effects of anchor wedge dimensional parameters on ......delay the occurrence of wire fracture inside...

63PCI Journal | May–June 2015

Although unbonded posttensioning for use in gravity load systems (for example, floor and roof slabs) has been available in the United States since the 1950s and standards exist for its application,1–4 this construction method is increasingly being considered and applied in more extreme loading environments, such as in primary earthquake-resisting structural components (for example, primary shear walls and moment-resisting frames). Recent advances in the seismic application of un-bonded posttensioning include precast concrete buildings, steel buildings, and bridge systems.5–24

The posttensioning tendon anchorages in unbonded posttensioned building and bridge systems are important structural components because of the transfer of the entire posttensioning force at these locations. Posttensioning anchorage designs, configurations, manufacturing pro-cesses, and materials have significantly changed since the initial research that led to their development.25–29 All of this early work focused on structures under gravity loads, with no consideration for extreme loads such as earth-quakes. As a potential limitation for seismic applications, premature strand wire fractures were observed by Weldon and Kurama30 during reversed-cyclic lateral load testing of unbonded posttensioned precast concrete coupled wall subassembly specimens. Subsequently, a detailed experi-mental study on the ultimate performance of industry-

■ This paper reports on an experimental investigation of the effects of anchor wedge dimensions on the ultimate strains of posttensioning strand.

■ The results demonstrate that slight increases in the taper angle of the anchor wedge outer surface and the thickness of the an-chor wedge can significantly improve the ultimate performance of the strand at failure.

Effects of anchor wedge dimensional parameters on posttensioning strand performance

Kevin Q. Walsh, Randy L. Draginis, Richard M. Estes, and Yahya C. Kurama

May–June 2015 | PCI Journal64

(ACI 318-11) and Commentary (ACI 318R-11).39 This was necessary to ensure that the expected strand strain demands would not exceed 0.01 at the prescribed validation-level roof drift of 2.3% (that is, the wall lateral drift at which the structure was required to be designed and validated per ACI ITG-5.1).40 Nonlinear dynamic response history analyses supporting the validation-level drift demand used in design were discussed by Smith and Kurama.41 From the design procedure in Smith and Kurama,36,37 the 0.01 maxi-mum posttensioning strand strain limit would result in a more severe constraint for the design of a wall with longer length and shorter height (for example, a three-story build-ing) or with strands placed farther away from the wall cen-terline because these conditions would result in increased strand strain demands at the same wall drift level.

The typical wire fracture in Fig. 1 indicates the presence of significant stress concentration at the narrow end of the tapered anchor housing cavity (that is, nonuniform stress transfer inside the anchorage). There is a need to de-velop an understanding of the anchorage design variables governing the stress transfer at the strand-wedge-anchor interface so that increased strand strains closer to the true strain capacity of the material can be developed at ultimate failure. Achieving this goal would not only improve the reliability of unbonded posttensioned structures in seismic regions but could also improve construction economy by eliminating the current design constraint imposed by pre-mature strand wire fracture. For example, the total tendon area could be decreased by allowing the use of the 0.70fpu ACI 318-11 limit instead of the fracture-controlled 0.55fpu limit for the initial posttensioning strand stress of the wall structure designed by Smith and Kurama.36,37

Previous research

The research by Walsh and Kurama31–33 involved the testing of approximately 400 specimens of seven-wire, uncoated, low-relaxation posttensioning strand meeting ASTM A41642 requirements with industry-representative standard anchorage components commonly available in the United States (Fig. 1). Both prominent types of mono-strand posttensioning anchors—cast anchors and machined barrel anchors—were tested. As examples of representative behavior, Fig. 2 shows the measured strand fracture stress and fracture strain results for strand-anchor assemblies tested according to the static testing requirements of ICC-ES.43 All of the specimens failed due to the fracture of one or more strand wires where the first few full-depth wedge teeth gripped the strand at the narrow end of the anchor housing cavity. The most significant observation from the data is that a large number of the specimens did not meet the acceptance criteria for unbonded posttensioning anchor performance set forth in ACI 318-11, ACI 423,1,2 and the Post-Tensioning Institute’s (PTI’s) Specification for Unbonded Single Strand Tendons.4 Furthermore, there was a large scatter in the strand ultimate strains at failure,

representative standard strand-anchorage components from the United States was conducted by Walsh and Kurama.31–33 Recently, premature strand wire fractures were also ob-served during the shake-table testing of a precast concrete building system.34

Walsh and Kurama31–33 showed that strand wire failures in industry-representative standard anchorage components can occur at strand strains as low as 0.01 or even smaller in some instances. The observed premature strand failures occurred due to the brittle fracture of individual strand wires inside the posttensioning anchors (Fig. 1), within the first few full-depth wedge teeth where the strand entered the narrow end at the front of the tapered anchor housing cavity. Significant variability was observed in the strand ultimate strains as a result of the brittle nature of the wire fractures. Based on the test data, a maximum strand strain limit of 0.01 was recommended for the design of unbonded posttensioned structures, unless anchors that have been proved to consistently achieve higher strand ultimate strains are specified.

Free-length failure tests of strand samples (that is, tensile tests performed using special sand-grip anchors to achieve strand failure within the free length away from the anchor-ages) conducted by Walsh and Kurama31,32 showed that the true (that is, not affected by the anchorages) ultimate fracture strain capacity of seven-wire, low-relaxation post-tensioning strand is generally between 0.060 and 0.075. Thus, the strain limit of 0.01 as governed by individual wire fractures inside the anchorages is restrictive relative to the actual material capacity of the strand.

As evidenced in the measured behavior of the coupled wall structure described in Weldon and Kurama,30 the strain limit of 0.01 represents a real and practical limit for the design of unbonded posttensioned structures in seismic regions. Premature posttensioning anchorage failure, even in the form of single wire fractures, can result in significant reductions in the self-centering capability as well as in the lateral stiffness and resistance of these structures under seismic loading.30 The residual behavior (that is, stress reduction through successive wire fractures) of monostrand anchorage systems beyond first wire fracture was recently investigated by Sideris et al.35

The practical implications of the 0.01 strain limit can also be considered with respect to the four-story precast concrete shear wall structure designed in the appendix of Smith and Kurama36,37 based on the experimental validation described in Smith et al.38 Following the recommendations from Walsh and Kurama,31–33 the initial posttensioning strand stress in this structure was limited to a relatively low value of 0.55fpu, where fpu is the nominal ultimate strand strength (compared with the maximum allowable stress of 0.70fpu specified by American Concrete Institute’s (ACI’s) Building Code Requirements for Structural Concrete


parameter; rather, it represents the measured heights of the industry-representative standard wedges that were tested in the sample pool. Despite the scatter in the data, on average, increased wedge height tended to result in greater fracture strains. A possible explanation for this trend may be that the increased wedge height provided a longer development length for the strand stresses, thus increasing the fracture strains. However, the improvement in strand performance from the increased wedge height alone was relatively small and the fractures still occurred where the first few full-depth wedge teeth gripped the strand at the narrow end of the tapered anchor housing cavity. Thus, it may be con-cluded that increased wedge height does not necessarily eliminate the development of stress concentrations at the narrow end of the anchor housing. Other dimensional vari-ables need to be explored, which is the focus of this paper.

