimen could reach almost 1300 kN (around 80% of the applied axial load of 1570 kN) before the displacement took off.   The axial load data from Phase 1 were plotted on the same graphs below to show the differences in stiffness before and after the test. 216   Figure A3.19 (a) – Axial Load vs. Vertical Displacement after Test (LVDT D8)  Figure A3.19 (b) – Axial Load vs. Vertical Displacement after Test (LVDT D10)  A3.2.7 Second Order Effects Estimation The load-displacement envelope of the test was plotted by finding the maximum load and specimen displacement obtained from the first cycle of each target specimen displacement in both the push and pull cycles.  Using the method as described in Section A2.2.5, the load used to overcome second order effects was calculated for all cycle peak points and the load-displacement curve after second order effects are deducted was plotted in the following section. 217   An axial load of 1400 kN was used to calculate second order effects for Phase 1 and an axial load of 1570 kN was used for all other phases.  A3.2.8 Load-Displacement Results and Prediction Comparison The lateral load-displacement envelope of the 1:4 column specimen, including the envelopes after second order effects were deducted, were plotted against the predicted load- displacement curves from Response2000 in Figure A3.20 below.  The original Response2000 prediction modeled the specimen with the design column-only height of 1370 mm, while the revised prediction modeled the specimen with the actual column plus footing height of 1760 mm.  The extra cycles for jack displacement +21/-25 and +23/-30 mm and their load- displacement points after second order effects were deducted were also plotted on the same graph as a yellow diamond and a light blue line.  It was noted that the maximum load reached during the test is even higher than the predicted maximum load.  The elastic stiffness is very similar to the revised prediction.  This may be due to movements in the footing (which was not monitored during the test), or it may be due to the weird behaviour of the concrete at the early cycles where there were residual displacements after each cycle, showing that the concrete was weakened. 218   Figure A3.20 – Results and Prediction Comparison 219  A3.2.9 Displacement due to Bar Slip Two extra LVDTs were installed at the base of the front face on both sides of the specimen before Phase 3 lateral testing.  The measured bar slip was translated into a displacement at the horizontal LVDTs to know how much of the measured displacement was caused by bar slip and how much was caused by section properties. The LVDTs were glued to the specimen with epoxy right at the edges.  The measurement point was at approximately 25 mm from the edge of the specimen and 50 mm from the top of the footing.  The left bar slip LVDT was able to take two readings before it fell off, and the right bar slip LVDT could only take one reading.  Table 3.3 below shows the bar slip measurement and the translated horizontal displacement at the horizontal LVDT position. Table A3.3 – Estimating Horizontal Displacement caused by Bar Slip Jack Displ [mm] Measured Displ [mm] Measured Slip [mm] Translated Horz Displ [mm] % of Measured Displ +15 +11.5 1.59 6.6 57.4% -30 -11.9 2.57 7.5 63.0% +25 +19.5 3.54 10.3 52.8%  A3.2.10 Curvatures and Section Strain Profiles  Sections were taken across where the LVDTs were located to determine the curvatures and strain profiles in the specimen during the push and pull phases.  Curvatures and strains were calculated (Tables A3.4 to A3.7) and plotted (Figures A3.21 (a) to (f)) at the following points during the test: 1.  When tension strain equaled to or was approximately 0.002 on the tension side (indicated with a blue line in the figures) 220  2.  When compression strain equaled to or was approximately 0.0035 on the compression side (indicated with a red line in the figures) 3.  When specimen displacement was approximately 11 mm (indicated with an orange line in the figures) 4.  When specimen displacement was approximately 18 mm (indicated with a green line in the figures) The strains were assumed to vary linearly across the section.  The measured displacements were approximately 20 mm from the edge of the specimen for all LVDTs.  The plots below show the strain profiles along the specimen length only (and not the distance between the LVDTs).  The top side of the graph is the left side of the specimen and the bottom side of the graph is the right side of the specimen.   Figure A3.21(a) – Strain Profile through Top LVDTs during Jack Pushing 221   Figure A3.21(b) – Strain Profile through Top LVDTs during Jack Pulling  Figure A3.21(c) – Strain Profile through Middle LVDTs during Jack Pushing  Figure A3.21(d) – Strain Profile through Middle LVDTs during Jack Pulling 222   Figure A3.21(e) – Strain Profile through Bottom LVDTs during Jack Pushing  Figure A3.21(f) – Strain Profile through Bottom LVDTs during Jack Pulling  Table A3.4 – Vertical Strains at Various Heights when Tension Strain ~0.002  Height = 525 mm Height = 372 mm Height = 226.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00212 0.00399 -0.00207 0.00458 -0.00213 0.00636 Pulling 0.00339 -0.00229 0.00351 -0.00210 0.00430 -0.00201 Note: Positive strain is compression and negative strain is tension.  Table A3.5 – Vertical Strains at Various Heights when Compression Strain ~0.0035  Height = 525 mm Height = 372 mm Height = 226.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00138 0.00333 -0.00104 0.00350 -0.00038 0.00360 Pulling 0.00339 -0.00229 0.00351 -0.00210 0.00338 0.00020 Note: Positive strain is compression and negative strain is tension.  223  Table A3.6 – Vertical Strains at Various Heights when Specimen Displacement ~ 11mm  Height = 525 mm Height = 372 mm Height = 226.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00403 0.00571 -0.00427 0.00722 -0.00439 0.01068 Pulling 0.00564 -0.00713 0.00665 -0.00931 0.00936 -0.01306 Note: Positive strain is compression and negative strain is tension.  Table A3.7 – Vertical Strains at Various Heights when Specimen Displ ~ 18mm  Height = 525 mm Height = 372 mm Height = 226.5 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.01163 0.00912 -0.01334 0.01183 -0.01717 0.01614 Pulling 0.00989 -0.01326 0.01039 -0.01644 0.01657 -0.02119 Note: Positive strain is compression and negative strain is tension.  The curvature at each section was calculated by the difference between the tension and compression strains measured at the LVDTs divided by the length between the LVDTs on both sides (in the case of this specimen, 800 mm + 2 x 20 mm = 840). Curvatures are tabulated in Table A3.8 below. Table A3.8 – Average Curvatures of Different Sections at Various Load Points [rad/km] Load Stage At Bot. LVDT At Mid. LVDT At Top LVDT Pushing Tens. strain > 0.002 10.63 8.31 7.64 Comp. strain > 0.0035 4.55 5.69 5.90 Displacement ~ 11 mm 18.82 14.35 12.18 Displacement ~ 18 mm 41.64 31.46 25.94 Pulling Tens. strain > 0.002 7.88 7.02 7.10 Comp. strain > 0.0035 3.97 7.02 7.10 Displacement ~ 11 mm 28.03 19.95 15.96 Displacement ~ 18 mm 47.20 33.54 28.93  Comparing the measured curvatures to the sectional curvatures at the base of the specimen obtained from predictions:  Hand prediction at compression strain = 0.0035: 11.3 rad/km  Response Prediction at maximum load (strain = 0.0035): 10.5 rad/km 224   Vector Prediction at maximum load (strain = 0.00326): 7.0 rad/km It is concluded that the estimated curvatures are mostly smaller than predicted, but most similar to the predicted values from VecTor2.  A3.2.11 Failure Mode  Concrete at the bottom corners started to break out after the first cycle of jack displacement +15/-30 mm.  However, severe cover spalling was mainly caused by the cycle with the largest displacement.  After cycling the specimen further at repeated jack displacements of +21/-25 and +23/-30 mm, the specimen failed by cracking and splitting across its length.  Heavy rebar buckling could also be seen at both ends near the base.  The failure mode is concluded to be bending with most of the concrete between the first and third ties crushed, which caused the split. The following page shows the failure plane of the specimen.  Heights and distances were measured approximately from the edge rebars.  225    226        APPENDIX A4 1:8 COLUMN SPECIMEN TEST   227  A4.1 1:8 COLUMN TESTING  The 1:8 column specimen was the third specimen to be tested.  It was tested on May 29, 2012, and the specimen was pushed to failure in the first cycle due to technical issues. The details of the test and issues are presented below.  A4.1.1 Specimen Information The 1:8 wall specimen has a width of 140 mm, length of 1100 mm and a height of 1570 mm from the top of the footing. It was casted on September 13, 2010 and tested on May 29, 2012, with a concrete age of 624 days during the test.  Figure A4.1 – 1:8 Column Specimen Plan View  A4.1.2 Instrumentation The following diagram shows the locations of the LVDTs from the side view of the specimen.  Measurements from the LVDTs were recorded every second. 228   Figure A4.2 –LVDT Locations for 1:8 Column  A4.1.3 Testing: Reverse Cyclic Lateral Load Test The test was done on May 29, 2012 and the initial plan was to test the specimen in the elastic range for jack displacements of +/-2 mm and +/-4 mm, and then adjust the jack displacements until the specimen gets the same displacements in the push and pull directions. However, during the first lateral cycle, there was a problem in the electronics and the jack pushed all the way towards maximum stroke, failing the specimen in the way.  It was later found out that the issue was caused by a broken wire in the jack feedback cable when the head of the cable was removed to check.  The system was unable to receive jack feedback, 229  thus the jack kept pushing against the specimen.  Moreover, it was also discovered that the data acquisition system was not picking up any load cell information.   The period of loading for the jack was set to be 120 seconds, but since there was no feedback, the exact rate of loading was unclear. The test was stopped by the emergency button at approximately four seconds after the jack started pushing laterally.  The only data managed to be recorded are the displacements from the LVDTs and the time in seconds relative to the start of the test. Photos were taken after the test was stopped.  A large patch of concrete fell off in the front around the third and fourth ties (Figure A4.3) and on the back around the second and third ties (Figure A4.4).  The concrete cover on the right side was completely off up to above the fourth tie, and the edge rebars buckled between the second, third and fourth tie (Figure A4.5).  The specimen failed after a split across the specimen, which was mostly visible from the second longitudinal rebar from the left to the right edge (Figure A4.6).  There were many cracks on the left side at the tie locations, going diagonally on the front and back sides towards the area where the concrete crushed. 230   Figure A4.3 –Concrete Cover fell off in Front & Cracking  Figure A4.4–Concrete Cover fell off at Back & Cracking 231   Figure A4.5 –Concrete Crushing and Rebar Buckling on Right  Figure A4.6 –Specimen Split along its Length  232  The following table shows the specimen displacement data.  The hydraulics was stopped at approximately 4 seconds, but the specimen split and kept moving until it stabilized. Figure A4.7 shows the specimen after testing. Table A4.1 – Loading on 1:8 Column Specimen Date Time Specimen Displ  [s] [mm] 2012-05-29 1 0.00  2 1.54  3 4.96  4 9.41  5 17.89  6 26.12  7 34.22  8 34.89  9 34.92   233    Figure A4.7 (a) to (d) –1:8 Column Specimen after Testing  234  A4.2 1:8 COLUMN DATA A4.2.1 Axial Load vs. Vertical Displacement  No axial load cycles were done on this specimen, but the data from the first application of axial load before lateral testing were plotted to check the axial strains at all the LVDT positions.  The graphs look linear, therefore the axial strains were calculated by dividing the displacement at maximum axial load over the heights which the LVDTs measured.  The axial load-displacement plots are shown in Figures 4.8 (a) to (f).  The calculated strains are presented in Table A4.2.  Figure A4.8(a) – Axial Load-Displacement Plot for LVDT D8  Figure A4.8(b) – Axial Load-Displacement Plot for LVDT D10 235   Figure A4.8(c) – Axial Load-Displacement Plot for LVDT D5  Figure A4.8(d) – Axial Load-Displacement Plot for LVDT D7  Figure A4.8(e) – Axial Load-Displacement Plot for LVDT D4 236   Figure A4.8(f) – Axial Load-Displacement Plot for LVDT D6 Table A4.2 – Estimated Compression Strains LVDT D8 D10 D5 D7 D4 D6 Location Left Top Right Top Left Mid. Right Mid. Left Bot. Right Bot. Strain 0.00115 0.00077 0.00136 0.00090 0.00209 0.00107  A4.2.2 Lateral Load Results  Due to technical issues as mentioned previously, data from the jack displacement and load cell were lost.  Therefore, all the LVDT displacements were plotted against time. Figure A4.9 below shows the displacement-time plot for the horizontal LVDTs.  The dots on the three plots are the data points at four seconds after the start of the test, which was approximately the time when the pressure was stopped.  The data from all vertical LVDTs are plotted in a similar manner in Figures A4.10 (a) to (f).  It is observed that the ranges of vertical displacements measured from LVDTs on both sides are very similar. 237   Figure A4.9 – Horizontal Displacement vs. Time Plot for 1:8 Column Specimen  Figure A4.10(a) –Vertical Displacement vs. Time at LVDT D8 238   Figure A4.10(b) –Vertical Displacement vs. Time at LVDT D10  Figure A4.10(c) –Vertical Displacement vs. Time at LVDT D5  Figure A4.10(d) –Vertical Displacement vs. Time at LVDT D7 239   Figure A4.10(e) –Vertical Displacement vs. Time at LVDT D4  Figure A4.10(f) –Vertical Displacement vs. Time at LVDT D6  A4.2.3 Second Order Effects Estimation Second order effects are unable to be computed due to a loss in load information.  A4.2.4 Load-Displacement Results and Prediction Comparison  Since the load data is unavailable, the maximum displacement measure is compared to the maximum predicted displacement.  When the test was stopped, the specimen had a displacement of approximately 9.4 mm. Response2000 predicted a maximum specimen 240  displacement of 3.6 mm.  Similar to the results from the other specimens, the 1:8 column specimen also exhibited a much flexible behaviour than predicted.  A4.2.5 Displacement due to Bar Slip Two extra LVDTs were installed in the front face of the specimen on both sides approximately 70 mm from the edges of the specimen and 50 mm above the top of footing to measure bar slip.  The measured bar slip went up to around 1.1 mm at maximum displacement of 9.4 mm before failure, which translates to a horizontal displacement at the top of approximately 3.7 mm (or 39.4% of total measured displacement).  Figure A4.11 shows the Slip-Time plot and Figure A4.12 shows the Slip vs. Horizontal Displacement plot.  Figure A4.11 – Slip at LVDT D1 vs. Time  Figure A4.12 –Slip at LVDT D1 vs. Specimen Displacement 241  A4.2.6 Curvatures and Section Strain Profiles  Sections were taken across where the LVDTs were located to determine the curvatures and strain profiles in the specimen during the push and pull phases.  Curvatures and strains were calculated (Tables A4.3 to A4.6) and plotted (Figures A4.13 (a) to (c)) at the following points during the test: 1.  After axial load was applied and before lateral load was applied (indicated with a blue line in the figures) 2.  Second data point, when displacement was approximately 1.5 mm and compression strains varied from 0.002 to 0.003 along the right side (indicated with a red line in the figures) 3.  Third data point, when displacement was approximately 5 mm and compression strains varied from 0.003 to 0.005 along the right side (indicated with an orange line in the figures) 4.  When specimen displacement was approximately 9.4mm (indicated with a green line in the figures) The strains were assumed to vary linearly across the section.  The measured displacements were approximately 20 mm from the edge of the specimen for the top LVDTs, 35 mm for the middle LVDTs and 50 mm for the bottom LVDTs.  The plots below show the strain profiles in the pushing direction along the specimen length only (and not the distance between the LVDTs).  The top side of the graph is the left side of the specimen and the bottom side of the graph is the right side of the specimen. 242   Figure A4.13(a) – Strain Profile through Top LVDTs during Jack Pushing  Figure A4.13(b) – Strain Profile through Middle LVDTs during Jack Pushing  Figure A4.13(c) – Strain Profile through Bottom LVDTs during Jack Pushing  243  Table A4.3 – Vertical Strains at Various Heights after Application of Axial Load  Height = 470 mm Height = 335 mm Height = 200 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing 0.00070 0.00133 0.00082 0.00152 0.00123 0.00184 Note: Positive strain is compression and negative strain is tension.  