Flexural and shear strength of prestressed ultra high strength fiber reinforced concrete composite girders

다국어 초록 (Multilingual Abstract)

Flexural and Shear Strength of Prestressed Ultra High Strength Fiber Reinforced Concrete Composite Girders

Xiang - Guo Wu

Department of Civil Engineering, Graduate School
Kumoh National Institute of Technology

Abstract
Ultra-High Performance Fiber-Reinforced Concretes (UHPFRC) has high compressive strength and exhibit strain hardening behavior. Post tensioned UHPFRC composites girder is a new type composites structure and application of UHPFRC material. Composites responses influence the main structural behavior including ultimate flexural and ultimate shear. The objectives of the study are to proposed estimate formula for ultimate loading capacity and cracking loading capacity. Towards this subject, the current knowledge of UHPFRC properties is to be modeled in order to predict the structural behaviour of such composite elements and to make recommendations for the main failure modes evaluations, i.e. flexural cracking load, ultimate flexural state and ultimate shear state, diagonal shear cracking load, ultimate shear connection capacity.
Experimental programs are performed to characterize the UHPFRC and determine the structural behaviour of composite elements through two full-scale UHPFRC composites and four full-scale UHPFRC girders with two kinds of mixing proportion UHPFRC. Prestressing losses are investigated during six weeks starting from the post tensioned UHPFRC girders. After the long-term measurements, two girders embedded with shear connectors are casted with Normal Concrete slab (NC). All the UHPFRC girder and composites are loaded under three point bending tests. Push tests are also carried out with the UHPFRC sandwich specimens to obtain the interfacial shear connection behavior which is the basis of the longitudinal interface shear analysis. Two shear connection parameters i.e. the initial elastic stiffness and slippage capacity are certificated as two constant parameters.
Ultimate flexural strength of UHPFRC composites and UHPFRC girder are analyzed. An overlapping method of the initial internal moment and the additive flexural moment is proposed to avoid the traditional complicate stress distribution of post tensioned girder. An equivalent rectangular tensile stress block is derived to simplify the flexural tensile stress distribution of UHPFRC girder. The initial internal moment of UHPFRC girder due to the effective prestressing stress is derived. Cracking loading capacity of UHPFRC composites and girder are also obtained. Full interaction behavior can be assumed at the mid-span section of the girder and ensure the compatibility response of the two elements. Finally, the moment capacity is obtained by superimposing of the additive moment due to extra loading with the initial internal moment. Overlapping method is also used to obtain the moment capacity of post tensioned UHPFRC girder. Calculation of the test specimens are carried out to predict the ultimate flexure strength and cracking loading capacity of UHPFRC composites and UHPFRC girder. Some parameters influences are discussed on the ultimate flexural capacity of post tensioned UHPFRC composites and girder. The ultimate flexural loading capacity formulae are simplified with the neglect of the bottom flange part in the equivalent tensile stress block. This part influence is small from the comparison analysis.
Based on two bounds theory which is an extension of the classical limit plasticity theory, ultimate shear behavior is investigated based on three point bending UHPFRC composites and UHPFRC girder. Beside the fiber parameters of fiber volume fraction, fiber length, diameter, interfacial bonding strength and tensile strength, fiber orientation is also considered in the fiber reinforcing model based on fiber uniform distribution assumption. This fiber reinforcing model is used to analyze the ultimate shear loading capacity and diagonal cracking loading capacity of UHPFRC composites and UHPFRC girder. Upper bound is derived based on the kinematical admissible failure mechanism and the low bound is derived based on cracking moment equilibrium analysis. According to the uniqueness theorem, the interaction of the two bounds constitutes the ultimate diagonal shear strength of UHPFRC structure. The two bounds expression is simplified approximately with constant diagonal cracking angle assumption. Some parameters influences on the ultimate shear strength are also analyzed. First diagonal cracking loading capacity formula is proposed based on the upper bound simplification by ignoring the influences of the fiber reinforcement. Beside the two bounds model, strut-tie models are constructed with strut compressive failure mode and strut splitting failure mode. Comparisons show that the two bounds theoretical model predictions and strut splitting failure model predictions are closer to the ultimate diagonal shear failure load of post tensioned UHPFRC composites girder.
For short span UHPFRC girder, large gap exists between the loading capacity of UHPFRC composites and UHPFRC girder. However, the gap decreases with the increasing of the span length of UHPFRC girder. For long span UHPFRC girder, the gap is small. This indicate the composites strengthen response is significant for short span girder and non-significant for long span girder.
Longitudinal interface shear force of UHPFRC composites is derived based on the linear elastic assumption. Two parameters of shear connection i.e. the initial elastic modulus and slippage capacity are obtained from the lateral direct push test of UHPFRC composites specimen. Test results proof that the initial elastic modulus and slippage capacity are two constant parameters of UHPFRC composites interface shear connection which is similar with steel composites interface shear characters. Shear connection degree is an important design parameter and it is the basis of criterion of full shear connection and partial shear connection. The ultimate state of longitudinal interface shear is assumed as the cracking state of the UHPFRC girder to define the shear connection degree which is a key parameter of the interface shear connection design. The shear connection degree can be used for the estimation of shear connector design. Calculations of the interface shear force and interface slippage are carried out. Based on the shear interfacial force distribution, shear connectors placement technology is recommended finally. Since cracking propagation of UHPFRC girder can influence the longitudinal interface shear force, the ultimate state of UHPFRC girder is different with the ultimate state of traditional steel composites girder, linear elastic interface analysis is certificated as the main character.
The formulae of the ultimate flexural and ultimate shear of post tensioned UHPFRC composites girder and UHPFRC girder are proposed which can be used to estimate the ultimate loading capacity of UHPFRC composites and girder. Beside the ultimate flexural and ultimate shear, the formulae of the flexural cracking loading capacity and the diagonal cracking loading capacity of the composites and girder are also proposed which can be used to estimate the cracking loading capacity of flexural and diagonal cracking for post tensioned UHPFRC composites and girder. The simplifications of the ultimate flexural and ultimate shear are more convience for practical UHPFRC ultimate behavior estimations.