Figure 2 also plots the strand fracture strains against the anchor housing cavity taper angle for the tested anchors.

with wire fractures occurring at strains as high as 0.04 and as low as 0.01 or less. Figure 2 includes data from a va-riety of parameters plotted together (for example, barrel anchors and cast anchors). A further breakdown of these results into different parameters can be found in Walsh and Kurama.31,32 Additional testing conducted under pos-tyield cyclic strand strain conditions showed that seismic loading can cause further reduction in the ultimate strand strains as well as further increase in the variation of these strains.31,33 More recent cyclic testing of monostrand-anchorage systems can be found in Sideris et al.35

It was provisionally observed by Walsh and Kurama31 that the geometric properties of the wedges and anchors affected the ultimate performance of the tested strands. For example, Fig. 2 plots the measured strand fracture strains against the anchor wedge height Hw. The variation of wedge height in Fig. 2 was not from a systematic study with controlled variation of the wedge height as a design

Figure 1. Previous research by Walsh and Kurama. Sources: Data from Walsh and Kurama (2009, 2010, and 2012). Note: Diagrams are not drawn to scale. ATA = anchor housing taper angle measured longitudinally; BID = anchor bottom inside diameter; BOD = anchor bottom outside diameter = TOD in case of barrel anchors; BW = wedge bottom outside width; dmw = diameter of middle strand wire; dow = diameter of outer strand wire; dp = outside crown-to-crown diameter of strand; Ha = anchor height; Hw = wedge height; IW = wedge inside width; L = cast anchor length; TID = anchor top inside diameter; TOD = anchor top outside diameter (equal to BOD in case of barrel anchors); TW = wedge top outside width; W = cast anchor width; WA = wedge taper angle measured longitudinally; WT = wedge thickness at top crown measured transversely.

TOD

Ha

TODTID

BIDBOD

ATA

Premature strand wire fracture inside anchor

Cast anchor Barrel anchor Nine-hole multistrand anchor

Anchor wedges

Seven-wire strand


Objectives, scope, and approach of current research

Posttensioning anchor wedges play a significant role by controlling the stress transfer from the strand to the anchor housing. It may be possible to improve the ultimate perfor-mance of a posttensioning strand at wire fracture (that is, higher fracture strains) by altering the dimensional proper-ties of the anchor wedges to result in a more uniform distribution of stresses within the strand-wedge-anchor interface, thereby reducing or even eliminating localized pinching of the strand at the narrow end of the tapered anchor housing cavity. In accordance with the objective to delay the occurrence of wire fracture inside the anchors, this paper experimentally investigates the effects of two important anchor wedge dimensional parameters on the ultimate strand strains at initial wire fracture.

The wedge dimensions were varied from industry-repre-sentative standard dimensions currently used in the manu-

The variation of anchor housing taper angle (Fig. 2) is dif-ferent from the wedge taper angle differential emphasized in the current research described in this paper. Because the specimens tested by Walsh and Kurama31 used standard anchor components, the configurations all had matched taper angles between the anchor housing and the outside surfaces of the wedges, consistent with industry practice. The anchor housing taper angle in a matched wedge-anchor configuration provides an indication of the stress transfer at the strand-wedge-anchor interface, perhaps overly concentrating the stress transfer if the angle is too steep and more evenly distributing it if the taper is shal-lower. Indeed, this trend is observed in Fig. 2, with the strand fracture strains generally increasing as the anchor housing taper angle decreases. However, strand slip rather than wire fracture can occur if the anchor housing taper angle is overly reduced. Thus, there is an effective working range for the dimensional design variables of the anchor components, which is another focus of the current research.

Figure 2. Representative results from Walsh and Kurama. Sources: Data from Walsh and Kurama (2009 and 2010). Note: ATA = arctan [(TID – BID)/(2Ha)]. 1 in. = 25.4 mm; 1 psi = 6.895 kPa.

Strand fracture strain versus fracture stress

Wedge height versus strand fracture strain

Anchor housing cavity taper angle versus strand fracture strain

Wedge height versus strand fracture strain


facture of these components as follows: the taper angle of the wedge outer surface was slightly increased to introduce a small (approximately 1.00 degree) differential with respect to the taper angle of the anchor housing cavity, and the thickness of the wedge cross section WT as measured at the crown was slightly increased (Fig. 3). These selected variations from standard wedge dimensions require no significant increase in the overall wedge size, and thus were considered to be more cost effective than increasing the height of the anchorage. Furthermore, while it may be possible to achieve an increase in the strand fracture strains by increasing the wedge height Hw, this parameter alone may not necessarily result in a significant reduction in the variance of the fracture strains (Fig. 2).

Most of the tests were conducted using machined barrel anchors, with a smaller number of tests conducted using cast anchors. While both two-piece and three-piece wedges were tested by Walsh and Kurama,31–33 only two-piece wedges were used in the new study. The use of two-piece wedges rather than three-piece wedges was favored due to the tighter quality control tolerances that are suggested later in this paper to consistently utilize the benefits of modified wedge dimensions. All anchors and wedges were obtained from a single manufacturer, and the anchors were not modified from their standard geometry (that is, only the wedges were modified). To test the limits of improvement in the strand ultimate strains at failure, the dimensional modifications on the wedges were made on the short-est height of wedge used in the industry. For all 0.5 in. (13 mm) diameter strand testing, the wedge height Hw was 1.2 in. (30 mm), and for all 0.6 in. (15 mm) diameter strand testing, the wedge height was 1.6 in. (40 mm) with a tolerance of ±0.010 in. (0.25 mm). To ensure that typical

dimensional and material variations for the posttensioning strand were represented in the test data, samples from three strand manufacturers were tested for each of the two sizes (0.5 and 0.6 in.).

The tests were conducted on monostrand specimens ac-cording to the static testing requirements of ICC-ES.43 The results were used to investigate the presence of optimal wedge taper angle differential and crown thickness that can consistently achieve significantly improved ultimate strand strains with reduced variability within the tested sample pool. A two-sample t-test with a one-sided alterna-tive hypothesis (a commonly used statistical examination of the difference in two population means) was used to verify that the increase in the ultimate strand strains using wedges with the presumed-optimal dimensions was signifi-cant. There are many different strand-anchorage systems and configurations used in practice, and the optimal wedge dimensions may be different from system to system. Thus, the primary goal in exploring the presence of optimal dimensions in this research was not to specify the values for these dimensions but rather to demonstrate the impor-tant dimensional principles for the design of wedges with improved strand performance at ultimate fracture.

A recent study using dimensionally-modified postten-sioning wedges in multistrand tendons was conducted by Abramson;44 however, to the best of the authors’ knowl-edge, there has been no previous systematic study on the effects of the wedge taper angle differential and crown thickness on the ultimate performance of the strand-an-chorage system. By empirically showing that small altera-tions in the wedge taper angle and crown thickness can significantly increase the strand fracture strains, the current

Figure 3. Anchor schematics. Note: Difference between minor and major diameters represents reduction in diameter due to depth of teeth. ATA =anchor housing ta-per angle = arctan [(TID – BID)/(2Ha)]; BID = anchor bottom inside diameter; Ha = anchor height; TID = anchor top inside diameter; WA = wedge taper angle measured longitudinally; WT = wedge thickness at crown measured transversely. 1 in. = 25.4 mm.

