Bursting and Spalling in Pretensioned U-Beams - Ferguson ...

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C.2 CONCRETE RELEASE STRENGTHA bottom-fiber stress limit of 0.65 (TxDOT Research Project 5197) and atop-fiber stress limit of 6 (ACI 318, 2008, Provision 18.4.1) are to be applied.where:= concrete release strengthEquation C.4Equation C.5The top-fiber stress limit is not satisfied, so “additional bonded reinforcement…shall be provided in the tensile zone to resist the entire tensile force with the assumptionof an uncracked section” (ACI 318, Provision 18.4.1).Equation C.6where:= height of tension zoneEquation C.7where:Ttz= tension in top portion of beam to be resisted by longitudinalreinforcement= stress in concrete, as a function of depthwhere:Equation C.8= stress in tension-zone longitudinal reinforcementAs,tz = provided longitudinal reinforcement, 4 – #7 in each top flange/web(double the tension-zone reinforcement compared to TxDOT standard)216
Allowable stress for tension-zone reinforcement at transfer range from 30 ksi(ACI 318, 2008, Provision 18.4.1) to 60 ksi (PCI Design Handbook, 2004,Section 4.2.2.2). Flexural cracking at the top of the beam was not expected to interferewith measurements of transverse-bar strains, as explained in Section 3.2.2.C.3 PRESTRESS LOSSES FROM ELASTIC SHORTENING OF BEAMEquation C.9where:h= stress in concrete at depth of prestress centroid= beam heightwhere:Eci= elastic modulus of concrete at releaseEquation C.10where:Ep= elastic modulus of prestressing strandEquation C.11Equation C.12Actual prestress losses from elastic shortening exceed assumed losses (10%).After a few iterations, convergence is reached, and design values are as shown inTable C.1217
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CopyrightbyDavid Andrew Dunkman2009
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Bursting and Spalling in Pretension
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Bursting and Spalling in Pretension
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2.4.2.3 Itani & Galbraith, 1986 ...
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4.2.2.4 Beam 1: Lateral-Bar Burstin
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List of TablesTable 2.1 Range of st
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Figure 2.25 Mechanical gage points
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Figure 3.30 Thermocouple placement
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CHAPTER 1Introduction1.1 IMPETUS FO
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At present, current end-region deta
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Figure 2.1 Severe cracking in a pre
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through use of tensioned, high-stre
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As splitting stress is bond-related
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Figure 2.6 Effect of bursting & spa
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magnitude of the end-region transve
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FEA can readily output color maps o
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2.3.1.3 Plastic Analysis of Beam En
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force can increase by 400% (Yettram
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2.4 EXPERIMENTAL STUDIES OF BURSTIN
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The trial specimens included one 40
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mechanical gage (2 in. gage length)
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Bursting stress(normalized by prest
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proprietary post-tensioning anchors
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Though Marshall and Mattock placed
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ectangular beam” (p. 21). At high
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Most beams observed to crack did so
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The behavior of these beams was dom
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2.4.2 Studies of End-Region Transve
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Figure 2.28 I-beams studied by Mars
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transverse forces compared to those
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(a) Actual spalling stress variatio
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stirrups in Gergely, Sozen and Sies
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50% more reinforcement than require
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strength concrete, increasingly hig
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the reinforcement located within th
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Typical crack patterns for the beam
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“Very common”crack locationPred
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Figure 2.38 Typical gage locations
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2.4.2.7 Smith et al., 2008Most rece
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the provided transverse reinforceme
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Itani and Galbraith (1986) reported
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Figure 2.45 Confining reinforcement
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cracks located along lines of prest
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odies relevant to pretensioned conc
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than that in another shape. For thi
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Figure 2.47 Required splitting rein
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No attempt was made in the Tentativ