Table A4.4 – Vertical Strains at Various Heights when Specimen Displacement ~1.5mm  Height = 470 mm Height = 335 mm Height = 200 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00012 0.00207 -0.00027 0.00247 -0.00047 0.00306 Note: Positive strain is compression and negative strain is tension.  Table A4.5 – Vertical Strains at Various Heights when Specimen Displacement ~5mm  Height = 470 mm Height = 335 mm Height = 200 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00144 0.00318 -0.00148 0.00404 -0.00259 0.00520 Note: Positive strain is compression and negative strain is tension.  Table A4.6 – Vertical Strains at Various Heights when Specimen Displacement ~9.4mm  Height = 470 mm Height = 335 mm Height = 200 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.00273 0.00480 -0.00312 0.00640 -0.00569 0.00898 Note: Positive strain is compression and negative strain is tension.  The curvature at each section was calculated by the difference between the tension and compression strains measured at the LVDTs divided by the length between the LVDTs on both sides (in the case of this specimen, 1100 mm + 2 x 20 mm = 1140 mm for top LVDT, 1100 + 2 x 50 mm = 1200 mm for middle LVDT and 1100 + 2 x 70 mm = 1240 mm for bottom LVDT).  Curvatures are tabulated in Table A4.7 below. Table A4.7 – Average Curvatures of Different Sections at Various Load Points [rad/km] Load Stage At Bot. LVDT At Mid. LVDT At Top LVDT Pushing Before Lateral Load 0.55 0.63 0.58 Displacement ~ 1.5 mm 3.21 2.49 2.00 Displacement ~ 5 mm 7.08 5.02 4.20 Displacement ~ 9.4 mm 13.34 8.65 6.85  244  The data at specimen displacement ~ 5mm is the closest to a compression strain equaled to 0.0035.  Comparing the measured curvatures to the sectional curvatures at the base of the specimen obtained from predictions:  Hand prediction at compression strain = 0.0035: 8.0 rad/km  Response Prediction at maximum load (strain = 0.0035): 7.3 rad/km  Vector Prediction at maximum load (strain = 0.0030): 4.75 rad/km It is concluded that the estimated curvatures are very similar to the predicted values.  A4.2.7 Failure Mode  The rate of loading for this specimen was unclear, but it was very quick.  The right side of the specimen start crushing soon after the lateral load was applied.  The crushing area enlarged quickly until above the fourth tie and the edge longitudinal rebars started buckling. The second layer of longitudinal rebars buckled soon afterwards and the specimen split across its length.  The major failure mode for this specimen was concrete crushing. The following page shows the failure plane of the specimen.  Heights and distances were measured approximately from the edge rebars.  245   246        APPENDIX A5 1:8 WALL SPECIMEN TEST   247  A5.1 1:8 WALL TESTING  The 1:8 wall specimen was the last specimen to be tested.  It was tested separately on two consecutive days (divided into 2 phases in this appendix), with elastic displacements on the first day and inelastic displacements on the second.  The details of the test are presented below.  A5.1.1 Specimen Information The 1:8 wall specimen has a width of 140 mm, length of 1100 mm and a height of 1570 mm from the top of the footing. It was casted on September 13, 2010 and tested on July 4 and 5, 2012, with a concrete age of 660 days during the first test phase. Different from the 1:8 column specimen, this specimen has ties formed by two hooked bars with a C-hook on one side and a 90-degree hook on the other.  There are no cross ties in the centre longitudinal bars.  Figure A5.1 – 1:8 Wall Specimen Plan View 248  A5.1.2 Instrumentation The following diagram shows the actual as-built locations of the LVDTs from the side view of the specimen.  Measurements from the LVDTs were recorded every second.  Figure A5.2 – As-Built LVDT Locations for 1:8 Wall  A5.1.3 Testing Phase 1: Reverse Cyclic Lateral Load Tests (Part 1)  Phase 1 of the test was done on July 4, 2012, and includes testing in the elastic range of the load-displacement behavior.  Target specimen displacements of 1 mm and 2 mm were set and the jack displacement was guessed to match the measured displacement to the target displacement.  Three cycles of each target displacement were done. 249   The horizontal load is applied at a height of approximately 1410 mm from the top of the footing, together with a constant axial load of 1570 kN.  Two LVDTs at 1218 mm on the left and 1214 mm on the right from the top of footing were used to measure the horizontal displacement of the specimen.  Jack displacements of +/-2 mm (where positive is jack pushing and negative is jack pulling), +3/-4 mm and +3.5/-7 mm were done for target specimen displacement +/-1 mm. The jack displacement of each cycle was guessed based on the reading of the actual displacement of the previous cycle.  Jack displacements of +5/-10 mm and two cycles of +5/- 13 mm were done for target specimen displacement of +/-2 mm.  The threaded rods holding the specimen on the sides were further tightened before the third cycle of target specimen displacement 2 mm due to a large slack observed in the pulling direction.  The period of loading for all cycles were 120 seconds.  The first phase of testing ended here so that the data could be analyzed to ensure they look reasonable.  During testing, it was observed that the right horizontal LVDT was having a large residual displacement after each push half-cycle, which was not detected by the left LVDT. An initial guess was that some dry glue on the right horizontal LVDT base plate was causing the weird readings.  However, after plotting up the load-displacement graphs of all LVDTs on the right (both horizontal and vertical), it was observed that this behavior was picked up by all the LVDTs, which showed that it was the actual specimen response.  As an extra check, a second horizontal LVDT was installed on the right before phase 2 of the test.  Nothing was observed after the first day of testing except a few small cracks.   250  5.1.4 Testing Phase 2: Reverse Cyclic Lateral Load Tests (Part II)  The second phase of testing was done on July 5, 2012.  The specimen was first cycled to target specimen displacements of +/-3 mm, +/-4 mm and +/-5 mm, with three cycles per displacement.  The jack displacements for the cycles were +6/-17 mm, +7/-21 mm and +8/- 25 mm respectively.  Period of loading was 120 seconds. After the third cycle of target specimen displacement +/-4 mm, the first concrete spalling was observed on the right side at the bottom of the specimen (Figure 5.3).  A lot of tensions cracks were observed at the back of the specimen after the first cycle of target specimen displacement +/-5 mm.  There are also visible vertical cracks along the interior longitudinal rebars (Figure 5.4).  Figure A5.3 – First Specimen Damage Observed  251   Figure A5.4 – Cracks after Target Specimen Displacement +/-5 mm Cycle 1   Next, three cycles each of target specimen displacement +/-6 mm, +/-7 mm and +/-9 mm are performed.  Jack displacements were +9/-28 mm, +10.5/-30 mm and +12.5/-33/5 mm respectively.  Period of loading was still 120 seconds.  After the first cycle of target specimen displacement +/-6 mm, the corner on the bottom right back side of the specimen has crushed and vertical cracks could be seen on the left side indicating the cover coming off soon (Figure A5.5).  Further cycles increased the amount of concrete spalling up to the third tie on the right (Figure A5.6(a)) and the bottom vertical LVDT on the left (Figure A5.6(b)) after the first cycle of target specimen displacement +/-9 mm. 252   By the end of the third cycle of target specimen displacement +/-9 mm, the concrete cover on the right side was totally gone up to the second tie (Figure A5.7).  The left side had obvious signs of cover spalling soon but it was still intact.   Figure A5.5 – Concrete Crushing on the Right 253   Figure A5.6 (a) – Right Side after Target Specimen Displacement 9mm Cycle 1  Figure A5.6 (b) – Left Side after Target Specimen Displacement 9mm Cycle 1 254   Figure A5.7 – Right Side Cover off after Target Specimen Displacement 9mm Cycle 3  Lastly, the specimen was cycled to a considerable amount by setting the target specimen displacement to +/-12 mm.  The period of loading was doubled to 240 seconds. The specimen was first pushed with jack displacement 15 mm.  The concrete on the right side crushed very severely during the push and the specimen failed at a displacement of around 11 mm during push.  The failure was a split across the specimen slanting between the second and fourth ties (Figures 5.8 (a) & (b)), buckling of the longitudinal bars and opening up of the ties (Figure 5.9).  The concrete cover was completely gone up to the fourth tie on both ends (Figure 5.10). 255    Figure A5.8 (a) & (b) – Specimen Split after Failure 256   Figure A5.9 – Rebar Buckling and Ties Opening   Figure A5.10 – Concrete Cover gone on Both Ends  257  The following diagram and Table A5.1 show the full loading sequence of the 1:2 column specimen. Figure A5.12 shows the specimen after testing.  Figure A5.11 – Actual Loading Cycles on 1:8 Wall Specimen  Table A5.1 – Loading on 1:8 Wall Specimen Date Jack Displ Specimen Displ # of Cycles Max Load  [mm] [mm]  [kN] 2012-07-04 +/-2 +0.62/-0.11 1 +133.52/-65.11  +3/-4 +0.98/-0.19 1 +205.39/-120.94  +3.5/-7 +1.16/-0.53 1 +242.98/-196.16  +5/-10 +1.97/-0.81 1 +349.82/-289.58  +5/-13 +1.93/-1.28 2 +343.97/-358.26 2012-07-05 +6/-17 +2.65/-2.03 3 +420.14/-423.86  +7/-21 +3.21/-2.57 3 +464.38/-456.59  +8/-25 +4.58/-4.77 3 +517.70/-542.79  +9/-28 +5.34/-5.59 3 +543.36/-565.75  +10/-30 +6.31/-6.45 1 +557.88/-577.30  +10.5/-30 +6.80/-6.42 2 +561.07/-571.75  +12.5/-33.5 +8.72/-6.48 3 +526.48/-577.30  +15 +11.32 1 +378.79  258    259   Figure A5.12 (a) to (d) –1:8 Wall Specimen after Testing    260  A5.2 1:8 WALL DATA A5.2.1 Axial Load vs. Vertical Displacement  When the axial load was first applied before the lateral cycles, one of the vertical jacks went out of stroke for the first cycle.  The jack was then adjusted and the axial load reapplied.  The following plots (Figures A5.13 (a) to (f)) show the axial load-displacement plots from all LVDTs before lateral load was applied.  The shape of the plots suggests the concrete was weakened when the axial load was applied, but no cracks were visible before the lateral load was applied. The quick increase in displacement when the load was applied and the slow decrease when load was removed may be due to the fact that there were no cross ties in the specimen to help holding the centre portion of the concrete together.  The axial concrete strains at each LVDT were estimated by matching a linear line near the end part of the plot, where most of the internal cracks, if there were any, were assumed to have closed.  The estimation was shown as a green dotted line on the plots and the estimated strains were presented in Table A5.2.    Figure A5.13(a) – Axial Load-Displacement Plot for LVDT D8 261    Figure A5.13(b) – Axial Load-Displacement Plot for LVDT D10    Figure A5.13(c) – Axial Load-Displacement Plot for LVDT D5    Figure A5.13(d) – Axial Load-Displacement Plot for LVDT D7  262    Figure A5.13(e) – Axial Load-Displacement Plot for LVDT D4    Figure A5.13(f) – Axial Load-Displacement Plot for LVDT D6  Table A5.2 – Estimated Compression Strains LVDT D8 D10 D5 D7 D4 D6 Location Left Top Right Top Left Mid. Right Mid. Left Bot. Right Bot. Strain 0.00063 0.00073 0.00075 0.00093 0.00103 0.00116  A5.2.2 Lateral Load Phase 1 Results Phase 1 of the test was done on July 4, 2012 and includes three cycles each for target specimen displacements of +/-1 and +/-2 mm.  The lateral load-displacement relation is plotted in Figure A5.14. 263    Figure A5.14 – Lateral Load-Displacement of 1:8 Wall Specimen (Phase 1)   It is observed that the right LVDT produced a much larger residual displacement after each cycle compared to the left.  This behaviour was shown similarly in all the other LVDTs on the right, thus it was concluded that it is the actual behavior of the specimen and not a problem in the setup or LVDTs.  It can also be seen that the specimen was displacing more in the push direction than the pull direction.  The slack on the setup during the pull direction was large, thus it took more guesses before the relation between the jack and specimen displacement can be obtained. 264  The following plots (Figures A5.15 (a) to (f)) show the lateral load – vertical displacement relation measured from each of the vertical LVDTs.  The shape of the plots is consistent with the plots from the horizontal LVDTs on both sides.   Figure A5.15(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 1)  Figure A5.15(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 1) 265   Figure A5.15(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 1)  Figure A5.15(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 1)  Figure A5.15(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 1) 266   Figure A5.15(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 1)  A5.2.3 Lateral Load Phase 2 Results Phase 2 of the lateral load test was done on July 5, 2012 and includes 3 cycles each of target specimen displacements of +/-3, +/-4, +/-5, +/-6, +/-7, +/-9 mm and one cycle of target specimen displacement +/-12 mm. The specimen showed approximately symmetrical behaviour in both the push and pull directions as shown in the load-displacement plot in Figure A5.16.  Load-displacements for all vertical LVDTs are shown in Figures A5.17 (a) to (f). 267   Figure A5.16 – Lateral Load-Displacement of 1:8 Wall Specimen (Phase 2)  Figure A5.17(a) – Lateral Load-Vertical Displacement at LVDT D8  (Phase 2) 268   Figure A5.17(b) – Lateral Load-Vertical Displacement at LVDT D10  (Phase 2)   Figure A5.17(c) – Lateral Load-Vertical Displacement at LVDT D5  (Phase 2)   Figure A5.17(d) – Lateral Load-Vertical Displacement at LVDT D7  (Phase 2) 269   Figure A5.17(e) – Lateral Load-Vertical Displacement at LVDT D4  (Phase 2)   Figure A5.17(f) – Lateral Load-Vertical Displacement at LVDT D6  (Phase 2)  A5.2.4 Second Order Effects Estimation The load-displacement envelope of the test was plotted by finding the maximum load and specimen displacement obtained from the first cycle of each target specimen displacement in both the push and pull cycles.  Using the method as described in Section A2.2.5, the load used to overcome second order effects was calculated for all cycle peak points and the load-displacement curve after second order effects are deducted was plotted in the following section. 270  A5.2.5 Load-Displacement Results and Prediction Comparison The lateral load-displacement envelope of the 1:8 wall specimen, including the envelopes after second order effects were deducted, were plotted against the predicted load- displacement curves from Response2000 in Figure A5.18 below.  The original Response2000 prediction modeled the specimen with the design column-only height of 1370 mm, while the revised prediction modeled the specimen with the actual column plus footing height of 1760 mm.  The peak points of all the cycles in the test are shown as light blue dots.  It was noted that the maximum load reached during the test is very close to the predicted maximum load.  The elastic stiffness, however, was similar to the original Response prediction in the pull direction and similar to the revised prediction in the push direction.  The difference in stiffness may be due to the initial weird behavior picked up during Phase 1, where the specimen was having large residual displacements after each cycle, weakening the specimen at every push.  A2.2.6 Displacement due to Bar Slip Two extra LVDTs were placed in the front face of the specimen on both sides approximately 70 mm from the edges of the specimen and 50 mm above the top of footing to measure bar slip.  The measured bar slip went up to around 0.003 mm at maximum displacement before failure, which translates to a horizontal displacement at the top of approximately 3.3 mm (or 29% of total measured displacement).  Figures A5.19 (a) and (b) show the horizontal load-lateral displacement plots for the slip LVDTs and Table A5.3 shows the slip at a few larger specimen target displacements, using the last cycle of each displacement. 271   Figure A5.18 – Results and Prediction Comparison 272   Figure A5.19(a) – Measured Slip at LVDT D1  (Left: Phase 1, Right: Phase 2)   Figure A5.19(b) – Measured Slip at LVDT D3  (Left: Phase 1, Right: Phase 2)  Table A5.3 – Estimating Horizontal Displacement caused by Bar Slip Target Displ [mm] Measured Displ [mm] Measured Slip [mm] Translated Horz Displ [mm] % of Measured Displ +6 +5.57 0.56 1.36 24.4% -6 -5.68 0.71 1.33 23.4% +7 +6.97 0.80 1.85 26.5% -7 -6.45 0.96 1.65 25.6% +9 +8.96 1.00 3.08 34.4% -9 -7.77 1.46 2.56 32.9% +12 +11.32 1.09 3.33 29.4%  A2.2.7 Curvatures and Section Strain Profiles  Sections were taken across where the LVDTs were located to determine the curvatures and strain profiles in the specimen during the push and pull phases.  Curvatures 273  and strains were calculated (Tables A5.4 to A5.7) and plotted (Figures A5.20 (a) to (f)) at the following points during the test: 1.  When tension strain equaled to or was approximately 0.002 on the tension side (indicated with a blue line in the figures) 2.  