njit-etd2003-032 - New Jersey Institute of Technology

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7 The traditional AO1 approach (AC1 Building Code 318-99) to design for shear strength is to consider the total nominal shear strength as the sum of two parts: Where 17,2 is the nominal shear strength; 17, is the shear strength of the beam attributable to the concrete; and 17, is the shear strength of the beam attributable to the shear reinforcement. 1. Strength 17, Attributable to Concrete. The development of the detailed equation for 17, is based on the test results. AOI-11.3.1 and 11.3.2 permit using either of the following: (1) For the simplified method,
Where A, is the area of shear reinforcement, Cy is the yield stress of the reinforcement, s is the spacing of the shear reinforcement, and a is the angle between the orientation of the shear reinforcement and the longitudinal axis of the beam. 1.4.2 Shear Strength of Deep Beams Classic literature review compiled by Albritton (1965), the Cement and Concrete Association (C&CA) (1969) and Construction Industry Research and Information Association (CIR1A) (1977) show that the early investigations are mostly on the elastic behavior with the beam assumed to be homogeneous, which can be carried out nowadays using the standard finite element method. Reinforcing is placed in regions where tensile stresses are above the estimated strength of the concrete. However, a serious disadvantage of elastic studies is the usual assumption of isotropic materials obeying Hooke's Law, which does not give sufficient guidance for practical design. It was not until the 196Os that systematic ultimate load tests were carried out by de Paiva and Siess (1965) and Leonhardt and Walther (1966). Leonhardt and Walther (1966) considered two states — the un-cracked and the cracked. They found that the cracking followed the tensile stress trajectories. However, after cracking and stress redistribution, the elastic approach did not adequately describe the stress distributions of deep beams. Actual stresses exceeded theoretical stresses at sections near supports and center of the spans. These tests were a major step forward in deep beam research. They revealed a concern for empirical evidence that emphasized the importance of
Page 1 and 2: Copyright Warning & Restrictions Th
Page 3 and 4: ABSTRACT SHEAR STRENGTHENING OF RC
Page 5 and 6: SHEAR STRENGTHENING OF RC BEAMS USI
Page 7 and 8: APPROVAL PAGE SHEAR STRENGTHENING O
Page 9 and 10: This dissertation is dedicated to m
Page 11 and 12: TABLE OF CONTENTS Chapter Page 1 IN
Page 13 and 14: TABLE OF CONTENTS (Continued) Chapt
Page 15 and 16: LIST OF TABLES Chapter Page 2.1 Max
Page 17 and 18: LIST OF FIGURES (Continued) Chapter
Page 23 and 24: 2 Additionally, special equipment i
Page 25 and 26: 4 5. To study the shear span to dep
Page 27: 6 1.4.1 Shear Strength of RC Beams
Page 31 and 32: 10 usually be the same throughout t
Page 33 and 34: 12 1.4.2.2 Shear Strength of Contin
Page 35 and 36: 14 based on the assumption that the
Page 37 and 38: CHAPTER 2 EXPERIMENTAL PROGRAM ON S
Page 39 and 40: 18 needed, which was 4Omm wide and
Page 41: 20 used for bonding of the strips t
Page 45 and 46: 24 2.2 Instrumentation and Test Pro
Page 47 and 48: 26 b) Beam Z4-90 The next beam was
Page 49 and 50: 28 CFRP strip suddenly detached fro
Page 51 and 52: 30 Figure 2.17 Failure of Beam ZC6.
Page 53 and 54: 32 capacity. The load went straight
Page 55 and 56: 34 Figure 2.22 Failure of Beam Z6-9
Page 58 and 59: 37 c) Failure Mechanism Apparently,
Page 60 and 61: 39 observed by a prolonged portion
Page 63 and 64: 42 c) Failure Mechanism Since diffe
Page 65 and 66: 44 The equation to compute CARP she
Page 67 and 68: 46 3.2 Design Approach Based on Mod
Page 70: 49 Arom Aigure 3.2, it can be obser
Page 74 and 75: 53 Equation 3.12 from curve fitting
Page 76 and 77: 55 strength. The method based on bo
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57 Chajes, M. J. et al. (1996) also
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3) CFRP continuous fiber sheet in t
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Figure 3.11 CARP strip in the form
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63 Thus, a relationship between the
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65 2 fc bi,d I f =wife • t f ' fi
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67 Arom Table 3.4, it can also be o
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69 equal to 3.75, the beam specimen
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71 laminates. The surfaces of the f
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Figure 4.3 Configuration of CARP st
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75 16 beams were tested in this res
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79 Figure 4.7 Typical test setup. 4
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81 intact. The CFRP strip delaminat
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83 4.5.1.4 Beam Z11-S45. The CFRP s
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85 4.5.2 Beam Group 2 4.5.2.1 Beam
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87 4.5.2.3 Beam Z22-S90. This beam
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89 (b) Right Side Figure 4.15 Failu
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91 of the delamination, which consi
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93 Figure 4.18 Failure of Beam Z31-
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95 4.5.4 Beam Group 4 4.5.4.1 Beam
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97 4.5.4.3 Beam Z42-FD. This was th
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99 (a) Side View of the Beam at Fai
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101 4.6 Test Results and Discussion
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103 failure along the inclined crac
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105
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107 4.6.3 Beam Group 3 A summary of
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109 4.6.3.3 Failure Mechanism. No i
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111 ;how deflections at ultimate lo
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113 All of the lines in Figure 4.28
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115 ratio; line Z-F90 means the var
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117 Unlike regular beams with large
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119 orientation of the CFRP strips
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121 As for shear design of deep bea
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123 provisions of ACI Code (ACI 318
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125 stress due to shear as well as
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Figure 5.3 Distribution of transver
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Figure 5.4 Estimation of effective
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131 Where A and Ah are the areas of
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Since the principal tensile stress
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135 laminates can be obtained from
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Table 5.1 Experimental and Computed
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139 Where i denote each type of rei
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141 the strongest beam in the 4-foo
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143 Figure 6.1 Failure of Beam ZC4-
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145 Figure 6.3 Failure of Beam Z22-
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147 6.2.4 Analysis of Test Results
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149 improves the performance of the
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Figure 6.7 Test result of beam Z22-
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Figure 6.8 Test result of Beam Z3I-
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155 equal to 69 degrees in this cas
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157 decreases, while the shear cont
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APPENDIX A LOAD DEFLECTION CURVES O
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161 Figure A.3 Load deflection curv
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163 Figure A.7 Load deflection curv
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Figure A.11 Load deflection curve o
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167 Figure B.1 Load deflection curv
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Page 192 and 193:
Page 194 and 195:
173 Figure B.13 Load deflection cur
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APPENDIX C LOAD DEFLECTION CURVES O
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177 Figure C.3 Load deflection curv
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179 Czaderski, Christoph. "Shear St
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181 4, No. 4, Nov. 2000, pp. 198-20
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