Taper angle differential (WA versus ATA) and wedge thickness WT

Typical manufacturing dimensions for presumed-optimal, higher-tapered wedges for 0.6 in. strand


research not only identifies these dimensional variables among the core principles for the design of the wedges but also presents significant quality control implications for the manufacture of posttensioning anchor components with consistent and improved strand performance. Ultimately, these findings can lead to new approaches for the design and manufacture of posttensioning tendon anchorages for unbonded posttensioned structural systems. Walsh et al.45 provide full results from the research.

Wedge taper angle differential

Industry-representative standard posttensioning anchor wedges in the United States are manufactured to achieve matched taper angles between the outside surface of the wedges and the inside surface of the anchor housing cavity. For example, for the typical standard anchor housing cavity taper angle ATA of about 7.00 degrees (within a tolerance of ±0.10 degrees), the standard wedge taper angle WA is also about 7.00 degrees (within a tolerance of ±0.10 de-grees). In a forensic examination of standard anchors and wedges tested to strand failure (Fig. 4), the stress transfer imprint (that is, marks of visible impression) left by the wedges on the anchor housing cavity surface suggested sig-nificant stress concentration at the wedge-anchor interface (and thereby at the strand-wedge interface) near the narrow end of the tapered anchor housing cavity. This observation is consistent with the occurrence of wire fractures at the narrow end of the anchor housing cavity (Fig. 1) and the increase in average fracture strains as the anchor housing taper angle is reduced (Fig. 2).

It may be possible to significantly reduce the stress concen-tration at the narrow end of the anchor housing cavity by increasing the wedge taper angle beyond what is com-

monly understood as the industry-representative standard matched angle to result in a differential of approximately 1.00 degree with respect to the anchor housing cavity taper. Figure 3 shows the typical manufacturing dimen-sions of the presumed-optimal, higher-tapered wedges for the 0.6 in. (15 mm) strand samples tested in this research program. There is an increased wedge taper angle of ap-proximately 8.00 degrees in the figure compared with the industry-representative standard taper angle of 7.00 de-grees.

Match-tapered wedges grip the strand mostly near the nar-row end of the anchor housing cavity (Fig. 4). In compari-son, higher-tapered wedges (wedges that have greater taper angle compared with the anchor housing cavity) initially

Figure 4. Wedge imprint photos (top) and schematics (bottom) inside anchor housing after strand wire fracture.

Standard, match-tapered wedges

Optimal, higher-tapered wedges

Over-tapered wedges

Figure 5. Anchorages of 0.6 in. strand systems with varying wedge gap control. Note: 1 in. = 25.4 mm.

Standard two-piece wedges

in barrel anchor

Standard three-piece wedges in

barrel anchor

Nonstandard two-piece wedges in barrel anchor

Nonstandard two-piece wedges in cast anchor

Standard two-piece wedges in cast anchor

Figure 6. Wedge crown thicknesses WT and wedge taper angle WA for test specimens. Note: 1 in. = 25.4 mm.


the tapered anchor housing cavity (Fig. 4 and 5). Increas-ing the wedge crown thickness WT reduces the size of the gaps between the wedge pieces, thereby not only increas-ing the effectively anchored circumference at the back of the strand but also reducing stress concentrations at the narrow end of the anchor housing cavity by preventing the wedges from seating too deeply into the anchor. Figures 4 and 5 illustrate this gap control principle, which is possible using a combination of wedge taper angle differential and increased wedge crown thickness.

The total gap between standard three-piece wedges is greater than the total gap between standard two-piece wedges (Fig. 5). Thus, gap reduction and control between the wedge pieces may be more effective with two-piece wedges compared with three-piece wedges. This may be a significant advantage for the choice of two-piece wedges rather than three-piece wedges in the use of nonstandard wedges in practice, in addition to the tighter quality control tolerances that can be achieved using two-piece wedges.

Similar to the wedge taper angle differential, there is an effective range for the wedge crown thickness. Beyond an optimal increase in the crown thickness, the wedge pieces may fully close prior to securing the strand with enough

grip the strand near the wide end of the anchor housing cavity, and ultimately the wedges rotate and deform to conform to the taper angle of the anchor housing cavity re-sulting in more uniform stress distribution over the wedge height. The inner edges of the wedge imprints in Fig. 4 for the optimal, higher-tapered wedges are now nearly even and approximately parallel to the strand. This may be viewed as evidence that a more uniform stress distribution at the wedge-anchor interface may exist in this case. Of course, wedges that are overtapered beyond an effective range of this action (that is, tapered at too great an angle) may likewise experience similar premature wire fractures as standard match-tapered wedges, but this would occur near the wide end of the anchor housing cavity rather than near the narrow end (Fig. 4).

Increased wedge thickness at crown

Similar to the wedge taper angle differential, the basic concept behind slightly increasing the wedge crown thick-ness WT is also an attempt to achieve more uniform stress transfer at the strand-wedge-anchor interface. The general principle in the design of industry-representative standard wedges is that the crown of the wedge pieces must remain in a near free-floating position inside the anchor housing cavity. A direct consequence of this standard design detail is that significant gaps remain between the wedge pieces at the back of a fully stressed strand near the wide end of

Table 1. Measured wedge dimensions

Strand diameter, in

Wedge ring Hw, in. TW, in. BW, in. IW, in.

0.5 No 1.2 1.00 0.730 0.516

0.6 No 1.6 1.12 0.780 0.616

Note: BW = wedge bottom outside width; Hw = wedge height; IW = wedge inside width; TW = wedge top outside width. 1 in. = 25.4 mm.

Table 2. Measured anchor dimensions

Anchor Ha, in. TOD, in. TID, in BID, in. BOD, in.

0.5 in. barrel 1.4 1.6 0.99 0.64 1.6

0.6 in. cast 1.3 1.7 0.97 0.68 1.4

0.6 in. barrel 1.8 1.8 1.15 0.70 1.8

0.6 in. cast 1.6 2.1 1.61 0.75 1.4

Note: BID = anchor bottom inside diameter; BOD = anchor bottom outside diameter = TOD for barrel anchors; Ha = anchor height; TID = anchor top inside diameter; TOD = anchor top outside diameter = BOD for barrel anchors. 1 in. = 25.4 mm.

Figure 7. Test setup (left) and determination of strand strains from measured strand stress and other data (right). Note: 1 in. = 25.4 mm; 1 psi = 6.895 kPa.