When compression strain equaled to or was approximately 0.0035 on the compression side (indicated with a red line in the figures) 3.  When specimen displacement was approximately 5 mm (indicated with an orange line in the figures) 4.  When specimen displacement was approximately 8 mm (indicated with a green line in the figures) The strains were assumed to vary linearly across the section.  The measured displacements were approximately 20 mm from the edge of the specimen for the top LVDTs, 50 mm for the middle LVDTs and 70 mm for the bottom LVDTs.  The plots below show the strain profiles along the specimen length only (and not the distance between the LVDTs). The top side of the graph is the left side of the specimen and the bottom side of the graph is the right side of the specimen.  Figure A5.20(a) – Strain Profile through Top LVDTs during Jack Pushing 274   Figure A5.20(b) – Strain Profile through Top LVDTs during Jack Pulling  Figure A5.20(c) – Strain Profile through Middle LVDTs during Jack Pushing  Figure A5.20(d) – Strain Profile through Middle LVDTs during Jack Pulling 275    Figure A5.20(e) – Strain Profile through Bottom LVDTs during Jack Pushing  Figure A5.20(f) – Strain Profile through Bottom LVDTs during Jack Pulling  Table A5.4 – Vertical Strains at Various Heights when Tension Strain ~0.002  Height = 471 mm Height = 334 mm Height = 196 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0020 0.0034 -0.0021 0.0042 -0.0019 0.0051 Pulling 0.0032 -0.0026 0.0032 -0.0016 0.0044 -0.0017 Note: Positive strain is compression and negative strain is tension.  Table A5.5 – Vertical Strains at Various Heights when Compression Strain ~0.0035  Height = 471 mm Height = 334 mm Height = 196 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0019 0.0035 -0.0021 0.0042 -0.00003 0.0040 Pulling 0.0036 -0.0031 0.0039 -0.0030 0.0037 -0.0012 Note: Positive strain is compression and negative strain is tension.  276  Table A5.6 – Vertical Strains at Various Heights when Specimen Displacement ~ 5mm  Height = 471 mm Height = 334 mm Height = 196 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0024 0.0040 -0.0026 0.0048 -0.0042 0.0070 Pulling 0.0036 -0.0031 0.0044 -0.0035 0.0055 -0.0041 Note: Positive strain is compression and negative strain is tension.  Table A5.7 – Vertical Strains at Various Heights when Specimen Displ ~8mm  Height = 471 mm Height = 334 mm Height = 196 mm  Left Side Right Side Left Side Right Side Left Side Right Side Pushing -0.0031 0.0077 -0.0035 0.0100 -0.0060 0.0158 Pulling 0.0049 -0.0041 0.0062 -0.0045 0.0060 -0.0073 Note: Positive strain is compression and negative strain is tension.  The curvature at each section was calculated by the difference between the tension and compression strains measured at the LVDTs divided by the length between the LVDTs on both sides (in the case of this specimen, 1100 mm + 2 x 20 mm = 1140 mm for top LVDT, 1100 + 2 x 50 mm = 1200 mm for middle LVDT and 1100 + 2 x 70 mm = 1240 mm for bottom LVDT).  Curvatures are tabulated in Table A5.8 below. Table A5.8 – Average Curvatures of Different Sections at Various Load Points [rad/km] Load Stage At Bot. LVDT At Mid. LVDT At Top LVDT Pushing Tens. strain > 0.002 6.37 5.72 4.89 Comp. strain > 0.0035 3.67 2.46 4.89 Displacement ~ 5 mm 10.09 6.72 5.75 Displacement ~ 8 mm 19.79 12.25 9.90 Pulling Tens. strain > 0.002 5.56 4.34 5.27 Comp. strain > 0.0035 4.49 6.21 6.09 Displacement ~ 5 mm 9.44 7.18 6.09 Displacement ~ 8 mm 12.11 9.68 8.21  Comparing the measured curvatures to the sectional curvatures at the base of the specimen obtained from predictions:  Hand prediction at compression strain = 0.0035: 8.0 rad/km  Response Prediction at maximum load (strain = 0.0035): 7.3 rad/km 277   Vector Prediction at maximum load (strain = 0.0030): 4.75 rad/km It is concluded that the estimated curvatures are similar to the predicted values from VecTor2, but much less compared to the other two predictions.  A2.2.8 Failure Mode  Severe concrete spalling was observed near the end of the test, with no visible damage in the elastic range.  Rebar slip caused by tension was not very obvious during the test due to small displacements.  The main failure mode of the specimen was concrete crushing (mainly on the right side), before the edge longitudinal bars buckled between the first and second ties, followed by opening up of the ties between the second and fourth ties, then buckling of the interior longitudinal bars and finally the splitting across the specimen. There were not a lot of cracking on the surface of the specimen compared to the other specimens. The following page shows the failure plane of the specimen.  Heights and distances were measured approximately from the edge rebars.   278     279       APPENDIX B COLUMN LOAD TAKEDOWN    280  B1 Maximum Span Length Equations Maximum span lengths allowed for different slab thicknesses were calculated according to the following equations from the Canadian Concrete Code CAN/CSA A23.3. For interior spans, [CSA A23.3Cl.13.2.3]        For exterior spans, [CSA A23.3Cl.13.2.4]       where hs = minimum slab thickness  ln = the longer clear span  fy = specified yield strength of reinforcing steel (assumed to be 400MPa)  B2 Live Load Reduction Equations Live load reductions were applied in the calculation of the gravitation load in high- rises acting on the columns at each storey according to the National Building Code of Canada (NBCC 05).  When the tributary area of a floor or roof or their combination is greater than 80m 2  designed for an assembly occupancy live load of 4.8kPa or more, the factor is      [NBCC05 Cl.4.1.5.9(2)] where  A = tributary area (m 2 ) When the tributary area of a floor or roof or their combination is greater than 20m 2  designed for an assembly occupancy live load of 4.8kPa or more, the factor is       [NBCC05 Cl.4.1.5.9(3)] 281  where  B = tributary area (m 2 )  B3 Column Load Resistance Equations Columns presented in the column takedown spreadsheets in Section B6.0 are designed according to CAN/CSA A23.3. For tied columns:                 [CSA A23.3 Cl.10.10.4]   where Pr,max = maximum factored axial load resistance a1 = ratio of average stress in rectangular compression block to the specified concrete strength = 0.85-0.0015f’c ≤ 0.67 [Cl.10.1.7]  ϕc = resistance factor for concrete =  f’c = specified compressive strength of concrete  Ag = gross sectional area  Ast = reinforcing steel sectional area  At = transverse torsion reinforcement area  Ap = area of prestressing tendons  ϕs = resistance factor for non-prestressed reinforcing bars  fy = specified yield strength of non-prestressed reinforcement  ϕa = resistance factor for structural steel  Fy = specified yield strength of structural steel section  fpr = stress in prestressing tendons at factored resistance 282  B4 Tributary Areas for 5, 10, 20, 30, 40 & 50-storey Columns The following tables list the tributary areas for interior and exterior columns with different width-to-length ratios for buildings with different storey heights and slab thicknesses. Table B4.1 (a) – Tributary Areas for Square Columns for a 5-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 300x300 16.89 300x300 2.35 152.4 300x300 23.74 300x300 5.65 203.2 350x350 41.55 300x300 9.43 254 450x450 65.12 300x300 14.16  Table B4.1 (b) – Tributary Areas for Square Columns for a 10-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 300x300 16.89 300x300 2.35 152.4 350x350 24.23 300x300 5.65 203.2 450x450 42.85 300x300 9.43 254 650x650 68.39 300x300 14.16  Table B4.1 (c) – Tributary Areas for Square Columns for a 20-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 400x400 17.72 300x300 2.35 152.4 500x500 25.73 300x300 5.65 203.2 700x700 46.19 350x350 9.74 254 900x900 72.59 450x450 15.32  Table B4.1 (d) – Tributary Areas for Square Columns for a 30-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 450x450 18.15 300x300 2.35 152.4 600x600 26.75 300x300 5.65 203.2 850x850 48.25 400x400 10.06 254 --- --- 550x550 16.11  283  Table B4.1 (e) – Tributary Areas for Square Columns for a 40-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 550x550 19.01 300x300 2.35 152.4 700x700 27.79 350x350 5.90 203.2 --- --- 500x500 10.70 254 --- --- 650x650 16.92  Table B4.1 (f) – Tributary Areas for Square Columns for a 50-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 650x650 19.89 300x300 2.35 152.4 800x800 28.86 400x400 6.14 203.2 --- --- 600x600 11.36 254 --- --- 800x800 18.18  Table B4.2 (a) – Tributary Areas for 1:2 Elongated Columns for a 5-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x500 17.50 250x500 2.57 152.4 250x500 24.46 250x500 6.00 203.2 250x500 41.86 250x500 9.88 254 325x650 65.71 250x500 14.72  Table B4.2 (b) – Tributary Areas for 1:2 Elongated Columns for a 10-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x500 17.50 250x500 2.57 152.4 250x500 24.46 250x500 6.00 203.2 325x650 43.32 250x500 9.88 254 450x900 68.76 250x500 14.72  Table B4.2 (c) – Tributary Areas for 1:2 Elongated Columns for a 20-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 275x550 17.81 250x500 2.57 152.4 325x650 25.57 250x500 6.00 203.2 500x1000 46.81 250x500 9.88 254 --- --- 300x600 15.29 284  Table B4.2 (d) – Tributary Areas for 1:2 Elongated Columns for a 30-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 325x650 18.44 250x500 2.57 152.4 435x850 27.09 250x500 6.00 203.2 600x1200 48.85 300x600 10.35 254 --- --- 375x750 16.17  Table B4.2 (e) – Tributary Areas for 1:2 Elongated Columns for a 40-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 400x800 19.41 250x500 2.57 152.4 500x1000 28.26 250x500 6.00 203.2 --- --- 350x700 10.83 254 --- --- 475x950 17.38  Table B4.2 (f) – Tributary Areas for 1:2 Elongated Columns for a 50-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 450x900 20.06 250x500 2.57 152.4 575x1150 29.45 275x550 6.18 203.2 --- --- 400x800 11.32 254 --- --- 525x1050 18.00  Table B4.3 (a) – Tributary Areas for 1:4 Elongated Columns for a 5-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x1000 19.53 250x1000 3.31 152.4 250x1000 26.87 250x1000 7.17 203.2 250x1000 45.03 250x1000 11.39 254 250x1000 67.84 250x1000 16.58  Table B4.3 (b) – Tributary Areas for 1:4 Elongated Columns for a 10-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x1000 19.53 250x1000 3.31 152.4 250x1000 26.87 250x1000 7.17 203.2 275x1100 45.85 250x1000 11.39 254 325x1300 70.87 250x1000 16.58 285  Table B4.3 (c) – Tributary Areas for 1:4 Elongated Columns for a 20-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x1000 19.53 250x1000 3.31 152.4 250x1000 26.87 250x1000 7.17 203.2 350x1400 48.32 250x1000 11.39 254 --- --- 250x1000 16.58  Table B4.3 (d) – Tributary Areas for 1:4 Elongated Columns for a 30-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x1000 19.53 250x1000 3.31 152.4 300x1200 28.12 250x1000 7.17 203.2 450x1800 51.69 250x1000 11.39 254 --- --- 300x1200 17.55  Table B4.3 (e) – Tributary Areas for 1:4 Elongated Columns for a 40-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 275x1100 20.06 250x1000 3.31 152.4 350x1400 29.39 250x1000 7.17 203.2 --- --- 250x1000 11.39 254 --- --- 325x1300 18.05  Table B4.3 (f) – Tributary Areas for 1:4 Elongated Columns for a 50-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 325x1300 21.13 250x1000 3.31 152.4 425x1700 31.34 250x1000 7.17 203.2 --- --- 275x1100 11.79 254 --- --- 375x1500 19.05  Table B4.4 (a) – Tributary Areas for 1:8 Elongated Columns for a 5-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x2000 23.59 250x2000 4.79 152.4 250x2000 31.69 250x2000 9.49 203.2 250x2000 51.38 250x2000 14.41 254 250x2000 75.71 250x2000 20.29 286  Table B4.4 (b) – Tributary Areas for 1:8 Elongated Columns for a 10-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x2000 23.59 250x2000 4.79 152.4 250x2000 31.69 250x2000 9.49 203.2 250x2000 51.38 250x2000 14.41 254 250x2000 75.71 250x2000 20.29  Table B4.4 (c) – Tributary Areas for 1:8 Elongated Columns for a 20-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x2000 23.59 250x2000 4.79 152.4 250x2000 31.69 250x2000 9.49 203.2 250x2000 51.38 250x2000 14.41 254 --- --- 250x2000 20.29  Table B4.4 (d) – Tributary Areas for 1:8 Elongated Columns for a 30-storey Building Slab Thk [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x2000 23.59 250x2000 4.79 152.4 250x2000 31.69 250x2000 9.49 203.2 325x2600 55.84 250x2000 14.41 254 --- --- 250x2000 20.29  Table B4.4 (e) – Tributary Areas for 1:8 Elongated Columns for a 40-storey Building Slab Thk  [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x2000 23.59 250x2000 4.79 152.4 275x2200 32.82 250x2000 9.49 203.2 --- --- 250x2000 14.41 254 --- --- 275x2200 21.17  Table B4.4 (f) – Tributary Areas for 1:8 Elongated Columns for a 50-storey Building Slab Thk  [mm] Int. Col. Size [mmxmm] Int. Tributary Area [mm 2 ] Ext. Col. Size [mmxmm] Ext. Tributary Area [mm 2 ] 127 250x2000 23.59 250x2000 4.79 152.4 325x2600 35.12 250x2000 9.49 203.2 --- --- 250x2000 14.41 254 --- --- 300x2400 22.07 287  B5 Gravitational Loads & Relation with Seismic Drift The following tables shows the unite dead load per area for different slab thickness, and the dead and live loads from column takedown.  The live load reduction factor had been applied in the calculations.  The ratios of D/(D+L) and Ps/Pf are also summarized below. Table B5.1 – Dead Load for Varying Slab Thicknesses Slab Thickness [mm] DL due to Slab Weight [kPa] DL due to Slab Weight & Partition [kPa] 127 3.048 3.548 152.4 3.6576 4.076 203.2 4.8768 5.377 254 6.096 6.596  Table B5.2 (a) – Loads for Square Interior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 327.92 655.84 1458.61 2313.04 3457.53 4855.08 LL [kN] 150.95 242.64 422.88 594.83 783.98 984.08 D/(D+L) 0.685 0.730 0.775 0.795 0.815 0.831 Ps=1.0D+0.5L 403.39 777.16 1670.05 2610.46 3849.52 5347.12 Pf=1.25D+1.5L 636.32 1183.76 2457.58 3783.56 5497.89 7544.97 Ps/Pf 0.634 0.657 0.680 0.690 0.700 0.709  Table B5.2 (b) – Loads for 1:2 Elongated Interior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 349.67 699.33 1453.76 2360.87 3558.03 4830.84 LL [kN] 155.25 249.67 424.60 603.08 798.26 991.61 D/(D+L) 0.693 0.737 0.774 0.797 0.817 0.830 Ps=1.0D+0.5L 427.29 824.17 1666.06 2662.41 3957.16 5326.64 Pf=1.25D+1.5L 669.96 1248.67 2454.11 3855.71 5644.93 7525.97 Ps/Pf 0.638 0.660 0.679 0.691 0.701 0.708  Table B5.2 (c) – Loads for 1:4 Elongated Interior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 424.92 849.83 1699.67 2549.50 3606.23 5074.75 LL [kN] 169.51 273.02 458.74 633.42 821.48 1237.92 D/(D+L) 0.715 0.757 0.787 0.801 0.814 0.830 Ps=1.0D+0.5L 509.67 986.34 1929.04 2866.22 4016.97 5593.71 Pf=1.25D+1.5L 785.42 1471.82 2812.70 4137.01 5740.00 7900.32 Ps/Pf 0.649 0.670 0.686 0.693 0.700 0.708 288  Table B5.2 (d) – Loads for 1:8 Elongated Interior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 575.42 1150.84 2301.69 3452.53 4603.37 5854.22 LL [kN] 197.53 318.94 538.36 745.65 946.86 1144.25 D/(D+L) 0.744 0.783 0.810 0.822 0.829 0.834 Ps=1.0D+0.5L 674.19 1310.31 2570.87 3825.35 5076.80 6326.24 Pf=1.25D+1.5L 1015.57 1916.96 3684.65 5434.14 7174.51 8909.15 Ps/Pf 0.664 0.684 0.698 0.704 0.708 0.710  Table B5.3 (a) – Loads for Square Exterior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 69.89 139.78 279.56 419.33 559.11 698.89 LL [kN] 28.16 55.37 87.91 116.62 143.42 169.01 D/(D+L) 0.713 0.716 0.761 0.782 0.796 0.805 Ps=1.0D+0.5L 83.97 167.46 323.51 477.65 630.82 783.39 Pf=1.25D+1.5L 129.61 257.78 481.31 699.10 914.02 1127.12 Ps/Pf 0.648 0.650 0.672 0.683 0.690 0.695  Table B5.3 (b) – Loads for 1:2 Elongated Exterior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 84.78 169.55 339.10 508.65 678.20 847.75 LL [kN] 30.80 58.90 93.74 124.58 153.41 180.98 D/(D+L) 0.733 0.742 0.783 0.803 0.816 0.824 Ps=1.0D+0.5L 100.18 199.00 385.97 570.94 754.91 938.24 Pf=1.25D+1.5L 152.17 300.30 564.49 822.68 1077.87 1331.16 Ps/Pf 0.658 0.663 0.684 0.694 0.700 0.705  Table B5.3 (c) – Loads for 1:4 Elongated Exterior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 137.16 274.32 548.64 822.96 1097.29 1371.61 LL [kN] 39.69 70.37 112.75 150.59 186.16 220.29 D/(D+L) 0.776 0.796 0.830 0.845 0.855 0.862 Ps=1.0D+0.5L 157.01 309.51 605.02 898.26 1190.37 1481.75 Pf=1.25D+1.5L 230.99 448.45 854.93 1254.59 1650.84 2044.95 Ps/Pf 0.680 0.690 0.708 0.716 0.721 0.725   289  Table B5.3 (d) – Loads for 1:8 Elongated Exterior Columns with 5”(127mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 241.93 483.86 967.73 1451.59 1935.45 2419.31 LL [kN] 57.48 91.86 148.69 200.06 248.68 295.58 D/(D+L) 0.808 0.840 0.867 0.879 0.886 0.891 Ps=1.0D+0.5L 270.67 529.79 1042.07 1551.62 2059.79 2567.11 Pf=1.25D+1.5L 388.63 742.62 1432.70 2114.57 2792.34 3467.52 Ps/Pf 0.696 0.713 0.727 0.734 0.738 0.740  Table B5.4 (a) – Loads for Square Interior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 372.24 1063.62 2407.99 3942.42 5750.15 7870.92 LL [kN] 150.95 326.07 579.77 831.99 1094.52 1369.91 D/(D+L) 0.711 0.765 0.806 0.826 0.840 0.852 Ps=1.0D+0.5L 447.71 1226.65 2697.87 4358.42 6297.41 8555.87 Pf=1.25D+1.5L 691.72 1818.62 3879.63 6176.01 8829.47 11893.51 Ps/Pf 0.647 0.674 