Shear strength evaluation of reinforced concrete members based on compatibility-aided truss model

국문 초록 (Abstract)

전단파괴는 매우 취성적인 파괴모드로 철근콘크리트 부재의 전단강도를 예측하는 것은 매우 어렵다. 현재까지 철근콘크리트 부재의 전단거동을 평가하기 위한 많은 연구들이 수행되었다. 개발된 다양한 이론들 중에서 트러스 모델은 부재의 전단거동을 평가하기 위한 가장 적합한 이론이다. 변형률 적합조건을 고려한 트러스 모델은 힘의 평형조건, 재료의 구성법칙 및 변형률 적합조건을 사용하여 철근콘크리트 부재의 전단강도와 변형을 동시에 예측할 수 있으며, 전단강도를 정확하게 평가할 수 있다. 그러나 변형률 적합조건을 고려한 트러스 모델을 사용해 전단강도를 계산하는 과정에서 많은 변수를 식별해야 하기 때문에 계산과정이 매우 복잡해진다. 이러한 계산과정은 전단철근의 항복조건을 사용할 경우 단순화시킬 수 있다. 전단철근이 항복한 후에는 변형률은 급격하게 증가하여 전단철근의 항복 전후의 변형률에 큰 차이가 발생한다. 그러나 전단철근이 항복한 시점에서의 전단강도와 최대 전단강도의 차이는 비교적 작다.
본 연구에서는 변형률 적합조건을 고려한 트러스 모델을 기반으로 하는 전단강도 평가식을 제안하였다. 전단강도 평가식의 간략화를 위해 전단철근이 항복하는 시점에서의 조건을 사용하였다. 전단강도 평가식의 검증범위의 확장을 위해 대형보의 실험적 연구도 수행하였다. 실험결과는 기존의 전단강도 평가식에 의해 계산된 전단강도와 비교를 통하여 분석되었다. 전단강도비는 전단철근량과 단면의 유효깊이에 큰 영향을 받았다. 이에 따라, 실험결과를 바탕으로 제안된 전단강도 평가식에는 단면의 유효깊이와 전단철근량에 대한 영향을 반영하였다. 제안식의 적용 범위를 확장하기 위해 휨 모멘트와 축력의 영향은 종방향 변형률에 반영되었다. 변형률 적합조건 트러스 모델에 의한 철근콘크리트 부재의 전단강도 평가식의 검증에는 기존에 수행된 1419개의 철근콘크리트 부재의 실험결과가 사용되었다. 1419개의 철근콘크리트 부재의 실험결과는 제안식과 KCI-17, ACI 318-19, EC2-04 및CSA A23.3-14에서 제시하고 있는 전단강도 평가식으로 계산된 결과와 비교하였다. 다양한 변수에 대한 비교 결과 본 연구에서 제안한 전단강도 평가식은 철근콘크리트 부재의 전단강도를 합리적으로 평가하였다.

다국어 초록 (Multilingual Abstract)

Shear failure is a very brittle failure mode, and it is very difficult to predict the shear strength of reinforced concrete (RC) members. Numerous studies have been conducted to evaluate the shear behavior of RC members. Among various theories for evaluating shear behavior of RC members, the truss model is the most suitable theory. The compatibility-aided truss model, one of the truss theories, can predict the shear strength and deformation of RC members simultaneously using stress equilibrium, constitutive laws of materials, and strain compatibility. This approach provides an accurate predicted shear strength of the RC member. However, analysis through the compatibility-aided truss model requires identification of numerous unknown variables. These processes can be simplified by using the conditions at the yielding of shear reinforcement. After the shear reinforcement yields, the strain increases rapidly, resulting in a large difference in the strain before and after yielding of the shear reinforcement. While, the difference between ultimate shear strength and shear strength at the yielding of shear reinforcement is not significant.
In this thesis, shear strength evaluation equation based on compatibility-aided truss model was proposed. For the simplification of the shear strength evaluation equation, the conditions at the yielding of shear reinforcement were used. Furthermore, the shear behavior of large-scale RC beams was experimentally investigated to better understand the effects of various parameters on shear strength. The experimental results were analyzed by comparing the shear strength calculated by the shear strength evaluation formula of KCI-17. The shear strength ratio was affected by the amount of shear reinforcement and the section depth. Based on the experimental results, the proposed equation considered the effect of the effective depth of the cross section and the amount of shear reinforcement on the shear strength. In addition, the effects of bending moments and axial forces were reflected in the longitudinal strain to expand the application range of the equation. The proposed equation based on compatibility-aided truss model for shear strength of RC members was verified against large experimental results. To verify the proposed equation, the measured shear strength values were compared with the calculated shear strengths according to the methods specified in KCI-17, ACI 318-19, EC2-04, and CSA A23.3-14 as well as the proposed equation. According to the comparison results with the actual shear strength of the RC members obtained from the previous literature, the proposed equation predicted the shear strength of RC members with reasonable accuracy.

