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80 3.1 Introduction The experimental portion of this study was completed in two phases. In phase 1, bond characteristics of unstressed seven-wire prestressing strands, with a particular emphasis on 0.7-in. diameter strands, were examined through (1) Hoyer effect testing, (2) beam-end tests, and (3) bond evaluation per ASTM A1081 (ASTM, 2015b). Full-scale girder testing, conducted in phase 2, is reported in ChapterÂ 4. 3.2 Bond Characterization of Prestressing Strand 3.2.1 Characterization of Strand Geometry and Material Properties Samples of four strand sizes were obtained (TableÂ 3.1 and FigureÂ 3.1). Samples of the same 0.6-in. and 0.7-in. strands having 90-degree hooks were also obtained; the hooks were bent around a 3.5-in.-diameter mandrel by the precaster who provided the strands. All strand samples of the same size came from the same spools; therefore, little variation was anticipated. Strand diameter (db) and individual wire (dc and dh; it is noted that in the seven-wire strand, the central straight wire is drawn slightly larger than the six helical wires) diameters were measured with a digital caliper. The twist angle, Î², was measured from photographs and confirmed with measurements of the wire pitch, s [i.e., Î² = tanâ1(2Ïdb/3s)]. Ultimate capacity, fpu, was obtained from tension tests using strand chucks as anchorage (not compliant with ASTM A1061). All strands satisfy the requirements of ASTM A416/AASHTO M203 (ASTM, 2015a) although the 0.7-in. strands only barely meet the â0.90fpu = 243 ksi at 1% elongationâ requirement. FigureÂ 3.2 shows representative measured stress-strain (Eq. 3.1) for each strand; the Ramberg- Osgood (Ramberg and Osgood, 1943) parameters are given in TableÂ 3.1. [ ]( ) = Îµ + â + Îµ ï£± ï£² ï£³ï£´ ï£¼ ï£½ ï£¾ï£´ â¤ Eq. 3.1 1 1 1 f E A A B fp p p p C C pu 3.2.2 Characterization of Strand âDeformationsâ A seven-wire strand, regardless of its dimension, has helical deformations formed by the helical wires; these deformations are proportional to the strand diameter. While there are no agreed-on means of quantifying the deformations of a helical strand, indices used to quantify nonprestressed steel reinforcing bar deformations (ACI 408-03, 2012) can provide relative measures of strand deformation. Rehm (1961) proposed a relative rib ratio, fR, given by Eq. 3.2, C H A P T E R Â 3 Experimental Research Approach and FindingsâComponent Tests
Experimental Research Approach and FindingsâComponent Tests 81Â Â 0.7 in. 0.6 in. 0.5 in. 3/8 in. Top to bottom: 0.7 in., 0.6 in., 0.5 in., and 3/8 in. in as-received condition. Nominal strand diameter, (in.) 0.7 0.6 0.5 3/8 Manufacturer Producer A Producer B Nominal strand area, (in.2) 0.294 0.217 0.153 0.085 Measured ultimate capacity, (ksi) 276(0.003) 287 (0.001) 286 (0.001) 287 (0.002) Measured capacity at 1% elongation 244(0.016) 269 (0.000) 260 (0.004) 257 (0.023) Measured tensile modulus obtained during Hoyer tests, (0.2 to 0.5 ) 31,206 (0.069) 31,985 (0.019) 30,415 (0.035) 30,234 (0.036) Ramberg-Osgood (ksi) 30,000 30,000 30,000 30,000 Ramberg-Osgood parameter A 0.060 0.030 0.035 0.030 Ramberg-Osgood parameter B 124 111 114 113 Ramberg-Osgood parameter C 12 15 11 10 Diameter of center wire, (in.) 0.239 0.206 0.170 0.128 Diameter of helical wire, (in.) 0.231 0.198 0.165 0.123 Pitch, (in.) 9.93 8.02 6.76 5.07 Twist angle, (deg.) 8.4 8.9 8.8 8.8 Relative rib area, (Eq. 3.2) 0.0085 0.0095 0.0093 0.0093 Note: Numbers in parentheses are coefficients of variation. TableÂ 3.1. Strand dimensions and material properties. FigureÂ 3.1. Strands used in this study.
82 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders specifically addressing helical deformation patterns; a variation of this ratio is promulgated by Eurocode 2 (British Standards Institution, 2014): ( ) = â Î² Eq. 3.2 4 2 2 f k d d sin ds R i in which k is the number of helical elements, k = 6 for seven-wire strand; d and di are the outer and minimum diameters of the deformations, respectively; for seven-wire strand: d = db and di = dc + dh; Î² is the twist angle; and s is the pitch. The values of relative rib area calculated with Eq. 3.2 are given in TableÂ 3.1. The relative rib areas for 0.6-in., 0.5-in., and 3â8-in. strands are similar, and the value for the 0.7-in. strand is 90% of the value calculated for the smaller strands. Hence, the mechanical interlock of the 0.7-in. strand may be expected to be marginally less efficient than that of the other strand sizes. 3.2.3 Hoyer Effect Testing Limited Hoyer effect testing had been performed prior to this study; a summary of previously available data is given in TableÂ 3.2; this includes limited testing of 0.7-in. strands in support of the proposal for this project. The present study allowed retesting a few strands from the earlier 2013 study by Briere etÂ al. As TableÂ 3.2 shows, the 0.6-in. strand behaved identically while there was some apparent reduction in dilation ratio of 0.5-in. strands. The differences are believed to be associated with improvements made to the clip gauge assembly for the current study. In this study, tests identical to those described by Briere etÂ al. (2013) were conducted (FigureÂ 3.3). Five strands of each diameter were tested. Each strand was tested with five load FigureÂ 3.2. Representative stress-strain curves and fitted Ramberg-Osgood (R-O) functions (Eq. 3.1) for strands tested.