0.695 0.706 0.713 0.719  Table B5.4 (b) – Loads for 1:2 Elongated Interior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 537.30 1074.59 2347.33 3986.84 5851.19 8057.78 LL [kN] 203.45 328.65 576.81 841.34 1110.83 1395.13 D/(D+L) 0.725 0.766 0.803 0.826 0.840 0.852 Ps=1.0D+0.5L 639.02 1238.92 2635.73 4407.51 6406.61 8755.35 Pf=1.25D+1.5L 976.79 1836.21 3799.37 6245.56 8980.24 12164.92 Ps/Pf 0.654 0.675 0.694 0.706 0.713 0.720  Table B5.4 (c) – Loads for 1:4 Elongated Interior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 625.29 1250.58 2501.17 4110.14 6011.05 8633.38 LL [kN] 219.75 355.42 601.79 869.22 1150.32 1475.36 D/(D+L) 0.740 0.779 0.806 0.825 0.839 0.854 Ps=1.0D+0.5L 735.17 1428.29 2802.06 4544.75 6586.20 9371.07 Pf=1.25D+1.5L 1111.24 2096.36 4029.15 6441.50 9239.28 13004.78 Ps/Pf 0.662 0.681 0.695 0.706 0.713 0.721   290  Table B5.4 (d) – Loads for 1:8 Elongated Interior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 801.28 1602.56 3205.13 4807.69 6856.23 9784.59 LL [kN] 251.91 408.29 693.94 965.51 1269.29 1635.05 D/(D+L) 0.761 0.797 0.822 0.833 0.844 0.857 Ps=1.0D+0.5L 927.24 1806.71 3552.10 5290.45 7490.87 10602.11 Pf=1.25D+1.5L 1379.47 2615.64 5047.31 7457.88 10474.21 14683.31 Ps/Pf 0.672 0.691 0.704 0.709 0.715 0.722  Table B5.5 (a) – Loads for Square Exterior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 143.23 286.45 572.90 859.35 1265.81 1748.83 LL [kN] 65.59 103.81 168.81 277.86 293.61 361.70 D/(D+L) 0.686 0.734 0.772 0.790 0.812 0.829 Ps=1.0D+0.5L 176.02 338.36 657.30 973.28 1412.61 1929.67 Pf=1.25D+1.5L 277.42 513.78 969.34 1415.98 2022.67 2728.58 Ps/Pf 0.634 0.659 0.678 0.687 0.698 0.707  Table B5.5 (b) – Loads for 1:2 Elongated Exterior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 161.17 322.34 644.69 967.03 1289.37 1730.43 LL [kN] 68.50 108.51 176.73 238.84 297.87 363.78 D/(D+L) 0.702 0.748 0.785 0.802 0.812 0.826 Ps=1.0D+0.5L 195.42 376.60 733.05 1086.45 1438.31 1912.32 Pf=1.25D+1.5L 304.21 565.70 1070.96 1567.04 2058.52 2708.71 Ps/Pf 0.642 0.666 0.684 0.693 0.699 0.706  Table B5.5 (c) – Loads for 1:4 Elongated Exterior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 223.75 447.51 895.01 1342.52 1790.02 2237.53 LL [kN] 78.06 123.97 202.89 275.12 344.00 410.78 D/(D+L) 0.741 0.783 0.815 0.830 0.839 0.845 Ps=1.0D+0.5L 262.78 509.49 996.45 1480.08 1962.02 2442.92 Pf=1.25D+1.5L 396.78 745.33 1423.09 2090.82 2753.53 3413.08 Ps/Pf 0.662 0.684 0.700 0.708 0.713 0.716   291  Table B5.5 (d) – Loads for 1:8 Elongated Exterior Columns with 6”(152.4mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 348.92 607.83 1395.66 2093.49 2791.32 3489.15 LL [kN] 96.42 153.75 253.56 345.67 433.93 519.76 D/(D+L) 0.783 0.819 0.846 0.858 0.865 0.870 Ps=1.0D+0.5L 397.13 774.71 1522.44 2266.33 3008.29 3749.03 Pf=1.25D+1.5L 580.78 1102.91 2124.92 3135.38 4140.05 5141.09 Ps/Pf 0.684 0.702 0.716 0.723 0.727 0.729  Table B5.6 (a) – Loads for Square Interior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 1154.43 2427.49 5564.16 9103.91 --- --- LL [kN] 316.25 528.05 965.23 1404.22 --- --- D/(D+L) 0.785 0.821 0.852 0.866 --- --- Ps=1.0D+0.5L 1312.56 2691.51 6046.78 9806.02 --- --- Pf=1.25D+1.5L 1917.41 3826.44 8403.05 13486.22 --- --- Ps/Pf 0.685 0.703 0.720 0.727 --- ---  Table B5.6 (b) – Loads for 1:2 Elongated Interior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 1163.46 2457.87 5642.98 9197.27 --- --- LL [kN] 318.23 532.99 976.68 1420.12 --- --- D/(D+L) 0.785 0.822 0.852 0.866 --- --- Ps=1.0D+0.5L 1322.57 2724.37 6131.32 9907.33 --- --- Pf=1.25D+1.5L 1931.66 3871.83 8518.75 13626.77 --- --- Ps/Pf 0.685 0.704 0.720 0.727 --- ---  Table B5.6 (c) – Loads for 1:4 Elongated Interior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 1324.76 2649.51 5793.61 9818.88 --- --- LL [kN] 343.81 559.72 1004.62 1494.16 --- --- D/(D+L) 0.794 0.826 0.852 0.868 --- --- Ps=1.0D+0.5L 1496.66 2929.38 6295.92 10565.96 --- --- Pf=1.25D+1.5L 2171.66 4151.48 8748.94 14514.83 --- --- Ps/Pf 0.689 0.706 0.720 0.728 --- ---   292  Table B5.6 (d) – Loads for 1:8 Elongated Interior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 1533.66 3067.33 6134.66 10552.28 --- --- LL [kN] 378.98 617.79 1060.89 1602.22 --- --- D/(D+L) 0.802 0.832 0.853 0.868 --- --- Ps=1.0D+0.5L 1723.15 3376.22 6665.10 11353.39 --- --- Pf=1.25D+1.5L 2485.55 4760.84 9259.65 15593.68 --- --- Ps/Pf 0.693 0.709 0.720 0.728 --- ---  Table B5.7 (a) – Loads for Square Exterior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 280.98 561.97 1196.85 1914.60 --- --- LL [kN] 95.94 152.97 258.84 362.38 --- --- D/(D+L) 0.745 0.786 0.822 0.841 --- --- Ps=1.0D+0.5L 328.95 638.45 1326.27 2095.79 --- --- Pf=1.25D+1.5L 495.14 931.91 1884.32 2936.82 --- --- Ps/Pf 0.664 0.685 0.704 0.714 --- ---  Table B5.7 (b) – Loads for 1:2 Elongated Exterior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 303.77 607.53 1215.07 1999.09 --- --- LL [kN] 99.41 158.60 261.85 371.18 --- --- D/(D+L) 0.753 0.793 0.823 0.843 --- --- Ps=1.0D+0.5L 353.47 686.83 1345.99 2184.69 --- --- Pf=1.25D+1.5L 528.82 997.32 1911.60 3055.64 --- --- Ps/Pf 0.668 0.689 0.704 0.715 --- ---  Table B5.7 (c) – Loads for 1:4 Elongated Exterior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 384.76 769.52 1539.04 2308.55 --- --- LL [kN] 110.87 177.24 293.72 401.77 --- --- D/(D+L) 0.776 0.813 0.840 0.852 --- --- Ps=1.0D+0.5L 440.19 858.14 1685.90 2509.44 --- --- Pf=1.25D+1.5L 647.25 1227.76 2364.38 3488.35 --- --- Ps/Pf 0.680 0.699 0.713 0.719 --- ---   293  Table B5.7 (d) – Loads for 1:8 Elongated Exterior Columns with 8”(203.2mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 544.46 1088.92 2177.83 3266.75 --- --- LL [kN] 133.15 213.56 356.10 489.14 --- --- D/(D+L) 0.804 0.836 0.859 0.870 --- --- Ps=1.0D+0.5L 611.03 1195.70 2355.88 3511.32 --- --- Pf=1.25D+1.5L 880.30 1681.49 3256.44 4817.15 --- --- Ps/Pf 0.694 0.711 0.723 0.729 --- ---  Table B5.8 (a) – Loads for Square Interior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 2208.30 4763.58 10543.85 --- --- --- LL [kN] 465.12 793.73 1446.28 --- --- --- D/(D+L) 0.826 0.857 0.879 --- --- --- Ps=1.0D+0.5L 2440.86 5160.45 11266.99 --- --- --- Pf=1.25D+1.5L 3458.06 7145.07 15349.23 --- --- --- Ps/Pf 0.706 0.722 0.734 --- --- ---  Table B5.8 (b) – Loads for 1:2 Elongated Interior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 2230.05 4777.10 --- --- --- --- LL [kN] 468.73 797.45 --- --- --- --- D/(D+L) 0.826 0.857 --- --- --- --- Ps=1.0D+0.5L 2464.41 5175.83 --- --- --- --- Pf=1.25D+1.5L 3490.65 7167.56 --- --- --- --- Ps/Pf 0.706 0.722 --- --- --- ---  Table B5.8 (c) – Loads for 1:4 Elongated Interior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 2312.01 4926.93 --- --- --- --- LL [kN] 481.96 819.07 --- --- --- --- D/(D+L) 0.828 0.857 --- --- --- --- Ps=1.0D+0.5L 2552.99 5336.46 --- --- --- --- Pf=1.25D+1.5L 3612.95 7387.26 --- --- --- --- Ps/Pf 0.707 0.722 --- --- --- ---   294  Table B5.8 (d) – Loads for 1:8 Elongated Interior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 2646.24 5292.47 --- --- --- --- LL [kN] 530.49 868.42 --- --- --- --- D/(D+L) 0.833 0.859 --- --- --- --- Ps=1.0D+0.5L 2911.48 5726.68 --- --- --- --- Pf=1.25D+1.5L 4103.53 7918.22 --- --- --- --- Ps/Pf 0.710 0.723 --- --- --- ---  Table B5.9 (a) – Loads for Square Exterior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 494.01 988.02 2262.35 --- --- --- LL [kN] 131.34 210.60 374.44 --- --- --- D/(D+L) 0.790 0.824 0.858 --- --- --- Ps=1.0D+0.5L 559.68 1093.32 2449.57 --- --- --- Pf=1.25D+1.5L 814.52 1550.92 3389.59 --- --- --- Ps/Pf 0.687 0.705 0.723 --- --- ---  Table B5.9 (b) – Loads for 1:2 Elongated Exterior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 522.75 1045.50 --- --- --- --- LL [kN] 135.36 217.17 --- --- --- --- D/(D+L) 0.794 0.828 --- --- --- --- Ps=1.0D+0.5L 590.43 1154.09 --- --- --- --- Pf=1.25D+1.5L 856.48 1632.63 --- --- --- --- Ps/Pf 0.689 0.707 --- --- --- ---  Table B5.9 (c) – Loads for 1:4 Elongated Exterior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 625.13 1250.26 --- --- --- --- LL [kN] 148.69 238.95 --- --- --- --- D/(D+L) 0.808 0.840 --- --- --- --- Ps=1.0D+0.5L 699.48 1369.74 --- --- --- --- Pf=1.25D+1.5L 1004.45 1921.25 --- --- --- --- Ps/Pf 0.696 0.713 --- --- --- ---   295  Table B5.9 (d) – Loads for 1:8 Elongated Exterior Columns with 10”(254mm) Slab Thickness # of storey 5 10 20 30 40 50 DL [kN] 826.08 1652.16 --- --- --- --- LL [kN] 174.81 281.69 --- --- --- --- D/(D+L) 0.825 0.854 --- --- --- --- Ps=1.0D+0.5L 913.49 1793.01 --- --- --- --- Pf=1.25D+1.5L 1294.81 2487.74 --- --- --- --- Ps/Pf 0.705 0.721 --- --- --- ---  B6 Column Load Takedown Spreadsheets The following appendix shows the summaries for column load takedown for both interior and exterior columns using the CSA and ACI codes.  One sample of detailed dead and live load calculations on a 50-storey building are included in each case.  The columns for other storeys and slab thicknesses are calculated in a similar way as the sample spreadsheets. However, the columns were designed according to the Canadian code and were not redesigned for the ACI spreadsheets.  296       APPENDIX B6.1 COLUMN LOAD TAKEDOWN INTERIOR COLUMNS (CSA)   COLUMN LOAD TAKEDOWN - Interior Columns (CSA) f'c[MPa] 30 Slab TH Ext Span Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm mm mm 5 STOREYS 127 2464 300 300 0.685 403.39 0.634 0.149 250 500 0.693 427.29 0.638 0.114 152.4 4156 300 300 0.711 447.71 0.647 0.166 250 500 0.725 639.02 0.654 0.170 203.2 5542 350 350 0.785 1312.56 0.685 0.357 250 500 0.785 1322.57 0.685 0.353 254 6927 450 450 0.826 2440.86 0.706 0.402 325 650 0.826 2464.41 0.706 0.389 10 storey 127 2464 300 300 0.730 777.16 0.657 0.288 250 500 0.737 824.17 0.660 0.220 152.4 4156 350 350 0.765 1226.65 0.674 0.334 250 500 0.766 1238.92 0.675 0.330 203.2 5542 450 450 0.821 2691.51 0.703 0.443 325 650 0.822 2724.37 0.704 0.430 254 6927 650 650 0.857 5160.45 0.722 0.407 450 900 0.857 5175.83 0.722 0.426 20 storey 127 2464 400 400 0.775 1670.05 0.680 0.348 275 550 0.774 1666.06 0.679 0.367 152.4 4156 500 500 0.806 2697.87 0.695 0.360 325 650 0.803 2635.73 0.694 0.416 203.2 5542 700 700 0.852 6046.78 0.720 0.411 500 1000 0.852 6131.32 0.720 0.409 254 6927 900 900 0.879 11266.99 0.734 0.464 650 1300 0.880 11474.80 0.734 0.453 30 storey 127 2464 450 450 0.795 2610.46 0.690 0.430 325 650 0.797 2662.41 0.691 0.420 152.4 4156 600 600 0.826 4358.42 0.706 0.404 425 850 0.826 4407.51 0.706 0.407 203.2 5542 850 850 0.866 9806.02 0.727 0.452 600 1200 0.866 9907.33 0.727 0.459 254 6927 1175 1175 0.892 18858.91 0.741 0.455 825 1650 0.892 19020.77 0.741 0.466 40 storey 127 2464 550 550 0.815 3849.52 0.700 0.424 400 800 0.817 3957.16 0.701 0.412 152.4 4156 700 700 0.840 6297.41 0.713 0.428 500 1000 0.840 6406.61 0.713 0.427 203.2 5542 1025 1025 0.878 14407.91 0.733 0.457 725 1450 0.877 14586.34 0.733 0.463 254 6927 1400 1400 0.900 27600.97 0.745 0.469 1000 2000 0.900 28135.05 0.745 0.469 50 storey 127 2464 650 650 0.831 5347.12 0.709 0.422 450 900 0.830 5326.64 0.708 0.438 152.4 4156 800 800 0.852 8555.87 0.719 0.446 575 1150 0.852 8755.35 0.720 0.441 203.2 5542 1200 1200 0.887 19894.83 0.738 0.461 850 1700 0.887 20176.23 0.738 0.465 254 6927 1650 1650 0.907 38334.97 0.749 0.469 1175 2350 0.907 39064.44 0.749 0.472 Square 1 to 2 COLUMN LOAD TAKEDOWN - Interior Columns (CSA) f'c[MPa] 30 Slab TH Ext Span mm mm 5 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 10 storey 127 2464 152.4 4156 203.2 5542 254 6927 20 storey 127 2464 152.4 4156 203.2 5542 254 6927 30 storey 127 2464 152.4 4156 203.2 5542 254 6927 40 storey 127 2464 152.4 4156 203.2 5542 254 6927 50 storey 127 2464 152.4 4156 203.2 5542 254 6927 Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm 250 1000 0.715 509.67 0.649 0.068 250 2000 0.744 674.19 0.664 0.045 250 1000 0.740 735.17 0.662 0.098 250 2000 0.761 927.24 0.672 0.062 250 1000 0.794 1496.66 0.689 0.200 250 2000 0.802 1723.15 0.693 0.115 250 1000 0.828 2552.99 0.707 0.340 250 2000 0.833 2911.48 0.710 0.194 250 1000 0.757 986.34 0.670 0.132 250 2000 0.783 1310.31 0.684 0.087 250 1000 0.779 1428.29 0.681 0.190 250 2000 0.797 1806.71 0.691 0.120 275 1100 0.826 2929.38 0.706 0.323 250 2000 0.832 3376.22 0.709 0.225 325 1300 0.857 5336.46 0.722 0.421 250 2000 0.859 5726.68 0.723 0.382 250 1000 0.787 1929.04 0.686 0.257 250 2000 0.810 2570.87 0.698 0.171 250 1000 0.806 2802.06 0.695 0.374 250 2000 0.822 3552.10 0.704 0.237 350 1400 0.852 6295.92 0.720 0.428 250 2000 0.853 6665.10 0.720 0.444 475 1900 0.880 12007.91 0.735 0.444 350 2800 0.881 12943.36 0.735 0.440 250 1000 0.801 2866.22 0.693 0.382 250 2000 0.822 3825.35 0.704 0.255 300 1200 0.825 4544.75 0.706 0.421 250 2000 0.833 5290.45 0.709 0.353 450 1800 0.868 10565.96 0.728 0.435 325 2600 0.868 11353.39 0.728 0.448 600 2400 0.892 20021.18 0.741 0.463 450 3600 0.893 22066.74 0.741 0.454 275 1100 0.814 4016.97 0.700 0.443 250 2000 0.829 5076.80 0.708 0.338 350 1400 0.839 6586.20 0.713 0.448 275 2200 0.844 7490.87 0.715 0.413 550 2200 0.880 15823.17 0.734 0.436 400 3200 0.880 17211.50 0.734 0.448 725 2900 0.900 29743.87 0.745 0.472 550 4400 0.902 33421.53 0.746 0.460 325 1300 0.830 5593.71 0.708 0.441 250 2000 0.834 6326.34 0.710 0.422 425 1700 0.854 9371.07 0.721 0.432 325 2600 0.857 10602.11 0.722 0.418 625 2500 0.887 21582.92 0.738 0.460 475 3800 0.889 24420.76 0.739 0.451 875 3500 0.908 42336.72 0.750 0.461 650 5200 0.909 47329.45 0.750 0.467 1 to 4 1 to 8 COLUMN NO: Square Column for 5in(127mm) slab (Interior Span) 50 Storeys [CSA] Note: For the reduction factor (RF) column, enter: 0 - no reduction factor is needed - area used for assembly occupancies designed for a live load of less than 4.8kPa and roofs designed for the minimum loading specified in Table 4.1.5.3. 1 - where a structural member supports a tributary area of a floor or roof, or a combination thereof, that is greater than 80m 2 and either used for assembly occupancies designed for a live load of 4.8kPa or more, or used for storage, manufacturing, retail stores, garages or as a footbridge, the specified live load due to use and occupancy is the load specified in Art. 4.1.5.3. 2 - where a structural member supports a tributary area of a floor or roof, or a combination thereof, that is greater than 20m 2 and used for any use or occupancy other than those indicated above, the specified live load due to use and occupancy is the load specified in Art. 4.1.5.3. = input Level Area Unfact. DL Unfact. LL Extra DL RF Accu. Unfact. DL Accu. Unfact. LL Fact. Load [m 2 ] [kN/m 2 ] [kN/m 2 ] [kN] [kN] [kN] [kN] Roof 19.8916 3.548 2.4 26.53 0 97.10 47.74 192.99 50 19.8916 3.548 2.4 26.53 2 194.20 95.48 385.97 49 19.8916 3.548 2.4 26.53 2 291.30 123.77 549.79 48 19.8916 3.548 2.4 26.53 2 388.41 148.74 708.63 47 19.8916 3.548 2.4 26.53 2 485.51 172.05 864.95 46 19.8916 3.548 2.4 26.53 2 582.61 194.28 1019.68 45 19.8916 3.548 2.4 26.53 2 679.71 215.75 1173.27 44 19.8916 3.548 2.4 26.53 2 776.81 236.65 1325.99 43 19.8916 3.548 2.4 26.53 2 873.91 257.09 1478.03 42 19.8916 3.548 2.4 26.53 2 971.02 277.16 1629.52 41 19.8916 3.548 2.4 26.53 2 1068.12 296.92 1780.53 40 19.8916 3.548 2.4 26.53 2 1165.22 316.42 1931.15 39 19.8916 3.548 2.4 26.53 2 1262.32 335.68 2081.42 38 19.8916 3.548 2.4 26.53 2 1359.42 354.74 2231.39 37 19.8916 3.548 2.4 26.53 2 1456.52 373.63 2381.09 36 19.8916 3.548 2.4 26.53 2 1553.63 392.35 2530.56 35 19.8916 3.548 2.4 26.53 2 1650.73 410.93 2679.80 34 19.8916 3.548 2.4 26.53 2 1747.83 429.37 2828.85 33 19.8916 3.548 2.4 26.53 2 1844.93 447.70 2977.72 32 19.8916 3.548 2.4 26.53 2 1942.03 465.92 3126.42 31 19.8916 3.548 2.4 26.53 2 2039.13 484.03 3274.97 30 19.8916 3.548 2.4 26.53 2 2136.24 502.06 3423.38 29 19.8916 3.548 2.4 26.53 2 2233.34 519.99 3571.66 28 19.8916 3.548 2.4 26.53 2 2330.44 537.85 3719.82 27 19.8916 3.548 2.4 26.53 2 2427.54 555.63 3867.86 26 19.8916 3.548 2.4 26.53 2 2524.64 573.33 4015.80 25 19.8916 3.548 2.4 26.53 2 2621.74 590.97 4163.64 24 19.8916 3.548 2.4 26.53 2 2718.85 608.55 4311.38 23 19.8916 3.548 2.4 26.53 2 2815.95 626.07 4459.03 22 19.8916 3.548 2.4 26.53 2 2913.05 643.53 4606.60 21 19.8916 3.548 2.4 26.53 2 3010.15 660.93 4754.09 20 19.8916 3.548 2.4 26.53 2 3107.25 678.29 4901.50 19 19.8916 3.548 2.4 26.53 2 3204.35 695.60 5048.84 18 19.8916 3.548 2.4 26.53 2 3301.46 712.86 5196.11 17 19.8916 3.548 2.4 26.53 2 3398.56 730.07 5343.31 16 19.8916 3.548 2.4 26.53 2 3495.66 747.25 5490.45 15 19.8916 3.548 2.4 26.53 2 3592.76 764.38 5637.53 14 19.8916 3.548 2.4 26.53 2 3689.86 781.48 5784.55 13 19.8916 3.548 2.4 26.53 2 3786.96 798.54 5931.51 12 19.8916 3.548 2.4 26.53 2 3884.07 815.56 6078.42 11 19.8916 3.548 2.4 26.53 2 3981.17 832.55 6225.28 10 19.8916 3.548 2.4 26.53 2 4078.27 849.50 6372.09 9 19.8916 3.548 2.4 26.53 2 4175.37 866.42 6518.85 8 19.8916 3.548 2.4 26.53 2 4272.47 883.32 6665.56 7 19.8916 3.548 2.4 26.53 2 4369.57 900.18 6812.23 6 19.8916 3.548 2.4 26.53 2 4466.68 917.01 6958.86 5 19.8916 3.548 2.4 26.53 2 4563.78 933.82 7105.45 4 19.8916 3.548 2.4 26.53 2 4660.88 950.60 7251.99 3 19.8916 3.548 2.4 26.53 2 4757.98 967.35 7398.50 2 19.8916 3.548 2.4 26.53 2 4855.08 984.08 7544.97 GND Resistance 8022 301       APPENDIX B6.2 COLUMN LOAD TAKEDOWN EXTERIOR COLUMNS (CSA)   