Lightweight Concrete for High Strength - Expanded Shale & Clay

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f * su lx ≤ 80d b ⎛ ⎞ ⎜135 ⎟ ⎜ + 31 1 ⎟ ⎜ 6 d ⎟ ⎝ b ⎠ ( A.17) For l x greater than 80d b : f 135 ≤ * su + 1 6 db 0.39l d b x ( A.18) Equation A.18 was rewritten in terms of l x in Table A.1 given in section A.11.14, Summary. A.11.4 Zia and Mostafa, 1977 Zia and Mostafa also realizing the inconsistencies with Equation A.16 suggested a new equation as well (Equation A.19) which incorporated their suggested transfer length equation, Equation A.8. l d = l t + l fb ⎛ = ⎜ 1.5 ⎝ f f si ' ci d b ⎞ − 4.6⎟ + 1.25( f ⎠ * su − f se ) d b ( A.19) A.11.5 FHWA Memorandum, 1988 Based on testing at the University of North Carolina in 1986 where poor transfer and development length results were recorded, the FHWA issued a memorandum specifying 4 interim restrictions as listed in Section A.8.7. Several research programs were initiated based on the FHWA restrictions. A.11.6 Deatherage, Burdette and Chew, 1989 Deatherage et al. conducted experimental testing on 20 AASHTO Type I girders with varying strand diameters and strand spacings and concrete design strengths of 5,000 psi. They suggested the flexural bond component suggested by AASHTO should be increased by 50 percent as shown in Equation A.20 below. A-20
l d = l t + l fb = f si 3 d b + 1.50( f * su − f se ) d b ( A.20) A.11.7 Russell, 1992 Russell performed an extensive series of testing of rectangular, scale model AASHTOtype and full-sized Texas Type C cross sections as part of a PhD Thesis under the supervision of Dr. Ned Burns. The specimens were all prestressed with ½-inch or 0.6-inch strand spaced at 2 inches except three rectangular sections that were prestressed with 0.6-inch strand spaced at 2.25 inches. In many of the specimens, strands were debonded to various distances from the girder ends. Russell concluded that “shear cracking through the transfer region will cause its bond to fail and that if cracks do not occur that the strand will develop is prestressing force plus any additional tension required by external loads.” To prevent cracking from occurring through the transfer region, Russell developed the criteria listed in Equation A.21 where l t was calculated using Equation A.10. where M cr > l V M cr = Cracking moment capacity of a member V u = Ultimate shear force at the critical section t u (A.21) In addition, Russell specified that if V u >V cw that vertical and longitudinal mild steel shear reinforcement should be provided to prevent web shear cracking from passing through the transfer region (V cw is the shear force causing web-shear cracking). 2.11.8 Mitchell, Cook, Khan and Tham, 1993 Mitchell et al. based their research on determining the effect of concrete strength on development length. They examined strand diameters of 3 / 8 -inch, ½-inch and 0.6-inch used to prestress rectangular sections made using concretes having strengths from 3,000 to 7,310 psi at release and from 4,500 to 12,900 psi at 28 days. Based on experimental results, Equation A.22 was suggested. A-21
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School of Civil and Environmental E
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ACKNOWLEDGMENTS The research presen
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A statistical evaluation based on f
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5.6 - Transfer Length 5-13 5.7 - Gi
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Report ACI 318- 99 AASHTO Standard
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Chapter 1. Introduction 1.1 Purpose
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Long term properties including pret
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ottom flange. Prestressing strands
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12500 12000 Concrete Strength, fc'
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Chapter 3. Mix Designs, Field Evalu
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Variation of coarse-to-fine aggrega
