Table Of ContentEffects of Anchor Wedge
Dimensional Parameters on
Post-Tensioning Strand Performance
December 2013
K.Q. Walsh, R.L. Draginis, R.M. Estes, and Y.C. Kurama Report #NDSE-2013-02
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Structural Engineering Research Report
Civil and Environmental Engineering and Earth Sciences
University of Notre Dame
Notre Dame, Indiana
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Effects of Anchor Wedge
Dimensional Parameters on
Post-Tensioning Strand Performance
December 2013 Report #NDSE-2013-02
by
Kevin Q. Walsh
University of Notre Dame
Randy L. Draginis
Hayes Industries Ltd
Richard M. Estes
University of Notre Dame
Yahya C. Kurama
University of Notre Dame
Structural Engineering Research Report
Civil and Environmental Engineering and Earth Sciences
University of Notre Dame
Notre Dame, Indiana
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ABSTRACT
This report describes the findings from an experimental investigation on the effects of important
anchor wedge dimensional parameters on the ultimate strains and stresses of seven-wire, low
relaxation unbonded post-tensioning (PT) strand at failure. Previous research on industry-
representative standard PT anchor components from the U.S. has shown that premature fracture
of the strand wires can occur at strand strains as low as 0.01 in./in., or even less in some
instances. This strain limit may pose a practical constraint for the use of this construction
technique under extreme conditions, such as emerging applications in earthquake-resistant
structures. Building on the previous findings, the current research experimentally investigates if
significant improvements in the ultimate strand strains can be made by: (1) slightly increasing
the taper angle of the wedge outer surface (approximately 1 degree increase) with respect to the
taper angle of the anchor housing cavity; and (2) slightly increasing the thickness of the wedge as
measured at the crown. The objective in controlling these wedge dimensions is to achieve a more
uniform distribution of stresses within the strand-wedge-anchor interface by maintaining a
uniform, minimized gap between the individual wedge pieces (i.e., wedge gap control) over the
height as well as the circumference of the anchor, and thereby reducing or even eliminating
stress concentrations at the narrow end of the anchor. The test results demonstrate that relatively
small, controlled deviations from industry-representative standard wedge dimensions can
significantly improve the ultimate performance of the strand-anchorage system at failure. A large
number of strand-anchorage systems were tested to evaluate the statistical validity of the results
involving presumed-optimal dimensions for the wedge taper angle and crown thickness. It is
concluded that these dimensional variations, which have not been previously investigated in a
systematic study, may represent core design variables affecting the stress transfer at the strand-
wedge-anchor interface. To this end, important quality control measures are identified and
should be considered for the manufacturing of the wedges as well as the anchor housing.
1
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CONTENTS
ABSTRACT .................................................................................................................................... 1
CONTENTS .................................................................................................................................... 2
LIST OF FIGURES ........................................................................................................................ 4
LIST OF TABLES .......................................................................................................................... 6
ACKNOWLEDGMENTS .............................................................................................................. 7
SYMBOLS AND NOTATION ...................................................................................................... 8
INTRODUCTION ........................................................................................................................ 10
1.1 Overview ................................................................................................................. 10
1.2 Objectives ............................................................................................................... 12
1.3 Previous Research at the University of Notre Dame .............................................. 13
1.4 Scope and Approach of Current Research .............................................................. 16
1.5 Organization of Report ........................................................................................... 17
WEDGE TAPER ANGLE DIFFERENTIAL AND CROWN THICKNESS .............................. 18
2.1 Wedge Manufacturing Process ............................................................................... 18
2.2 Introducing a Wedge Taper Angle Differential ...................................................... 18
2.3 Increasing Wedge Thickness Measured at Crown .................................................. 20
EXPERIMENTAL PROGRAM ................................................................................................... 22
3.1 Wedge Dimensions ................................................................................................. 22
3.2 Anchor Dimensions ................................................................................................ 23
3.3 Strand Properties ..................................................................................................... 23
3.4 Test Equipment ....................................................................................................... 24
3.5 Test Setup and Procedure ........................................................................................ 25
3.6 Test Measurements ................................................................................................. 26
TEST RESULTS AND FINDINGS ............................................................................................. 28
4.1 The Effects of Wedge Dimensional Variations on Ultimate Strand Strain ............ 28
4.2 The Effects of Wedge Dimensional Variations on Strand Failure Modes .............. 33
4.3 Statistical Validation of Results .............................................................................. 35
4.4 Quality Control Measures for PT Anchor Components ......................................... 38
SUMMARY AND CONCLUSIONS ........................................................................................... 39
REFERENCES ............................................................................................................................. 41
2
APPENDIX A: TABULATED DATA BY TEST GROUP ......................................................... 44
APPENDIX B: DETERMINATION OF STRAND CROSS-SECTIONAL AREA .................... 53
APPENDIX C: STATISTICAL ANALYSIS DATA AND RESULTS ....................................... 55
3
LIST OF FIGURES
Figure 1.1: Strand wire fracture at anchor entry point .................................................................. 11
Figure 1.2: Coupled wall subassembly test results (Weldon and Kurama 2007) showing strand
wire fractures (1 kip=4.448 kN) ................................................................................................... 11
Figure 1.3: Plan view of full-scale structure and elevation view of full-scale wall (Smith et al.
