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

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Figure 2.57 Harped strands in webs of Washington trapezoidal tub girder(Tadros, 2005)....................................................................................................... 92Figure 2.58 Transverse reinforcement in end region of WSDOT trapezoidal tub girder(after AASHTO LRFD, 2008, Interim) .................................................................. 93Figure 2.59 Transverse reinforcement in the end block of a Texas U-beam, dividedinto that provided within the projected areas of the void & the webs .................. 94Figure 2.60 Standard end-region reinforcement for U-beams(54 in. deep, 78 – 0.5-in. strands) vs. code requirements(counting all transverse reinforcement in end block) ........................................... 95Figure 2.61 Standard end-region reinforcement for U-beams(54 in. deep, 78 – 0.5-in. strands) vs. code requirements(neglecting transverse reinforcement within projection of void in end block) ..... 95Figure 3.1 Elastic stress trajectories in a post-tensioned concrete beam, illustrating thedivision into D- and B-regions (after Schlaich, Schäfer & Jennewein, 1987) ..... 98Figure 3.2 Concrete modulus equations from ACI 318 & 363 ...................................... 100Figure 3.3 Tension-zone longitudinal reinforcement ..................................................... 103Figure 3.4 Beam 1 & 2 design summary ........................................................................ 103Figure 3.5 U-beam end-block design alternatives for skewed ends ............................... 106Figure 3.6 Cylinder compressive-strength testing ......................................................... 107Figure 3.7 Schematic for splitting tensile-strength test (after Tuchsherer, 2007) ......... 108Figure 3.8 Maturity-age concept (Kehl & Carrasquillo, 1998) ..................................... 109Figure 3.9 Sure Cure temperature-match-curing system (Tuchsherer, 2007) ............... 110Figure 3.10 Reinforcing bar used in U-beam specimens ............................................... 112Figure 3.11 Reinforcing-bar tension testing in 60-kip test machine .............................. 113Figure 3.12 Extensometer on reinforcing-bar sample ................................................... 113Figure 3.13 Failure modes for Grade 60 rebar & deformed wire ................................. 114Figure 3.14 Typical strain-gage installation along pitched wire within strand(O’Callaghan, 2007) ........................................................................................... 115Figure 3.15 Extensometer & strain gage on strand sample ........................................... 116Figure 3.16 Strands epoxied into black pipe for tensile-strength testing....................... 117Figure 3.17 Typical strand failure mode ........................................................................ 118Figure 3.18 Setup used for Beam 2 elastic-modulus testing for strand ......................... 119Figure 3.19 Crack map for Beam 0, as received five months after cast & release ........ 120Figure 3.20 Typical strain-gage placement in beam end-region ................................... 121Figure 3.21 Instrumentation for transverse reinforcement within end block ................ 122Figure 3.22 Strand strain-gage installation process (Beam 2, 45°-skewed end) ........... 124Figure 3.23 Completed strand strain gaging (inset from O’Callaghan, 2007) ............. 124Figure 3.24 Strand strain-gage locations (Beam 2) ....................................................... 125Figure 3.25 Interface board used to connect strain-gage leads to quarter-bridges ...... 126Figure 3.26 Heuristic for checking quarter-bridge channels ........................................ 126Figure 3.27 Heuristic for checking half-bridge channels .............................................. 127Figure 3.28 Typical thermocouple instrumentation (Beam 2) ....................................... 128Figure 3.29 Typical thermocouple data (after Tuchscherer, 2007) ............................... 128xiv
Figure 3.30 Thermocouple placement in small skewed end block (Beam 1) ................. 129Figure 3.31 Placing concrete using sidewinder (concrete buggy) ................................. 131Figure 3.32 Consolidating bottom-flange concrete using internal vibrators& external form vibrators (not shown) .............................................................. 131Figure 3.33 Installing the interior-void form ................................................................. 132Figure 3.34 Filling the webs and end blocks around the interior-void form,held in place with hangers .................................................................................. 132Figure 3.35 Finishing the top surface ............................................................................ 133Figure 3.36 FSEL pretensioning bed (O’Callaghan, 2007)........................................... 134Figure 3.37 Wider bulkhead in place at stressing end ................................................... 135Figure 3.38 Special tapered side form fabricated by Hamilton Form ........................... 136Figure 3.39 U-beam formwork in pretensioning bed ..................................................... 136Figure 3.40 Modifications to beam header .................................................................... 137Figure 3.41 Strands installed, tensioned to nominal stress for instrumentation............ 138Figure 3.42 Linear potentiometers (circled) used to monitor strand elongation........... 139Figure 3.43 Slump testing............................................................................................... 141Figure 3.44 Cylinder molds set out for beam cast ......................................................... 141Figure 3.45 Placing concrete in the bottom flange ........................................................ 142Figure 3.46 Consolidating bottom-flange concrete using internal vibrators& external form vibrators .................................................................................. 142Figure 3.47 Moving interior void into position after bottom flange is cast ................... 143Figure 3.48 Positioning interior-void hangers .............................................................. 143Figure 3.49 Casting end block (and webs) around the interior void ............................. 144Figure 3.50 Placing concrete in large triangular end block(Beam 2, 45°-skewed end) .................................................................................. 