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38 3.4 Measured Transfer Lengths on transfer lengths. Three different sources for 0.5 in. diam- versus Varying Concrete eter strand and one source for 0.6 in. diameter strand were Strengths and Varying NASP employed in this research program. Bond Test Values Figure 3.18 shows the details of the I-shaped cross section. In the I-shaped beams made with 0.5 in. diameter strands, The research aims at assessing the effects that varying con- four strands were located within the bottom bulb of the cross crete strength can have on strand bond. This section deals section with a fifth strand located 2 in. from the top of the primarily with transfer lengths measured on pretensioned cross section. In the I-beams made with 0.6 in. diameter beams. Variables included strand with varying bond quality strands, three strands were located within the bottom bulb of and concrete strengths varying between 4 ksi at release and 10 the cross section with a fourth strand located 2 in. from the ksi at release. Beams were either rectangular in shape or top of the cross section. I-shaped. A total of 43 rectangular-shaped beams and 8 I-shaped beams were cast using 4 different strand sources. 3.4.1 Fabrication of Beams The number of beams made and the corresponding research variables are reported in Table 3.7. Two-strand rectangular Transfer lengths were measured at release on all the beams beams included two strands placed near the bottom of the using strand end slips. On some of the beams, transfer lengths cross section. The four-strand rectangular beams had two were measured using a detachable mechanical strain gage strands placed near the bottom and two strands placed near (DEMEC gage), which effectively measures changes in con- the top. Beams were cast using both 0.5 in. and 0.6 in. diam- crete surface strains. The transfer lengths measured from eter strands. Figure 3.14 illustrates the beam numbering strand end slips are compared with those measured using the system that describes the variables that are contained within DEMEC gage. each beam specimen. Cross section details for the rectangu- The rectangular beams were 17 ft in length with a cross lar beams are found in Figures 3.15 and 3.16. section that was 6.5 in. wide by 12 in. high. Two #6 bars Figure 3.17 depicts some of the rectangular beams during were placed within 1 in. of the top of the cross section in all fabrication, prior to release of the prestressing strands. Beams rectangular beams to ensure ductile flexural failures. The were made with a target 1-day concrete strength of 4,000, cross section for the I-shaped beams is shown in Figure 6,000, 8,000 and 10,000 psi. The 6,000-psi release strength 3.18. The beams were fabricated 24 ft in length. The beams concrete beams were made using both air-entrained and non- cast had 0.5 in. diameter strands and 0.6 in. diameter air-entrained concrete to study the effects of air entrainment strands. All of the I-beams contained horizontal web rein- Table 3.7. Number of transfer length beams and research variables employed. 0.6 in Target Concrete 0.5 in Diameter Strands Diameter Target Air Release Design Strands Content Strength Strength (%) (ksi) (ksi) Strand A Strand B Strand D Strand A6 Two-Strand Rectangular Beams 4 6 2 0 2 2 2 6 10 2 2 0 2 3 6 10 6 2 0 2 0 8 14 2 2 0 2 3 10 15 2 2 0 2 3 Four-Strand Rectangular Beams 6 10 2 2 0 2 0 8 14 2 2 0 2 0 10 16 2 2 0 2 0 I-Shaped Beams 6 10 2 1 0 1 2 10 15 2 1 0 1 2

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39 Beam Shape Internal hoop reinforcements were placed in the form of R: Rectangular 6.5" x 12" triangular cages at both ends of the beam. I: "I" Shaped beams Strands were tensioned to 75 percent of fpu (the guaran- teed breaking strength) or 202.5 ksi. The expected elonga- Strand Source A, B, or D for 0.5 in. strand tions were calculated and compared with the measured A for 0.6 in. strand elongations to ensure proper stressing. The strands were stressed to an initial level of 2,000 lb. Once the force on the Nominal Concrete Strength at Release strand reached 2,000 lb, the strand was marked with a per- 4, 6, 8, or 10 ksi A6: for 6 ksi with Air Entrainment manent marker coinciding with the datum level marking on the prestressing bed. The strand was then stressed to 202.5 ksi. The elongation was then measured as the distance the mark on the strand moved from the datum marking on RA6-5-1-T the prestressing bed. Concrete was batched onsite at Coreslab's batch plant. Fresh properties of concrete, slump, unit weight, and air con- tent were checked before casting the concrete. Extensive trial batching was performed (Tessema 2006) to determine the Strand Size 5 for 0.5 in. diameter fresh and hardened properties of the concrete mix designs. If 6 for 0.6 in. diameter the fresh properties of unit weight, slump, or air content did not meet with the design expectations, the concrete was not used. Concrete cylinders were made at the site and placed in Specimen Number the same prestressing bed as the test beams until transfer. 1, 2, or 3 is the number in a series Steam curing was used if the ambient temperatures were low. of companion beams The test beams together with the concrete cylinders were kept under cover if steam curing was used. Top Strand 3.4.2 Measuring Transfer Lengths If the rectangular beam contains top strands, T is used. Not applicable for "I" shaped beams Transfer lengths were measured on all strands by measur- ing the distance each strand slipped into the concrete after prestress release. A depth micrometer was used in combina- Figure 3.14. Beam number identification. tion with specially made clamps to measure the strand end slip. Figure 3.19 shows the depth micrometer measuring forcement consisting of four or two #4 bars, 96 in. long, lo- strand end slips immediately after prestress release. cated near the ends of the beams and anchored with stan- Strand end slips are directly related to measured transfer dard hooks. Two horizontal #4 bars were placed at the lengths, as shown in Figure 3.20. In Figure 3.20, stresses are south end of every beam, and four horizontal #4 bars were used to indicate the loss of prestress caused by elastic short- placed at the north end. The deck slab contained two #3 ening (ES). After release, ES is the primary prestress loss. The straight bars in the longitudinal direction in the deck slab. transfer length of the strand is directly related to the area of 17' 6 2 2 in. Strands 2- #6 Bars 16'-8" 12 #3 Tie at 6" c/c 2 2- in. Strands Figure 3.15. Details of four-strand beams.

