TABLE OF CONTENTS
DECLARATION................................................................................................ i
v
APPROVAL..................................................................................................... ii
ACKNOWLEDGEMENT ....................................................................................iii
ABSTRACT ................................................................................................... iv
TABLE OF CONTENTS ................................................................................... iv
LIST OF FIGURES .........................................................................................vii
LIST OF TABLES ........................................................................................... ix
CHAPTER ONE: INTRODUCTION ............................................................ 1
1.1 Background ............................................................................................. 1
1.2 PROBLEM STATEMENT............................................................................. 2
1.3 MAIN OBJECTIVES ................................................................................... 3
1.4 SPECIFIC OBJECTIVES ............................................................................. 3
1.5 RESEARCH SIGNIFICANCE: ...................................................................... 3
CHAPTER TWO: LITERATURE REVIEW ................................................... 4
2.1 COMPARISION BETWEEN SOLID AND HOLLOW REINFORCED CONCRETE
BEAMS .......................................................................................................... 4
2.2 REINFORCEMENT DETAILING IN HOLLOW SECTIONS................................ 6
2.3 FINITE ELEMENT ANALYSIS ..................................................................... 6
2.3.1 FEM Solution Process Procedures ........................................................... 7
2.3.2 Basic Theory ......................................................................................... 7
2.3.3 Element types ....................................................................................... 8
2.4 DEVELOPING MATERIALS MODELS AND FAILURE BEHAVIORS IN MODELS10
2.4.1 Concrete Plastic Damage Model. .......................................................... 10
2.4.2 Damage Parameters............................................................................ 11
2.5 FAILURE MODES.................................................................................... 11
2.5.1 Fracture.............................................................................................. 11
2.5.2 Flexural shear cracking ........................................................................ 12
2.5.3 Splitting failure.................................................................................... 13
2.5.4 Web crushing...................................................................................... 14
2.5.6 STRESS –STRAIN BLOCK OF RECTANGULAR HOLLOW SECTION............ 16
2.5.7 CONFINEMENT OF REINFORCED CONCRTE COLUMN............................ 17
vi
2.5.9 CRACK PROPAGATION......................................................................... 19
2.5.9.1 SMEARED CRACK MODELS................................................................ 20
2.6 SOLUTION METHOD .............................................................................. 21
CHAPTER THREE: METHODOLOGY ...................................................... 21
3.0 Introduction........................................................................................... 21
3.1 Data collection Establishing study parameters.......................................... 22
3.2 Pre process modeling of the structural models in FEM using Abaqus ......... 26
3.2.1 Flowchart of the pre-process modeling and post process analysis in
Abaqus ....................................................................................................... 26
3.3 MODELING OF PARTS ............................................................................ 26
3.5 ASSIGNING MATERIAL PROPERTIES TO PARTS ....................................... 27
3.5.1 Concrete Beam models ........................................................................ 27
3.5.2 REINFORCEMENTS.............................................................................. 29
3.6 ASSEMBLING THE MODLED PARTS ......................................................... 31
3.8 MESHING / DISCRETISATION OF THE MODELS ....................................... 35
3.9 SUBMITION OF THE JOB/STATIC ANALYSIS............................................ 37
CHAPTER FOUR: RESULTS AND DISCUSSION...................................... 38
4.1. STRESS AND STRAIN DISTRIBUTION..................................................... 38
4.4.1 Stress distribution in reinforcements..................................................... 41
CHAPTER FIVE : CONCLUSIONS AND RECCOMMENDATION................ 54
5.1 Conclusion............................................................................................. 54
5.2 RECOMMENDATIONS ............................................................................. 55
REFERENCES............................................................................................... 57
APPENDEX 1: FORMULAES ........................................................................... 60
APPENDIX 2: MODIFIED STRESS- STRAIN CURVES UNDER COMPPRESSION
AND TENSION............................................................................................. 61
ABSTRACT Performance of beams with pvc pipes embedded at the center or with an eccentric pipes needs design consideration of influencing variables such as the pipe size and the location of the pipe being embedded. This was performed analytically where six RC beams of dimension (300x450 and span of 3500) were modeled in Abaqus 6.10-3 of which one was a solid beam and the 5 had varying pipe sizes and location of the pipe as designated (B-25.4, B-50.8mm,B-76.2mm,B-101.2mmE50 and 127mmE 100mm).The models were assigned correctly with their material properties both elastically and plastically of which CDP(concrete damaged plasticity) and other damage parameters from Abaqus manual were incorporated which helped in defining the failure mechanisms in concrete. The beam models were treated as simply supported beam and loaded with a concentrated load(500KN) in addition meshing was done and the concrete elements were assigned with an element type C3D8R hexagonal elements and meshed with 50x50mm mesh size and for reinforcements were meshed with global size of 100mm. The analysis was submitted and results (stresses, strain, load-deflection ductility index and crack patterns) of beams were compared to solid beam. The results indicated an increase in stresses in concrete and bottom reinforcement as the pipe size increases and reduction in loading capacity and ductility index as the pipe size and location varied. Therefore, the size and location of the pipes in beams affects the strength, stiffness and ductility of the RC beams.