다국어 초록 (Multilingual Abstract)

Flexural and Shear Strength of Prestressed Ultra High Strength Fiber Reinforced Concrete Composite Girders

Wu Xiang-Guo

Department of Civil Engineering, Graduate School
Kumoh National Institute of Technology

요약

UHPFRC 합성거더는 새로운 형태의 합성 구조물로서, 구조적으로 강합성 거더와는 다른 거동 특성을 보인다. 본 논문에서는 UHPFRC 합성부재 및 거더에 대한 구조실험을 수행하고, 실험결과를 바탕으로 포스트텐션 방식의UHPFRC 거더 및 합성부재에 대해 극한 휨강도, 극한 전단력, 휨균열, 사인장 전단균열 및 합성계면에서의 전단균열저항력 등에 대한 구조해석을 실시하였다. 구조해석 시 적용한 섬유보강 모델은 섬유혼입률, 섬유길이, 섬유직경, 섬유와 매트릭스의 부착강도, 섬유의 인장강도와 같은, 섬유와 관련한 변수뿐만 아니라 섬유의 방향성도 고려하였으며, 섬유는 임의적으로 분포되어 있어 모든 방향에 대해 동일한 확률로 분포하는 것으로 가정하였다. 섬유보강 모델은 UHPFRC 합성부재 또는 거더에서의 극한 전단력 산정 및 사인장 균열 발생 하중을 산정하기 위한 상한계, 하한계 모델에 적용되었다. UHPFRC 합성부재의 전단연결 성능은 합성단면에서의 전단력 평가를 통해 이루어졌다. 본 연구에서는 포스트텐션 방식의 UHPFRC 거더 및 합성부재의 내하력 평가가 가능하도록 극한 휨강도 및 전단력에 관한 모델식을 간편식의 형태로 제안하였다. 또한 포스트텐션 방식의 UHPFRC 거더 및 합성부재에 대해 균열발생 하중을 평가할 수 있도록 휨균열 및 전단균열 발생강도에 관한 모델식을 제안하였다. 그리고 본 연구에서 제안한 전단 연결도(shear connection degree)는 UHPFRC 합성부재의 완전부착과 부분부착에 대한 기준으로 사용될 수 있다.