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40 17' 6 2 2 #6 Bars 16'-8" 12 #3 Tie at 6" c/c 2 2- in. Strands Figure 3.16. Details of two-strand beams. the shaded triangle shown in Figure 3.20. The shaded area di- vided by the elastic modulus of the strand gives the strand end slip measurement. Thus, by measuring the strand end slip, the transfer length can be calculated directly. Over time, the beam experiences additional losses and a lengthening of the transfer length. The transfer length over time is illustrated in Figure 3.20 by the larger, unshaded triangle. In Figure 3.20, fsi is the stress in the prestressing strand just prior to release, and fse is the strand stress after all losses. ES is the elastic shorten- ing loss that occurs immediately upon release of the pre- stressing force. Changes in concrete surface strains were measured on some of the specimens using a DEMEC gage. The DEMEC gage is pictured in Figure 3.21. DEMEC target points were set at 100-mm spacings. The DEMEC gage spans 200 mm, so read- Figure 3.17. Fabrication of rectangular beams. ings were taken over a 200-mm gage length. The procedure 23 # 3 bars on deck at 9" c/c and 2 bars throughout the length 1.5 2 # 3 stirrups at 7" c/c 3 24 # 4 bars with standard hooks 2" c/c for 96" 23 20.5 20 from ends 4 bars at north end and 2 bars at south end # 3 bars 4" c/c shape for internal hoop 6.5 reinforcement for 72" from end 3 Prestressing strand 10 Mild steel reinforcement Figure 3.18. Details of I-shaped beams.

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41 Figure 3.21. Concrete surface strain measurements with DEMEC gage. requires initial readings to be made prior to strand cutting. After release, the measurements are repeated, and the differ- ences can be plotted as a strain profile, such as the one shown Figure 3.19. Strand end slip measurement using a in Figure 3.22. As shown, concrete strains on the north end micrometer. and the south end are plotted along the length of the beam. The strain profile is "smoothed" by averaging three measure- ment points. The Average Mean Strain (AMS) is found out by averaging the points on the strain plateau on the north and the Initial Losses south sides independently. The measured transfer length obtained from the DEMEC readings is the location where the 95-percent AMS line intersects the Smoothed Strain profile. f si (f si ES) f se 3.4.3 Results of the Transfer Length Measurements Results of the transfer length measurements are reported Lt in several tables, generally organized by strand type. Table 3.8 reports the transfer lengths computed from measured Figure 3.20. Variation in strand stress variations strand end slips on Strands A and B. Table 3.8 reports trans- with length and relation to strand end slip fer lengths only on strands located at the bottom of the measurements. cross sections. Table 3.8 reports a transfer length for each Concrete Strains (10-6 in/in) 450 400 350 300 250 200 150 100 50 0 0 2 4 6 8 10 12 14 16 Length of the Beam (north to south) Unsmoothed Profile Smoothed Profile Figure 3.22. Concrete strain profile highlighting strand transfer lengths.