Experimental Research Approach and FindingsâComponent Tests 83Â Â repetitions, sufficient to establish a steady-state load-strain-dilation response. Typically, for a strand that has not been previously stressed, the initial stressing operation is a âshakedownâ of sorts, and larger dilation ratios are obtained. Second and subsequent stress cycles approach a steady-state behavior. Each strand was stressed to 0.8fpu and released while measuring both axial strain (strain gauge) and transverse dilation (clip gauge). The dilation ratio from the first cycle (initial prestress) and the average ratio obtained over five cycles are given in TableÂ 3.3. The average ratios are expected to be smaller due to the âshakedownâ effect. The longitudinal offset strain following the first and after all five cycles is also reported in TableÂ 3.3; most offset strain occurs in the first cycle. 22.214.171.124 Instrument Precision and Correction The clip gauge used (FigureÂ 3.3) does not measure dilation strain directly, but rather the change in strand diameter. The diameter was measured with a precision of 0.000014Â in.; this is equivalent to a strain resolution (in microstrain) of 14.3/db. Therefore, the strain resolution is improved for larger strand diameter (20 ÂµÎµ for 0.7-in. strand and 38 ÂµÎµ for 3â8-in. strand). The longitudinal strain gauge was aligned along the axis of a helical wire (FigureÂ 3.3). Therefore, a correction is necessary to transform the strain measured along the axis of the helical wire, Îµh, to the strain oriented along the longitudinal axis of the strand, Îµc (Machida and Durelli, 1973): Îµ = Îµ Î² Eq. 3.32cosc h gage (Epsilon gage) Nominal strand diameter, (in.) 0.7a 0.6b 0.5b Nominal strand area, (in.2) 0.294 0.217 0.153 Measured ultimate capacity, (ksi) 282 278 306 Measured tensile modulus, (ksi) 29,800 29,200 31,100 Twist angle, (deg.) 8.4 8.2 8.1 Average dilation ratio 0.32 0.34 0.40 Average dilation ratio of retested strands onlyb 0.34 0.37 Retests of Briereb strands conducted in 2019 0.34 0.32 aPreliminary sample strands tested by the research team. bBriere et al. (2013). TableÂ 3.2. Data from previous Hoyer tests. FigureÂ 3.3. Hoyer effect test setup and instrumentation.
84 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders The correction given by Eq. 3.3 is applied before calculating the dilation ratio and offset strains reported in TableÂ 3.3. The dilation ratio is calculated as the ratio of transverse (dilation) strain to the longitudinal strain oriented along the strand axis, Îµc. 3.3 Beam-End Tests Thirty beam-end tests were conducted. The test matrix, shown in TableÂ 3.4, included three straight strand development lengths (20db, 30db, and 40db) and three 90-degree hooked strands with varying embedment lengths (10db, 20db, and 30db). Normal weight concrete (NWC) and lightweight concrete (LWC) were used in the straight strand specimens with 30db development length. All other specimens were tested with NWC only. Each straight strand test consisted of two duplicate specimens (designated by final letter, A or B, in TableÂ 3.4). The test specimen and loading arrangement are shown in FigureÂ 3.4. All dimensions and internal reinforcement are compliant with ASTM A944-10 (ASTM, 2015c) except for five tests having longer embedment, for which 6Â in. was added to the 25-in. standard specimen length (see TableÂ 3.4). The longer specimens also contained an additional pair of No. 4 stirrups (FigureÂ 3.4). For both strand sizes, 0.6Â in. and 0.7Â in., the 90-degree hooks were formed around a 3.5-in.- diameter mandrel. This diameter is smaller than that required for standard reinforcing bar hooks, which require 3.75Â in. and 4.5Â in. for 0.6-in. and 0.7-in. bars, respectively. The smaller bend diameter used for the strand is not believed to be a concern since the standard bend diameter is prescribed to ensure that there is no cracking of a solid bar when bent. The individual Nominal strand diameter, (in.) 0.7 0.6 0.5 3/8 First cycle dilation ratio 0.373(0.043) 0.312 (0.124) 0.346 (0.145) 0.301 (0.289) Average dilation ratio (five cycles) 0.333(0.180) 0.302 (0.169) 0.297 (0.229) 0.289 (0.198) Longitudinal strain ( ) offset following initial cycle 522(0.142) 317 (0.182) 201 (0.417) 139 (0.382) Longitudinal strain ( ) offset following five cycles 805(0.411) 311 (0.172) 223 (0.389) 201 (0.165) Note: Numbers in parentheses are coefficients of variation. TableÂ 3.3. Results from Hoyer test. Strand Concrete Straight strand embedment length and specimen labels 90o hook embedment and specimen labels = 40 = 30 = 20 = 30 = 20 = 10 0.7 in. NWC1 = 28 in.a 7-40-A/B = 21 in. 7-30-A/B = 14 in. 7-20-A/B = 21 in.a H7-30 = 14 in. H7-20 = 7 in. H7-10 12 in. NWC2 na 7-30-C/D na na na na na LWC na L7-30-E/F na na na na na 0.6 in. NWC1 = 24 in.a 6-40-A/B = 18 in. 6-30-A/B = 12 in. 6-20-A/B = 18 in. H6-30 = 12 in. H6-20 = 6 in. H6-10 10 in. NWC2 na 6-30-C/D na na na na na LWC na L6-30-E/F na na na na na 0.5 in. NWC1 na na = 10 in. 5-20-A/B na na na na 3/8 in. NWC1 na na = 7.5 in. 3-20-A/B na na na na aRequires nonstandard 31-in.-long specimen. See Figure 3.4 for the definition of and . na = Not applicable. TableÂ 3.4. Beam-end test matrix and specimen identification.
Experimental Research Approach and FindingsâComponent Tests 85Â Â wires of a seven-wire strand will slip past each other, and thus each wire is bent individually; this permits a smaller diameter to be used without affecting the cracking of the wires. The length of the hook âtail,â dimension A in TableÂ 3.4 and FigureÂ 3.4a, was 10Â in. and 12Â in. for 0.6-in. and 0.7-in. strands, respectively. These values are required for standard reinforcing bar hooks, and they also ensure that the straight portion of the tail exceeds 12db. All strand samples were placed in the concrete in their as-received conditions. All strands appeared clean, free of laitance, oil, residue, and corrosion. While samples were stored in the laboratory before testing in a controlled environment, no history or chain of custody is available (a) Test arrangement and specimen details. (b) Test setup showing single 60-kip ram (left) and two-ram arrangement (120-kip capacity) used for three high-force tests (right). (c) Free end of strand showing slip transducer. FigureÂ 3.4. Beam-end test.