목차 (Table of Contents)

• TABLE OF CONTENTS
• 1 Introduction 1
• 1.1 Development and application of UHPFRC 1
• 1.2 UHPFRC composites girder 5
• 1.3 Failure modes of UHPFRC composites girder 7
• 1.4 Aim of this study 7
• 1.5 Thesis structure 8
• 2 Material Characterizations and Constitutive Model 9
• 2.1 Development of UHPFRC 9
• 2.1.1 Definition 9
• 2.1.2 Historical overview 10
• 2.1.3 Principles of UHPFRC 11
• 2.2 Mixing and curing process 12
• 2.2.1 Mixing proportion 12
• 2.2.2 Curing procedure 13
• 2.2.3 Mixing method 13
• 2.3 Material mechanical properties and constitutive model 14
• 2.3.1 Compressive experiment results of UHPFRC 14
• 2.3.2 Compressive strength, modulus and equivalent stress block 16
• 2.3.3 Tension behavior of UHPFRC 18
• 2.3.4 Tensile model of UHPFRC 20
• 2.3.5 Reinforcement steel bar 25
• 2.3.6 Prestressed tendon 25
• 2.3.7 Steel shear connector 25
• 2.3.8 Normal concrete 26
• 3 Structure Tests 27
• 3.1 Structure specimen dimension 27
• 3.1.1 Composites structure specimen dimension 27
• 3.1.2 Push test specimen dimension 28
• 3.2 Specimens construction 30
• 3.2.1 Constructions of UHPFRC girder and push test specimen 30
• 3.3 Loading test of UHPFRC girder and composites 35
• 3.3.1 Test results of specimen UPoG-6-3 35
• 3.3.2 Test results of specimen UPoG-6-4 37
• 3.3.3 Test results of specimen UPoCG-6-5 39
• 3.3.4 Test results of specimen UPoCG-3-7 41
• 3.3.5 Test results of specimen UPoG-3-6 43
• 3.3.6 Test results of specimen UPoG-3-2 45
• 3.4 Push tests 48
• 3.4.1 Push test experiment 48
• 3.4.2 Push tests procedure 49
• 3.4.3 Test results analysis 54
• 4 Ultimate Flexure of UHPFRC Girder and Composites 57
• 4.1 Limit state of the composites material 57
• 4.2 Effective width of the NC slab 58
• 4.3 Initial effective strain of post tensioned UHPFRC girder 60
• 4.3.1 Elastic shortening of concrete 61
• 4.3.2 Prestressing losses by steel stress relaxation 61
• 4.3.3 Anchorage seating stress losses 62
• 4.3.4 Initial effective prestressing force of UHPFRC girder 62
• 4.4 Flexural cracking loading capacity of UHPFRC girder 63
• 4.4.1 Flexural cracking loading capacity evaluation 63
• 4.4.2 Initial design step with constant tendon eccentricity 66
• 4.4.3 Initial internal moment after prestress losses 67
• 4.4.4 Ultimate flexural strength of post tension UHPFRC girder 69
• 4.5 Flexural srength of post tensioned UHPFRC composites girder 74
• 4.5.1 Equavilent cross section and area moment 74
• 4.5.2 The cracking loading capacity evaluation 75
• 4.6 Ultimate flexural strength of UHPFRC-NC composites girder 77
• 4.6.1 Equilibrium analysis 77
• 4.6.2 Ultimate flexural anaysis with NC compression failure 79
• 4.6.3 Ultimate flexural anaysis of tension failure of tendon 84
• 4.6.4 Ultimate flexural anaysis of UHPFRC tension failure 87
• 4.6.5 Degree of UHPFRC-NC shear connection 90
• 4.6.6 Global distribution of shear connectors 92
• 5 Ultimate Shear of UHPFRC Composites and Girder 93
• 5.1 General 93
• 5.2 Fiber reinforcing parameter 95
• 5.3 Ultimate shear failure of UHPFRC-NC composites girder 97
• 5.3.1 Ultimate shear failure mechanism 97
• 5.3.2 Geometrical parameters of the model 98
• 5.3.3 Internal dissipation works and external work 99
• 5.3.4 External work 105
• 5.3.5 Total internal work 105
• 5.4 Diagonal cracking load analysis 110
• 5.5 Shear capacity of UHPFRC-NC composites beams 111
• 5.6 FDCL of UHPFRC-NC composites girder 112
• 5.7 Calculation of the ultimate shear strength 112
• 5.7.1 Variation of the two bounds with cracking position 112