2012) (1 in. = 25.4 mm) ................................................................................................................ 12
Figure 1.4: Materials tested by Walsh and Kurama (2009, 2010, 2012) ...................................... 14
Figure 1.5: Representative strand fracture stress versus fracture strain results from Walsh and
Kurama (2009, 2010) (1 in.=25.4 mm; 1 psi=6.895 kPa) ............................................................. 14
Figure 1.6: Wedge height versus strand fracture strain (and associated linear trend lines) from
Walsh and Kurama (2009) (1 in.=25.4 mm) ................................................................................. 15
Figure 1.7: Anchor housing cavity taper angle versus strand fracture strain (and associated linear
trend line) from Walsh and Kurama (2009) (ATA= arctan[(TID–BID)/(2H )]) (1 in.=25.4 mm) 15
a
Figure 1.8: Anchor schematic depicting taper angle differential and wedge cross-section as
measured at crown ........................................................................................................................ 16
Figure 2.1: Wedge imprint photos (top) and schematics (bottom) inside anchor housing after
ultimate strand fracture ................................................................................................................. 19
Figure 2.2: Typical manufacturing dimensions for presumed-optimal, higher tapered wedges in a
0.6-in. PT strand anchorage (ϕ=center hole diameter; difference between minor and major ϕ
represents reduction in diameter due to teeth height) ................................................................... 20
Figure 2.3: Anchorages of typical 0.6-in. strand systems with varying wedge gap control ......... 21
Figure 3.1: Wedge crown thicknesses, WT, versus wedge taper angle, WA, for individual test
specimens ...................................................................................................................................... 22
Figure 3.2: Testing equipment ...................................................................................................... 24
Figure 3.3: General test setup (1 in.=25.4 mm) ............................................................................ 25
Figure 3.4: Determination of strand strains from measured strand stress and other data ............. 26
Figure 4.1: Wedge taper angle, WA, versus ultimate strand strain for individual test specimens
(with second-order trend lines and optimal ranges also shown) ................................................... 29
Figure 4.2: Wedge crown thickness, WT, versus ultimate strand strain for individual test
specimens (with second-order trend lines and optimal ranges also shown) ................................. 29
Figure 4.3: Wedge taper angle, WA, versus coefficient of variation, CV, of ultimate strand strain
for selected test groups (with second-order trend lines and optimal ranges also shown) ............. 30
Figure 4.4: Wedge crown thickness, WT, versus coefficient of variation, CV, of ultimate strand
strain for test groups (with second-order trend lines and optimal ranges also shown) ................. 30
4
Figure 4.5: Number of outer wire slips (top + bottom anchorages) versus ultimate strand strain
for individual test specimens (with linear trend lines also shown) ............................................... 34
Figure 4.6: Number of wire fractures (top + bottom anchorages) versus ultimate strand strain for
individual test specimens (with linear trend lines also shown) ..................................................... 34
Figure 4.7: Wedge taper angle, WA, versus number of wire fractures (top + bottom anchorages)
for individual test specimens (with second-order trend lines and previously-defined optimal
ranges also shown) ........................................................................................................................ 35
Figure 4.8: Wedge top thickness, WT, versus number of wire fractures (top + bottom anchorages)
for individual test specimens (with second-order trend lines and previously-defined optimal
ranges also shown) ........................................................................................................................ 35
5
Description:relaxation unbonded post-tensioning (PT) strand at failure. uniform, minimized gap between the individual wedge pieces (i.e., wedge gap control)