86 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders for the samples before their receipt. Because of the relatively lower bond stress observed for the 0.6-in. strand in NWC1 (see TableÂ 3.6), the same strand used in NWC2 and LWC specimens was wiped clean with a commercial degreasing agent before use. Although the 0.6-in. strand is identical in all tests, the improvement in results (TableÂ 3.6), despite the lower concrete strength, suggests that this strand may have been contaminated to some degree when used in NWC1. Bond breakers (FigureÂ 3.4a) consisted of 0.75-in. inside diameter pultruded glass fiber reinforced tubes for the 0.6-in. and 0.7-in. strand, and plastic strand debonding tubes for the 0.5-in. and 3â8-in. strands. Linear variable differential transformer (LVDT) collars (FigureÂ 3.4c) were located at the loaded and free ends of the embedded strands to measure slip. Only loaded- end LVDTs were possible for the hooked embedments. Both NWC and LWC were specified as a 5-ksi ready-mix concrete having Â¾ in. aggregate top size. NWC1 specimens were cast on 13 December 2018 from a 4-cy batch. NWC2 was used as a control for LWC and was cast on 14 August 2020. LWC was cast on 21 August 2020. Both NWC2 and LWC were cast from 1-cy batches. Mix design and material properties are given in TableÂ 3.5; all specimens were cured in ambient laboratory conditions. Properties were obtained from three 4-in.-diameter standard cylinders in all cases except 56-day strength for NWC for which only two cylinders were available. As seen in TableÂ 3.5, NWC2 did not achieve its specified strength. FigureÂ 3.5 shows representative specimens prior to concrete place- ment. Specimens are cast (FigureÂ 3.5) inverted to how they are tested (FigureÂ 3.4)âthe strand is located at the bottom of the cast and has 24-in. concrete placed above it. Mix design NWC1 NWC2 LWC Type I/II cement (ASTM C150) 574 lb/cy 574 lb/cy Fine aggregate 1,205 lb/cy(ASTM C33) 1,285 lb/cy (ASTM C330) #67 coarse aggregate 1,700 lb/cy(ASTM C33) 900 lb/cy (ASTM C330 expanded shale) GGBFS (ASTM C989) 101 lb/cy 101 lb/cy AE: Sika Air 260 (ASTM C260) 4 oz/cwt 3.5 oz/cwt Water 270 lb/cy(w/c = 0.40) 270 lb/cy (w/c = 0.40) Material Properties Slump 5.5 in. 5.75 in. Air content (ASTM C231) 6.7% 6.5% Dry unit weight 142.8 pcf 116.0 pcf Measured unit weight Not measured 132.5 pcf(COV = 0.007) 115.0 pcf (COV = 0.013) 28-day compressive strength (ASTM C39) = 6,895 psi (COV = 0.03) = 3,369 psi (COV = 0.08) = 5,196 psi (COV = 0.01) 56-day compressive strength (ASTM C39) = 7,553 psi = 4,075 psi (COV = 0.04) Obtained from cores = 5,750 psi (COV = 0.06) 84-day compressive strength (ASTM C39) = 7,862 psi (COV = 0.02) NA NA 28-day splitting cylinder strength (ASTM C496) 595 psi = 7.16 (COV = 0.16) 413 psi = 7.12 (COV = 0.03) 449 psi = 6.23 (COV = 0.09) 56-day splitting cylinder strength (ASTM C496) 613 psi (COV = 0.26) Not determined due to need for cores 671 psi (COV = 0.08) Note: GGBFS, ground granulated blast-furnace slag; COV, coefficient of variance; NA, not available. TableÂ 3.5. Concrete mix designs and material properties.
Experimental Research Approach and FindingsâComponent Tests 87Â Â 3.3.1 Straight Strand Beam-End Test Results All straight strand beam-end tests were compliant with the method of ASTM A944-10 (ASTM, 2015c). The testing frame (FigureÂ 3.4b) was designed around a large self-contained reaction frame. The load was applied concentrically to the strand using a 60-kip hollow-core hydraulic ram (two rams in parallel were used for specimens 7-40 and H7-30). Hydraulic pres- sure was used to calculate the applied load with a precision of 70Â lb. The slip was measured using an LVDT collar (seen in FigureÂ 3.4c) having a stroke of 0.5Â in. and precision of 0.00005Â in., far over that required by ASTM A944-10 (0.001Â in.). The load was applied slowly (at a rate to result in slip failure between 1 and 3Â minutes) until slip was recorded. Due to the sensitivity of the instrument, the initial slip was defined as a relative movement of the free end of the strand over 0.0001Â in. Once the slip was observed, load and slip data were recorded. Cracking, if observed, was also reported. Due to the nature of the test setup, the slip at the free end represents the ultimate capacity of the embedded strand. It is not possible to reliably obtain the descending branch of the stress-slip curves. FigureÂ 3.6 shows the strand stress versus free-end slip recorded for each test. Failure of all straight strand specimens in NWC1 (FigureÂ 3.6a) was by pullout failure. In this case, the applied load remained constant or decreased marginally as the slip continued (i.e., load-slip stiffness was negligible). The test was stopped once the slip exceeded 0.5Â in. (so as to not damage the slip transducer). None of the specimens exhibited any distress to the concrete, thus, indicating pullout failure (rather than splitting). In these cases, the slip behavior is âbrittleâ with low ultimate slip displacements, and brittle pullout failure closely followed initial slip. Hairline flexural cracks were observed in both 6-40 and 7-40 specimens at loads exceeding the initiation of slip. These cracks are believed to be an artifact of using a longer, 31-in., test specimen and the small degree of flexure that is induced in the beam-end specimen over this larger span. NWC2 was a relatively poor concrete mix exhibiting a âsofterâ slip behavior; that is, once slip initiated, a relatively ductile response ensued, resulting in larger slip measurements. This behavior is seen in FigureÂ 3.6b. LWC, having a strength falling between NWC1 and NWC2 and having a lightweight expanded shale coarse aggregate, also exhibited a more ductile response. In these specimens, concrete splitting failure was observed as shown in FigureÂ 3.7. Splitting resulted from excessive slip generating greater radial forces as the strand deformations âmovedâ through the concrete (FigureÂ 3.6a). Splitting began at the loaded end of the strand and propagated to the free end as the bond resistance was redistributed. LWC exhibited a higher split tensile capacity than NWC1 (a) Specimens 7-30B and 3-20A showing strand embedment and debonding (b) Series of 90Â° bent 0.6-in. strand specimens having embedments of ldh = 10db, 20db, and 30db Bond breaker Bonded strand FigureÂ 3.5. Beam-end specimens prior to concrete placement (loaded end at bottom of all images).
88 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders (a) NWC1 specimens. (b) NWC2 and LWC specimens. FigureÂ 3.6. Strand stress versus free-end slip.