• 5.7.2 Influence of fiber volume fraction on ultimate shear load 114
• 5.7.3 Fiber parameters influences on the shear failure load 115
• 5.7.4 Ultimate shear load variation with NC element parameters 115
• 5.8 Ultimate shear analysis of post tension UHPFRC girder 116
• 5.8.1 Geometrical parameters of the model 116
• 5.8.2 Ultimate shear analysis (Upper Bound) 117
• 5.8.3 Diagonal cracking load (Low Bound) 119
• 5.8.4 Calculations of the two bounds 120
• 5.9 FDCL of post tensioned UHPFRC girder 121
• 5.10 Strut-tie model analysis 123
• 5.10.1 Strut compressive failure mode of UHPFRC composites 123
• 5.10.2 Strut splitting failure mode of UHPFRC composites 127
• 5.10.3 Strut compressive failure mode of UHPFRC girder 127
• 5.10.4 Strut splitting failure mode of UHPFRC girder 128
• 6 Longitudinal Interface Shear Connection Capacity of UHPFRC Composites 130
• 6.1 Proposal formulae for interfacial shear connection 130
• 6.1.1 Strength of shear connections in UHPFRC-NC 131
• 6.1.2 Load-slip relationship 132
• 6.1.3 Maximum load, maximum slip and initial mean stiffness 132
• 6.2 Linear elastic analysis 133
• 6.2.1 General analysis 133
• 6.2.2 Fracture strength analysis 140
• 6.2.3 Calculations of the interface shear force 141
• 7 Conclusions 144
• References 146
• Paper List 155
• Acknowledgements 157
• LIST OF FIGURES
• Fig. 1.1 Standard UHPFRC composites analysis element 6
• Fig. 1.2 Thesis structure 8
• Fig. 2.1 Definition of UHPFRC 9
• Fig. 2.2 Mixing method 14
• Fig. 2.3 Test results of the compressive constituents relation of UHPFRC 15
• Fig. 2.4 Equivalent stress block of UHPFRC linear compression 16
• Fig. 2.5 Equivalent stress block of UHPFRC nonlinear compression 17
• Fig. 2.6 Geometrical dimension of the specimen 19
• Fig. 2.7 Variation of tensile stress with deformation strain of UHPFRC 20
• Fig. 2.8 Cracking definition in tension for UHPFRC section 21
• Fig. 2.9 Localized crack in pure bending for UHPFRC section 22
• Fig. 2.10 Simplified tensile constitutive model of UHPFRC 22
• Fig. 2.11 Equvalent stress block 23
• Fig. 2.12 Equvalent stress blokc for claculation 24
• Fig. 2.13 Equvalent renctangular stress block at the ultimate state 24
• Fig. 2.14 Mechanical shear connector geometrical dimension 25
• Fig. 2.15 Idealized stress-strain curve of compressive concrete 26
• Fig. 3.1 UHPFRC-NC composites structural system 28
• Fig. 3.2 Specimen embedded with one shear connector 28
• Fig. 3.3 Specimen embedded with two shear connectors 29
• Fig. 3.4 Specimen embedded with three shear connectors 29
• Fig. 3.5 Variation of load with midspan deflection of UPG-6-3 36
• Fig. 3.6 Strain distribution at the vertical critical section 36
• Fig. 3.7 Stress distribution at the vertical critical section 37
• Fig. 3.8 Variation of load with midspan deflection of UPoG-6-4 38
• Fig. 3.9 Strain distribution at the vertical critical section 38
• Fig. 3.10 Stress distribution at the vertical critical section 39
• Fig. 3.11 Variation of load with midspan deflection of UPoCG-6-5 40
• Fig. 3.12 Strain and stress distributions 41
• Fig. 3.13 Variation of load with midspan deflection of UPoCG-3-7 42
• Fig. 3.14 Strain distribution at the vertical critical section 43
• Fig. 3.15 Variation of load with midspan deflection of UPoG-3-6 44
• Fig. 3.16 Strain distribution at the vertivcal critical section 44
• Fig. 3.17 Stress distribution at the vertical critical section 45
• Fig. 3.18 Variation of load with midspan deflection of UPoG-3-2 46