COLUMN LOAD TAKEDOWN - Exterior Columns (CSA) f'c [MPa] 30 Slab TH Ext Span Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm mm mm 5 STOREYS 127 2464 300 300 0.7128 83.97 0.648 0.0311 250 500 0.7335 100.18 0.658 0.0267 152.4 4156 300 300 0.6859 176.02 0.634 0.0652 250 500 0.7017 195.42 0.642 0.0521 203.2 5542 300 300 0.7455 328.95 0.664 0.1218 250 500 0.7534 353.47 0.668 0.0943 254 6927 300 300 0.7900 559.68 0.687 0.2073 250 500 0.7943 590.43 0.689 0.1574 10 STOREYS 127 2464 300 300 0.7289 167.46 0.650 0.0620 250 500 0.7422 199.00 0.663 0.0531 152.4 4156 300 300 0.7399 338.36 0.659 0.1253 250 500 0.7481 376.60 0.666 0.1004 203.2 5542 300 300 0.7860 638.45 0.685 0.2365 250 500 0.7930 686.83 0.689 0.1832 254 6927 300 300 0.8243 1093.32 0.705 0.4049 250 500 0.8280 1154.09 0.707 0.3078 20 STOREYS 127 2464 300 300 0.7635 323.51 0.672 0.1198 250 500 0.7834 385.97 0.684 0.1029 152.4 4156 300 300 0.7747 657.30 0.678 0.2434 250 500 0.7848 733.05 0.684 0.1955 203.2 5542 350 350 0.8222 1326.27 0.704 0.3609 250 500 0.8227 1345.99 0.704 0.3589 254 6927 450 450 0.8580 2449.57 0.723 0.4032 300 600 0.8571 2430.46 0.722 0.4501 30 STOREYS 127 2464 300 300 0.7840 477.65 0.683 0.1769 250 500 0.8033 570.94 0.694 0.1523 152.4 4156 300 300 0.7904 973.28 0.687 0.3605 250 500 0.8019 1086.45 0.693 0.2897 203.2 5542 400 400 0.8408 2095.79 0.714 0.4366 300 600 0.8434 2184.69 0.715 0.4046 254 6927 550 550 0.8749 4025.94 0.732 0.4436 375 750 0.8737 3999.77 0.731 0.4740 40 STOREYS 127 2464 300 300 0.7969 630.82 0.690 0.2336 250 500 0.8155 754.91 0.700 0.2013 152.4 4156 350 350 0.8117 1412.61 0.698 0.3844 250 500 0.8123 1438.31 0.699 0.3835 203.2 5542 500 500 0.8593 3168.87 0.723 0.4225 350 700 0.8587 3187.55 0.723 0.4337 254 6927 650 650 0.8863 5879.83 0.738 0.4639 475 950 0.8874 6082.19 0.738 0.4493 50 STOREYS 127 2464 300 300 0.8053 783.39 0.695 0.2901 250 500 0.8241 938.24 0.705 0.2502 152.4 4156 400 400 0.8286 1929.67 0.707 0.4020 275 550 0.8263 1912.32 0.706 0.4214 203.2 5542 600 600 0.8736 4487.96 0.731 0.4156 400 800 0.8703 4350.73 0.729 0.4532 254 6927 800 800 0.8980 8458.58 0.744 0.4406 525 1050 0.8948 8118.31 0.742 0.4909 1 to 2Square COLUMN LOAD TAKEDOWN - Exterior Columns (CSA) f'c [MPa] 30 Slab TH Ext Span mm mm 5 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 10 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 20 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 30 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 40 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 50 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm 250 1000 0.7756 157.01 0.680 0.0209 250 2000 0.8080 270.67 0.696 0.0180 250 1000 0.7414 262.78 0.662 0.0350 250 2000 0.7835 397.13 0.684 0.0265 250 1000 0.7763 440.19 0.680 0.0587 250 2000 0.8035 611.03 0.694 0.0407 250 1000 0.8078 699.48 0.696 0.0933 250 2000 0.8253 913.49 0.705 0.0609 250 1000 0.7959 309.51 0.690 0.0413 250 2000 0.8404 529.79 0.713 0.0353 250 1000 0.7831 509.49 0.684 0.0679 250 2000 0.8195 774.71 0.702 0.0516 250 1000 0.8128 858.14 0.699 0.1144 250 2000 0.8360 1195.70 0.711 0.0797 250 1000 0.8395 1369.74 0.713 0.1826 250 2000 0.8543 1793.01 0.721 0.1195 250 1000 0.8295 605.02 0.708 0.0807 250 2000 0.8668 1042.07 0.727 0.0695 250 1000 0.8152 996.45 0.700 0.1329 250 2000 0.8463 1522.44 0.716 0.1015 250 1000 0.8397 1685.90 0.713 0.2248 250 2000 0.8595 2355.88 0.723 0.1571 250 1000 0.8621 2700.45 0.725 0.3601 250 2000 0.8746 3541.20 0.731 0.2361 250 1000 0.8453 898.26 0.716 0.1198 250 2000 0.8789 1551.62 0.734 0.1034 250 1000 0.8299 1480.08 0.708 0.1973 250 2000 0.8583 2266.33 0.723 0.1511 250 1000 0.8518 2509.44 0.719 0.3346 250 2000 0.8698 3511.32 0.729 0.2341 300 1200 0.8778 4440.12 0.733 0.4111 250 2000 0.8833 5283.77 0.736 0.3523 250 1000 0.8550 1190.37 0.721 0.1587 250 2000 0.8861 2059.79 0.738 0.1373 250 1000 0.8388 1962.02 0.713 0.2616 250 2000 0.8655 3008.29 0.727 0.2006 250 1000 0.8589 3330.87 0.723 0.4441 250 2000 0.8758 4664.39 0.732 0.3110 325 1300 0.8860 6197.13 0.738 0.4889 275 2200 0.8919 7536.28 0.741 0.4152 250 1000 0.8616 1481.75 0.725 0.1976 250 2000 0.8911 2567.11 0.740 0.1711 250 1000 0.8449 2442.92 0.716 0.3257 250 2000 0.8703 3749.03 0.729 0.2499 275 1100 0.8683 4432.08 0.728 0.4884 250 2000 0.8800 5815.96 0.734 0.3877 375 1500 0.8947 8523.01 0.742 0.5051 300 2400 0.8984 10077.29 0.744 0.4665 1 to 4 1 to 8 COLUMN NO: Square Column for 5in(127mm) slab (Exterior Span) 50, 40, 30, 20, 10 & 5 Storeys [CSA] Note: For the reduction factor (RF) column, enter: 0 - no reduction factor is needed - area used for assembly occupancies designed for a live load of less than 4.8kPa and roofs designed for the minimum loading specified in Table 4.1.5.3. 1 - where a structural member supports a tributary area of a floor or roof, or a combination thereof, that is greater than 80m 2 and either used for assembly occupancies designed for a live load of 4.8kPa or more, or used for storage, manufacturing, retail stores, garages or as a footbridge, the specified live load due to use and occupancy is the load specified in Art. 4.1.5.3. 2 - where a structural member supports a tributary area of a floor or roof, or a combination thereof, that is greater than 20m 2 and used for any use or occupancy other than those indicated above, the specified live load due to use and occupancy is the load specified in Art. 4.1.5.3. = input Level Area Unfact. DL Unfact. LL Extra DL RF Accu. Unfact. DL Accu. Unfact. LL Fact. Load [m 2 ] [kN/m 2 ] [kN/m 2 ] [kN] [kN] [kN] [kN] Roof 2.347024 3.548 2.4 5.65 0 13.98 5.63 25.92 50 2.347024 3.548 2.4 5.65 2 27.96 11.27 51.84 49 2.347024 3.548 2.4 5.65 2 41.93 16.90 77.76 48 2.347024 3.548 2.4 5.65 2 55.91 22.53 103.69 47 2.347024 3.548 2.4 5.65 2 69.89 28.16 129.61 46 2.347024 3.548 2.4 5.65 2 83.87 33.80 155.53 45 2.347024 3.548 2.4 5.65 2 97.84 39.43 181.45 44 2.347024 3.548 2.4 5.65 2 111.82 45.06 207.37 43 2.347024 3.548 2.4 5.65 2 125.80 50.70 233.29 42 2.347024 3.548 2.4 5.65 2 139.78 55.37 257.78 41 2.347024 3.548 2.4 5.65 2 153.76 58.93 280.59 40 2.347024 3.548 2.4 5.65 2 167.73 62.40 303.26 39 2.347024 3.548 2.4 5.65 2 181.71 65.78 325.81 38 2.347024 3.548 2.4 5.65 2 195.69 69.10 348.26 37 2.347024 3.548 2.4 5.65 2 209.67 72.36 370.62 36 2.347024 3.548 2.4 5.65 2 223.64 75.56 392.90 35 2.347024 3.548 2.4 5.65 2 237.62 78.71 415.10 34 2.347024 3.548 2.4 5.65 2 251.60 81.82 437.23 33 2.347024 3.548 2.4 5.65 2 265.58 84.88 459.30 32 2.347024 3.548 2.4 5.65 2 279.56 87.91 481.31 31 2.347024 3.548 2.4 5.65 2 293.53 90.91 503.28 30 2.347024 3.548 2.4 5.65 2 307.51 93.87 525.19 29 2.347024 3.548 2.4 5.65 2 321.49 96.80 547.06 28 2.347024 3.548 2.4 5.65 2 335.47 99.70 568.88 27 2.347024 3.548 2.4 5.65 2 349.45 102.58 590.67 26 2.347024 3.548 2.4 5.65 2 363.42 105.43 612.42 25 2.347024 3.548 2.4 5.65 2 377.40 108.26 634.14 24 2.347024 3.548 2.4 5.65 2 391.38 111.07 655.82 23 2.347024 3.548 2.4 5.65 2 405.36 113.86 677.48 22 2.347024 3.548 2.4 5.65 2 419.33 116.62 699.10 21 2.347024 3.548 2.4 5.65 2 433.31 119.37 720.70 20 2.347024 3.548 2.4 5.65 2 447.29 122.10 742.27 19 2.347024 3.548 2.4 5.65 2 461.27 124.82 763.81 18 2.347024 3.548 2.4 5.65 2 475.25 127.52 785.34 17 2.347024 3.548 2.4 5.65 2 489.22 130.20 806.83 16 2.347024 3.548 2.4 5.65 2 503.20 132.87 828.31 15 2.347024 3.548 2.4 5.65 2 517.18 135.53 849.77 14 2.347024 3.548 2.4 5.65 2 531.16 138.17 871.20 13 2.347024 3.548 2.4 5.65 2 545.13 140.80 892.62 12 2.347024 3.548 2.4 5.65 2 559.11 143.42 914.02 11 2.347024 3.548 2.4 5.65 2 573.09 146.02 935.40 10 2.347024 3.548 2.4 5.65 2 587.07 148.62 956.76 9 2.347024 3.548 2.4 5.65 2 601.05 151.20 978.11 8 2.347024 3.548 2.4 5.65 2 615.02 153.77 999.44 7 2.347024 3.548 2.4 5.65 2 629.00 156.34 1020.76 6 2.347024 3.548 2.4 5.65 2 642.98 158.89 1042.06 5 2.347024 3.548 2.4 5.65 2 656.96 161.43 1063.34 4 2.347024 3.548 2.4 5.65 2 670.93 163.97 1084.62 3 2.347024 3.548 2.4 5.65 2 684.91 166.49 1105.88 2 2.347024 3.548 2.4 5.65 2 698.89 169.01 1127.12 GND Resistance 1709 306       APPENDIX B6.3 COLUMN LOAD TAKEDOWN INTERIOR COLUMNS (ACI)   COLUMN LOAD TAKEDOWN - Interior Columns (ACI) f'c [MPa] 30 Slab TH Ext Span Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm mm mm 5 STOREYS 127 2464 300 300 0.722 456.58 0.767 0.169 250 500 0.729 484.54 0.772 0.129 152.4 4156 300 300 0.747 509.77 0.786 0.189 250 500 0.758 730.57 0.795 0.195 203.2 5542 350 350 0.810 1520.39 0.837 0.414 250 500 0.811 1532.09 0.837 0.409 254 6927 450 450 0.846 2850.52 0.866 0.469 325 650 0.847 2878.21 0.866 0.454 10 storey 127 2464 300 300 0.767 886.69 0.802 0.328 250 500 0.773 941.85 0.807 0.251 152.4 4156 350 350 0.798 1411.31 0.826 0.384 250 500 0.798 1425.58 0.826 0.380 203.2 5542 450 450 0.846 3133.94 0.866 0.516 325 650 0.846 3172.52 0.866 0.501 254 6927 650 650 0.877 6051.06 0.891 0.477 450 900 0.877 6068.88 0.891 0.499 20 storey 127 2464 400 400 0.809 1922.95 0.835 0.401 275 550 0.807 1917.85 0.834 0.423 152.4 4156 500 500 0.835 3127.71 0.857 0.417 325 650 0.832 3053.68 0.854 0.482 203.2 5542 700 700 0.874 7076.90 0.889 0.481 500 1000 0.875 7176.31 0.890 0.478 254 6927 900 900 0.897 13255.32 0.909 0.545 650 1300 0.898 13500.94 0.909 0.533 30 storey 127 2464 450 450 0.827 3018.22 0.850 0.497 325 650 0.828 3079.03 0.851 0.486 152.4 4156 600 600 0.852 5072.10 0.871 0.470 425 850 0.852 5129.29 0.871 0.473 203.2 5542 850 850 0.887 11504.91 0.900 0.531 600 1200 0.887 11623.59 0.900 0.538 254 6927 1175 1175 0.908 22232.38 0.919 0.537 825 1650 0.908 22422.31 0.918 0.549 40 storey 127 2464 550 550 0.844 4468.92 0.864 0.492 400 800 0.845 4595.44 0.865 0.479 152.4 4156 700 700 0.865 7349.00 0.882 0.500 500 1000 0.865 7477.03 0.882 0.498 203.2 5542 1025 1025 0.897 16937.75 0.908 0.537 725 1450 0.897 17147.16 0.908 0.544 254 6927 1400 1400 0.916 32583.32 0.925 0.554 1000 2000 0.916 33214.84 0.925 0.554 50 storey 127 2464 650 650 0.858 6227.98 0.876 0.491 450 900 0.856 6202.01 0.874 0.510 152.4 4156 800 800 0.875 10007.06 0.890 0.521 575 1150 0.876 10241.78 0.891 0.516 203.2 5542 1200 1200 0.905 23426.54 0.915 0.542 850 1700 0.904 23757.26 0.915 0.548 254 6927 1650 1650 0.922 45310.94 0.930 0.555 1175 2350 0.922 46173.38 0.930 0.557 Square 1 to 2 COLUMN LOAD TAKEDOWN - Interior Columns (ACI) f'c [MPa] 30 Slab TH Ext Span mm mm 5 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 10 storey 127 2464 152.4 4156 203.2 5542 254 6927 20 storey 127 2464 152.4 4156 203.2 5542 254 6927 30 storey 127 2464 152.4 4156 203.2 5542 254 6927 40 storey 127 2464 152.4 4156 203.2 5542 254 6927 50 storey 127 2464 152.4 4156 203.2 5542 254 6927 Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm 250 1000 0.749 581.00 0.788 0.077 250 2000 0.776 773.75 0.809 0.052 250 1000 0.771 843.26 0.805 0.112 250 2000 0.789 1068.47 0.820 0.071 250 1000 0.818 1736.87 0.843 0.232 250 2000 0.825 2003.01 0.848 0.134 250 1000 0.848 2982.40 0.867 0.398 250 2000 0.852 3404.90 0.871 0.227 250 1000 0.791 1132.31 0.821 0.151 250 2000 0.813 1512.96 0.839 0.101 250 1000 0.809 1648.12 0.836 0.220 250 2000 0.825 2092.98 0.848 0.140 275 1100 0.850 3413.91 0.869 0.376 250 2000 0.855 3940.13 0.874 0.263 325 1300 0.877 6257.96 0.892 0.494 250 2000 0.878 6717.81 0.893 0.448 250 1000 0.819 2227.17 0.844 0.297 250 2000 0.839 2982.83 0.860 0.199 250 1000 0.835 3248.74 0.857 0.433 250 2000 0.849 4132.10 0.868 0.275 350 1400 0.874 7368.82 0.889 0.501 250 2000 0.875 7801.76 0.890 0.520 475 1900 0.898 14130.15 0.910 0.522 350 2800 0.899 15233.67 0.910 0.518 250 1000 0.831 3317.99 0.854 0.442 250 2000 0.850 4448.28 0.869 0.297 300 1200 0.852 5288.87 0.871 0.490 250 2000 0.858 6166.09 0.876 0.411 450 1800 0.888 12400.51 0.901 0.510 325 2600 0.888 13325.87 0.901 0.526 600 2400 0.909 23604.05 0.919 0.546 450 3600 0.909 26021.26 0.919 0.535 275 1100 0.843 4662.90 0.863 0.514 250 2000 0.856 5911.51 0.874 0.394 350 1400 0.864 7685.28 0.881 0.523 275 2200 0.868 8749.01 0.884 0.482 550 2200 0.898 18608.85 0.910 0.513 400 3200 0.898 20242.74 0.910 0.527 725 2900 0.916 35116.31 0.925 0.557 550 4400 0.917 39467.43 0.926 0.544 325 1300 0.857 6513.89 0.875 0.514 250 2000 0.860 7373.34 0.877 0.492 425 1700 0.877 10965.84 0.892 0.506 325 2600 0.879 12413.68 0.894 0.490 625 2500 0.905 25418.00 0.916 0.542 475 3800 0.906 28769.04 0.917 0.531 875 3500 0.923 50050.26 0.931 0.545 650 5200 0.923 55956.86 0.931 0.552 1 to 4 1 to 8 COLUMN NO: Square Column for 5in(127mm) slab (Interior Span) 50 Storeys [ACI] Note: For the reduction factor (RF) column, enter: 0 - no reduction factor is needed - area used for assembly occupancies designed for a live load of less than 4.8kPa and roofs designed for the minimum loading specified in Table 4.1.5.3. 2 - where a structural member supports a tributary area of a floor or roof, or a combination thereof, that is greater than 20m 2 and used for any use or occupancy other than those indicated above, the specified live load due to use and occupancy = input 1.2D+1.6L Level Area Unfact. DL Unfact. LL Extra DL RF Accu. Unfact. DL Accu. Unfact. LL Fact. Load [m 2 ] [kN/m 2 ] [kN/m 2 ] [kN] [kN] [kN] [kN] Roof 19.8916 3.548 2.4 26.53 0 97.10 47.74 192.91 50 19.8916 3.548 2.4 26.53 2 194.20 95.48 385.81 49 19.8916 3.548 2.4 26.53 2 291.30 106.20 519.49 48 19.8916 3.548 2.4 26.53 2 388.41 125.91 667.54 47 19.8916 3.548 2.4 26.53 2 485.51 144.40 813.64 46 19.8916 3.548 2.4 26.53 2 582.61 162.11 958.50 45 19.8916 3.548 2.4 26.53 2 679.71 179.26 1102.47 44 19.8916 3.548 2.4 26.53 2 776.81 196.00 1245.77 43 19.8916 3.548 2.4 26.53 2 873.91 212.40 1388.54 42 19.8916 3.548 2.4 26.53 2 971.02 228.53 1530.87 41 19.8916 3.548 2.4 26.53 2 1068.12 244.43 1672.84 40 19.8916 3.548 2.4 26.53 2 1165.22 260.14 1814.49 39 19.8916 3.548 2.4 26.53 2 1262.32 275.69 1955.88 38 19.8916 3.548 2.4 26.53 2 1359.42 291.08 2097.04 37 19.8916 3.548 2.4 26.53 2 1456.52 306.35 2237.98 36 19.8916 3.548 2.4 26.53 2 1553.63 321.49 2378.74 35 19.8916 3.548 2.4 26.53 2 1650.73 336.53 2519.33 34 19.8916 3.548 2.4 26.53 2 1747.83 351.48 2659.76 33 19.8916 3.548 2.4 26.53 2 1844.93 366.34 2800.06 32 19.8916 3.548 2.4 26.53 2 1942.03 381.12 2940.23 31 19.8916 3.548 2.4 26.53 2 2039.13 395.82 3080.28 30 19.8916 3.548 2.4 26.53 2 2136.24 410.46 3220.22 29 19.8916 3.548 2.4 26.53 2 2233.34 425.03 3360.05 28 19.8916 3.548 2.4 26.53 2 2330.44 439.54 3499.80 27 19.8916 3.548 2.4 26.53 2 2427.54 454.00 3639.45 26 19.8916 3.548 2.4 26.53 2 2524.64 468.41 3779.02 25 19.8916 3.548 2.4 26.53 2 2621.74 482.76 3918.52 24 19.8916 3.548 2.4 26.53 2 2718.85 497.07 4057.93 23 19.8916 3.548 2.4 26.53 2 2815.95 511.34 4197.28 22 19.8916 3.548 2.4 26.53 2 2913.05 525.57 4336.57 21 19.8916 3.548 2.4 26.53 2 3010.15 539.75 4475.79 20 19.8916 3.548 2.4 26.53 2 3107.25 553.90 4614.95 19 19.8916 3.548 2.4 26.53 2 3204.35 568.02 4754.05 18 19.8916 3.548 2.4 26.53 2 3301.46 582.10 4893.10 17 19.8916 3.548 2.4 26.53 2 3398.56 596.15 5032.10 16 19.8916 3.548 2.4 26.53 2 3495.66 610.16 5171.05 15 19.8916 3.548 2.4 26.53 2 3592.76 624.15 5309.95 14 19.8916 3.548 2.4 26.53 2 3689.86 638.11 5448.81 13 19.8916 3.548 2.4 26.53 2 3786.96 652.04 5587.62 12 19.8916 3.548 2.4 26.53 2 3884.07 665.95 5726.39 11 19.8916 3.548 2.4 26.53 2 3981.17 679.83 5865.13 10 19.8916 3.548 2.4 26.53 2 4078.27 693.68 6003.82 9 19.8916 3.548 2.4 26.53 2 4175.37 707.52 6142.47 8 19.8916 3.548 2.4 26.53 2 4272.47 721.33 6281.09 7 19.8916 3.548 2.4 26.53 2 4369.57 735.12 6419.68 6 19.8916 3.548 2.4 26.53 2 4466.68 748.89 6558.23 5 19.8916 3.548 2.4 26.53 2 4563.78 762.63 6696.75 4 19.8916 3.548 2.4 26.53 2 4660.88 776.36 6835.23 3 19.8916 3.548 2.4 26.53 2 4757.98 790.07 6973.69 2 19.8916 3.548 2.4 26.53 2 4855.08 803.76 7112.12 GND Resistance 8022 311       APPENDIX B6.4 COLUMN LOAD TAKEDOWN EXTERIOR COLUMNS (ACI)      COLUMN LOAD TAKEDOWN - Exterior Columns (ACI) f'c [MPa] 30 Slab TH Ext Span Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm mm mm 5 STOREYS 127 2464 300 300 0.713 97.95 0.760 0.036 250 500 0.733 117.13 0.776 0.031 152.4 4156 300 300 0.679 205.80 0.734 0.076 250 500 0.691 229.42 0.743 0.061 203.2 5542 300 300 0.781 376.66 0.813 0.140 250 500 0.788 405.47 0.818 0.108 254 6927 300 300 0.819 647.44 0.843 0.240 250 500 0.823 683.66 0.846 0.182 10 STOREYS 127 2464 300 300 0.713 195.90 0.760 0.073 250 500 0.733 234.26 0.776 0.062 152.4 4156 300 300 0.780 385.36 0.808 0.143 250 500 0.787 430.37 0.818 0.115 203.2 5542 300 300 0.819 736.40 0.844 0.273 250 500 0.825 793.44 0.848 0.212 254 6927 300 300 0.851 1271.82 0.870 0.471 250 500 0.855 1343.56 0.873 0.358 20 STOREYS 127 2464 300 300 0.804 369.97 0.830 0.137 250 500 0.821 443.78 0.846 0.118 152.4 4156 300 300 0.811 754.92 0.836 0.280 250 500 0.820 844.31 0.844 0.225 203.2 5542 350 350 0.851 1540.73 0.870 0.419 250 500 0.852 1563.83 0.870 0.417 254 6927 450 450 0.881 2867.27 0.895 0.472 300 600 0.880 2844.43 0.895 0.527 30 STOREYS 127 2464 300 300 0.822 549.06 0.845 0.203 250 500 0.838 659.45 0.859 0.176 152.4 4156 300 300 0.825 1122.32 0.848 0.416 250 500 0.835 1256.02 0.857 0.335 203.2 5542 400 400 0.867 2443.89 0.884 0.509 300 600 0.870 2548.91 0.885 0.472 254 6927 550 550 0.896 4727.44 0.908 0.521 375 750 0.895 4695.69 0.907 0.557 40 STOREYS 127 2464 300 300 0.833 727.44 0.854 0.269 250 500 0.849 874.39 0.868 0.233 152.4 4156 350 350 0.843 1636.59 0.863 0.445 250 