목차 (Table of Contents)

• Chapter 1 INTRODUCTION 1
• 1.1 Research Objective 1
• 1.2 Summary of Research 4
• Chapter 2 LITERATURE REVIEW 6
• 2.1 Introduction 6
• 2.2 Basic Theory 7
• 2.2.1 Shear Stresses in an Uncracked Elastic Member 7
• 2.2.2 Average Shear Stress 7
• 2.3 Shear Resistance Mechanism in RC Member without Shear Reinforcement 10
• 2.3.1 Resistances of RC Members without Shear Reinforcement 10
• 2.3.2 Beam and Arch Action 10
• 2.3.3 Shear Failure Mechanism 12
• 2.3.4 Influencing Parameters for RC Members without Shear Reinforcement 17
• 2.4 Shear Resistance Mechanism in RC Member with Shear Reinforcement 20
• 2.4.1 Resistances of RC Members with Shear Reinforcement 20
• 2.4.2 45° Truss Model 21
• 2.4.3 Plasticity Truss Mechanism 23
• 2.4.4 Compression Field Theory 27
• 2.4.5 Modified Compression Field Theory 30
• 2.4.6 Rotating-Angle Softened Truss Model 34
• 2.4.7 Fixed-Angle Softened Truss Model 38
• 2.5 Current Shear Design Procedure 42
• 2.5.1 KCI-17 42
• 2.5.2 ACI 318-19 45
• 2.5.3 Eurocode2 (EC2) Part 1 47
• 2.5.4 CSA A23.3-14 49
• 2.6 Conclusions 52
• Chapter 3 EXPERIMENTAL PROGRAM 55
• 3.1 Introduction 55
• 3.2 Test Specimen and Procedure 56
• 3.2.1 Specimens Details 56
• 3.2.2 Test Setup and Measurements 70
• 3.3 Test Results 71
• 3.3.1 General Observation 71
• 3.3.2 Shear Force-Deflection Relations 76
• 3.3.3 Strain Distributions of Shear and Longitudinal Reinforcements 83
• 3.4 Shear Strength Reduction of RC Beams 96
• 3.4.1 Factors Affecting the Shear Strength of RC Beams 96
• 3.4.2 Considering Size Effect 100
• 3.5 Conclusions 104
• Chapter 4 SHEAR STRENGTH EVALUATION EQUATIONS 105
• 4.1 Introduction 105
• 4.2 Basic Concept of Proposed Equation 106
• 4.3 Derivation of Shear Strength Evaluation Equation Based on Compatibility-Aided Truss Model 109
• 4.3.1 Shear Stress 109
• 4.3.2 Crack Angle (θ) 110
• 4.3.3 Longitudinal Strain (ε_x) 116
• 4.3.4 Size Effect 120
• 4.3.5 Effect of Amount of Shear Reinforcement 121
• 4.3.6 Proposed Shear Strength Evaluation Equations 124
• Chapter 5 VERIFICATION OF PROPOSED EQUATION 128
• 5.1 Introduction 128
• 5.2 RC Members without Shear Reinforcement 129
• 5.2.1 Effect of Effective Depth (d) 132
• 5.2.2 Effect of Shear Span to Depth Ratio (a/d) 134
• 5.2.3 Effect of Compressive Strength of Concrete (f_c^') 137
• 5.2.4 Effect of Longitudinal Tensile Reinforcement Ratio (p_l) 137
• 5.3 RC Members with Shear Reinforcement 141
• 5.3.1 Effect of Effective Depth (d) 144
• 5.3.2 Effect of Shear Span to Depth Ratio (a/d) 145
• 5.3.3 Effect of Compressive Strength of Concrete (f_c^') 149
• 5.3.4 Effect of Longitudinal Tensile Reinforcement Ratio (p_l) 151
• 5.3.5 Effect of Amount of Shear Reinforcement (ρ_t f_yt/√(f_c^' )) 153
• 5.4 RC Members Subjected to Axial Load 155
• 5.4.1 Effect of Shear Span to Depth Ratio (a/d) 158
• 5.4.2 Effect of Compressive Strength of Concrete (f_c^') 161
• 5.4.3 Effect of Longitudinal Tensile Reinforcement Ratio (p_l) 163
• 5.4.4 Effect of Amount of Shear Reinforcement (ρ_t f_yt/√(f_c^' )) 163
• 5.4.5 Effect of Axial Force Ratio (N/bhf_c^') 167
• 5.5 Conclusions 169
• Chapter 6 SUMMARY AND CONCLUSIONS 171
• References 176
• APPENDIX A: EXPERIMENTAL DATA FOR VERIFICATION OF RC MEMBERS WITHOUT SHEAR REINFORCEMENT 199
• APPENDIX B: EXPERIMENTAL DATA FOR VERIFICATION OF RC MEMBERS WITH SHEAR REINFORCEMENT 239
• APPENDIX C: EXPERIMENTAL DATA FOR VERIFICATION OF RC MEMBERS SUBJECTED TO AXIAL LOAD 267