• Fig. 3.19 Strain distribution at the critical section 47
• Fig. 3.20 Stress distribution at the vertical section 48
• Fig. 3.21 Push test results of the first loading scheme 51
• Fig. 3.22 Push test results of the modified loading scheme 54
• Fig. 3.23 Initial elastic modulus of shear connection 55
• Fig. 3.24 Ultimate slippage of interfacial shear connection 56
• Fig. 4.1 Idealized stress distribution for ultimate strength of NC 58
• Fig. 4.2 Effective width 59
• Fig. 4.3 Effective span for simply supported structure 60
• Fig. 4.4 Cross section of post tension UHPFRC girder 63
• Fig. 4.5 Comparison of the cracking loading capacity of UHPFRC girder 65
• Fig. 4.6 Variation of the cracking failure load and midspan deflection 66
• Fig. 4.7 Elastic fiber stresses after losses 68
• Fig. 4.8 Ultimate flexural analysis of post tension UHPFRC girder 69
• Fig. 4.9 Influence of the last term on the total moment in Eq.4-42 71
• Fig. 4.10 Comparison of the ultimate flexural strength of UHPFRC girder 73
• Fig. 4.11 Variation of the ultimate loading capacity 73
• Fig. 4.12 Variation of the midspan deflection 74
• Fig. 4.13 Transformed section of composites elements 74
• Fig. 4.14 Comparison of the cracking loading capacity 76
• Fig. 4.15 Variation of the cracking failure load 77
• Fig. 4.16 UHPFRC composites mid-span cross section equilibrium analysis 78
• Fig. 4.17 UHPFRC composites ultimate flexure with NC compression failure 80
• Fig. 4.18 Tensile stress distribution of UHPFRC 81
• Fig. 4.19 Tensile stress block in the web and the flange 81
• Fig. 4.20 UHPFRC composites ultimate flexure of tension failure of tendon 84
• Fig. 4.21 Ultimate flexure of UHPFRC tension failure 87
• Fig. 4.22 Comparison of the ultimate flexural loading capacity of UHPFRC composites 89
• Fig. 4.23 Shear analysis along the UHPFRC composites structure 92
• Fig. 5.1 Arbitrary distribution of fibers on unit section 95
• Fig. 5.2 Vertical projection and embedding length of fibers 96
• Fig. 5.3 Diagonal shear crack propagation model of UHPFRC composites 98
• Fig. 5.4 Ultimate diagonal shear model of UHPFRC composites 99
• Fig. 5.5 Stress distribution in the membrane due to the extral load 102
• Fig. 5.6 Stress element analysis of UHPFRC composites girder 106
• Fig. 5.7 Cross section of UHPFRC composites girder 106
• Fig. 5.8 Stress distribution along the critical diagonal crack 110
• Fig. 5.9 FDCL of UHPFRC composites girder 112
• Fig. 5.10 Variation of the two bounds with the cracking position 113
• Fig. 5.11 Comparison of test results with predictions 113
• Fig. 5.12 Variation of ultimate shear load with fiber volume fraction 114
• Fig. 5.13 Variation of the ratio of ultimate shear load with and without fiber 114
• Fig. 5.14 Variation of the ultimate shear load with fiber diameter and length 115
• Fig. 5.15 Variation of the ultimate shear load with NC element width and height 116
• Fig. 5.16 Ultimate shear failure state of post tension UHPFRC girder 116
• Fig. 5.17 Ultimate shear model of UHPFRC girder 117
• Fig. 5.18 Diagonal cracking model (Low Bound analysis) 119
• Fig. 5.19 Two bounds numerical calculation 121
• Fig. 5.20 FDCL variation along the girder with different girder net span length 122
• Fig. 5.21 Comparisons of the ultimate failure load 123
• Fig. 5.22 Comparison of the ultimate shear between composites and girder 123
• Fig. 5.23 UHPFRC composites girder strut and tie model-I 124
• Fig. 5.24 Typical nodal zones analysis of UHPFRC composites composites model 124