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No citation is provided in the PCI
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Section Propertiesy b22.4 in.A 1120
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minimum for greater skews. For beam
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treatment (counting the transverse
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Pretensioned/post-tensioned beams h
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Figure 2.57 Harped strands in webs
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transversereinforcementwithin voidp
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2.8 SUMMARYIn this chapter, literat
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3.2.1.1 Linear and Nonlinear Stress
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Empirical expressions can be used t
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where: 0.021 = spalling force,
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3.3 CONCRETE PROPERTIES3.3.1 Concre
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It was reasoned that the dimensiona
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Splitting tensile-strength testing
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For temperature-match curing, therm
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3.4.1 Reinforcing-Bar Mechanical Te
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Grade 60 rebar yielded at 65 ksi an
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Equation 3.10where:ε1,2 = gage str
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Figure 3.17 Typical strand failure
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SouthNorth North120NorthSouthFigure
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Beam 1 also included an additional
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Figure 3.22 Strand strain-gage inst
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Figure 3.25 Interface board used to
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eam has a “hot spot” (measureme
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3.6 BEAM FABRICATION3.6.1 Beam Cast
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Figure 3.33 Installing the interior
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In order to use a pretensioning bed
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standardside-formprofilespecialtape
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Figure 3.41 Strands installed, tens
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Correspondence between the values o
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Figures 3.45 to 3.50 show the fabri
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Figure 3.49 Casting end block (and
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Figure 3.52 Detensioning by gradual
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CHAPTER 4Results & Discussion4.1 OV
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The strain time history for each ga
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1DNorthSouth1E18 ksi1C1C,E1D1521B1B
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Figure 4.4 Beam 1 prestress losses
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crack adjacent to this location was
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The temperatures in the end blocks
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Table 4.4 Beam 2 applied prestressi
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Figure 4.10 Beam 2 prestress losses
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terms of force distribution seems t
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Page 184 and 185: spalling stresses were measured in
Page 186 and 187: transverse reinforcement contained
Page 188 and 189: Based on Figure 4.18, the 4% Pi des
Page 190 and 191: Uniform and linearly-decreasing tra
Page 192 and 193: 4.3.5 Contributing Factors to High
Page 194 and 195: stress ratio multiplied by a typica
Page 196 and 197: Figure 4.25 Relation between total
Page 198 and 199: 4.4.1 Recommended Texas U-Beam Rein
Page 200 and 201: Figure 4.28 Proposed end-region det
Page 202 and 203: At present, AASHTO LRFD (2009) lack
Page 204 and 205: CHAPTER 5Conclusions5.1 SUMMARY OF
Page 206 and 207: tested at transfer and under shear
Page 208 and 209: APPENDIX ADatabase of Transverse-Ba
Page 210 and 211: 194Figure A.1 U-beam with skewed en
Page 212 and 213: 196Figure A.3 Shallow Texas bulb te
Page 214 and 215: 198Figure A.5 Lightweight-concrete
Page 216 and 217: 200Figure A.7 Washington bulb tee (
Page 218 and 219: 202Figure A.9 Nebraska bulb tees an
Page 220 and 221: 204Figure A.11 Nebraska bulb tees a
Page 222 and 223: 206Figure A.13 Shallow I-beams
Page 224 and 225: where:= lower-bound concrete tensil
Page 226 and 227: B.3.4 Transmission Length (Clause 6
Page 228 and 229: Equation B.11where:= bursting force
Page 230 and 231: 50High Web gage4030Max Moment heigh
Page 234 and 235: Table C.1 Specimen Design for Beams
Page 236 and 237: Table D.1 Beam 1 match-cured cylind
Page 238 and 239: D.1.2 Beam 28Release-Point Cylinder
Page 240 and 241: Cylinder Strength (ksi)131197Ambien
Page 242 and 243: D.2 REINFORCING-BAR MODULUS & STREN
Page 244 and 245: APPENDIX EEnd-Block Temperature Pro
Page 246 and 247: E.2 BEAM 2T max = 142°F∆T = 30°
Page 248 and 249: REFERENCESREFERENCED STANDARDSAmeri
Page 250 and 251: Fédération Internationale du Bét
Page 252 and 253: Davis, R.T.; Buckner, C.D. & Ozyild
Page 254 and 255: Lin, T.Y. & Burns, N.H. (1981), Des
Page 256 and 257: Stone, W.C. & Breen, J.E. (1984),
Page 258: VITADavid Andrew Dunkman was born 2
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Bursting and Spalling in Pretensioned U-Beams - Ferguson ...

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