Experimental Research Approach and FindingsâComponent Tests 89Â Â (TableÂ 3.5); thus, the splitting behavior observed is attributable to the nature of the LWCâlikely the relatively brittle nature of the LWC shale aggregateârather than to the cylinder-derived strength. Bond capacities resulting from tests exhibiting a splitting failure must be interpreted as being lower-bound bond capacities (making resulting extrapolation of development length upper-bound values). The average bond stress, Ï, was calculated from Eq. 3.4 and is summarized in TableÂ 3.6 for the first instance of slip and the ultimate capacity of each specimen. Applied load, P, is also normalized by strand area to give strand stress: fs = P/Aps. Ï = Ï = ÏP d l f A d lb e s ps b e Eq. 3.4 Finally, assuming a linear relationship between strand stress and development length, the embedment length required to develop the fpu = 270 ksi strand capacity, ld, can be extrapolated using Eq. 3.5; this is also reported in TableÂ 3.6. ( )= Eq. 3.5l l f fd e pu max 126.96.36.199 Discussion of Straight Strand Beam-End Test Results The primary conclusion observed from the data presented in TableÂ 3.6 and summarized in TableÂ 3.7 is that different performance was observed for different strand sizes and differ- ent concrete. The performance of a given strand size in a particular concrete was consistent, however. The variation in bond behavior is not attributed to the strand size itself since there is no size-dependent trend evident. Similarly, the variation is not attributed to the mechanical interlock of the strand since the relative rib areas are similar for each strand (TableÂ 3.1). There appears to be some impact of concrete strength (as reported by Ramirez and Russell, 2008 and described in Section 188.8.131.52) although the data are insufficient to quantify this. (a) L6-30 F. (b) L6-30-E. (c) L7-30-E. (d) L7-30-F. FigureÂ 3.7. LWC beam-end specimens showing splitting behavior (pullout to right).
90 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders Specimen Concrete Slip >0.0001 in. Initial splitting Maximum load = ( / ) (Splitting if applicable) in. in.2 In. kips ksi ksi kips ksi ksi kips ksi ksi in. 7-40-A NWC1 7.9 ksi 0.7 0.294 28 21.8 74.1 0.35 n.o. a n.o. n.o. 55.2 187.8 0.90 40.2 = 57.5 7-40-B 21.2 72.1 0.34 n.o. n.o. n.o. 56.0 190.5 0.91 39.7 = 56.7 7-30-A 21 5.5 18.7 0.12 n.o. n.o. n.o. 43.4 148.6 0.94 38.2 = 54.5 7-30-B 6.2 21.1 0.13 n.o. n.o. n.o. 45.1 153.4 0.98 37.0 = 52.8 7-30-C NWC2 4.1 ksi 16.0 54.4 0.35 n.o. n.o. n.o. 29.0 98.6 0.63 57.5 = 82.2 7-30-D 18.0 61.2 0.39 n.o. n.o. n.o. 41.0 139.5 0.89 40.6 = 58.1 L7-30-E LWC 5.8 ksi 22.0 74.8 0.48 36.0 122.4 0.78 36.0 122.4 0.78 46.3 = 66.2 L7-30-F 15.0 51.0 0.32 23.0 78.2 0.50 39.0 132.7 0.84 42.7 = 61.0(72.5 = 103.5 ) 7-20-A NWC1 7.9 ksi 14 6.0 20.4 0.19 n.o. n.o. n.o. 30.2 102.7 0.98 36.8 = 52.67-20-B 4.0 13.6 0.13 n.o. n.o. n.o. 29.0 98.6 0.94 38.3 = 54.8 6-40-A 0.6 0.217 24 20.0 92.2 0.44 n.o. n.o. n.o. 24.5 112.9 0.54 57.4 = 95.76-40-B 7.2 33.2 0.16 n.o. n.o. n.o. 22.2 102.3 0.49 63.3 = 105.5 6-30-A 18 12.1 55.8 0.36 n.o. n.o. n.o. 20.2 93.1 0.60 52.2 = 87.0 6-30-B 6.4 29.5 0.19 n.o. n.o. n.o. 20.1 92.7 0.59 52.4 = 87.4 6-30-C NWC2 4.1 ksi 14.0 64.5 0.41 n.o. n.o. n.o. 35.0 161.3 1.03 30.1 = 50.2 6-30-D 15.0 69.1 0.44 n.o. n.o. n.o. 35.0 161.3 1.03 30.1 = 50.2 L6-30-E LWC 5.8 ksi 2.0 9.2 0.06 21.0 96.8 0.62 35.0 161.3 1.03 30.1 = 50.2(50.2 = 83.7d ) L6-30-F 7.0 32.3 0.21 27.7 127.6 0.82 35.0 161.3 1.03 30.1 = 50.2(38.1 = 63.5 ) 6-20-A NWC1 7.9 ksi 12 3.1 14.3 0.14 n.o. n.o. n.o. 15.8 72.8 0.70 44.5 = 74.26-20-B 5.9 27.2 0.26 n.o. n.o. n.o. 11.8 54.4 0.52 59.6 = 99.3 5-20-A 0.5 0.153 10 4.0 26.1 0.25 n.o. n.o. n.o. 21.0 137.3 1.34 19.7 = 39.45-20-B 4.9 32.0 0.32 n.o. n.o. n.o. 20.5 134.0 1.31 20.1 = 40.3 3-20-A 3/8 0.085 7.5 2.8 32.9 0.32 n.o. n.o. n.o. 7.6 89.4 0.86 22.7 = 60.43-20-B 2.0 23.5 0.23 n.o. n.o. n.o. 7.6 89.4 0.86 22.7 = 60.4 an.o., Not observed. Nominal strand diameter, (in.) 0.7 0.7 0.7 0.6 0.6 0.6 0.5 3/8 Concrete NWC1 NWC2 LWC NWC1 NWC2 LWC NWC1 NWC1 Bond stress at initial slip, (ksi) 0.21 (0.52) 0.37 0.40 0.30 (0.38) 0.42 0.13 0.28 0.28 Bond stress at maximum load, (ksi) 0.94 (0.04) 0.76 0.81 0.57 (0.13) 1.03 1.03 1.32 0.86 Extrapolated development length, 38.4 (0.04) 49.0 59.4 a 54.9 (0.12) 30.1 44.2 a 19.9 22.7 55 70 85 92 50 74 40 60 aControlled by splitting failure; interpreted as upper-bound value. TableÂ 3.6. Straight strand slip results. TableÂ 3.7. Summary of straight strand test results (COV in parentheses where applicable). From the results of NWC1 and NWC2, it is hypothesized that the condition of the strand has affected both the relatively high bond results for the 0.5-in. strand and the low results for the 0.6-in. strands in NWC1. For the NWC2 and LWC tests, both the 0.6-in. and 0.7-in. strands were degreased in advance. This process has apparently improved the bond of the 0.6-in. strands in NWC2, despite the poorer concrete quality. Two primary questions were to be addressed through beam-end tests: (1) Is there a difference between bond characteristics of 0.6-in. and 0.7-in. strands? (2) Does concrete density affect the bond of 0.7-in. strands? The average values of lb/db (shown in the last column of TableÂ 3.6) are summarized for NWC and LWC for each strand size and both strand sizes combined in