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3.2.1 Compressive Strength Figure 3
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Table 3.5 Chloride Permeability --
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12,000 11,500 11,000 Compressive St
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1,400 1,300 1,200 1,100 Experimenta
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strength (10L made in the laborator
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The 50% and 90% of the 620-day cree
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700 600 10,000-psi Measured Shams &
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a Creep Coefficient 3.0 2.5 2.0 1.5
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Chapter 5. Behavior of AASHTO Type
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Portion of Girder Damaged During Te
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2” End Cover (Typ both ends) 4 Sp
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5.3 Instrumentation The surface of
Page 47 and 48: Figure 5.7 Installation of stirrups
Page 49 and 50: Table 5.3 Girder concrete propertie
Page 51 and 52: 120 100 80 Stress (ksi) 60 40 20 0
Page 53 and 54: Table 5.5 -Transfer Length Results
Page 55 and 56: Figure 5.12 Typical flexural failur
Page 57 and 58: Since G2 girders had a higher concr
Page 59 and 60: V " pc cw− Pr ed = ft −Pr ed 1
Page 61 and 62: Test # Table 5.9 Predicted vs. Expe
Page 63 and 64: this research project, modification
Page 65 and 66: Chapter 6. Prestress Losses in HPLC
Page 67 and 68: losses in the 10,000-psi girders to
Page 69 and 70: Microstrains (in/inx10 -6 ) 0 500 1
Page 71 and 72: 6.3 Conclusions Regarding Prestress
Page 73 and 74: 7.3 Transfer Length An evaluation o
Page 75 and 76: Shrinkage after 620 days of drying
Page 77 and 78: More research is required to examin
Page 79 and 80: Appendix A. Background A.1 Introduc
Page 81 and 82: Raithby and Lydon described the use
Page 83 and 84: are normally recognized as being on
Page 85 and 86: aggregate must be saturated by pres
Page 87 and 88: A.7.2 Strength Ceiling Harmon discu
Page 89 and 90: compared to lower strength specimen
Page 91 and 92: A.8.8 Deatherage, Burdette and Chew
Page 93 and 94: 3. Concrete compressive strength at
Page 95 and 96: findings were comments that the AAS
Page 97: including strand diameter, embedmen
Page 101 and 102: l d = l t + l fb ⎛ = ⎜ ⎝ f d
Page 103 and 104: Table A.1 Summary of Development Le
Page 105 and 106: strand release, the strand attempts
Page 107 and 108: Appendix B. Creep and Shrinkage B.1
Page 109 and 110: Changes in moisture migration: the
Page 111 and 112: t′: age of concrete at loading (d
Page 113 and 114: s: slump (in) γ ψ ⎧ 0.30 −1.4
Page 115 and 116: t: age of concrete (days) t 0 : age
Page 117 and 118: where ε sh ∞ ⎧ 510 µε for st
Page 119 and 120: left girder-end. The dimension L wa
Page 121 and 122: 6” 85” 50” Segment of girder
Page 123 and 124: 146” 89” 96” 137” Stirrups
Page 125 and 126: were added in a specific sequence f
Page 127 and 128: C.2.3 Formwork Removal, Detensionin
Page 129 and 130: Figure C.19 Mostafa Prestressing St
Page 131 and 132: Figure C.22 Ms. Lyn Clements (GDOT)
Page 133 and 134: If significant strand end slip over
Page 135 and 136: CSS at Level of Bottom Strands (µ
Page 137 and 138: Appendix D. Prestress Losses in HPL
Page 139 and 140: E ps : elastic modulus of prestress
Page 141 and 142: D.2.2. AASHTO-LRFD Refined Estimate
Page 143 and 144: ∆f log(24 ⋅t) ⎛ f ⎜ ⎞ 55
Page 145 and 146: P i : initial prestressing force af
Page 147 and 148: References AASHTO (1996), Standard
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ASTM C 618, Standard Specification
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Guide for Structural Lightweight Ag
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Martin, L. D., Scott, N. L., “Dev
Page 155:
Shahawy, M. A., Batchelor, B., “S
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Lightweight Concrete for High Strength - Expanded Shale & Clay

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