Lightweight Concrete for High Strength - Expanded Shale & Clay

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Shrinkage of concrete. The final prestress loss due to drying shrinkage is given by member geometry and relative humidity at which member is exposed. Equation D.4 shows PCI expression to estimate shrinkage loss. SH ⎛ V ⎞ ( × 6 8.2 10 ) ⋅ K ⋅ E ⋅ ⎜1 − 0.06 ⎟ ⋅ ( 100 − RH ) = − sh ps ⎝ S ⎠ where, SH: shrinkage loss (ksi) K sh : 1.0 for pretensioned members E ps : elastic modulus of prestressing steel (ksi) V: specimen volume (in 3 ) S: specimen surface area (in 2 ) RH: relative humidity, % (D.4) Steel relaxation. defined as the loss of stress over a certain period of time, steel relaxation depends on the type of prestressing steel (stress-relieved or lo relaxation) and the other prestress losses. Equation D.5 gives the loss of prestress due to steel relaxation. [ K − J ⋅ ( SH + CR + ES ) ⋅ ( − RH )] C RE = re 100 ⋅ (D.5) where RE: steel relaxation loss (ksi) K re : maximum relaxation stress, 5,000 psi for grade 270, low relaxation strands J: parameter, 0.04 for grade 270, low relaxation strands, ES: elastic shortening loss (ksi) CR: creep of concrete loss (ksi) SH: shrinkage of concrete loss (ksi) C: parameter depending on the initial prestress to ultimate strand strength and strand type, 0.70 in this case. D-4
D.2.2. AASHTO-LRFD Refined Estimates of Time-Dependent Losses According to AASHTO-LRFD (1998), the total loss of prestress, not including anchorage seating loss, is the sum of the elastic shortening, creep, shrinkage, and steel relaxation losses, given by Equation D.6. Equation D.6 applies to prestressed members with spans no greater than 250 ft., NWC and compressive strength above 3,500 psi. ∆ f = ∆f + ∆f + ∆f + ∆f + ∆f (D.6) pT pES pCR pSH pR1 pR2 where ∆f pT : total prestress losses (ksi) ∆f pES : elastic shortening loss (ksi) ∆f pCR : creep of concrete loss (ksi) ∆f pSR : shrinkage of concrete loss (ksi) ∆f pR1 : initial steel relaxation loss (ksi) ∆f pR2 : after transfer steel relaxation loss (ksi) Elastic Shortening. According to AASHTO-LRFD, the Elastic shortening loss is given by Equation D.7. E p ∆ f pES = ⋅ f cgp (D.7) E ci where, ∆f pES : elastic shortening loss (ksi) f cgp ⎛ Pi = ⎜ ⎝ Ag Pi ⋅ e + I g 2 ⎞ M ⎟ − ⎠ I g g ⋅ e ( f cgp ) : sum of the stresses in the concrete at the cgs due to prestress force at transfer and the maximum dead load moment (ksi) P i : initial prestressing force after anchorage seating loss (kip) e: eccentricity of the cgs. with respect to the center of gravity of the section at the cross section considered. Eccentricity is negative if below concrete section neutral axis (in) A g : gross area of the section (in 2 ) I g : gross moment of inertia (in 4 ) M g : the dead load gravity moment applied to the section at time of prestressing (kip-in) D-5
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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
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Figure 5.7 Installation of stirrups
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Table 5.3 Girder concrete propertie
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120 100 80 Stress (ksi) 60 40 20 0
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Table 5.5 -Transfer Length Results
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Figure 5.12 Typical flexural failur
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Since G2 girders had a higher concr
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V " pc cw− Pr ed = ft −Pr ed 1
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Test # Table 5.9 Predicted vs. Expe
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this research project, modification
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Chapter 6. Prestress Losses in HPLC
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losses in the 10,000-psi girders to
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Microstrains (in/inx10 -6 ) 0 500 1
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6.3 Conclusions Regarding Prestress
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7.3 Transfer Length An evaluation o
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Shrinkage after 620 days of drying
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More research is required to examin
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Appendix A. Background A.1 Introduc
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Raithby and Lydon described the use
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are normally recognized as being on
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aggregate must be saturated by pres
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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 and 98: including strand diameter, embedmen
Page 99 and 100: l d = l t + l fb = f si 3 d b + 1.5
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: E ps : elastic modulus of prestress
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
Page 149 and 150: ASTM C 618, Standard Specification
Page 151 and 152: Guide for Structural Lightweight Ag
Page 153 and 154: 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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