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

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List of FiguresFigure 1.1 Cross section of pretensioned concrete U-beam .............................................. 2Figure 1.2 DEF damage in end block of dapped trapezoidal box beam(after 13 years exposure) ........................................................................................ 2Figure 1.3 U-beam end-block design alternatives for skewed ends ................................... 3Figure 2.1 Severe cracking in a pretensioned concrete beam end region(Marshall & Mattock, 1962) .................................................................................. 7Figure 2.2 Convention for end-region stress direction .................................................... 10Figure 2.3 Development of splitting stress (Uijl, 1991) ................................................... 10Figure 2.4 End-region stress terminology (after Sanders, 1990) .................................... 12Figure 2.5 Bursting & spalling stress distributions (after Lenschow & Sozen, 1965) .... 12Figure 2.6 Effect of bursting & spalling stresses through exaggerated deformationsof beam with discontinuities (after Hawkins, 1966) ............................................. 13Figure 2.7 Analytical approaches for prestressed beam end regions .............................. 14Figure 2.8 Symmetrical prism method of Guyon for a beam under eccentric prestress(Sanders, 1990) ..................................................................................................... 15Figure 2.9 Symmetrical prism method of Guyon for a beam subject tomultiple lines of prestress (Sanders, 1990) ........................................................... 16Figure 2.10 Gergely-Sozen analysis model (Gergely & Sozen, 1967) ............................. 18Figure 2.11 STM of Davis, Buckner & Ozyildirim (2005) ............................................... 20Figure 2.12 Transverse reinforcement required for Virginia bulb tee based on STM(after Davis, Buckner & Ozyildirim, 2005) .......................................................... 21Figure 2.13 Effect of end blocks of various lengths on bursting force distribution(after Yettram & Robbins, 1971) ......................................................................... 22Figure 2.14 Shear stress distribution in Florida U-beam under prestress load only(Huang & Shahawy, 2005) ................................................................................... 23Figure 2.15 Bursting & spalling strains in Base rectangular beam ................................ 26Figure 2.16 Spalling strains in Base IT-beams ................................................................ 27Figure 2.17 Concrete prism with extensive surface gaging (Zieliński & Rowe, 1960).... 28Figure 2.18 Analytical stress at various locations compared to Zieliński & Rowe’sexperimental results (Yettram & Robbins, 1969) ................................................. 30Figure 2.19 Specimen with failure near flange/web junction(Zieliński & Rowe, 1962) ...................................................................................... 31Figure 2.20 Surface instrumentation & strains at beam end(after Marshall & Mattock, 1962) ........................................................................ 33Figure 2.21 Surface instrumentation & strains over beam length(after Marshall & Mattock, 1962) ........................................................................ 33Figure 2.22 Prestressing force & spalling strains for a rectangular beam(after Gergely, Sozen & Siess, 1963) .................................................................... 35Figure 2.23 Pretensioning frame at Glasgow (Arthur & Ganguli, 1965) ....................... 37Figure 2.24 Mechanical gage points on I-beam specimen(after Arthur & Ganguli, 1965) ............................................................................ 37xii
Figure 2.25 Mechanical gage points on I-beam specimen(after Krishnamurthy, 1970) ................................................................................. 39Figure 2.26 Typical bursting/splitting crack in hollow-core ribs (Uijl, 1983) ................ 40Figure 2.27 “Internal cracking” viewed in saw-cut specimen (Uijl, 1983) .................... 41Figure 2.28 I-beams studied by Marshall & Mattock ...................................................... 44Figure 2.29 Typical transverse tensile strain variation(after Marshall & Mattock, 1962) ........................................................................ 45Figure 2.30 Linear regression analysis forming basis of Marshall & Mattockdesign equation (after Marshall & Mattock, 1962) .............................................. 47Figure 2.31 Actual spalling stress variation & uniform stress variationassumed for design ................................................................................................ 48Figure 2.32 Stirrups serving as both transverse & confining reinforcement(Gergely, Sozen & Siess, 1963)............................................................................. 49Figure 2.33 Typical transverse-bar strain gage locations (Itani & Galbraith, 1986) ..... 52Figure 2.34 Typical strain-gage location for I- & IT-beams ........................................... 55Figure 2.35 Strain-gage location for 43-in. I-beams ....................................................... 55Figure 2.36 Typical crack pattern in Virginia bulb tee (after Crispino, 2007) ............... 58Figure 2.37 Typical gage locations (after Crispino, 2007) ............................................. 60Figure 2.38 Typical gage locations (O’Callaghan, 2007) ............................................... 62Figure 2.39 Typical crack pattern with widths (O’Callaghan, 2007) .............................. 63Figure 2.40 Wide IT-beam monitored by Smith et al. ...................................................... 64Figure 2.41 Beam with two strand groups (Fountain, 1963) ........................................... 65Figure 2.42 Prevalence of crack patterns noted in pretensioned I-beams(after Gamble, 1997) ............................................................................................. 67Figure 2.43 Cracking in Texas U-beam, one week after release (Barrios, 1994) ........... 68Figure 2.44 Confining reinforcement details tested by Barrios (1994) ........................... 69Figure 2.45 Confining reinforcement provided at end of beamswith both details shown in Figure 2.44 ................................................................. 70Figure 2.46 Common cracks in pretensioned beams (PCI, 1985) ................................... 71Figure 2.47 Required splitting reinforcement for a trapezoidal tub girder(after AASHTO LRFD, 2008, Interim) .................................................................. 78Figure 2.48 U-beam as replacement for two I-beams (Ralls, Ybanez & Panak, 1993) ... 83Figure 2.49 Texas/Florida U-beam section properties (54 in. standard) ........................ 84Figure 2.50 Two- & three-strand-row design standards for 54-in. Texas U-beam(Ralls, Ybanez & Panak, 1993) ............................................................................. 84Figure 2.51 End-block design alternatives for Texas U-beam(minimum end-block dimensions drawn for maximum skew) ............................... 86Figure 2.52 Skewed end-block dimensions for extreme cases ......................................... 86Figure 2.53 Additional transverse reinforcement near center of end block .................... 87Figure 2.54 Colorado U-girder section properties(48 in. deep, pretensioned standard) .................................................................... 89Figure 2.55 Curved pretensioned/post-tensioned Colorado U-girder (Endicott, 2005) .. 90Figure 2.56 Washington trapezoidal-tub-girder section properties (54 in. standard) .... 91xiii
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: List of TablesTable 2.1 Range of st
Page 15 and 16: Figure 3.30 Thermocouple placement
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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