Strand properties

Samples from three strand manufacturers were tested for each of the two sizes (0.5 and 0.6 in. [13 and 15 mm]) (Table 3). Strands 0.5A and 0.6A were also the primary strands tested by Walsh and Kurama,31–33 while strands 0.5F, 0.6F, 0.5G, and 0.6G represent new spools used in this new research program only. All strand samples met the dimensional requirements of ASTM A41642 with diam-eters measured across the crowns ranging from 0.500 to 0.510 in. (12.7 to 13.0 mm) and 0.600 to 0.615 in. (15.2 to 15.6 mm) for the 0.5 and 0.6 in. (13 and 15 mm) strand samples, respectively. Given the acute attention to the control of wedge dimensions in this research, the tested strand spools were chosen specifically because of their slight dimensional differences to gauge the effects of this real-world variable on the ultimate strand performance. The strand cross-sectional area ap was calculated45 from the following measurements of the strand samples: length of sample ls, weight of sample ws; weight of middle wire wm from sample (to determine the steel unit weight γs), and diameter of middle wire dmw. The other strand properties listed in Table 3 were determined by testing strand samples (three from each strand spool listed) with special sand-grip anchors to result in near-simultaneous free-length fracture of all seven wires in each specimen.33,35

Test setup and procedure

Figure 7 depicts the basic test setup and equipment, which are the same as those used in the previous study by Walsh and Kurama.31–33 Each strand specimen was positioned through the crossheads of the testing machine with a posttensioning anchor placed on the outer surface of each crosshead. The anchors bore directly on 1.5 in. (38 mm) thick steel plates, each with a central hole oversized 1⁄16 in. (1.6 mm) with respect to the nominal strand diameter. The bearing plates were screwed to the machine crossheads, and the central holes were aligned vertically using a laser align-ment tool such that each strand sample was placed in the

transverse pressure to keep the outer wires from slipping. Thus, it is important to control the wedge gap to a small but nonzero value through the entire range of the strand stress-strain behavior. The implications of outer wire slip (due to overthickened wedges) on the strand ultimate performance are discussed as part of the test results in this paper.

Experimental program

Wedge dimensions

A total of 334 strand samples with wedges of varying dimensions (including industry-representative stan-dard control wedges as well as modified wedges) were tested.45 Figure 6 shows the taper angle WA and crown thickness WT of the tested wedge pieces for the 0.5 in. (13 mm) and 0.6 in. (15 mm) diameter strand samples. As stated previously, the dimensional modifications of the wedges were made on the shortest height of wedge (that is, Hw in Fig. 1) commonly used in the industry. The taper angle WA was measured for each manufactured and heat-treated wedge piece by using an optical comparator to determine the angle of the outside surface with respect to the teeth-line profile. The crown thickness WT of each wedge piece was measured with digital calipers across the thickest area of the wedge segment (Fig. 3). The wedge dimensions in Fig. 6 are the average dimensions of the two wedges from the top or bottom anchor associated with ultimate strand failure (that is, the wedges from the unfailed anchor in each test are not included in the data). In the few cases where strand failure occurred near-simultaneously in both anchors, dimensions from all four wedges (that is, the two top and two bottom wedges) were averaged. The selection of the wedges in each test was controlled such that the differences in the dimensions of the four wedge pieces used on the same strand specimen were minimal.

The data points in Fig. 6 along the horizontal line for WA equal to 7.00 degrees represent the industry-representa-tive standard wedges. While the measured wedge taper angle WA was consistent (and close to the 7.00-degree standard) for these samples, the corresponding range for the wedge crown thickness WT was greater. The current industry standard tolerance for the wedge crown thickness is ±0.015 in. Table 1 summarizes other geometric proper-ties associated with the wedges tested in this program (the geometric variables listed in Table 1 are shown in Fig. 1).

Anchor dimensions

The study was conducted on standard anchors with the shortest anchor height Ha commonly used in the industry. Table 2 summarizes the geometric properties associated with the tested anchors (the geometric variables listed in Table 2 are shown in Fig. 1).

Table 3. Measured strand properties

Strand pool ap, in.

2 fpm,free-length, ksi εpf,free-length

Ep, ksi

0.5A 0.149 286.7 0.0736 28,028

0.5F 0.151 285.5 0.0726 28,767

0.5G 0.151 287.6 0.0680 29,874

0.6A 0.219 280.9 0.0752 27,872

0.6F 0.218 282.5 0.0677 28,811

0.6G 0.220 285.2 0.0675 28,985

Note: ap = strand cross-sectional area; fpm,free-length = strand peak stress; Ep = strand linear-elastic modulus; εpf,free-length = strand ultimate (frac-ture) strain. 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.


seating and the strand was loaded to failure by moving the top machine crosshead upward at a constant speed of 1.44 in./ min (36.6 mm/min) while the bottom crosshead remained stationary. This position rate resulted in a strain rate of 0.02 / min, which is at the upper limit of the ICC-ES required strain rate range of 0.0047 to 0.021 /min.

Test measurements

During each test, the time elapsed, applied load, and crosshead displacement were recorded continuously at a frequency of 100 Hz. All test equipment components were calibrated on-site by a calibration laboratory technician. The strand stress was found by dividing the measured force with the area ap listed in Table 3. An extensometer was not used to measure the strand strains due to risk of damage to the sensor from multiple explosive wire fractures under the high strand stresses that were possible using the modified wedges. Therefore, different from Walsh and Kurama,31–33 the strand strains were determined by using other measured data in three stages of behavior

same position with minimal eccentricity between the ends of the strand. Unlike the study by Walsh and Kurama,31–33 the cast anchors were not fitted with support plates that at-tempted to use the full bearing area underneath the anchor but instead were placed directly on the 1.5 in. thick bearing plates so that all of the bearing occurred through the anchor boss (Fig. 1). The potential effects of this test variation from the previous research program were not investigated.

In accordance with the static testing requirements of ICC-ES,43 the crossheads of the testing machine were positioned to provide an initial strand free-length of about 71 in. (1800 mm) between the top and bottom bearing surfaces such that a strand free-length of about 72 in. (1830 mm) was achieved after seating of the anchor wedges. That is, the wedges were assumed to seat approximately 0.5 in. (13 mm) in each of the top and bottom anchors dur-ing testing. The anchor wedges were tapped in lightly by hand using the back of a spare anchor barrel before a preload of approximately 750 lb (3300 N) was applied to the strand. Then, the wedges were checked for proper

Figure 8. Wedge taper angle WA (top) and crown thickness WT (bottom) versus ultimate strand strain for individual test specimens (with second-order trend lines and optimal ranges also shown). Note: 1 in. = 25.4 mm.

0.5 in. strand (optimal 8.00 ±0.25 deg)

0.5 in. strand (optimal 0.484 ±0.010 in.)




curve in this range (that is, a large change in strain occurs with a small change in stress). Thus, the incre-mental crosshead displacement of the testing machine was used to determine the elongation increment of the strand, which was then divided by the free length of the strand (that is, length between the anchors) mea-sured at the start of this third stage of the test.

To validate this three-stage process, the strains for the strand specimens tested by Walsh and Kurama31–33 were estimated using the same procedure and then compared with direct extensometer measurements. At the point of wire fracture, the differences between the estimated and direct-measured strains were typically less than 0.001.

Test results and findings

Effects of wedge dimensional variations on ultimate strand strain

The experimental program included wedges with a

(Fig. 7) and described as follows:

• Up to a strand stress of 130 ksi (896 MPa), the strand strains were calculated by dividing the stress with the measured elastic modulus Ep of the strand. The elastic modulus was determined from the strand strains measured using an extensometer during the free-length failure tests of each strand spool as listed in Table 3 and described in Walsh and Kurama.31,33

• Between stresses of 130 and 250 ksi (900 and 1700 MPa), the strand strains were determined by find-ing the corresponding strain on the measured stress-strain relationship of the strand from the free-length failure tests. Again, the strains in these free-length failure tests were measured using an extensometer.