• Fig. 5.25 Two struts ultimate strength 126
• Fig. 5.26 UHPFRC girder strut and tie model 127
• Fig. 5.27 Typical nodal zones analysis of UHPFRC model 128
• Fig. 5.28 Comparisons of the short span UHPFRC composites girder 129
• Fig. 5.29 Comparisons of the short span UHPFRC composites girder 129
• Fig. 6.1 Push test Shear connection characteristics 131
• Fig. 6.2 The load slip model of the shear connection in this project 132
• Fig. 6.3 Linear elastic analysis of UHPFRC composites analysis 134
• Fig. 6.4 General analysis procedure for fracture 138
• Fig. 6.5 Variation of interfacial shear force with external load 141
• Fig. 6.6 Interfacial shear force with external load and longitudinal coordinates (half span) 141
• Fig. 6.7 Interfacial shear force with external load and longitudinal coordinates (full span) 142
• Fig. 6.8 Variation of supporting end slippage with concentrated load 142
• LIST OF PHOTOES
• Photo 1.1 UHPFRC composites structure application 5
• Photo 2.1 Workability and ductility of UHPFRC 10
• Photo 2.2 Steel fiber used in set A and set B 13
• Photo 2.3 Normal sand and fine sand 13
• Photo 2.4 High energy mixture 14
• Photo 2.5 Compressive experiment of UHPFRC 14
• Photo 2.6 Compressive experiment of normal concrete(NC) 15
• Photo 2.7 Direct tensile test and cracking propagation 19
• Photo 3.1 UHPFRC girder formwork 30
• Photo 3.2 Strain gauge attachment 30
• Photo 3.3 Post tension tendon pipe and the anchorage head 31
• Photo 3.4 Casting of UHPFRC girder 31
• Photo 3.5 Preparation of steam curing 32
• Photo 3.6 Post tension 32
• Photo 3.7 Construction and installation of the push test specimen UHPFRC part 32
• Photo 3.8 Formwork of the NC slab 33
• Photo 3.9 Reinforcement steel bar placement 33
• Photo 3.10 Strain gage and optical fiber placement 34
• Photo 3.11 Normal concrete casting 34
• Photo 3.12 NC part construction of the push test specimen 34
• Photo 3.13 Spray curing process 35
• Photo 3.14 Loading process of Specimen UPoG-6-3 35
• Photo 3.15 Loading process of Specimen UPoG-6-4 38
• Photo 3.16 Loading process of Specimen UPoCG-6-5 39
• Photo 3.17 Loading process of Specimen UPoCG-3-7 42
• Photo 3.18 Loading process of UPoG-3-6 43
• Photo 3.19 Loading process of UPoG-3-2 46
• Photo 3.20 The first push test scheme (symmetrical loading) of S2-1 50
• Photo 3.21 The first push test scheme (symmetrical loading) of S1-1 50
• Photo 3.22 The second push test scheme (one side direct push) of S2m-1 51
• Photo 3.23 The second push test scheme (one side direct push) of S2m-2 52
• Photo 3.24 The second push test scheme (one side direct push) of S1m-1 52
• Photo 3.25 The second push test scheme (one side direct push) of S1m-2 52
• Photo 3.26 The second push test scheme (one side direct push) of S3m-1 53
• Photo 3.27 The second push test scheme (one side direct push) of S3m-2 53
• Photo 3.28 The second push test scheme (one side direct push) of S3m-3 53
• LIST OF TABLES
• Table 2.1 Mechanics Properties Comparison of UHPFRC with NC and FRC 9
• Table 2.2 Durability Comparison of UHPFRC with OPC and HSC 10
• Table 2.3 Mix compositions of UHPFRC (by weight) 12
• Table 2.4 Compression parameters results 15
• Table 2.5 Model parameters of UHPFRC tensile constitutive model 23
• Table 3.1 Push test results statistics 55
• Table 4.1 UHPFRC girder section parameters 65
• Table 4.2 Predictions and test results of the UHPFRC girder cracking loading capacity 65
• Table 4.3 Comparisons of ultimate flexural loading capacity of UHPFRC girder 73