500 0.844 1666.61 0.864 0.444 203.2 5542 500 500 0.883 3708.93 0.897 0.495 350 700 0.882 3730.40 0.896 0.508 254 6927 650 650 0.905 6919.26 0.916 0.546 475 950 0.906 7158.99 0.917 0.529 50 STOREYS 127 2464 300 300 0.840 905.39 0.860 0.335 250 500 0.856 1088.87 0.874 0.290 152.4 4156 400 400 0.858 2243.79 0.875 0.467 275 550 0.856 2222.56 0.874 0.490 203.2 5542 600 600 0.895 5267.66 0.907 0.488 400 800 0.892 5103.32 0.905 0.532 254 6927 800 800 0.915 9975.66 0.924 0.520 525 1050 0.912 9568.76 0.922 0.579 Square 1 to 2 COLUMN LOAD TAKEDOWN - Exterior Columns (ACI) f'c [MPa] 30 Slab TH Ext Span mm mm 5 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 10 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 20 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 30 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 40 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 50 STOREYS 127 2464 152.4 4156 203.2 5542 254 6927 Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg Col Dim1 Col Dim2 D/D+L Ps Ps/Pf Ps/f'cAg mm mm mm mm 250 1000 0.776 184.44 0.809 0.025 250 2000 0.808 319.06 0.835 0.021 250 1000 0.722 311.50 0.767 0.042 250 2000 0.815 458.38 0.840 0.031 250 1000 0.808 507.56 0.834 0.068 250 2000 0.831 708.76 0.853 0.047 250 1000 0.834 812.26 0.856 0.108 250 2000 0.849 1064.69 0.868 0.071 250 1000 0.776 368.88 0.809 0.049 250 2000 0.868 617.32 0.884 0.041 250 1000 0.817 586.97 0.842 0.078 250 2000 0.848 899.77 0.868 0.060 250 1000 0.842 995.62 0.862 0.133 250 2000 0.862 1394.14 0.879 0.093 250 1000 0.864 1598.45 0.881 0.213 250 2000 0.877 2098.77 0.891 0.140 250 1000 0.860 702.93 0.878 0.094 250 2000 0.891 1220.48 0.904 0.081 250 1000 0.846 1155.45 0.866 0.154 250 2000 0.872 1777.13 0.888 0.118 250 1000 0.866 1965.79 0.883 0.262 250 2000 0.883 2758.23 0.896 0.184 250 1000 0.885 3163.65 0.898 0.422 250 2000 0.895 4159.02 0.907 0.277 250 1000 0.873 1047.16 0.889 0.140 250 2000 0.901 1821.64 0.912 0.121 250 1000 0.859 1721.48 0.876 0.230 250 2000 0.882 2651.67 0.896 0.177 250 1000 0.877 2932.89 0.891 0.391 250 2000 0.892 4118.85 0.904 0.275 300 1200 0.898 5216.91 0.910 0.483 250 2000 0.903 6215.16 0.914 0.414 250 1000 0.881 1390.56 0.895 0.185 250 2000 0.907 2421.81 0.917 0.161 250 1000 0.866 2286.30 0.883 0.305 250 2000 0.888 3524.81 0.901 0.235 250 1000 0.883 3898.44 0.896 0.520 250 2000 0.897 5477.74 0.908 0.365 325 1300 0.905 7292.48 0.916 0.575 275 2200 0.910 8878.71 0.920 0.489 250 1000 0.887 1733.43 0.900 0.231 250 2000 0.911 3021.34 0.921 0.201 250 1000 0.871 2850.34 0.887 0.380 250 2000 0.893 4397.07 0.905 0.293 275 1100 0.890 5196.95 0.903 0.573 250 2000 0.900 6835.54 0.911 0.456 375 1500 0.912 10045.85 0.922 0.595 300 2400 0.915 11886.65 0.925 0.550 1 to 4 1 to 8 COLUMN NO: Square Column for 5in(127mm) slab (Exterior Span) 50, 40, 30, 20, 10 & 5 Storeys [ACI] Note: For the reduction factor (RF) column, enter: 0 - no reduction factor is needed - area used for assembly occupancies designed for a live load of less than 4.8kPa and roofs designed for the minimum loading specified in Table 4.1.5.3. 2 - where a structural member supports a tributary area of a floor or roof, or a combination thereof, that is greater than 37.2m 2 and used for any use or occupancy other than those indicated above, the specified live load due to use and occupancy = input 1.2D+1.6L Level Area Unfact. DL Unfact. LL Extra DL RF Accu. Unfact. DL Accu. Unfact. LL Fact. Load [m 2 ] [kN/m 2 ] [kN/m 2 ] [kN] [kN] [kN] [kN] Roof 2.347024 3.548 2.4 5.65 0 13.98 5.63 25.79 50 2.347024 3.548 2.4 5.65 2 27.96 11.27 51.57 49 2.347024 3.548 2.4 5.65 2 41.93 16.90 77.36 48 2.347024 3.548 2.4 5.65 2 55.91 22.53 103.14 47 2.347024 3.548 2.4 5.65 2 69.89 28.16 128.93 46 2.347024 3.548 2.4 5.65 2 83.87 33.80 154.72 45 2.347024 3.548 2.4 5.65 2 97.84 39.43 180.50 44 2.347024 3.548 2.4 5.65 2 111.82 45.06 206.29 43 2.347024 3.548 2.4 5.65 2 125.80 50.70 232.07 42 2.347024 3.548 2.4 5.65 2 139.78 56.33 257.86 41 2.347024 3.548 2.4 5.65 2 153.76 61.96 283.65 40 2.347024 3.548 2.4 5.65 2 167.73 67.59 309.43 39 2.347024 3.548 2.4 5.65 2 181.71 73.23 335.22 38 2.347024 3.548 2.4 5.65 2 195.69 78.86 361.00 37 2.347024 3.548 2.4 5.65 2 209.67 84.49 386.79 36 2.347024 3.548 2.4 5.65 2 223.64 90.13 412.57 35 2.347024 3.548 2.4 5.65 2 237.62 61.77 383.98 34 2.347024 3.548 2.4 5.65 2 251.60 64.21 404.66 33 2.347024 3.548 2.4 5.65 2 265.58 66.63 425.29 32 2.347024 3.548 2.4 5.65 2 279.56 69.01 445.88 31 2.347024 3.548 2.4 5.65 2 293.53 71.37 466.43 30 2.347024 3.548 2.4 5.65 2 307.51 73.71 486.94 29 2.347024 3.548 2.4 5.65 2 321.49 76.02 507.42 28 2.347024 3.548 2.4 5.65 2 335.47 78.31 527.86 27 2.347024 3.548 2.4 5.65 2 349.45 80.59 548.28 26 2.347024 3.548 2.4 5.65 2 363.42 82.85 568.66 25 2.347024 3.548 2.4 5.65 2 377.40 85.09 589.02 24 2.347024 3.548 2.4 5.65 2 391.38 87.31 609.35 23 2.347024 3.548 2.4 5.65 2 405.36 89.52 629.66 22 2.347024 3.548 2.4 5.65 2 419.33 91.71 649.94 21 2.347024 3.548 2.4 5.65 2 433.31 93.90 670.21 20 2.347024 3.548 2.4 5.65 2 447.29 96.07 690.45 19 2.347024 3.548 2.4 5.65 2 461.27 98.22 710.68 18 2.347024 3.548 2.4 5.65 2 475.25 100.37 730.88 17 2.347024 3.548 2.4 5.65 2 489.22 102.50 751.07 16 2.347024 3.548 2.4 5.65 2 503.20 104.62 771.24 15 2.347024 3.548 2.4 5.65 2 517.18 106.74 791.39 14 2.347024 3.548 2.4 5.65 2 531.16 108.84 811.53 13 2.347024 3.548 2.4 5.65 2 545.13 110.94 831.66 12 2.347024 3.548 2.4 5.65 2 559.11 113.02 851.77 11 2.347024 3.548 2.4 5.65 2 573.09 115.10 871.86 10 2.347024 3.548 2.4 5.65 2 587.07 117.17 891.95 9 2.347024 3.548 2.4 5.65 2 601.05 119.23 912.02 8 2.347024 3.548 2.4 5.65 2 615.02 121.28 932.07 7 2.347024 3.548 2.4 5.65 2 629.00 123.32 952.12 6 2.347024 3.548 2.4 5.65 2 642.98 125.36 972.15 5 2.347024 3.548 2.4 5.65 2 656.96 127.39 992.18 4 2.347024 3.548 2.4 5.65 2 670.93 129.42 1012.19 3 2.347024 3.548 2.4 5.65 2 684.91 131.43 1032.19 2 2.347024 3.548 2.4 5.65 2 698.89 133.45 1052.18 GND Resistance 1709 316        APPENDIX C SPECIMEN DRAWINGS    317        APPENDIX C1 COLUMN REINFORCEMENT DETAILS           326        APPENDIX C2 AS-BUILT COLUMN TIE LOCATIONS        332        APPENDIX C3 TEST SET-UP DRAWINGS          340        APPENDIX C4 LVDT MOUNTS DRAWINGS       345        APPENDIX C5 OTHER DESIGN DRAWINGS       347        APPENDIX D SPECIMEN PREDICTIONS BY HAND CALCULATIONS    348        APPENDIX D1 1:1 COLUMN SPECIMEN   349        APPENDIX D1.1 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITH CONRETE COVER)  1:1 Column with Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 400 mm Length, l 400 mm Clear cover 15 mm Longitudinal bar spacing 167.5 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.904 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.002366 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm2 mm x109mm4 x106mm3 x109mm4 mm2 MPa kN mm2 mm2 Concrete 400 400 160000 200 2.13 32.00 0.00 Steel S1 3 15M 3661 32.5 0.1190 0.10 600 -0.0027 -450.00 -270.00 13806 4260.6217 S2 2 15M 2440 200 0.4881 0.00 400 0.0012 233.34 93.34 2500 2840.4145 S3 3 15M 3661 367.5 1.3453 0.10 600 0.0051 450.00 270.00 47307 4260.6217 S 169762 2.13 33.95 0.21 yCG = SAy/SA 200.00 mm Ix = SI0 + SA(y-yNA) 2 2.34 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 0.659 x109mm4 Compression block depth, c 149.99827 mm Concrete compression force, Pc = a1f'cb1cw -1575 kN ycc = 137.85 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 75.00 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -289.00 kN ys1 = 167.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 93.34 kN ys2 = 0.00 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 270.00 kN ys3 = 167.50 mm Force equilibrium, Pr = Pc+Ps -1500.34 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 310.69 kNm 1:1 Column with Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.00064 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.00064 -5.2E-05 1.599 102.67468 400 -0.000668 -2.93E-05 1.739 109.89542 384.32936 -0.000697 -4.74E-06 1.884 116.45769 370.01869 -0.000726 1.746E-05 2.022 121.47694 358.86376 -0.000754 4.553E-05 2.176 128.11198 346.57772 -0.000783 7.447E-05 2.333 134.28869 335.57496 -0.000926 0.0002402 3.173 160.79777 291.80285 -0.001069 0.0004362 4.095 182.51575 260.98612 -0.001212 0.0006573 5.086 201.39424 238.26342 -0.001355 0.0008935 6.118 218.47919 221.45471 -0.001498 0.0011438 7.188 234.29027 208.37865 -0.001641 0.0013879 8.242 249.27682 199.09209 -0.001784 0.0016459 9.333 263.35037 191.13905 -0.001927 0.0019068 10.432 276.67419 184.70923 -0.00207 0.0021664 11.527 289.30152 179.56447 -0.002213 0.0024751 12.756 296.42836 173.47215 -0.002356 0.0028121 14.063 300.59674 167.52903 -0.002499 0.0031507 15.373 304.19943 162.54935 -0.002642 0.0034917 16.690 307.21457 158.29296 -0.002785 0.0038232 17.981 309.87635 154.87911 -0.002928 0.0041235 19.188 311.47214 152.59544 -0.003071 0.0043888 20.299 312.00049 151.28956 -0.003214 0.0046377 21.365 312.05136 150.43025 -0.003357 0.0048677 22.380 311.61704 149.99827 -0.0035 0.0050751 23.334 310.69447 149.99827 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 2.5 150 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 12.000 304 23.334 310.69447 0 50 100 150 200 250 300 350 0 5 10 15 20 25 M o m e n t [k N m ] Curvature [rad/km] 1:1 Column with Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 2.5 150 @ f1 12 304 @ f2 23.33360301 310.6944716 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 21.90 30.00 0.5000 1.3700 0.0000 0.313 43.80 60.00 1.0000 1.3700 0.0000 0.626 65.69 90.00 1.5000 1.3700 0.0000 0.938 87.59 120.00 2.0000 1.3700 0.0000 1.251 109.49 150.0 2.5000 1.3700 0.0000 1.564 131.97 180.80 4.4000 1.1366 0.2334 2.094 154.45 211.60 6.3000 0.9712 0.3988 2.891 176.93 242.40 8.2000 0.8478 0.5222 3.827 199.42 273.20 10.1000 0.7522 0.6178 4.843 221.90 304.00 12.0000 0.6760 0.6940 5.909 222.88 305.34 14.2667 0.6730 0.6910 5.966 223.85 306.68 16.5334 0.6701 0.6880 6.039 224.83 308.02 18.8002 0.6672 0.6850 6.131 226.78 310.7 23.3336 0.6614 0.6791 6.365 226.78 9.244 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 200.000 mm 0.00227 rad Di = Ѳi(hw-0.5lp) 2.879 mm 0 50 100 150 200 250 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 H o rz  L o ad  [ kN ] Displacement [mm] 353         APPENDIX D1.2 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITHOUT CONRETE COVER)   1:1 Column without Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 400 mm Length, l 370 mm Clear cover 0 mm Longitudinal bar spacing 167.5 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.904 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.002366 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm2 mm x109mm4 x106mm3 x109mm4 mm2 MPa kN mm2 mm2 Concrete 400 370 148000 185 1.69 27.38 0.00 Steel S1 3 15M 3661 17.5 0.0641 0.10 600 -0.0031 -450.00 -270.00 16999 4260.6217 S2 2 15M 2440 185 0.4515 0.00 400 0.0009 175.71 70.28 1378 2840.4145 S3 3 15M 3661 352.5 1.2904 0.10 600 0.0048 450.00 270.00 41869 4260.6217 S 157762 1.69 29.19 0.21 yCG = SAy/SA 185.00 mm Ix = SI0 + SA(y-yNA) 2 1.89 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 0.613 x109mm4 Compression block depth, c 147.87978 mm Concrete compression force, Pc = a1f'cb1cw -1552 kN ycc = 123.72 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 73.94 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -289.00 kN ys1 = 167.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 70.28 kN ys2 = 0.00 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 270.00 kN ys3 = 167.50 mm Force equilibrium, Pr = Pc+Ps -1501.15 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 285.71 kNm 1:1 Column without Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.000693 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.000693 -3.28E-05 1.873 96.498713 370 -0.000721 -8.21E-06 2.022 102.56619 356.55994 -0.000749 1.293E-05 2.162 106.79861 346.52057 -0.000777 4.023E-05 2.319 112.97418 335.15498 -0.000805 6.825E-05 2.478 118.72611 324.95871 -0.000833 9.775E-05 2.642 124.1809 315.49708 -0.000974 0.000264 3.511 147.97205 277.30804 -0.001114 0.0004584 4.461 167.87101 249.7347 -0.001254 0.0006743 5.472 185.38285 229.25884 -0.001395 0.000905 6.524 201.33555 213.78174 -0.001535 0.0011488 7.614 216.17777 201.62086 -0.001675 0.0013999 8.724 230.15932 192.04531 -0.001816 0.0016441 9.815 243.4465 185 -0.001956 0.0018916 10.916 256.05962 179.20662 -0.002097 0.0021434 12.028 268.02605 174.30026 -0.002237 0.0024387 13.264 275.55761 168.64234 -0.002377 0.0027706 14.604 279.68502 162.78105 -0.002518 0.0031053 15.951 283.28765 157.82763 -0.002658 0.0033981 17.180 285.00373 154.7089 -0.002798 0.0036748 18.363 286.18443 152.38254 -0.002939 0.0039407 19.516 286.93955 150.5766 -0.003079 0.004193 20.630 287.27375 149.24819 -0.003219 0.0044298 21.699 287.17977 148.35871 -0.00336 0.0046487 22.719 286.64414 147.87978 -0.0035 0.0048429 23.668 285.70509 147.87978 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 2.5 130 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 12.000 275 23.668 285.70509 0 50 100 150 200 250 300 350 0 5 10 15 20 25 M o m e n t [k N m ] Curvature [rad/km] 1:1 Column without Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 2.5 130 @ f1 12 275 @ f2 23.6678739 285.7050882 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 18.98 26.00 0.5000 1.3700 0.0000 0.313 37.96 52.00 1.0000 1.3700 0.0000 0.626 56.93 78.00 1.5000 1.3700 0.0000 0.938 75.91 104.00 2.0000 1.3700 0.0000 1.251 94.89 130.0 2.5000 1.3700 0.0000 1.564 116.06 159.00 4.4000 1.1201 0.2499 2.129 137.23 188.00 6.3000 0.9473 0.4227 2.959 158.39 217.00 8.2000 0.8207 0.5493 3.923 179.56 246.00 10.1000 0.7240 0.6460 4.962 200.73 275.00 12.0000 0.6476 0.7224 6.046 202.29 277.14 14.3336 0.6426 0.7168 6.143 203.86 279.28 16.6671 0.6377 0.7113 6.271 205.42 281.42 19.0007 0.6329 0.7059 6.430 208.54 285.7 23.6679 0.6234 0.6953 6.835 208.54 9.592 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 185.000 mm 0.00216 rad Di = Ѳi(hw-0.5lp) 2.758 mm 0 50 100 150 200 250 0.000 2.000 4.000 6.000 8.000 10.000 12.000 H o rz  L o ad  [ kN ] Displacement [mm] 357         APPENDIX D2 1:2 COLUMN SPECIMEN   358       APPENDIX D2.1 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITH CONRETE COVER) 1:2 Column with Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 275 mm Length, l 550 mm Clear cover 15 mm Longitudinal bar spacing 161.67 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.904 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.002366 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm 2 mm x10 9 mm 4 x10 6 mm 3 x10 9 mm 4 mm 2 MPa kN mm 2 mm 2 Concrete 275 550 151250 275 3.81 41.59 0.00 Steel S1 2 15M 2440 32.5 0.0793 0.14 400 -0.0030 -450.00 -180.00 36089 2840.4145 S2 2 15M 2440 194.17 0.4739 0.02 400 -0.0004 -89.05 -35.62 801 2840.4145 S3 2 15M 2440 355.84 0.8684 0.02 400 0.0021 419.65 167.86 17788 2840.4145 S4 2 15M 2440 517.5 1.2629 0.14 400 0.0046 450.00 180.00 87043 2840.4145 S 161012 3.81 44.28 0.18 yCG = SAy/SA 275.00 mm Ix = SI0 + SA(y-yNA) 2 3.99 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 1.062 x109mm4 Compression block depth, c 222.47014 mm Note: This is a random guess Concrete compression force, Pc = a1f'cb1cw -1606 kN ycc = 182.82 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 111.24 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -192.67 kN ys1 = 242.