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

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mechanical gage (2 in. gage length) and closely spaced gage points. These specimens(one shown in Figure 2.17) represented anchorage zones of post-tensioned concretemembers. As the strains measured were located near the axis of prestress, they should beclassified as bursting strains.While the applicability of their study to the present work is indirect at best, theirstudy is mentioned for the very high bursting stresses and forces reported by theresearchers. Zieliński and Rowe reported bursting forces of 20 to 35% of the appliedprestressing force, 50 to 100% higher than those predicted by the available theories.“Mainly because they indicate tensile stresses far in excess of the theoretical twodimensionalvalues,” noted Yettram and Robbins (1969), the results of this experimentalstudy were “widely accepted by designers” (p. 104).Figure 2.17 Concrete prism with extensive surface gaging (Zieliński & Rowe, 1960)28
It is now understood (Gergely, Sozen & Siess, 1963; Yettram and Robbins, 1969)that the magnitude of the bursting stresses reported by Zieliński and Rowe were likelyexaggerated due to inelastic deformations (e.g. microcracking). Zieliński and Rowe hadconverted their measured strains to the stress domain assuming that the concrete surfaceshad behaved as linear elastic plates.The level of prestress (longitudinal stress) corresponding to reported stress data inZieliński and Rowe’s study was 10 to 20% of the cube strength. While members subjectto uniform compression of this magnitude respond elastically, the same cannot be said formembers under a general state of stress. Gergely, Sozen and Siess (1963) found inelasticaction at low levels of prestress in a study of post-tensioned beams (Section 2.4.1.4).Yettram and Robbins (1969) also challenged the general approach of measuringconcrete surface strains. Through linear elastic FEM studies of specimens similar to thosetested by Zieliński and Rowe, they found disparities in the stress conditions at the surfaceof the beam compared to the interior. The surface stresses were higher for most realisticloading conditions (majority of beam width loaded). It is clear from Figure 2.18,however, that increases in stress from the surface-measurement technique cannot accountfor the entire discrepancy between the experimental and analytical results.In summary, the maxim put forward by Hawkins (1966) should not be ignored:“Care taken in instrumentation and observation is vital… particularly for calculations oftransverse tensile stress” (p. 198, emphasis added).In a second study completed by Zieliński and Rowe (1962), 20 eccentrically posttensionedI-beams were examined. Most I-beams had rectangular end blocks; many hadtwo or more anchorages; and none had transverse reinforcement. As in their previousstudy, mechanical strain readings were taken using a 2-in. gage.29
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 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 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
Page 64 and 65: (a) Actual spalling stress variatio
Page 66 and 67: stirrups in Gergely, Sozen and Sies
Page 68 and 69: 50% more reinforcement than require
Page 70 and 71: strength concrete, increasingly hig
Page 72 and 73: the reinforcement located within th
Page 74 and 75: Typical crack patterns for the beam
Page 76 and 77: “Very common”crack locationPred
Page 78 and 79: Figure 2.38 Typical gage locations
Page 80 and 81: 2.4.2.7 Smith et al., 2008Most rece
Page 82 and 83: the provided transverse reinforceme
Page 84 and 85: Itani and Galbraith (1986) reported
Page 86 and 87: Figure 2.45 Confining reinforcement
Page 88 and 89: cracks located along lines of prest
Page 90 and 91: odies relevant to pretensioned conc
Page 92 and 93: 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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