Experimental Research Approach and FindingsâComponent Tests 91Â Â TableÂ 3.8. Within the scatter that is expected when measuring a local phenomenon such as a bond, the results do not indicate a significant difference (1) in terms of strand size: lb/db = 81 for 0.6-in. versus lb/db = 59 for 0.7-in. in NWC and lb/db = 50 for 0.6-in. versus lb/db = 64 for 0.7-in. in LWC or (2) in terms of concrete density: lb/db = 70 for NWC versus lb/db = 57 for LWC. Finally, these tests were intended to be âproof testsâ of current AASHTO provisions. The results suggest that current development length equations are conservative for NWC and LWC. AASHTO LRFD Bridge Design Specifications Article 184.108.40.206.2 (AASHTO, 2020) specifies the development length of the bonded strand to be: = Îº âï£« ï£ï£¬ ï£¶ ï£¸ï£· Eq. 3.6 2 3 l f f dd ps pe b ACI 318R-19 (2019) Article 220.127.116.11 specifies an essentially identical equation with Îº = 1. Taking Îº = 1 and fpe = 0.56fpu, the length required to develop fpu is 169db. In this study, no extrapolated value of ld exceeded 106db (TableÂ 3.6). The 0.5-in. strand exhibited apparent values of ld as low as 40db. Both 0.6-in. and 0.7-in. strands embedded in LWC resulted in split- ting failures at bond stresses lower than observed in comparable NWC, although concrete strengths were relatively low. 3.3.2 90-Degree Hooked Strand Embedment Beam-End Tests An identical test arrangement using only concrete mix NWC1 was used to test hooked strands. For the hooked strands, slip cannot be measured directly. In this case, the LVDT collar was located on the loaded end of the strand. This transducer now measured elongation of the unbonded portion of the strand plus the effect of bond deformation and eventually slip. A longer stroke transducer (1.5Â in.) was used for the hook embedment tests, resulting in a resolution of 0.00015Â in. for these tests. Slip at the loaded end of the strand, however, begins at the initiation of load and will be gradual; thus, it is not possible to identify a true initial slip. Plots showing the relationship between applied load and elongation are shown in FigureÂ 3.8. A summary of results for the hooked strand specimens is given in TableÂ 3.9. Each test progressed as shown schematically in FigureÂ 3.9. The load was applied, and the strand bond increased and then began to deteriorate at the loaded end (FigureÂ 3.9a). As the loading Strand Concrete NWC LWC 0.7-in. 59 64 0.6-in. 81 50 0.6-in. and 0.7-in. 70 57 TableÂ 3.8. Average values of ld/db. FigureÂ 3.8. Elongation at loaded end of hooked strands.
92 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders continued, the region of deteriorated bond progressed toward the hook, and the hook became engaged in sharing the strand pullout force. At some point, the entire straight portion of the strand was essentially debonded at which point the strand was anchored only by the hooked embedment (FigureÂ 3.9b). Shortly after this, a tension crack occurred at the top of the specimen at the location of the hook. This crack is an artifact of the test arrangement and results from the small degree of flexure at the âbeam endâ modeled by the beam-end test. Once this crack appeared, the behavior was no longer a âpulloutâ behavior per se but rather a strut developing between the hook anchorage and the horizontal reaction (FigureÂ 3.9b). The strut angle and the number of No. 4 stirrups it engages are a function of the embedment, ldh, provided. Specimen behavior takes one of two forms: 1. For short embedment (H6-10 and H7-10), a steep strut engages only two stirrup legs (FigureÂ 3.9c). The block of concrete engaged by the hooked bar fails in shear along the inclined strut and rotates away from the specimen (FigureÂ 3.9c). 2. For longer embedment in which the strut is shallower and engages more stirrup legs, the shear resistance is increased. In this case, a splitting failure occurs (FigureÂ 3.9d), including the typical âwishboneâ crack at the end of the hook. This failure is initiated by a combination of the hook being unable to fully anchor the tapered strut that develops (shown in the plan view of FigureÂ 3.9b) and the vertical force that results as the hook is âunbentâ (see FigureÂ 3.10g). Side or back splitting of the specimen is mitigated by the greater concrete cover in both of these dimensions. Specimen (in.) (in.2) (in.) Occurrence of transverse crack Maximum load (kips) (kips) (kips) (ksi) Failure mode H7-30 0.7 0.294 21 60.0 204 69.0 235 Splitting (Figure 3.9d) H7-20 14 39.0 133 57.5 196 Splitting (Figure 3.9d) following initial formation of shear crack H7-10 7 43.5 148 Shear (Figure 3.9c) H6-30 0.6 0.217 18 not observed 45.5 210 Splitting (Figure 3.9d) H6-20 12 32.0 147 36.5 168 Splitting (Figure 3.9d) H6-10 6 28.0 129 32.5 150 Shear (Figure 3.9c) TableÂ 3.9. Hooked strand test results. (a) Increasing load. (b) Straight portion of bar effectively debonded. (c) Failure of short embedment length. (d) Splitting failure of long embedment length. FigureÂ 3.9. Schematic representation of beam-end specimen loading and failure modes.