• For strains beyond that corresponding to a stress of 250 ksi (1700 MPa), the stress-strain relationship from the free-length failure tests could no longer be used reliably because of the shallowness of the stress-strain

Figure 9. Wedge taper angle WA (top) and crown thickness WT (bottom) versus coefficient of variation CV of ultimate strand strain for selected test groups (with second-order trend lines and optimal ranges also shown). Note: 1 in. = 25.4 mm.






end(s) from all of the specimens included in that group are plotted. Each test group was sorted to include specimens with a narrow range of wedge geometries (WA and WT) in addition to having common strand spools and anchor types (Tables 4 and 5). The sample sizes of the test groups varied (some with as high as 20 test samples and others with as low as 3 samples) because of the need to consider a wide range of wedge dimensions, WA and WT, while also building a statistically sound sample size for the dimensions that were ultimately chosen as being close to optimal.

The data in Fig. 8 and 9 and Tables 4 and 5 suggest that modified wedges with increased taper angle and crown thickness can result in improved strand performance by not only increasing the average ultimate strand strains

relatively wide range of dimensional alterations (that is, changes in the wedge taper angle and crown thickness) to approximate the presumed-optimal wedge dimensions for the sample test pool. The ultimate strains from the indi-vidual strand tests are plotted against the wedge taper angle WA and crown thickness WT in Fig. 8 and 9. The ultimate strand strain for each test was determined as the point at which fracture of the strand wire(s) or slippage of the outer wires (that is, outer six wires) (Fig. 1) caused at least a 10% drop in stress. Generally, the ultimate strain was clearly defined by sudden failures.

The entire data set from the study is in Walsh et al.45 Figure 9 illustrates the coefficient of variation CV of the ultimate strand strains from selected test groups. For each test group, the average wedge dimensions at the failure

Table 4. Data by test group for 0.5 in. strand configurations

Strand spool

Anchor WedgeNumber of tests

Wedge taper angle, WA, degrees

Wedge thickness WT, in.

Average ultimate

strains, in./in.

Coefficient of varia-

tion CV of ultimate strains

Average number of

exterior wire slips

Average number of

wire fracturesRange Average Range Average

0.5A Barrel Standard 15 6.98 to 7.03 7.00 0.468 to 0.469 0.468 0.0218 0.33 0.00 1.13

0.5A Barrel Modified 3* 8.02 to 8.03 8.02 0.473 to 0.475 0.474 0.0255 0.56 0.00 1.33

0.5A Barrel Modified 6 8.02 to 8.04 8.03 0.481 0.481 0.0376 0.05 0.00 3.00

0.5A Barrel Modified 9 7.48 to 7.51 7.50 0.486 to 0.490 0.488 0.0322 0.20 0.56 2.67

0.5A† Barrel Optimal 15 8.03 to 8.04 8.03 0.487 to 0.489 0.488 0.0357 0.19 0.07 2.60





0.5A Cast Standard 9 7.00 to 7.02 7.00 0.467 to 0.469 0.468 0.0122 0.33 0.00 1.00

0.5A Cast Modified 3 8.02 to 8.04 8.03 0.480 to 0.481 0.481 0.0222 0.50 0.00 2.00

0.5A Cast Modified 3 7.49 to 7.50 7.50 0.482 0.482 0.0367 0.05 0.00 2.00

0.5A† Cast Optimal 9 8.03 to 8.06 8.04 0.487 to 0.489 0.488 0.0291 0.34 0.11 1.78




0.5F Barrel Standard 3 7.01 to 7.03 7.02 0.461 to 0.467 0.464 0.0124 0.28 0.33 1.00

0.5F Barrel Modified 3 7.48 to 7.50 7.49 0.486 to 0.487 0.487 0.0329 0.04 2.00 2.33


0.5F† Barrel Optimal 5 8.03 to 8.04 8.03 0.487 to 0.491 0.489 0.0373 0.06 0.20 3.00



0.5F† Cast Optimal 3 8.08 to 8.11 8.10 0.488 0.488 0.0383 0.02 0.00 4.00

0.5G Barrel Standard 10 6.99 to 7.02 7.01 0.466 to 0.470 0.468 0.0182 0.46 0.00 1.10

0.5G† Barrel Optimal 10 8.03 to 8.05 8.04 0.487 to 0.489 0.488 0.0511 0.09 0.00 5.90

0.5G Cast Standard 10 6.99 to 7.02 7.01 0.466 to 0.470 0.468 0.0126 0.29 0.40 1.50

0.5G† Cast Optimal 10 8.03 to 8.05 8.04 0.487 to 0.489 0.488 0.0399 0.33 0.10 3.00

Note: The listed wedge dimensions are average values measured at the anchorage end(s) that experienced ultimate failure. The number of outer wire slips and wire

fractures in each test was determined as the sum between the anchorage end(s) that experienced ultimate failure. 1 in. = 25.4 mm.

*One test had differential wedge seating > 0.10 in., which greatly decreased the average value and increased the coefficient of variation CV of the ultimate strains in this

test group. As discussed in Walsh and Kurama (2010 and 2012), poor wedge seating is generally associated with unusually low fracture strains. † These rows show the approximate presumed-optimal wedge dimensions for the assessment of statistical significance summarized in Table 6.


• 0.6 in. (15 mm) strand: wedge taper angle of 8.10 de-grees (that is, a differential of about 1.10 degrees from the anchor housing cavity taper angle) with a toler-ance of ±0.40 degrees and crown thicknesses of about 0.548 in. (13.9 mm) with a tolerance of ±0.010 in. (0.254 mm)

The data ranges associated with the these presumed-opti-mal dimensions and their tolerances are represented by the shaded regions in Fig. 8 and 9. The tolerances were chosen to include portions of the polynomial trend lines in Fig. 8 above an ultimate strand strain of approximately 0.03. These tolerance ranges also coincide with a reduction in the coefficient of variation CV polynomial trend lines, thus indicating a generally decreased amount of variability in the ultimate strand strains (Fig. 9). The true improvement in the ultimate strand performance may not be clearly evi-dent within the optimal ranges in Fig. 8 and 9 because only one dimensional variable is controlled in each plot. (For example, the data points within the shaded optimal WA ranges in Fig. 8 include specimens with presumed-optimal

at failure but also decreasing the variability in the ultimate strains (represented by the CV of the data). In fact, wedges of almost every combination of modified dimensions tested in this investigation outperformed the standard wedges for each test group. Furthermore, an optimal wedge geometry could potentially exist, and the polynomial trend lines in Fig. 8 and 9 can be used to determine provisionally such presumed-optimal geom-etries (that is, dimensions that significantly increase the ultimate strand strains in Fig. 8 while also reducing the coefficient of variation CV in Fig. 9). Based on the ul-timate strand strains only (Fig. 8), the following wedge dimensions and tolerances can be considered presumed optimal:

• 0.5 in. (13 mm) strand: wedge taper angle of 8.00 de-grees (that is, a differential of about 1.00 degree from the anchor housing cavity taper angle) with a toler-ance of ±0.25 degrees and crown thickness of about 0.484 in. (12.3 mm) with a tolerance of ±0.010 in. (0.254 mm)

Figure 10. Number (from top + bottom anchorages) of outer wire slips (top) and wire fractures (bottom) versus ultimate strand strain for individual test specimens (with linear trend lines also shown). Note: 1 in. = 25.4 mm.