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 -48.29 kN ys2 = 80.83 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 167.86 kN ys3 = 80.84 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S4 180.00 kN ys4 = 242.50 mm Force equilibrium, Pr = Pc+Ps -1498.74 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 401.38 kNm 1:2 Column with Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.000677 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.000677 -4E-05 1.231 139.95102 550 -0.000705 -1.65E-05 1.331 149.13292 529.92828 -0.000734 6.131E-06 1.430 156.10385 513.21179 -0.000762 3.285E-05 1.536 164.85326 496.10905 -0.00079 6.072E-05 1.644 172.98732 480.56916 -0.000818 9.008E-05 1.756 180.62921 466.18839 -0.00096 0.0002563 2.349 213.11283 408.41686 -0.001101 0.0004516 2.999 239.12504 366.95673 -0.001242 0.0006581 3.671 261.45767 338.24827 -0.001383 0.0008896 4.391 282.38039 314.92761 -0.001524 0.0011332 5.135 301.52396 296.81592 -0.001665 0.0013842 5.893 319.31344 282.59676 -0.001806 0.0016392 6.658 335.98343 271.30228 -0.001947 0.0018954 7.426 351.66161 262.2585 -0.002089 0.0021503 8.191 366.41253 254.98507 -0.00223 0.0024307 9.006 376.47378 247.59666 -0.002371 0.0027285 9.854 383.254 240.60384 -0.002512 0.0030271 10.704 389.20553 234.69001 -0.002653 0.0033094 11.522 394.19033 230.27204 -0.002794 0.0035636 12.286 397.27042 227.44403 -0.002935 0.003811 13.037 399.53836 225.16959 -0.003077 0.0040379 13.748 401.23757 223.78781 -0.003218 0.0042541 14.438 402.10384 222.85907 -0.003359 0.0044544 15.098 402.18759 222.47014 -0.0035 0.0046415 15.732 401.38109 222.47014 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 1.9 205 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 8.700 385 15.732 401.38109 0 50 100 150 200 250 300 350 400 450 0 2 4 6 8 10 12 14 16 18 M o m e n t [k N m ] Curvature [rad/km] 1:2 Column with Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 1.9 205 @ f1 8.7 385 @ f2 15.73244848 401.3810937 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 29.93 41.00 0.3800 1.3700 0.0000 0.238 59.85 82.00 0.7600 1.3700 0.0000 0.475 89.78 123.00 1.1400 1.3700 0.0000 0.713 119.71 164.00 1.5200 1.3700 0.0000 0.951 149.64 205.0 1.9000 1.3700 0.0000 1.189 175.91 241.00 3.2600 1.1654 0.2046 1.534 202.19 277.00 4.6200 1.0139 0.3561 2.064 228.47 313.00 5.9800 0.8973 0.4727 2.697 254.74 349.00 7.3400 0.8047 0.5653 3.395 281.02 385.00 8.7000 0.7295 0.6405 4.133 283.41 388.28 10.1065 0.7233 0.6351 4.212 285.80 391.55 11.5130 0.7173 0.6298 4.311 288.20 394.83 12.9195 0.7113 0.6246 4.429 292.98 401.4 15.7324 0.6997 0.6144 4.721 292.98 7.105 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 275.000 mm 0.00193 rad Di = Ѳi(hw-0.5lp) 2.384 mm 0 50 100 150 200 250 300 350 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 H o rz  L o ad  [ kN ] Displacement [mm] 362       APPENDIX D2.2 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITHOUT CONRETE COVER)  1:2 Column without Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 275 mm Length, l 520 mm Clear cover 0 mm Longitudinal bar spacing 161.67 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.904 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.002366 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm 2 mm x10 9 mm 4 x10 6 mm 3 x10 9 mm 4 mm 2 MPa kN mm 2 mm 2 Concrete 275 520 143000 260 3.22 37.18 0.00 Steel S1 2 15M 2440 17.5 0.0427 0.14 400 -0.0032 -450.00 -180.00 40549 2840.4145 S2 2 15M 2440 179.17 0.4372 0.02 400 -0.0006 -126.97 -50.79 1576 2840.4145 S3 2 15M 2440 340.84 0.8318 0.02 400 0.0020 390.10 156.04 14877 2840.4145 S4 2 15M 2440 502.5 1.2263 0.14 400 0.0045 450.00 180.00 80447 2840.4145 S 152762 3.22 39.72 0.18 yCG = SAy/SA 260.00 mm Ix = SI0 + SA(y-yNA) 2 3.40 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 1.008 x109mm4 Compression block depth, c 218.86851 mm Note: This is a random guess Concrete compression force, Pc = a1f'cb1cw -1580 kN ycc = 169.31 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 109.43 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -192.67 kN ys1 = 242.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 -63.45 kN ys2 = 80.83 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 156.04 kN ys3 = 80.84 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S4 180.00 kN ys4 = 242.50 mm Force equilibrium, Pr = Pc+Ps -1499.73 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 375.56 kNm 1:2 Column without Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.000717 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.000717 -2.41E-05 1.379 133.67091 520 -0.000745 -2.92E-07 1.482 141.63662 502.69724 -0.000773 2.311E-05 1.584 148.23204 487.90904 -0.000801 5.064E-05 1.694 156.12848 472.60473 -0.000828 7.898E-05 1.806 163.47691 458.76217 -0.000856 0.0001087 1.920 170.41527 445.89001 -0.000995 0.0002754 2.529 200.24837 393.591 -0.001135 0.0004691 3.191 224.49077 355.50533 -0.001274 0.0006725 3.873 245.18368 328.85357 -0.001413 0.0009 4.603 264.97502 306.9618 -0.001552 0.001139 5.355 283.14418 289.80108 -0.001691 0.0013853 6.122 300.06205 276.22618 -0.00183 0.0016355 6.897 315.93968 265.37131 -0.001969 0.0018869 7.674 330.89403 256.62632 -0.002109 0.0021372 8.449 344.98548 249.55194 -0.002248 0.0024106 9.270 354.99115 242.46117 -0.002387 0.0027048 10.133 361.53126 235.55896 -0.002526 0.0029806 10.958 366.10731 230.5086 -0.002665 0.0032371 11.746 369.50455 226.90217 -0.002804 0.0034853 12.516 372.22979 224.04613 -0.002943 0.0037249 13.270 374.25464 221.80566 -0.003083 0.0039479 13.991 375.68275 220.3254 -0.003222 0.0041593 14.688 376.37798 219.33557 -0.003361 0.0043553 15.356 376.35318 218.86851 -0.0035 0.0045356 15.991 375.56224 218.86851 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 1.9 185 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 8.700 360 15.991 375.56224 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 M o m e n t [k N m ] Curvature [rad/km] 1:2 Column without Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 1.9 185 @ f1 8.7 360 @ f2 15.99133619 375.5622435 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 27.01 37.00 0.3800 1.3700 0.0000 0.238 54.01 74.00 0.7600 1.3700 0.0000 0.475 81.02 111.00 1.1400 1.3700 0.0000 0.713 108.03 148.00 1.5200 1.3700 0.0000 0.951 135.04 185.0 1.9000 1.3700 0.0000 1.189 160.58 220.00 3.2600 1.1520 0.2180 1.555 186.13 255.00 4.6200 0.9939 0.3761 2.107 211.68 290.00 5.9800 0.8740 0.4960 2.760 237.23 325.00 7.3400 0.7798 0.5902 3.474 262.77 360.00 8.7000 0.7040 0.6660 4.226 265.05 363.11 10.1583 0.6980 0.6603 4.304 267.32 366.22 11.6165 0.6921 0.6547 4.405 269.59 369.34 13.0748 0.6862 0.6491 4.525 274.13 375.6 15.9913 0.6749 0.6384 4.825 274.13 7.176 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 260.000 mm 0.00190 rad Di = Ѳi(hw-0.5lp) 2.351 mm 0 50 100 150 200 250 300 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 H o rz  L o ad  [ kN ] Displacement [mm] 366        APPENDIX D3 1:4 COLUMN SPECIMEN  367        APPENDIX D3.1 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITH CONRETE COVER)   1:4 Column with Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 200 mm Length, l 800 mm Clear cover 15 mm Longitudinal bar spacing 245 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.904 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.002366 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm 2 mm x10 9 mm 4 x10 6 mm 3 x10 9 mm 4 mm 2 MPa kN mm 2 mm 2 Concrete 200 800 160000 400 8.53 64.00 0.00 Steel S1 2 15M 2440 32.5 0.0793 0.33 400 -0.0031 -450.00 -180.00 76840 2840.4145 S2 2 15M 2440 277.5 0.6772 0.04 400 -0.0004 -72.78 -29.11 1037 2840.4145 S3 2 15M 2440 522.5 1.2751 0.04 400 0.0024 450.00 180.00 45284 2840.4145 S4 2 15M 2440 767.5 1.8730 0.33 400 0.0052 450.00 180.00 209581 2840.4145 S 169762 8.53 67.90 0.40 yCG = SAy/SA 400.00 mm Ix = SI0 + SA(y-yNA) 2 8.94 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 2.112 x109mm4 Compression block depth, c 309.69998 mm Note: This is a random guess Concrete compression force, Pc = a1f'cb1cw -1626 kN ycc = 271.67 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 154.85 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -192.67 kN ys1 = 367.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 -41.78 kN ys2 = 122.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 180.00 kN ys3 = 122.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S4 180.00 kN ys4 = 367.50 mm Force equilibrium, Pr = Pc+Ps -1500.05 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 605.75 kNm 1:4 Column with Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.00064 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.00064 -2.6E-05 0.800 204.5835 800 -0.000668 -1.01E-06 0.869 219.01865 768.65916 -0.000697 2.338E-05 0.939 231.10973 742.58603 -0.000726 5.162E-05 1.013 244.72028 716.52408 -0.000754 8.249E-05 1.090 257.54964 691.82374 -0.000783 0.0001141 1.169 269.42045 669.83737 -0.000926 0.0002943 1.590 319.67137 582.34573 -0.001069 0.0005013 2.046 358.94963 522.43331 -0.001212 0.0007352 2.537 395.32461 477.68678 -0.001355 0.000987 3.051 428.02906 444.02286 -0.001498 0.0012535 3.585 458.1138 417.82651 -0.001641 0.0015281 4.129 486.23424 397.40489 -0.001784 0.0018069 4.678 512.72537 381.28966 -0.001927 0.0020867 5.229 537.75903 368.46308 -0.00207 0.002388 5.808 556.97669 356.36379 -0.002213 0.0027161 6.422 568.92063 344.5689 -0.002356 0.003046 7.038 579.60821 334.72224 -0.002499 0.0033764 7.655 589.0811 326.4348 -0.002642 0.0036656 8.218 595.18457 321.46939 -0.002785 0.0039462 8.770 600.16343 317.54557 -0.002928 0.0042143 9.306 604.07673 314.63414 -0.003071 0.0044683 9.823 606.89517 312.62647 -0.003214 0.0047063 10.320 608.58044 311.44243 -0.003357 0.0049385 10.808 608.3912 310.5886 -0.0035 0.0051737 11.301 605.75241 309.69998 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 1.2 300 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 5.800 575 11.301 605.75241 0 100 200 300 400 500 600 700 0 2 4 6 8 10 12 M o m e n t [k N m ] Curvature [rad/km] 1:4 Column with Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 1.2 300 @ f1 5.8 575 @ f2 11.30125994 605.7524059 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 43.80 60.00 0.2400 1.3700 0.0000 0.150 87.59 120.00 0.4800 1.3700 0.0000 0.300 131.39 180.00 0.7200 1.3700 0.0000 0.450 175.18 240.00 0.9600 1.3700 0.0000 0.601 218.98 300.0 1.2000 1.3700 0.0000 0.751 259.12 355.00 2.1200 1.1577 0.2123 0.985 299.27 410.00 3.0400 1.0024 0.3676 1.347 339.42 465.00 3.9600 0.8839 0.4861 1.780 379.56 520.00 4.8800 0.7904 0.5796 2.256 419.71 575.00 5.8000 0.7148 0.6552 2.759 424.20 581.15 6.9003 0.7072 0.6483 2.827 428.69 587.30 8.0005 0.6998 0.6415 2.914 433.18 593.45 9.1008 0.6926 0.6348 3.019 442.16 605.8 11.3013 0.6785 0.6220 3.283 442.16 5.857 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 400.000 mm 0.00220 rad Di = Ѳi(hw-0.5lp) 2.575 mm 0 50 100 150 200 250 300 350 400 450 500 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 H o rz  L o ad  [ kN ] Displacement [mm] 371        APPENDIX D3.2 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITHOUT CONRETE COVER)   1:4 Column without Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 200 mm Length, l 770 mm Clear cover 0 mm Longitudinal bar spacing 245 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.904 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.002366 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm 2 mm x10 9 mm 4 x10 6 mm 3 x10 9 mm 4 mm 2 MPa kN mm 2 mm 2 Concrete 200 770 154000 385 7.61 59.29 0.00 Steel S1 2 15M 2440 17.5 0.0427 0.33 400 -0.0033 -450.00 -180.00 84111 2840.4145 S2 2 15M 2440 262.5 0.6406 0.04 400 -0.0005 -102.48 -40.99 2027 2840.4145 S3 2 15M 2440 507.5 1.2385 0.04 400 0.0023 450.00 180.00 39992 2840.4145 S4 2 15M 2440 752.5 1.8364 0.33 400 0.0051 450.00 180.00 198007 2840.4145 S 163762 7.61 63.05 0.40 yCG = SAy/SA 385.00 mm Ix = SI0 + SA(y-yNA) 2 8.01 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 2.058 x109mm4 Compression block depth, c 307.5197 mm Note: This is a random guess Concrete compression force, Pc = a1f'cb1cw -1614 kN ycc = 257.57 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 153.76 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -192.67 kN ys1 = 367.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 -53.66 kN ys2 = 122.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 180.00 kN ys3 = 122.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S4 180.00 kN ys4 = 367.50 mm Force equilibrium, Pr = Pc+Ps -1500.49 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 581.34 kNm 1:4 Column without Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.000665 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.000665 -1.51E-05 0.864 198.26866 770 -0.000693 8.35E-06 0.933 209.53327 743.54632 -0.000722 3.518E-05 1.006 223.09121 717.53096 -0.00075 6.477E-05 1.083 235.93127 692.69143 -0.000778 9.512E-05 1.161 247.78295 670.56498 -0.000807 0.0001271 1.241 258.93115 650.09106 -0.000949 0.0003078 1.670 306.46867 568.15168 -0.00109 0.0005197 2.140 344.81998 509.60731 -0.001232 0.0007451 2.628 378.70608 468.90827 -0.001374 0.0009944 3.147 410.25269 436.52616 -0.001516 0.0012578 3.686 439.34369 411.21624 -0.001657 0.0015291 4.234 466.56837 391.38684 -0.001799 0.0018046 4.789 492.23969 375.66903 -0.001941 0.0020813 5.345 516.52054 363.10761 -0.002083 0.0023748 5.923 535.60941 351.58096 -0.002224 0.0027038 6.549 547.1064 339.63885 -0.002366 0.0030316 7.173 557.54594 329.85831 -0.002508 0.0033307 7.759 564.27267 323.2199 -0.00265 0.0036165 8.327 569.89854 318.1876 -0.002791 0.0038925 8.882 574.51125 314.26012 -0.002933 0.0041611 9.427 577.9785 311.11752 -0.003075 0.0044067 9.942 580.66988 309.2668 -0.003217 0.0046415 10.443 582.15643 308.01849 -0.003358 0.0048594 10.920 582.52599 307.5197 -0.0035 0.0050645 11.381 581.34437 307.5197 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 1.2 270 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 5.800 555 11.381 581.34437 0 100 200 300 400 500 600 700 0 2 4 6 8 10 12 M o m e n t [k N m ] Curvature [rad/km] 1:4 Column without Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 1.2 270 @ f1 5.8 555 @ f2 11.3813847 581.3443667 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 39.42 54.00 0.2400 1.3700 0.0000 0.150 78.83 108.00 0.4800 1.3700 0.0000 0.300 118.25 162.00 0.7200 1.3700 0.0000 0.450 157.66 216.00 0.9600 1.3700 0.0000 0.601 197.08 270.0 1.2000 1.3700 0.0000 0.751 238.69 327.00 2.1200 1.1312 0.2388 1.012 280.29 384.00 3.0400 0.9633 0.4067 1.402 321.90 441.00 3.9600 0.8388 0.5312 1.860 363.50 498.00 4.8800 0.7428 0.6272 2.356 405.11 555.00 5.8000 0.6665 0.7035 2.875 408.96 560.27 6.9163 0.6602 0.6969 2.933 412.80 565.54 8.0326 0.6541 0.6904 3.008 416.65 570.81 9.1488 0.6480 0.6840 3.101 424.34 581.3 11.3814 0.6363 0.6716 3.336 424.34 5.866 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 385.000 mm 0.00215 rad Di = Ѳi(hw-0.5lp) 2.530 mm 0 50 100 150 200 250 300 350 400 450 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 H o rz  L o ad  [ kN ] Displacement [mm] 375        APPENDIX D4 1:8 COLUMN SPECIMEN  376        APPENDIX D4.1 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITH CONRETE COVER)  1:8 Column with Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 140 mm Length, l 1100 mm Clear cover 15 mm Longitudinal bar spacing 345 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.9039 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.0023664 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm 2 mm x10 9 mm 4 x10 6 mm 3 x10 9 mm 4 mm 2 MPa kN mm 2 mm 2 Concrete 140 1100 154000 550 15.53 84.70 0.00 Steel S1 2 15M 2440 32.5 0.0793 0.65 400 -0.0032 -450.00 -180.00 165498 2840.4145 S2 2 15M 2440 377.5 0.9213 0.07 400 -0.0005 -98.49 -39.40 3821 2840.4145 S3 2 15M 2440 722.5 1.7632 0.07 400 0.0023 450.00 180.00 80194 2840.4145 S4 2 15M 2440 1067.5 2.6051 0.65 400 0.0050 450.00 180.00 394618 2840.4145 S 163762 15.53 90.07 0.80 yCG = SAy/SA 550.00 mm Ix = SI0 + SA(y-yNA) 2 16.33 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 4.195 x109mm4 Compression block depth, c 439.313856 mm Note: This is a random guess Concrete compression force, Pc = a1f'cb1cw -1614 kN ycc = 367.96 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 219.66 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -192.67 kN ys1 = 517.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 -52.06 kN ys2 = 172.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 180.00 kN ys3 = 172.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S4 180.00 kN ys4 = 517.50 mm Force equilibrium, Pr = Pc+Ps -1498.89 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 826.84 kNm 1:8 Column with Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.000665 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.000665 -1.97E-05 0.605 282.60436 1100 -0.000693 3.453E-06 0.653 298.31479 1062.2099 -0.000722 2.989E-05 0.704 317.61669 1025.045 -0.00075 5.908E-05 0.758 335.89042 989.55989 -0.000778 8.903E-05 0.813 352.75148 957.95062 -0.000807 0.0001206 0.869 368.60603 928.7021 -0.000949 0.000299 1.169 436.14001 811.64565 -0.00109 0.0005084 1.498 490.52163 728.01072 -0.001232 0.0007313 1.839 538.36608 669.86914 -0.001374 0.0009779 2.203 582.9202 623.60893 -0.001516 0.0012385 2.580 623.94862 587.45188 -0.001657 0.0015069 2.964 662.30127 559.12413 -0.001799 0.0017795 3.352 698.42998 536.67009 -0.001941 0.0020532 3.741 732.57138 518.7252 -0.002083 0.00234 4.143 760.85586 502.67888 -0.002224 0.0026626 4.578 777.16969 485.88171 -0.002366 0.0029858 5.013 791.84923 471.93823 -0.002508 0.0032904 5.432 802.50036 461.70724 -0.00265 0.0035728 5.829 810.50304 454.55493 -0.002791 0.0038458 6.217 817.03675 448.943 -0.002933 0.0041116 6.599 821.93638 444.45357 -0.003075 0.0043545 6.959 825.73116 441.80971 -0.003217 0.0045867 7.310 827.80665 440.02642 -0.003358 0.0048021 7.644 828.28917 439.31386 -0.0035 0.0050047 7.967 826.83794 439.31386 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 0.85 400 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 4.100 780 7.967 826.83794 0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 6 7 8 9 M o m e n t [k N m ] Curvature [rad/km] 1:8 Column with Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 0.85 400 @ f1 4.1 780 @ f2 7.966969289 826.8379404 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 58.39 80.00 0.1700 1.3700 0.0000 0.106 116.79 160.00 0.3400 1.3700 0.0000 0.213 175.18 240.00 0.5100 1.3700 0.0000 0.319 233.58 320.00 0.6800 1.3700 0.0000 0.425 291.97 400.0 0.8500 1.3700 0.0000 0.532 347.45 476.00 1.5000 1.1513 0.2187 0.702 402.92 552.00 2.1500 0.9928 0.3772 0.963 458.39 628.00 2.8000 0.8726 0.4974 1.274 513.87 704.00 3.4500 0.7784 0.5916 1.614 569.34 780.00 4.1000 0.7026 0.6674 1.972 576.18 789.37 4.8734 0.6942 0.6595 2.025 583.02 798.74 5.6468 0.6861 0.6518 2.093 589.86 808.10 6.4202 0.6781 0.6442 2.175 603.53 826.8 7.9670 0.6628 0.6296 2.380 603.53 4.709 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 550.000 mm 0.00213 rad Di = Ѳi(hw-0.5lp) 2.329 mm 0 100 200 300 400 500 600 700 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 H o rz  L o ad  [ kN ] Displacement [mm] 380        APPENDIX D4.2 COLUMN SPECIMEN MOMENT-CURVATURE AND LOAD-DISPLACEMENT PREDICTIONS (WITHOUT CONRETE COVER)   1:8 Column without Concrete Cover: Section Properties CSA INPUT - MATERIAL PROPERTIES A23.3 Concrete Strength, f'c 35 MPa Uniform concrete tensile strength, ft 0 MPa Steel yield strength, fy 450 MPa Ultimate steel strength, fu 451 MPa Steel modulus of elasticity, Es 200000 MPa Concrete density, gc 2400 kg/m 3 Maximum Top compression strain, etop 0.0035 Note: Input as positive Steel resistance factor, fs 1 Concrete resistance factor, fc 1 INPUT - CROSS-SECTION PROPERTIES Width, b 140 mm Length, l 1070 mm Clear cover 0 mm Longitudinal bar spacing 345 mm Axial Load, Pf -1500 kN Tie diameter 10 mm Height of specimen, h 1370 mm CALCULATIONS - MATERIAL PROPERTIES Top compression strain, etop Current value -0.0035 Concrete modulus of elasticity, Ec =  (3300*√f'c+6900)(gc/2300) 1.5 28164.9039 MPa Compression block parameter, a1 = [(etop/e'c) - (etop/e'c) 2 /3]/b1 0.905 Compression block parameter, b1 = 4-(etop/e'c) / 6-2*(etop/e'c) 0.829 Compression strain, e'c = √f'c/2500 -0.0023664 n = Es/Ec 7.101 CALCULATIONS - CROSS SECTION PROPERTIES Width Height Area y I0 Ay A(y-yCG) 2 As ec = es fs T =fsfsAs (y-c) 2 nAs mm mm mm 2 mm x10 9 mm 4 x10 6 mm 3 x10 9 mm 4 mm 2 MPa kN mm 2 mm 2 Concrete 140 1070 149800 535 14.29 80.14 0.00 Steel S1 2 15M 2440 17.5 0.0427 0.65 400 -0.0034 -450.00 -180.00 174943 2840.4145 S2 2 15M 2440 362.5 0.8847 0.07 400 -0.0006 -117.69 -47.07 5367 2840.4145 S3 2 15M 2440 707.5 1.7266 0.07 400 0.0022 436.52 174.61 73842 2840.4145 S4 2 15M 2440 1052.5 2.5685 0.65 400 0.0050 450.00 180.00 380367 2840.4145 S 159562 14.29 85.37 0.80 yCG = SAy/SA 535.00 mm Ix = SI0 + SA(y-yNA) 2 15.09 x109mm4 Icr = bc 3/12+SAtrans*(d-c) 2 4.086 x109mm4 Compression block depth, c 435.761356 mm Note: This is a random guess Concrete compression force, Pc = a1f'cb1cw -1601 kN ycc = 354.43 mm Concrete tension force, Pt = ft (l-c) 0 kN yct = 217.88 Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S1 -192.67 kN ys1 = 517.