Experimental Research Approach and FindingsâComponent Tests 93Â Â FigureÂ 3.10 shows the hooked embedment strand tests following testing. The shear failure of H6-10 and H7-10 is evident as is the shear crack that developed before the splitting failure of H7-20. Splitting failures of H6-20, H6-30, and H7-30 were not accompanied by any cracking on the sides of the specimen. FigureÂ 3.10g shows evidence of the hook beginning to unbend (compare the hook with its imprint in the concrete). The effect of pulling the hook out of its embedment is a vertical force that helps to drive the splitting. The result of this is evident in H7-30 in which the entire top cover of the specimen spalled as a result of the failure (the concrete cover shown in FigureÂ 3.10f was simply lifted away by hand). FigureÂ 3.10h shows the strand imprint in the concrete, illustrating excellent consolidation and well-defined helical deformations. 18.104.22.168 Discussion of Hooked Strand Beam-End Tests As expected and shown in FigureÂ 3.11, the capacity of the hooked strands increases with increased embedment length. TableÂ 3.10 summarizes the observed relationships for the 0.6-in. c) H6-30 a) H6-10 d) H7-10 e) H7-20 f) H7-30 b) H6-20 g) embedment of H6-30 showing unbending of hooked strand h) imprint of bonded strand H6-30 (debonding region shown at right) FigureÂ 3.10. Images of hook embedment specimens following testing illustrate failure modes.
94 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders and 0.7-in. strands tested. As an approximation, the intercept (capacity at zero embedment)â 106 ksi and 116 ksi for 0.7-in. and 0.6-in. strands, respectivelyârepresents the contribution of the hook geometry, while the ldh/db term represents the bonded straight portion of the strand. The results reflect the better bond of the 0.7-in. strand in NWC1 (TableÂ 3.7). Extrapolating the relationships given in TableÂ 3.10 to determine the hook embedment required to develop fpu, it is clear the presence of the hook reduces the theoretical development length from that determined for a straight strand embedment. The reduction is on the order of 31% and 45% for 0.7-in. and 0.6-in. strands, respectively. By comparison, similar reductions are implied for deformed reinforcing bars. The ratio of the hooked bar to straight bar devel- opment length prescribed by AASHTO LRFD Bridge Design Specifications (AASHTO, 2020) is ldh = 0.26ld and that prescribed by ACI 318R-19 (2019) is ldh = 0.50ld (No. 6 bars and smaller). 3.3.3 Potential Utility of 90-Degree Strand Anchorage Because of the expected high stresses in the beam-end region, girders constructed with 0.7-in. prestressing strands may be more susceptible to anchorage shear failure. When a crack initiates near the beam end, a tension force, T, is developed in the prestressing strand, as shown in FigureÂ 3.12a. If there is an inadequate anchorage of the steel crossing the crack, a shear anchorage failure occurs. This anchorage failure mode is taken into consideration in AASHTO LRFD Bridge Design Specifications Article 22.214.171.124 (AASHTO, 2020). Eq. 3.7 prescribes the longitudinal reinforce- ment required to develop the required tension force T as a combination of the moment, shear, and axial force acting at the critical section. FigureÂ 3.11. Hook embedment versus beam-end pullout capacity. Nominal strand diameter, 0.7 0.6 Observed relationship (Figure 3.11) = 4.4 / + 106( = 0.99) = 3.0 / + 116 ( = 0.95) Extrapolated hook embedment required to develop = 6.6 in. = 38 = 30.8 in. = 51.3 TableÂ 3.10. Observed relationships for hooked strands.
Experimental Research Approach and FindingsâComponent Tests 95Â Â 0.5 0.5 cotâ â= + â¥ Ï + Ï + Ï â â ï£« ï£ï£¬ ï£¶ ï£¸ï£· Î¸T A f A f M d N V V Vs y ps ps u v f u c u v p s Eq. 3.7 where (see FigureÂ 3.12a) âAs = area of nonprestressed steel on the flexural tension side of the member at the section under consideration; fy = specified yield strength of the nonprestressed steel; âAps = area of prestressing steel on the flexural tension side of the member; fps = stress that may be developed in the prestressed reinforcement based on development at the critical section; Mu = factored moment, not to be taken less than |Vu â Vp | dv; dv = effective shear depth; Ïf = resistance factor for flexure; Nu = factored axial force, taken as positive if tensile and negative if compressive; Ïc = resistance factor for axial force; Vu = factored shear force at the section; Ïv = resistance factor for shear and torsion; Vp = component in the direction of the applied shear of the effective prestressing force (positive if resisting the applied shear; Vp = 0 when only straight strand is present); Vs = shear resistance provided by the transverse reinforcement at the section under investigation limited to a value of Vu/Ïv; Î¸ = angle of inclination of diagonal compressive stresses used in determining the nominal shear resistance of the section under investigation. It is desirable to provide the force T with only the âAps fps term; this mitigates the need to add additional longitudinal steel in the already congested end region. However, 1. Due to the need to debond strands to mitigate end-region cracking, the number of bonded strands (âAps) at the critical section is reduced. Greater debonding will be required for the larger forces inherent in using 0.7-in. strands; and 2. Due to the proximity to the end of the girder and the larger strand diameter, the strand is only able to develop limited stress, fps, at the critical section. For larger strands, fps will be reduced due to longer development lengths. Taken together, this leads to limited tension capacity, T. A parametric study (Shahrooz etÂ al., 2017) concluded that increasing the prestressing force in a girder (requiring an increase in the debonding ratio) also increases the possibility for potential shear anchorage failure. Because debonding is necessary to control cracking at prestress transfer, Aps cannot be increased and will likely be reduced when 0.7-in. strands are used. Therefore, only increasing fps is available to mitigate the need for additional reinforcing steel, âAs fy in Eq. 3.7. By casting the strand extensions into cast-in-place end diaphragms, it is proposed that the strand extension can (1) provide some degree of development to the partially debonded strand (giving these strands a value of fps > 0), and (2) improve the development of bonded strands (increasing the available fps for these strands); this is shown schematically in FigureÂ 3.12b. (a) Straight strand anchorage (after AASHTO, 2020). (b) Hooked strand. FigureÂ 3.12. Strand anchorage free-body diagrams at beam end.