0.5 in. strand

0.5 in. strand

0.6 in. strand

0.6 in. strand


occurred inside an anchor and resulted in an abrupt and significant reduction in the strand force. A small amount of slip in the center wire was a regular occurrence with strand-anchorage specimens of all performance levels. However, this center-wire slip did not result in a significant drop in the strand force, and, therefore, was not identified as an ultimate failure mode.

For each test group, Tables 4 and 5 list the average number of outer-wire slips and average number of wire fractures associated with ultimate strand failure. To demonstrate the undesirable nature of outer-wire slip failure, Fig. 10 illustrates the moderate correlation between the number of wire slips and ultimate strand strain from individual test specimens. The number of outer-wire slips and wire frac-tures in each test was determined as the sum between the anchorage end(s) that experienced ultimate failure. Within the range of no slip to three wire slips, a reduction in the ultimate strand strain tended to occur with an increase in

as well as nonoptimal WT values). The presumed-optimal wedge dimensions and tolerances are limited to the speci-mens tested in this research program and may be further limited by the small sample size, as few as three samples, in some of the test groups (Tables 4 and 5). However, the different sample sizes between the different test groups did not significantly affect the presumed-optimal dimensions. (That is, the polynomial trends in Fig. 8 and 9 remained consistent as more samples were added to a particular test group).

Effects of wedge dimensional variations on strand failure mode

Two different ultimate failure modes, namely strand wire fracture and outer-wire slip (defined in this paper as the movement of an outer wire by more than 0.25 in. [6 mm] relative to the majority of the other outer wires), were manifested in the test program. Both of these failure modes

Table 5. Data by test group for 0.6 in. strand configurations

Strand spool




Average ultimate strains, in./in.

Coefficient of varia-tion CV of ultimate strains

Average number of

exterior wire slips

Average number of

wire fracturesRange Average Range Average

0.6A Barrel Standard 25* 6.99 to 7.03 7.00 0.524 to 0.536 0.530 0.0303 0.39 0.04 1.84

0.6A Barrel Modified 3 7.37 7.37 0.540 0.540 0.0410 0.01 0.00 3.00


0.6A Barrel Modified 3 7.35 to 7.38 7.37 0.549 to 0.550 0.549 0.0281 0.15 2.33† 1.33†


0.6A ‡ Barrel Optimal 20 8.03 to 8.05 8.04 0.549 to 0.551 0.549 0.0400 0.04 0.00 4.05



0.6A Barrel Modified 3 8.03 8.03 0.555 to 0.556 0.555 0.0363 0.09 0.00 3.00

0.6A Cast Standard 9 7.00 to 7.01 7.01 0.529 to 0.531 0.531 0.0138 0.63 0.00 1.00



0.6A‡ Cast Optimal 9 8.03 to 8.04 8.04 0.549 to 0.550 0.550 0.0298 0.32 0.11 1.67



0.6F Barrel Standard 6 7.00 to 7.03 7.01 0.524 to 0.536 0.531 0.0307 0.43 0.00 1.17

0.6F Barrel Modified 3 7.36 to 7.39 7.37 0.549 0.549 0.0311 0.44 1.00 2.00


0.6F‡ Barrel Optimal 3 8.12 to 8.18 8.16 0.549 0.549 0.0446 0.03 0.00 4.33

0.6F‡ Cast Optimal 3 8.08 to 8.14 8.11 0.549 0.549 0.0468 0.03 0.00 3.67

0.6G Barrel Standard 10 6.99 to 7.01 7.00 0.528 to 0.531 0.530 0.0217 0.28 0.10 1.20

0.6G‡ Barrel Optimal 10 8.03 to 8.05 8.04 0.549 to 0.551 0.550 0.0297 0.40 0.30 2.00

0.6G Cast Standard 10 6.99 to 7.01 7.00 0.528 to 0.531 0.530 0.0104 0.34 0.20 1.30

0.6G‡ Cast Optimal 10 8.03 to 8.05 8.04 0.549 to 0.551 0.550 0.0246 0.46 0.00 1.50

Note: The listed wedge dimensions are average values measured at the anchorage end(s) that experienced ultimate failure. The number of outer wire slips and wire

fractures in each test was determined as the sum between the anchorage end(s) that experienced ultimate failure. 1 in. = 25.4 mm.

*Five tests from this group were not included in the statistical analysis described in Table 6 because of their outlier wedge dimensions. †All wires slipped through the anchor in one test. ‡ These rows show the approximate presumed-optimal wedge dimensions for the assessment of statistical significance summarized in Table 6.


It is hypothesized that, in general, the 0.6 in. specimens are less sensitive to changes in wedge dimensions.

Statistical validation of results

The results from the experimental program were used to validate, with widely accepted statistical principles, that an improvement in ultimate strand performance can be expected using dimensionally-modified wedges over industry-representative standard wedges. This task was achieved by monitoring for optimal dimensions during the course of the experimental program (these optimal dimensions remained relatively consistent as more sam-ples were tested) and ultimately building a statistically sound sample size for the dimensions that were identi-fied as being close to optimal. These wedge dimensions that most closely approximate the presumed-optimal values in Fig. 8 are in Tables 4 and 5 as wedge taper angle just over 8.00 degrees and wedge crown thickness of about 0.488 in. (12.4 mm) for 0.5 in. (13 mm) strand and 0.549 in. (13.9 mm) for 0.6 in. (15 mm) strand. The

the number of wire slips. Conversely, Fig. 10 shows that the ultimate strand strain increased notably with increased number of near-simultaneous wire fractures. Furthermore, the data in Tables 4 and 5 indicate a strong correlation between an increased average number of wire fractures per test group and decreased CV. These results demonstrate that multiple wire fractures should be sought as a more desirable failure mode for the ultimate performance of posttensioning strand-anchor systems.

Considering the goal to develop dimensionally-modified wedges so as to increase the number of near-simultaneous wire fractures (to improve the ultimate strand perfor-mance), Fig. 11 illustrates correlations between the varied wedge dimensions and the number of wire fractures, with shaded presumed-optimal dimensional ranges coinciding with those in Fig. 8 and 9. It can be concluded that the presumed-optimal wedge dimensional ranges also resulted in a generally increased number of wire fractures. The correlations are stronger for the 0.5 in. (13 mm) strand specimens than they are for the 0.6 in. (15 mm) specimens.