144Figure 3.51 Removing interior void form in preparation for transfer ........................... 145Figure 3.52 Detensioning by gradually decreasing pressure in stressing rams ............ 146Figure 3.53 Lifting Beam 0 from delivery truck ............................................................. 146Figure 4.1 Strain time histories for two gages ............................................................... 149Figure 4.2 Beam 1 cast & release timeline with key events ........................................... 150Figure 4.3 Beam 1 transverse-bar bursting & spalling stresses,with cracking from transfer ................................................................................ 152Figure 4.4 Beam 1 prestress losses in instrumented strands, after transfer .................. 154Figure 4.5 Beam 1 effective prestress & distance from beam end, after transfer .......... 154Figure 4.6 Beam 1 lateral-bar bursting stresses ............................................................ 156Figure 4.7 Beam 1 end-block temperature profiles, at transfer of prestress ................. 157Figure 4.8 Beam 2 cast & release timeline with key events ........................................... 159Figure 4.9 Beam 2 transverse-bar bursting & spalling stresses,with cracking from transfer ................................................................................ 161Figure 4.10 Beam 2 prestress losses in instrumented strands, after transfer ................ 162Figure 4.11 Beam 2 effective prestress & distance from beam end, after transfer ........ 162Figure 4.12 Beam 2 lateral-bar stresses ........................................................................ 164Figure 4.13 Beam 2 end-block temperature profiles, at transfer of prestress ............... 165xv
Page 1 and 2: CopyrightbyDavid Andrew Dunkman2009
Page 3 and 4: Bursting and Spalling in Pretension
Page 5 and 6: Bursting and Spalling in Pretension
Page 7 and 8: 2.4.2.3 Itani & Galbraith, 1986 ...
Page 9 and 10: 4.2.2.4 Beam 1: Lateral-Bar Burstin
Page 11 and 12: List of TablesTable 2.1 Range of st
Page 13: Figure 2.25 Mechanical gage points
Page 17: CHAPTER 1Introduction1.1 IMPETUS FO
Page 20: At present, current end-region deta
Page 23 and 24: Figure 2.1 Severe cracking in a pre
Page 25 and 26: through use of tensioned, high-stre
Page 27 and 28: As splitting stress is bond-related
Page 29 and 30: Figure 2.6 Effect of bursting & spa
Page 31 and 32: magnitude of the end-region transve
Page 33 and 34: FEA can readily output color maps o
Page 35 and 36: 2.3.1.3 Plastic Analysis of Beam En
Page 38 and 39: force can increase by 400% (Yettram
Page 40 and 41: 2.4 EXPERIMENTAL STUDIES OF BURSTIN
Page 42 and 43: The trial specimens included one 40
Page 44 and 45: mechanical gage (2 in. gage length)
Page 46 and 47: Bursting stress(normalized by prest
Page 48 and 49: proprietary post-tensioning anchors
Page 50 and 51: Though Marshall and Mattock placed
Page 52 and 53: ectangular beam” (p. 21). At high
Page 54 and 55: Most beams observed to crack did so
Page 56 and 57: The behavior of these beams was dom
Page 58 and 59: 2.4.2 Studies of End-Region Transve
Page 60 and 61: Figure 2.28 I-beams studied by Mars
Page 62 and 63: 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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limits were only exceeded at locati
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spalling stresses were measured in
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transverse reinforcement contained
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Based on Figure 4.18, the 4% Pi des
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Uniform and linearly-decreasing tra
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4.3.5 Contributing Factors to High
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stress ratio multiplied by a typica
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Figure 4.25 Relation between total
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4.4.1 Recommended Texas U-Beam Rein
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Figure 4.28 Proposed end-region det
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At present, AASHTO LRFD (2009) lack
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CHAPTER 5Conclusions5.1 SUMMARY OF
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tested at transfer and under shear
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APPENDIX ADatabase of Transverse-Ba
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194Figure A.1 U-beam with skewed en
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196Figure A.3 Shallow Texas bulb te
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198Figure A.5 Lightweight-concrete
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200Figure A.7 Washington bulb tee (
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202Figure A.9 Nebraska bulb tees an
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204Figure A.11 Nebraska bulb tees a
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206Figure A.13 Shallow I-beams
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where:= lower-bound concrete tensil
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B.3.4 Transmission Length (Clause 6
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Equation B.11where:= bursting force
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50High Web gage4030Max Moment heigh
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C.2 CONCRETE RELEASE STRENGTHA bott
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Table C.1 Specimen Design for Beams
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Table D.1 Beam 1 match-cured cylind
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D.1.2 Beam 28Release-Point Cylinder
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Cylinder Strength (ksi)131197Ambien
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D.2 REINFORCING-BAR MODULUS & STREN
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APPENDIX EEnd-Block Temperature Pro
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E.2 BEAM 2T max = 142°F∆T = 30°
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REFERENCESREFERENCED STANDARDSAmeri
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Fédération Internationale du Bét
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Davis, R.T.; Buckner, C.D. & Ozyild
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Lin, T.Y. & Burns, N.H. (1981), Des
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Stone, W.C. & Breen, J.E. (1984),
Page 258:
VITADavid Andrew Dunkman was born 2
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