96 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders It is unlikely that a short straight strand extension will provide much effect, but providing a hook on this strand may be significant. Both cases were considered in the testing program of this chapter. Shahrooz etÂ al. (2017) reported an extensive finite element-based study of 39 girders having either 0.6-in. or 0.7-in. strands. The intent of the study was to investigate the effects of large amounts of strand debonding. As a result, the examples have large prestress forces and relatively large amounts of strand debonding. When tension capacity (Eq. 3.7) at the critical section was checked for shear (dv /2 from the end of the cast girder), seven examples were found to require additional nonprestressed reinforcement. The seven cases are shown in TableÂ 3.11. The inadequate longitudinal reinforcement is indicated in the far right-hand column as a ratio less than 1. To maintain the initial beam designs, two approaches satisfy Eq. 3.7: 1. Add more nonprestressed steel (âAs fy); this is Case A in each instance reported in TableÂ 3.11 and is reported by Shahrooz etÂ al. (2017). 2. Increase fps by providing hooked anchorage; this is Case B and is described further below. Model parameters Aps at dv/2 at /2 at /2 â Case â straight hooked = 10 in. â straight hooked = 10 in. in. ksi ft in. in. in.2 in.2 in.2 ksi ksi Nebraska DOT NU-900 girders spaced at 8 ft ( /2 = 28.2 in.) 8 0.6 14 0.14 6 55 102 na 2.604 na na 118 na 0.89 8A Case 8 with additional = 0.88 in. na 2.604 na 0.88 118 na 0.98 8B Case 8 with 7 hooked strands having = 10 in. 71.4 1.085 1.519 na 118 144 1.00 9 0.7 14 0.43 6 65 119 na 2.352 na na 102 na 0.82 9A Case 9 with additional = 1.32 in. na 2.352 na 1.32 102 na 0.99 9B Case 9 with 8 hooked strands having = 10 in. 83.3 na 2.352 na 102 124 1.00 11 0.6 14 0.00 8 55 102 na 3.038 na na 118 na 0.93 11A Case 11 with additional =0.62 in. na 3.038 na 0.62 118 na 0.99 11B Case 11 with 5 hooked strands having = 10 in. 71.4 1.953 1.085 na 118 144 1.00 12 0.7 14 0.29 8 65 119 na 2.94 na na 102 na 0.81 12A Case 12 with additional =1.32 in. na 2.94 na 1.32 102 na 1.01 12B Case 12 with 10 hooked strands having = 10 in. 83.3 na 2.94 na 102 124 0.99 AASHTO BIV-48 adjacent box girders spaced at 4 ft ( /2 = 33.6 in.) 29 0.7 46 0.7 12 165 119 na 4.116 na na 121 na 0.90 29A Case 29 with additional =1.32 in. na 4.116 na 1.32 121 na 1.01 29B Case 29 with 10 hooked strands having = 10 in. 83.3 1.176 2.94 na 121 141 1.01 31 0.6 46 0.52 15 145 102 na 4.774 na na 141 na 0.98 31A Case 31 with additional =0.44 in. na 4.774 na 0.44 141.12 na 1.00 31B Case 32 with 12 hooked strands having = 10 in. 71.4 4.123 0.651 na 141.12 164.87 1.00 32 0.7 46 0.65 15 165 119 na 4.704 na na 120.96 na 0.89 32A Case 32 with additional =1.32 in. na 4.704 na 1.32 120.96 na 1.00 32B Case 32 with 12 hooked strands having = 10 in. 83.3 1.176 3.528 na 120.96 141.32 1.00 na = Not applicable. TableÂ 3.11. Summary of stress checks (after Shahrooz etÂ al., 2017).
Experimental Research Approach and FindingsâComponent Tests 97Â Â Without a hooked embedment, the value of fps,straight = design stress in a straight pretensioned strand at nominal flexural strength at the section under consideration (ksi) is given by AASHTO (2020) Equations 126.96.36.199.2-2 and 188.8.131.52.2-1, respectively, as: From the point where bonding commences to the end of transfer length: 60 , =f f l d ps straight pe px b Eq. 3.8 From the end of the transfer length to the end of the development length: 60 60 , ( )= + â â âf f l d l d f fps straight pe px b d b ps pe Eq. 3.9 where lpx = distance (in.) from the free end of the pretensioned strand to the section under consideration. Providing a hooked embedment allows fps,hook to be taken as: , ( )( )= + â +f f f f x l lps hook hook pu hook hook dh Eq. 3.10 where fhook = constant stress that is attributed to the hook, which may be conservatively taken as fhook = 0; fpu = specified tensile strength of prestressing steel; lhook = embedment length of hooked strand into diaphragm; ldh = hooked strand development length, proposed as 0.7ld (TableÂ 3.10); ld = straight strand development length, ld = 170db; x = length along girder measured from end of girder; hook embedment is shown as negative values of x. 184.108.40.206 Illustrative Example, Case 11 from TableÂ 3.11 Case 11 reported in TableÂ 3.11 is an NU-900 girder having geometry reported in TableÂ 3.12; this case had no strand debonding. As shown in TableÂ 3.11, Case 11 had only 93% of the required tensile capacity T (Eq. 3.7) from the available strand (âAps fps). The following steps are taken to calculate the potential effect of adding a hooked embedment as shown schematically in FigureÂ 3.12b: 1. Embedment length of the hooked strand into the diaphragm, lh, taken as 10-in. in all cases (FigureÂ 3.12b); fhook is conservatively assumed to be zero. 2. Critical section: 2 2 12 32.4 2 28.2 in.( ) ( )= + = + =d support dv v 3. Hooked strand development length: ( )= = = = Ã =l l d ddh d b b0.7 0.17 170 119 119 0.6 71.4 in. Girder properties Strands along girder Case (in.) (in.) (in.) (in.2) (in.) (in.) 0â36 (in.) 36â72 (in.) 72â108 (in.) 108+ (in.) 11 36 32.4 0.6 0.217 36 102 14 14 14 14 TableÂ 3.12. Case 11 geometric details.