Figure 11. Wedge taper angle WA (top) and crown thickness WT (bottom) versus number of wire fractures (top + bottom anchorages) for individual test specimens (with second-order trend lines and previously defined optimal ranges also shown). Note: 1 in. = 25.4 mm.






identified wedge dimensions did not necessarily provide the greatest improvement for every tested strand-anchor configuration but were nonetheless chosen to investi-gate the statistical significance of the improvement over industry-representative standard wedges. This deci-sion was made because the purpose of the study was to determine approximate wedge dimensions that provided overall improvement on the ultimate strand performance rather than explicitly optimized for each strand-anchor configuration.

The statistical analysis performed on the test data45 was a two-sample t-test with a one-sided alternative hypothesis assuming unequal population variances.47 Both barrel and cast anchors were considered in combination with strand samples from spools 0.5A, 0.5G, 0.6A, and 0.6G (Fig. 12 and Table 6). Different sample pool sizes were necessary to determine statistically significant differences between the presumed-optimal and standard wedges for the different strand-anchor configurations (for example, 15 samples for strand 0.5A and 20 samples for strand 0.6A). The p-value is the estimated probability of rejecting the null hypothesis when the null hypothesis is valid. In this case, the null hypothesis is that the average ultimate strand strain achievable with an infinite population of standard wedges (that is, using an infinitely large sample pool size) is greater than or equal to the average ultimate strand strain achievable with an infinite population of presumed-optimal wedges. A p-value less than the generally accept-

ed threshold of 0.05 indicates that the null hypothesis can be rejected. Because the p-values in Table 6 for the tested strand-anchor configurations are all low (that is, most much lower than 0.05), it can be concluded that the im-provement observed in the average ultimate strand strains from each finite sample pool using the presumed-optimal wedges is statistically significant and that the alternative hypothesis that the presumed-optimal wedges will, on average, outperform the standard wedges is validated. De-spite the improvement in average fracture strains from the use of the presumed-optimal wedges, a few test samples with the presumed-optimal wedges were still limited to a fracture strain of about 0.01 (Fig. 12).

The comparisons for coefficient of variation CV in Table 6 are mixed, though the three lowest CV values are associated with the presumed-optimal wedges. An improvement in CV can be observed for four of the strand-anchor configurations tested (0.5A-barrel, 0.5G-barrel, 0.6A-barrel, 0.6A-cast), while two configurations are inconclusive (0.5A-cast, 0.5G-cast) and two configu-rations resulted in increased CV using the presumed-optimal wedges (0.6G-barrel, 0.6G-cast). These results point to the possibility for increased uncertainty and variability associated with cast anchors and 0.6 in. (15 mm) strand compared with machined barrel anchors and 0.5 in. (13 mm) strand. No statistical significance study was conducted for the CV values; larger sample sizes would likely be needed to validate the statistical

Table 6. Summary results from statistically significant testing phase

Strand spool




Average ulti-mate strain,

in./in.

Coefficient of variation CV of ultimate

strains

p-valuep-value <

0.05Range Average Range Average

0.5A BarrelStandard 15 6.98 to 7.03 7.00 0.468 to 0.469 0.468 0.0218 0.33

3.17 × 10-6 YesOptimal 15 8.03 to 8.04 8.03 0.487 to 0.489 0.488 0.0357 0.19

0.5A CastStandard 9 7.00 to 7.02 7.00 0.467 to 0.469 0.468 0.0122 0.33

3.26 × 10-4 YesOptimal 9 8.03 to 8.06 8.04 0.487 to 0.489 0.488 0.0291 0.34

0.5G BarrelStandard 10 6.99 to 7.02 7.01 0.466 to 0.470 0.468 0.0182 0.46

1.60 × 10-8 YesOptimal 10 8.03 to 8.05 8.04 0.487 to 0.489 0.488 0.0511 0.09

0.5G CastStandard 10 6.99 to 7.02 7.01 0.466 to 0.470 0.468 0.0126 0.29

3.20 × 10-5 YesOptimal 10 8.03 to 8.05 8.04 0.487 to 0.489 0.488 0.0399 0.33

0.6A BarrelStandard 20* 6.99 to 7.03 7.00 0.528 to 0.531 0.530 0.0292 0.43

6.14 × 10-4 YesOptimal 20 8.03 to 8.05 8.04 0.549 to 0.551 0.549 0.0400 0.04

0.6A CastStandard 9 7.00 to 7.01 7.01 0.529 to 0.531 0.531 0.0138 0.63

9.62 × 10-4 YesOptimal 9 8.03 to 8.04 8.04 0.549 to 0.550 0.550 0.0298 0.32

0.6G BarrelStandard 10 6.99 to 7.01 7.00 0.528 to 0.531 0.530 0.0217 0.28

3.94 × 10-2 YesOptimal 10 8.03 to 8.05 8.04 0.549 to 0.551 0.550 0.0297 0.40

0.6G CastStandard 10 6.99 to 7.01 7.00 0.528 to 0.531 0.530 0.0104 0.34

1.66 × 10-3 YesOptimal 10 8.03 to 8.05 8.04 0.549 to 0.551 0.550 0.0246 0.46

Note: p-value = estimated probability of rejecting the null hypothesis when the null hypothesis is actually true. 1 in. = 25.4 mm. *For this test group, 5 of the 25 total tests listed in Table 5 using industry-standard wedges were not included in the statistical validation analysis because of their outlier

dimensions from the other industry-standard wedges. Compared with the 25-sample test group in Table 5, the range of standard wedge thicknesses for the 20-sample

test group in this table is more consistent with the range of standard wedge thicknesses in the other test groups.


significance of the differences in CV for many of the test groups.

Quality control measures for posttensioning anchor components

A major theme from the test results in this paper as well as those in Walsh and Kurama31–33 is the high variance (mea-sured using the coefficient of variation CV) in the ultimate strand strains, even among strand-anchor samples that are identical in make, model, and configuration. Given the understanding that relatively small variations in the anchor wedge taper angle differential and wedge crown thickness represent the potential for significant improvements in the strand performance, the next step in implementing these principles within the industry is the development and speci-fication of measuring techniques and a set of requirements for qualifying the anchor components to consistently meet target strand performance ranges.

The quality control measures for the anchor components for each strand size should include specified targets as well as tolerance ranges for the wedge taper angle differential,

wedge crown thickness, and wedge height. Established requirements on these dimensions should be integrated with requirements on other anchor properties (for ex-ample, housing taper angle and material composition) to achieve consistently improved ultimate performance at the strand-wedge-anchor interface. There are no specifications provided by the American Association of Highway and Transportation Officials, the American Concrete Institute, the American Segmental Bridge Institute, the American Society of Civil Engineers, or the Post-tensioning Institute that require certification of product quality with respect to the wedge taper angle differential or crown thickness. As the importance and validity of these dimensional param-eters are better understood, future specification standards for finished wedge and anchor housing components should require this certification, especially for applications that involve strand strains greater than 0.01.

For the industry-typical material properties used in this study and the industry-standard anchor housing taper angle of approximately 7.00 degrees, a wedge taper angle dif-ferential of approximately 1.00 degree should be main-tained within a tolerance of ±0.10 degrees. (That is, the

Figure 12. Strand fracture strain versus fracture stress results (that is, failure point on strand stress versus strain curve). Note: 1 in. = 25.4 mm; 1 psi = 6.895 kPa.