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S2 -59.74 kN ys2 = 172.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S3 174.61 kN ys3 = 172.50 mm Steel force, Ps = SfsAs or Ps,comp = As (fs - a1f'c) S4 180.00 kN ys4 = 517.50 mm Force equilibrium, Pr = Pc+Ps -1498.91 kN Pf/Pr 1.00 Moment, Mr = Cyc + STyT 800.77 kNm 1:8 Column without Concrete Cover: Moment-Curvature CALCULATE THE STARTING POINT When c = length Top Strain = -0.000684 rad/km kNm mm Top Strain Bot Strain Phi Moment c 0 0 -0.000684 -1.12E-05 0.639 276.2911 1070 -0.000712 1.217E-05 0.688 291.45012 1034.8102 -0.00074 3.969E-05 0.741 309.94188 998.93847 -0.000768 6.836E-05 0.795 327.07297 966.51336 -0.000797 9.862E-05 0.851 343.1547 936.54734 -0.000825 0.0001304 0.907 358.29955 908.82523 -0.000966 0.0003091 1.211 423.18449 797.23189 -0.001106 0.0005178 1.543 475.81461 716.94743 -0.001247 0.0007379 1.886 522.04477 661.2514 -0.001388 0.0009838 2.253 565.45925 615.92404 -0.001529 0.0012422 2.633 605.51543 580.66565 -0.00167 0.0015083 3.019 642.99618 552.94929 -0.00181 0.0017786 3.410 678.33027 530.90883 -0.001951 0.00205 3.802 711.74468 513.24219 -0.002092 0.0023337 4.205 739.71311 497.50572 -0.002233 0.0026546 4.644 755.74269 480.83134 -0.002374 0.0029688 5.076 769.12581 467.6195 -0.002514 0.0032588 5.485 777.95651 458.39059 -0.002655 0.0035382 5.884 785.53035 451.21657 -0.002796 0.003808 6.275 791.71439 445.60303 -0.002937 0.0040699 6.657 796.3645 441.147 -0.003078 0.004311 7.020 799.86749 438.39833 -0.003218 0.0045409 7.372 801.75967 436.55248 -0.003359 0.0047543 7.709 802.12228 435.76136 -0.0035 0.0049536 8.032 800.76912 435.76136 TRI-LINEAR APPROXIMATE (BILINEAR FOR NOW WITHOUT INELASTIC PORTION) Phi Moment 0 0 0.85 380 Note: Change the moment and curvature to match a tri-linear model to the M-phi curve 4.100 755 8.032 800.76912 0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 6 7 8 9 M o m e n t [k N m ] Curvature [rad/km] 1:8 Column without Concrete Cover: Load-Displacement Note: This load-displacement approximation is based on the tri-linear M-phi approximation on the previous page MOMENT CURVATURE MODEL Curvature Moment [rad/km] [kNm] 0 0 0.85 380 @ f1 4.1 755 @ f2 8.031919193 800.7691162 LOAD-DEFORMATION RELATIONSHIP Displacement = sum of moment of curvature about the point of loading along the length of the member If f < f1, D = fL 2/3 If f2≥f≥ f1, D = f1L1 2/3+f1(L 2-L1 2)/2+(f-f1)(L-L1)(2L+L1)/6 If f≥ f2, D = f1L1 2/3+f1L2(2L1+L2)/2+L2(f2-f1)(2L2+3L1)/6+f2[L 2-(L1+L2) 2]/2+(f-f2)(L-L1-L2)(2L+L1+L2)/6 Elastic Deformation Horz. Load P Moment = Plw Curvature Length @ f1 Length @ f2 Displ. D [kN] [kNm] [rad/km] L1 [m] L2 [m] [mm] 0 0.00 0.0000 0.0000 0.0000 0.000 55.47 76.00 0.1700 1.3700 0.0000 0.106 110.95 152.00 0.3400 1.3700 0.0000 0.213 166.42 228.00 0.5100 1.3700 0.0000 0.319 221.90 304.00 0.6800 1.3700 0.0000 0.425 277.37 380.0 0.8500 1.3700 0.0000 0.532 332.12 455.00 1.5000 1.1442 0.2258 0.707 386.86 530.00 2.1500 0.9823 0.3877 0.974 441.61 605.00 2.8000 0.8605 0.5095 1.289 496.35 680.00 3.4500 0.7656 0.6044 1.633 551.09 755.00 4.1000 0.6895 0.6805 1.994 557.78 764.15 4.8864 0.6813 0.6723 2.047 564.46 773.31 5.6728 0.6732 0.6644 2.116 571.14 782.46 6.4592 0.6653 0.6566 2.199 584.50 800.8 8.0319 0.6501 0.6416 2.407 584.50 4.726 Note: This row is for inelastic displacement Inelastic Deformation Ѳi = (fcap - fy)*lp where lp [mm] = 535.000 mm 0.00210 rad Di = Ѳi(hw-0.5lp) 2.319 mm 0 100 200 300 400 500 600 700 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 H o rz  L o ad  [ kN ] Displacement [mm] 384         APPENDIX E THE CHILEAN WALL SPECIMEN   385  E1 INTRODUCTION The main reason for this research originally was to determine the bending behaviour of Chilean columns under an applied lateral displacement.  In February 2010, an earthquake of magnitude 8.8 occurred in the coast of the Maule Region, Chile.  Observations show that most buildings collapsed because of failures of columns and walls on the ground level. These Chilean walls, as referred to in this thesis due to their long and slender appearances, have a large cross sectional length-to-width ratio, which is similar to the 1:8 column specimen in this test.  They were designed as columns, and expected to perform like columns under earthquake loads. However, due to their length and slenderness, it was of concern that they may actually act like walls more than columns, but since they were not shear walls, their displacement and bending capacities are questionable.   The main reason for this test was to determine the differences in behaviour of columns with different cross-sectional width-to-length rations, and to determine whether shape played an important part in the failure of the Chilean columns. The Chilean Wall specimen, as discussed in Chapter 2, has the same cross sectional dimensions and longitudinal rebars as the 1:8 column specimen.   The only difference is the arrangement of ties.  In the Chilean Wall specimen (later changed to 1:8 Wall specimen), the tie hoops were formed by putting two G-shape ties together, one on top of each other in opposite directions.  There were no cross-ties or U-shape hooks at the end of the ties (Figure E1.1). 386   Figure E1.1 – Chilean Wall Specimen  E2 TESTING PROCEDURE While all the column specimens were tested with axial compression and lateral load, the Chilean Wall specimen was originally designed to be tested with both axial tension and compression with lateral load.   The Chilean Wall specimen simulates a small part of a larger wall on the edge, which, during an earthquake, will experience both tension and compression with a rotation (Figure E2.1).  Figure E2.1 – Element Experiences both Tension and Compression in Earthquake  387  The original testing protocol of the specimen includes the application of axial tension in the specimen until a certain extent (eg. cracking) to weaken the specimen, before applying axial compression and cycling it laterally.  E3 TEST SET-UP Much design work had been done on the test frame for the application of axial tension. To apply tension, the connection from the vertical jack to the floor must be solid to allow the jack pushing onto a support.  A small supporting ‘table’ made from steel HSS and plates was first proposed to be installed below the vertical jacks on both sides (Figure E3.1).  The vertical jack is connected to the I-beam in the loading cruciform on top, and the table stands on the ground on its own.  Four Dywidag rods connected to the bottom swivel plate of the jack go through four enlarged holes at the top plate of the table and connected to a steel plate that is placed inside the table.  A single Dywidag rod ties this steel plate to the floor.  During axial compression, the vertical jacks will be pulling up on the four Dywidag rods which will be pulling the rod connected to the ground.  The table will play no part in compression loading.  During axial tension, the jack will push outward, and the bottom swivel plate will rest on the top of the table which helps to transmit the load to the floor by the four HSS.  388   Figure E3.1 – Set-up for Tension Application  In the case of the square foundation, where the vertical jack is not in alignment with the hole on the ground, an extra HSS is placed horizontally on top of the steel plate inside the table to span over two adjacent holes (Figure E3.2). 389   Figure E3.2 – Different Set-up for Different Footings  On the specimen, four rods were added to the top when casted which would be connected to the loading cruciform for applying tension (Figure E3.3). 390   Figure E3.3 – Extra Rods on Chilean Wall Specimen for Applying Tension  E4 CHILEAN WALL ANALYSIS E4.1 Modeling the Specimen with VecTor2 Vector2 was used to model the Chilean Wall Specimen.  The model was set up in Formworks, the pre-processor of VecTor2.  The concrete and steel material properties were first defined in the program.  The column model was built by specifying the dimensions in terms of nodes and meshing it into a number of elements.  The column was then assigned the concrete properties defined earlier.  The reinforcing bars were modeled as line trusses and assigned the steel properties according to the designation of the bars used (Figure E4.1). 391   Figure E4.1 – Chilean Wall Specimen Model in VecTor2  E4.2 Specimen Model Push-over Analysis with Axial Compression Two load cases were considered in the model, gravitational loading and reverse cyclic loading due to a lateral load applied at the top of the column.  A constant load of 1500 kN acted on the top of the specimen.  Distributing it evenly over 12 nodes, a force of 125 kN was applied at each node at the top, which was kept constant by a factor of 1.0 throughout the analysis.  The lateral load was defined as a unit displacement on the top node on the left, pushing to the right.  During the analysis, the unit displacement was increased from a factor of 0 to 10, with displacement increments of 0.05 mm.  The maximum displacement factor of 392  10 was used according to double the value of the predicted maximum displacement due to cross-sectional properties, 8.4 mm. The FormWorks model was then run in VecTor2, and the results viewed in Augustus, the post-processor of VecTor2.  Looking at the load-displacement graph of the output, the specimen model is observed to fail at around 5 mm displacement (Figure E4.2).  From the crack patterns at failing displacement, it can be seen that most cracks are concentrated at the bottom tension side of the specimen, with less diagonal cracks across the face (Figure E4.3). This indicates that the failure mode is bending and not shear.  Figure E4.2 – Load-Displacement for Chilean Wall Specimen in VecTor2  393   Figure E4.3 – Crack Patterns for Chilean Wall Specimen at Failure  Since there is a limitation on VecTor2 and it was not possible to simulate a tension load before the compression and lateral loads, only push-over analyses with compression load were done in the prediction phase.  E4.3 Modeling the Chilean Wall with VecTor2 Vector2 was also used to model the Chilean Wall specimen as an element in a larger wall prototype.  The results from this analysis were used to determine the loading forces for testing this specimen.  The Chilean Wall specimen is a piece of a larger wall located near the 394  base.  Using Vector2, a wall of length 30 ft (9900 mm) and height approximately ten times the length (98640 mm) was modeled with elements of size the same as the Chilean wall specimen (1100 mm length x 1370 mm) (Figure E4.4).  An axial load of 0.5f’cAg (2079 kN) was applied on the wall while the wall was pushed sideways by an increasing force at the top, simulating earthquake forces.  Figure E4.4 – Wall Prototype Model in VecTor2  The model was tested by applying a unit displacement at the top left corner of the wall in FormWorks and increasing it from a displacement factor of 0 to 3000.  The value of 3000 was determined by multiplying the length of the wall, 98640 mm, by 0.03, assuming 395  around 3% maximum drift.   Figure E4.5 shows the load-displacement plot of the wall and Figure E4.6 shows the crack pattern.  Figure E4.5 – Load-Displacement of Wall Prototype Model in VecTor2  Figure E4.6 – Crack Patterns for Wall Prototype Model in VecTor2 396  E4.4 Element Behaviour in the Wall Prototype Model Elements at approximately lw from the base of the wall were further looked into in terms of the axial force, shear force and lateral displacement on the element.  Elements 64, 65, 66, 70, 71 and 72 (Figure E4.7) were considered.  Figure E4.7 – Elements at One Wall Length from Base  E4.4.1 Edge Elements – Elements 64 & 72 Since the push-over analysis was done with the displacement applied from the left of the wall specimen, element 64 will experience axial tension while element 72 will experience axial compression.  Figures E4.8 to E4.10 below show the plots of lateral load vs. axial load on element, element shear stress vs. total displacement and element shear stress vs. element strain. 397   Figure E4.8 – Lateral Load vs. Axial Load for Edge Elements  Figure E4.9 – Element Shear Stress vs. Total Displacement for Edge Elements  398   Figure E4.10 – Element Shear Stress vs. Element Strains for Edge Elements  Looking at the earthquake case as illustrated in Figure E2.1, the red line simulates pulling on the specimen (data collected from element 64 in the model), where the element will experience axial tension and the blue line simulates pushing on the specimen (data collected from element 72 in the model), where the element will experience axial compression.  E4.4.2 Second Elements – Elements 65 & 71 Similar to the edge elements, the different behaviour for the second element from the edge are plotted and shown in Figures E4.11 to E4.13 below.    399   Figure E4.11 – Lateral Load vs. Axial Load for Second Elements   Figure E4.12 – Element Shear Stress vs. Total Displacement for Second Elements 400   Figure E4.13 – Element Shear Stress vs. Element Strains for Second Elements  E4.4.3 Third Elements – Elements 66 & 70 Lastly, the different behaviour for the third element from the edge are plotted and shown in Figures E4.14 to E4.16 below.  Figure E4.14 – Lateral Load vs. Axial Load for Third Elements 401   Figure E4.15 – Element Shear Stress vs. Total Displacement for Third Elements   Figure E4.16 – Element Shear Stress vs. Element Strains for Third Elements  402  Coming paring the three sets of elements, the specimen can take much more axial compression while pushing sideways than axial tension.  This is also due to the applied constant axial load of 0.05f’cAg which increased the lateral force needed before the element experiences axial tension.  From the lateral vs. axial load plots of the interior elements, it can be seen that at very large displacements, the initial axial compression force becomes stable, then decreases as the rotation caused by the lateral force governs, deflecting the whole wall and pulling on the elements on the compression side. Similarly, shear stress on the compression side is much larger than that on the tension side due to the effect of the initially applied axial load.  E5 CONCLUSION  In the end, it was decided that the Chilean Wall specimen was not to be tested in tension due to the complexity in constructing the test set-up and actually running the jacks with the desired loading protocol.  Moreover, the Chilean Wall specimen could also be viewed as a bearing wall due to its height and slenderness and can be tested like a wall specimen rather than an elongated column specimen.  In order to make the test uniform and the results comparable, the Chilean Wall specimen was changed to the 1:8 wall specimen and was test the same way as the other column specimens.  A constant axial load of 1500 kN was applied while the specimen was cycled horizontally in both directions.  The only difference in this specimen to the column specimens would be the lack of cross ties and tie arrangement.  Further research is to be done to study the behaviour of these slender columns under tension and lateral forces.

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