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

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Table of ContentsCHAPTER 1: Introduction ...................................................................................11.1 Impetus for Study of End-Region Stresses in U-Beams ........................11.2 Overview of TxDOT Research Project 5831 .........................................31.3 Thesis Organization ...............................................................................4CHAPTER 2: Literature Review .........................................................................62.1 Overview ................................................................................................62.2 End-Region Tensile Stress Terminology ...............................................82.3 Bursting & Spalling Analysis in Prestressed Beam End Regions .......132.3.1 General Approaches to Analysis .................................................132.3.1.1 Elastic Analysis of Beam End Regions ........................142.3.1.2 Inelastic Analysis of Beam End Regions .....................172.3.1.3 Plastic Analysis of Beam End Regions ........................192.3.2 Effect of End Blocks ...................................................................212.3.3 Analysis of U-Beams ..................................................................232.4 Experimental Studies of Bursting & Spalling Effects .........................242.4.1 Studies of End-Region Surface Strains .......................................242.4.1.1 Base, 1958 ....................................................................252.4.1.2 Zieliński & Rowe, 1960 & 1962 ..................................272.4.1.3 Marshall & Mattock, 1962 ...........................................322.4.1.4 Gergely, Sozen & Siess, 1963 ......................................342.4.1.5 Arthur & Ganguli, 1965 ...............................................362.4.1.6 Krishnamurthy, 1970 ....................................................382.4.1.7 Uijl, 1983 ......................................................................392.4.1.8 Summary ......................................................................412.4.2 Studies of End-Region Transverse-Reinforcement Strains ........422.4.2.1 Marshall & Mattock, 1962 ...........................................432.4.2.2 Gergely, Sozen & Siess, 1963 ......................................48vi
2.4.2.3 Itani & Galbraith, 1986 ................................................512.4.2.4 Tuan et al., 2004 ...........................................................532.4.2.5 Crispino, 2007 ..............................................................572.4.2.6 O’Callaghan, 2007 .......................................................602.4.2.7 Smith et al., 2008..........................................................642.4.2.8 Summary ......................................................................642.5 State of Practice ...................................................................................642.5.1 Field Experience with End-Region Cracking .............................642.5.2 Best Practices for Minimizing End-Region Cracking ................702.5.3 Acceptable End-Region Cracking Criteria .................................722.6 Design Code Requirements ..................................................................732.6.1 AASHTO Provisions ..................................................................742.6.2 ASCE-ACI 323 Tentative Recommendations ............................792.6.3 ACI 318 Provisions .....................................................................802.6.4 PCI Recommendations................................................................812.6.5 CEB-FIP Recommendations .......................................................822.7 DOT Standards for U-Beams ...............................................................822.7.1 Texas U-Beam ............................................................................832.7.2 Florida U-Beam ..........................................................................882.7.3 Colorado U-Girder ......................................................................892.7.4 Washington Trapezoidal Tub Girder ..........................................902.7.5 Comparison of End-Region Reinforcement................................922.8 Summary ..............................................................................................96CHAPTER 3: Experimental Methods ...............................................................973.1 Overview ..............................................................................................973.2 Specimen Design .................................................................................973.2.1 Prestressed Beam Theory ............................................................973.2.1.1 Linear and Nonlinear Stress Distributions ...................983.2.1.2 Elastic Shortening of Beam ..........................................993.2.1.3 Transfer Length of Prestressing Strand ......................100vii
Page 1 and 2: CopyrightbyDavid Andrew Dunkman2009
Page 3 and 4: Bursting and Spalling in Pretension
Page 5: Bursting and Spalling in Pretension
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 and 14: Figure 2.25 Mechanical gage points
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
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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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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),
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VITADavid Andrew Dunkman was born 2
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Bursting and Spalling in Pretensioned U-Beams - Ferguson ...

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