0.5A and 0.6A strands with barrel anchors

0.5G and 0.6G strands with barrel anchors

0.5A and 0.6A strands with cast anchors

0.5G and 0.6G strands with cast anchors


interface when using modified wedges compared with industry-representative standard wedges.

• Two different failure modes limit the ultimate strain capacity of posttensioning strand, namely outer-wire slippage and wire fracture within the anchor. Gen-erally, the ultimate strand strain increases with an increased number of near-simultaneous wire fractures. Conversely, a reduction in the ultimate strain occurs with an increase in the number of outer-wire slips. Thus, outer-wire slippage should be avoided and multiple-wire fractures should be sought for improved strand performance.

• Increasing the wedge taper angle or crown thickness too far outside the effective ranges can lead to reduced ultimate strand strains and increased variability. To this end, important quality control measures should be specified related to the manufacturing of the wedges as well as the anchor housing.

• While no three-piece wedges were tested in the cur-rent study, two-piece wedges may be more desirable because the two-piece wedge configuration may allow better control of the wedge crown thickness during manufacture.

• The current study was conducted on the shortest height of wedges (and anchors) commonly used in the industry. As future research, slightly longer wedges with increased taper differential angle and crown thickness should be investigated. It may be possible to develop the full free-length fracture strength and strain capacity of the strand using a combination of these parameters in the design and manufacturing of the anchor components.

Acknowledgments

The work detailed herein was partially funded by Hayes Industries Inc. in Sugar Land, Texas (now Precision-Hayes International) with in-kind donations provided by the University of Notre Dame. This work built on previous research at the University of Notre Dame that was funded by PCI under a Daniel P. Jenny Fellowship. The authors recognize the support provided by Brent Bach, Theresa Aragon, Eric Herbert, and Steven Walsh at the University of Notre Dame. The opinions, findings, and conclusions expressed in the paper are those of the authors and do not necessarily reflect the views of PCI or the individuals and organizations acknowledged.

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Varying the wedge taper angle or crown thickness too far outside the effective ranges can lead to reduced ultimate strand strains and increased variability. Furthermore, for different anchor housing taper angles and different anchor housing and wedge material properties (yield and ulti-mate strength), the optimal wedge taper angle differential and wedge crown thickness may be different. Given the generally better manufacturing control of machined barrel anchors compared with cast anchors, consistent improve-ments are more likely to be achieved for barrel anchors. Also, the importance of the wedge crown thickness in de-termining the ultimate strand performance suggests that a two-piece wedge configuration may be more desirable than a three-piece configuration by allowing better control of the wedge dimensions during the manufacturing process.

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This paper experimentally investigates the effects of anchor wedge taper angle differential (with respect to the anchor housing cavity) and wedge thickness (measured at the crown) on the ultimate strain of unbonded posttensioning strand at failure. The main conclusions from the research follow. The specific conclusions regarding optimal dimen-sions are likely limited to the materials and components tested in this particular research program.

• Increasing the wedge crown thickness and introduc-ing a wedge taper angle differential of approximately 1.00 degree can significantly improve ultimate strand performance. These dimensional variations from stan-dard wedges require no increase in the overall anchor size and thus are considered to be more cost effective than simply increasing the height of the anchorage. The best-performing specimens in the tested data pool had a wedge taper angle of just over 8.00 degrees (placed within an anchor housing taper angle of about 7.00 degrees) and wedge crown thickness of about 0.488 in. (12.4 mm) for 0.5 in. (13 mm) strand and 0.549 in. (13.9 mm) for 0.6 in. (15 mm) strand.

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esis when null hypothesis is actually true

TID = anchor top inside diameter

TOD = anchor top outside diameter = BOD for barrel anchors

TW = wedge top outside width

W = cast anchor width

WA = wedge taper angle measured longitudinally

wm = weight of middle wire of strand sample tested to determine cross-sectional area

ws = weight of strand sample tested to determine cross-sectional area

WT = wedge thickness at crown measured trans-versely

γs = unit weight of steel strand

εpf,free-length = maximum (at fracture) strand strain from free-length failure tests

able for download at http://www3.nd.edu/~concrete/homepage_files/NDSE-13-02.pdf.

46. ASTM Subcommittee A01.13. 2008. “Standard Test Methods and Definitions for Mechanical Testing of Steel Products.” Annex A7 Method of Testing Multi-Wire Strand for Prestressed Concrete. ASTM A370. West Conshohocken, PA: ASTM International.

47. Devore, J. L., and N. R. Farnum. 2005. Applied Statis-tics for Engineers and Scientists. 2nd ed. Boston, MA: Cengage Learning.

Notation

ap = single posttensioning strand cross-sectional area

ATA = anchor housing taper angle = arctan[(TID–BID)/(2Ha)]

BID = anchor bottom inside diameter

BOD = anchor bottom outside diameter = TOD for barrel anchors

BW = wedge bottom outside width

CV = coefficient of variation (ratio of sample stan-dard deviation to sample mean)

dmw = diameter of middle strand wire

dow = diameter of outer strand wire

dp = outside crown-to-crown diameter of strand

Ep = elastic modulus of posttensioning strand

fpm,free-length = actual strand strength (maximum strand stress) from free-length failure tests

fpu = nominal ultimate strand strength

Ha = anchor height

Hw = wedge height

IW = wedge inside width

L = cast anchor length

ls = length of strand sample tested to determine cross-sectional area

p-value = estimated probability of rejecting null hypoth-


About the authors

Kevin Q. Walsh, MS, PE, is a doctoral student at the University of Auckland and a structural engineer at the Auckland Council in Auckland, New Zealand. He conducted the work documented in this paper while serving as an

adjunct professor at the University of Notre Dame in Notre Dame, Ind.

Randy L. Draginis is technical manager at Precision-Hayes International in Sugar Land, Tex., and is a voting member of the Post-Tensioning Institute’s M-10 Unbonded Tendon Committee.

Richard M. Estes is a field engineer at Schlumberger in Laredo, Tex. He conducted the work documented in this paper while serving as an undergraduate research assistant at the University of Notre Dame.

Yahya C. Kurama, PhD, PE, MPCI, is a professor at the University of Notre Dame.

Abstract

Previous research using industry-representative standard posttensioning anchor components from the United States has shown that premature wire fractures of seven-wire, low-relaxation unbonded posttensioning strand can occur at strand strains of 0.01 or less. Building on this research, this paper describes an experimental investigation into whether significant improvements in the ultimate strand strains at wire fracture can be made by slightly increasing the taper angle of the anchor wedge outer surface with respect to the taper angle of the anchor housing cavity and slightly increasing the thickness of the anchor wedge as measured at the crown. The test results demonstrate that relatively small, controlled deviations from industry-rep-resentative standard wedge dimensions can significantly improve the ultimate performance of the strand at failure. Quality control measures are recommended related to the manufacturing of the wedges as well as the anchor housing for use in extreme design load conditions.

Keywords

Anchor, posttensioning, seismic, strand, stress-strain relationship, unbonded, wedge, wire fracture, wire slip.

Review policy

This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute’s peer-review process.

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effects of anchor wedge dimensional parameters on ......delay the occurrence of wire fracture inside...

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