98 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders 4. Stress in pretensioned strand at nominal flexural strength at the section of the member under consideration: since dv/2 is less than transfer length, lt, Eq. 3.8 is used. 60 0.56 28.2 60 0.6 118.4 ksi, ( )( ) ( ) = = =f f l d f ps straight pe px b pu 5. For hooked strand: ( )( )= + â +f f f f x l lps hook pu hook hook dh; thus, 270 ksi 28.2 in.+10 in. 71.4 in. 144.4 ksi, ( )= =f ps hook 6. Aps,straight = (No. of strands â No. of hooked strands) Aps = (14 â 5) Ã· 0.217 = 1.953 in.2 7. Aps,hook = No. of hooked strands Ã Aps = 5 Ã 0.217 = 1.085Â in.2 8. âAps fps/T = (Aps fps,straight + Aps fps,hook)/T = (231.3 + 156.7)/387.7 = 1.0008 > 1.00 Therefore, by providing 90-degree hooks, the improved capacity of the now-anchored straight strands is adequate to resist the tension force T, and anchorage failure is prevented. 220.127.116.11 Possible Effect of Hooked Strand Embedment on AASHTO LRFD Equations 18.104.22.168-1 and 22.214.171.124-2 To illustrate the potential effect of hooked strand embedment, two similar cases, Cases 11 and 12 (TableÂ 3.11), are shown in FigureÂ 3.13. Case 11 has fourteen 0.6-in. strands, and Case 12 has fourteen 0.7-in. strands. Two approaches are shown in each case. The first approach, I, assumes the hooked bar to have zero stress developed by the tail of the hook ( fhook = 0); the second approach, II, assumes the tail is able to provide a capacity (0.37fpu = 100 ksi). The second approach reflects the results shown in TableÂ 3.10. In both approaches, the development length of the hooked strand is assumed to be ldh = 0.7ld. The increase in available fps varies. For Case 11 (FigureÂ 3.13a), considering approach I ( fhook = 0), there is an increase in fps of about 27% at the critical section dv/2. From Case 12 (TableÂ 3.11 and FigureÂ 3.13b), the increase is less than that of Case 11 due to the debonding present. Hooked anchorages are not believed to provide additional capacity for partially debonded strands. While they do so in theory, the strand stress must be accompanied by a strain over the partially debonded regions of the strand; this results in unacceptable levels of concrete cracking to engage the anchored debonded strand. Similar analyses and conclusions should result from using post-installed strand anchors on straight strands embedded in a cast-in-place diaphragm. This is not within the scope of the present study. 3.4 Bond Evaluation per ASTM A1081 Six samples meeting the specifications of ASTM A1081 (ASTM, 2015c) were produced to determine the bond capacity of 0.7-in. strands used in the full-scale test specimens reported in ChapterÂ 4. In this test, strands are embedded in a steel-confined 4.75-in. mortar cylinder.
Experimental Research Approach and FindingsâComponent Tests 99Â Â (a) Case 11 NU-900 girder having fourteen 0.6-in. strands and no partial debonding. (b) Case 12 NU-900 girder having fourteen 0.7-in. strands and partial debonding ratio, = 0.29 (dotted lines are debonded strands from 0 to 36 in.). FigureÂ 3.13. Schematic development of strand stress in strands with and without hooked anchorage into a cast-in-place diaphragm.
100 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders The strand is embedded over a length of 16Â in. (22.9db). The test is intended as an acceptance test for the bond quality of the strand and is explicitly intended for 0.5-in. and 0.6-in. strands. After several trials, the mortar mix design shown in TableÂ 3.13 was selected. The average compressive strength from three 2-in. cubes was 4,600 psi before starting the test, and 4,830 psi after testing, meeting the 4,500 to 5,000 psi range specified in ASTM A1081 (ASTM, 2015c). The strands were placed inside steel casings, the mortar was placed and consolidated with the use of a vibrator, and the strand was centered while the mortar was fresh (see FigureÂ 3.14). The setup shown in FigureÂ 3.15 was used to apply the load and measure slip. The load was applied by a hand pump with a valve to regulate the rate of loading. The measured load-slip relationships for five samples are shown in FigureÂ 3.16, and the loads corresponding to 0.10-in. slip (per ASTM A1018 requirements) are summarized in TableÂ 3.14. Type III cement 60 lb/ft3 Sand (SSD) 62 lb/ft3 Water 28 lb/ft3 TableÂ 3.13. Mortar mix design. (a) Casings and strands before casting. (b) Procedure to center the strands. FigureÂ 3.14. Setup for casting ASTM A1081 samples. FigureÂ 3.15. Apparatus for conducting ASTM A1081 tests.
Experimental Research Approach and FindingsâComponent Tests 101Â Â e device for measuring the slip malfunctioned, and no slip data are available for sample 6. e average load to cause 0.10-in. slip was found to be 20 kips with a coecient of variation of 13%. e load at 0.10-in. slip varies considerably, e.g., (1) average 22 kips (COV: 3.1%) by Morcous etÂ al. (2012); (2) average 33.5 kips (COV: 15%) by a series of tests conducted for the supplier of strands used in this project (Curry, 2018). e average value of 20 kips (TableÂ 3.14) meets recommended acceptance criteria for 0.7-in. strands (Morcous etÂ al., 2012). e average value of 20 kips exceeds the recently approved PCI-recommended practice for 0.5-in. strands: 14 kips for all strands and 18 kips for high-bond-strength strands (Brewe, 2020). 3.5 Summary of Component Test Results and Observations e rst phase of the experimental program focused on the bond characterization of seven-wire prestressing strands, specically 0.7-in. strands. Four types of tests were conducted: (1) direct tension, (2) Hoyer eect testing, (3) beam-end tests, and (4) bond evaluation per ASTM A1081. Based on analysis and synthesis of the observed responses, the following observations can be drawn: 1. All strands tested met the requirements of ASTM A416/AASHTO M203 (ASTM, 2015a). 2. e Hoyer eect results in strand contraction and dilation that exceed the value predicted by the Poisson eect. e trend of decreasing dilation eect with increasing strand diameter reported by Briere etÂ al. (2013) was not observed in the present study. Indeed, dilation is relatively uniform with the 0.7-in. strand, if anything, exhibiting greater dilation. e reason for this divergence from the limited previous data has not been identied. 3. e bond characteristics of the strand used in this study were quantied using ASTM A944-10 (ASTM, 2015c) beam-end tests and ASTM A1018 (ASTM. 2015b) pullout tests. From the ASTM A944-10 beam-end tests, no extrapolated value of development length exceeded 106db. Both 0.6-in. and 0.7-in. strands embedded in LWC resulted in splitting failures at bond stresses lower than observed in comparable NWC, although concrete strengths were relatively low. e bond performance of the 0.7-in. strand used in the experimental program, estab- lished using the ASTM A1018 test, was found to be comparable to the range of the values reported by others. Sample Load (kips) 1 19.9 2 17.0 3 22.1 4 23.5 5 18.0 Average 20.1 Std. dev. 2.71 COV 13.5% FigureÂ 3.16. Load-slip relationships for ASTM A1081 samples 1â5. TableÂ 3.14. Load at 0.10-in. slip.
102 Use of 0.7-in. Diameter Strands in Precast Pretensioned Girders 4. The potential for using the embedment of hooked strands into cast-in-place end diaphragms to increase the strand stress that may be developed near girder ends is illustrated. Experimental validation of this approach is necessary and should consider strand anchors in addition to hooked strands. 5. Although only a limited number of tests were conducted, ASTM A944-10 beam-end tests of strands having short embedment length and a 90-degree hook illustrated that, like for nonprestressed reinforcement, providing a hook reduces the development length, and the hook itself provides a residual capacity (seen to be equivalent to about 100 ksi in this study) provided the concrete remains intact.