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

More documents

Recommendations

Info

extremes and averages of stresses under concentrated loads, but rather it is aboutthe formation and extent of cracks (Gergely, Sozen & Siess, 1963, p. 120).Around that time, two landmark studies were completed at the laboratories of thePortland Cement Association (Marshall & Mattock, 1962) and the University of Illinois(Gergely, Sozen & Siess, 1963). Both studies examined, among other items, the amountof transverse reinforcement necessary to control end-region cracking. The Marshall andMattock end-region reinforcement design procedure, in a simplified form, wasimmediately incorporated into the American Association of State Highway Officials(AASHO) Standard Specifications (1961, Interim), and later adopted more directly forthe Precast/Prestressed Concrete Institute (PCI) Design Handbook (1999). The analyticaltreatment of beam end regions first proposed by Gergely, Sozen and Siess (1963) hasproved influential in the prestressed concrete research community.The organization of this literature review is as follows. First, terminology relevantto end-region tensile stresses is defined. Discussion then touches on analytical techniquesand findings before moving on to experimental studies. Experimental studies reviewedinclude those in which surface strains were measured and those, like the present study, inwhich strains in transverse reinforcement were measured. Results from fieldinvestigations and surveys of Department of Transportation (DOT) and other bridgedesign/construction professionals are presented. Current code provisions and their historyare examined, followed by discussion of standard U-beam designs in Texas and threeother states.2.2 END-REGION TENSILE STRESS TERMINOLOGYAs stated by Lin and Burns (1981), the purpose of prestressing is to“counterbalance undesirable strains and stresses” (p. 12). In a typical prestressedconcrete beam, the flexural tension zone (lower portion of the beam) is precompressed8
through use of tensioned, high-strength steel reinforcement. By prestressing, an engineercan reduce or eliminate the longitudinal tensile stresses to be experienced by theprecompressed tension zone under service loads.Not all tensile stresses are reduced by prestressing, however. In the end regions ofprestressed beams, tensile stresses are induced by the spread of the prestressing force,concentrated in the bottom, and often top, portions of the beam, to the entire crosssection. This spread of forces occurs nonlinearly—i.e. the end region experiences adisturbed state of stress or in strut-and-tie terminology, is a D-region.The direction, location and magnitude of end-region tensile stresses are highlydependent on section properties (e.g. prestressing force level and distribution, beamsection geometry) and local variations in material properties (e.g. concrete tensilestrength). End-region stresses are often categorized based on their direction and location.The direction of the stresses can be categorized as longitudinal (horizontal), transverse(vertical) or lateral (out-of-plane), as shown in Figure 2.2. Longitudinal stresses areprimarily compressive, though along the top edge, tensile stresses may exist. Lateralstresses are often small as the strand pattern for most beams is symmetric about the beamvertical axis (y-axis in Figure 2.2). The strand pattern for a highway beam is rarelysymmetric about the z-axis, however, making the transverse tensile stresses the mostsignificant—and the most studied—of the end-region tensile stresses.Based on their location, end-region stresses acting at transfer of prestress can beclassified as bursting or spalling stresses. Bursting stresses occur along or near the line ofaction for the prestressing force, and typically reach their peak some distance into thebeam. Bursting stresses are caused by equilibrium: the spreading of the concentratedprestressing force to the rest of the section. Cracks due to bursting stresses are typicallyhorizontal.9
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: Figure 2.1 Severe cracking in a pre
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
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
Page 94 and 95:
Figure 2.47 Required splitting rein
Page 96 and 97:
No attempt was made in the Tentativ
Page 98 and 99:
No citation is provided in the PCI
Page 100 and 101:
Section Propertiesy b22.4 in.A 1120
Page 102 and 103:
minimum for greater skews. For beam
Page 104 and 105:
treatment (counting the transverse
Page 106 and 107:
Pretensioned/post-tensioned beams h
Page 108 and 109:
Figure 2.57 Harped strands in webs
Page 110 and 111:
transversereinforcementwithin voidp
Page 112 and 113:
2.8 SUMMARYIn this chapter, literat
Page 114 and 115:
3.2.1.1 Linear and Nonlinear Stress
Page 116 and 117:
Empirical expressions can be used t
Page 118 and 119:
where: 0.021 = spalling force,
Page 120 and 121:
3.3 CONCRETE PROPERTIES3.3.1 Concre
Page 122 and 123:
It was reasoned that the dimensiona
Page 124 and 125:
Splitting tensile-strength testing
Page 126 and 127:
For temperature-match curing, therm
Page 128 and 129:
3.4.1 Reinforcing-Bar Mechanical Te
Page 130 and 131:
Grade 60 rebar yielded at 65 ksi an
Page 132 and 133:
Equation 3.10where:ε1,2 = gage str
Page 134 and 135:
Figure 3.17 Typical strand failure
Page 136 and 137:
SouthNorth North120NorthSouthFigure
Page 138 and 139:
Beam 1 also included an additional
Page 140 and 141:
Figure 3.22 Strand strain-gage inst
Page 142 and 143:
Figure 3.25 Interface board used to
Page 144 and 145:
eam has a “hot spot” (measureme
Page 146 and 147:
3.6 BEAM FABRICATION3.6.1 Beam Cast
Page 148 and 149:
Figure 3.33 Installing the interior
Page 150 and 151:
In order to use a pretensioning bed
Page 152 and 153:
standardside-formprofilespecialtape
Page 154 and 155:
Figure 3.41 Strands installed, tens
Page 156 and 157:
Correspondence between the values o
Page 158 and 159:
Figures 3.45 to 3.50 show the fabri
Page 160 and 161:
Figure 3.49 Casting end block (and
Page 162 and 163:
Figure 3.52 Detensioning by gradual
Page 164 and 165:
CHAPTER 4Results & Discussion4.1 OV
Page 166 and 167:
The strain time history for each ga
Page 168 and 169:
1DNorthSouth1E18 ksi1C1C,E1D1521B1B
Page 170 and 171:
Figure 4.4 Beam 1 prestress losses
Page 172 and 173:
crack adjacent to this location was
Page 174 and 175:
The temperatures in the end blocks
Page 176 and 177:
Table 4.4 Beam 2 applied prestressi
Page 178 and 179:
Figure 4.10 Beam 2 prestress losses
Page 180 and 181:
terms of force distribution seems t
Page 182 and 183:
limits were only exceeded at locati
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 232 and 233:
C.2 CONCRETE RELEASE STRENGTHA bott
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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?