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42 Table 3.8. Summary of transfer lengths at release for bottom Strands A/B. X S f ci f c (56d ) Beam Number Location North South (kips) (kips) (psi) (psi) RB4-5-1 East 17.06 18.31 20.12 West 19.78 18.66 2.56 4,033 7,050 RB4-5-2 East 24.13 22.47 West 18.1 22.45 RA6-5-1 East 20.66 20.24 West 17.68 16.16 RA6-5-2 East 15.94 11.78 18.02 West 17.12 18.23 2.23 6,183 8,500 RA6-5-1T East 19.39 18.7 West 20.62 18.93 RA6-5-2T East 18.7 18.84 West 19.07 16.27 RA8-5-1 East 12.01 13.09 West 14.58 13.9 RA8-5-2 East 13.9 11.74 13.63 West 15.93 12.42 1.32 8,570 13,490 RA8-5-1T East (a) 12.51 West (b) 14.71 RA8-5-2T East 14.52 15.6 West 12.55 13.36 RA10-5-1 East (c) (d) West (e) 13.57 RA10-5-2 East 12.75 15.25 13.72 West 12.75 14.8 2.27 9,711 14,470 RA10-5-1T East 17.74 12.06 West 18.16 11.32 RA10-5-2T East 12.2 11.78 West 11.46 14.53 (a) Lt of 1.48 in. not included (c) Lt of 25.65 in. not included (b) Lt of 5.26 in. not included (d) Lt of 5.82 in. not included (e) Lt of 22.89 in. not included strand, two at each end of the beam, with each end of the Table 3.10 reports the measured transfer lengths for Strand beam designated as either north or south; thus, all together, A, placed near the tops of cross sections in the respective four transfer length measurements are reported for each beams. Again, no clear pattern emerges of the top strands beam. having longer transfer lengths than the bottom strands. Table 3.8 also reports the average transfer length for all of Table 3.11 reports the measured transfer lengths for 0.5 in the transfer length measurements on beams for a particular diameter Strand D. Table 3.11 includes the beam number, the concrete strength, X . The standard deviation, S is reported in measured transfer length for each strand, the average transfer inches for the data set. The release strength, fci (psi), is the length for Strand D by concrete strength, the standard devia- average of at least three 4 in. by 8 in. cylinders. The 56-day tion of the transfer lengths, and 1-day and 56-day concrete strength, fci (56d), is the average of three cylinders placed in strengths. laboratory curing conditions. Table 3.12 reports transfer lengths measured on Strand D Table 3.9 reports the measured transfer lengths on beams placed in top locations of four-strand beams. Again, there is that contained air-entrained concrete. Only Strand A was used no clear pattern of top strands having longer transfer lengths for this set of beams. While the transfer lengths measured in than bottom strands. air-entrained concrete appear to be longer than the transfer Table 3.13 reports transfer lengths measured on I-shaped lengths measured in the companion beams without air en- beams, including data from both 0.5 in. diameter strands-- trainment, no clear pattern emerges with the limited data. Strand A and Strand D--and data from the 0.6 in. diameter

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43 Table 3.9. Summary of transfer lengths at release of bottom Strands A/B in air-entrained concrete. Beam Number Location North South X S f ci f c (56d ) (kips) (kips) (psi) (psi) RA6A-5-1 East 19.26 17.47 West 16.22 17.88 20.49 3.39 7,960 11,420 RA6A-5-2 East 26.41 22.63 West 22.6 21.42 RD6A-5-1 East 36.25 30.04 West 34.55 28.15 26.26 6.93 7,960 11,420 RD6A-5-2 East 21.16 21.79 West 19.79 18.36 strand, Strand A6. As in Tables 3.8 through 3.12, measured transfer length measured using both methods. Figure 3.23 transfer lengths are reported for each strand, the average and presents the data from Tables 3.15 through 3.17 graphically standard deviation are reported for each beam, along with and shows that generally the transfer lengths measured by the concrete strengths at release and at 56 days. Table 3.13 DEMEC gage are approximately the same as the transfer includes data collected from strands located in the bottom lengths obtained from strand end slip measurements. bulbs on the I-shaped beams only. Tables 3.18 through 3.22 provide the transfer length meas- Table 3.14 reports the measured transfer lengths on top urements over time, from release through 240 days after strands from the I-shaped beams. The data are erratic, so release. Strand end slips can be measured individually for no conclusions can be drawn from these measurements. each strand. In the tables reporting measured transfer All of the transfer lengths reported in Tables 3.8 through lengths from strand end slips, the east strand is represented 3.14 report transfer lengths measured immediately after in the column headed by "E" whereas the west strand is re- release. ported in the columns headed by "W." Transfer lengths were Tables 3.15, 3.16 and 3.17 all include both transfer length not measured beyond release for beams RB4-5-1 and RB4-5-2. measurements made with the DEMEC gage and transfer As the data indicate, transfer lengths grow over time, and the length measurements made from strand end slips for com- 240-day transfer lengths are considerably longer than parison. Approximately 43 percent of the beam ends had the transfer lengths measured at release. All of the transfer Table 3.10. Summary of transfer lengths at release of Strand A in top locations. X S f ci f c (56d ) Beam Number Location North South (kips) (kips) (psi) (psi) RA6-5-1T East 21.03 19.11 19.04 West 19.47 20.58 2.07 6,183 8,500 RA6-5-2T East 17.07 16.52 West 21.82 16.71 RA8-5-1T East 13.38 14.88 14.55 West 10.74 14.42 1.96 8,570 13,490 RA8-5-2T East 17.61 15.7 West 15.12 14.56 RA10-5-1T East 14.93 13.5 West 14.53 11.32 12.90 1.65 9,711 14,470 RA10-5-2T East 10.63 11.2 West 14.11 12.99

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44 Table 3.11. Summary of transfer lengths at release for bottom Strand D. X S f ci f c (56d ) Beam Number Location North South (kips) (kips) (psi) (psi) RD4-5-1 East 31.69 32.11 32.90 West 33.88 29.93 2.64 4,033 7,050 RD4-5-2 East 36.9 (a) West (b) (c) RD6-5-1 East 29.88 30.42 West 30.6 25.71 RD6-5-2 East 25.35 30.15 26.19 West 25.84 28.29 2.99 6,183 8,500 RD6-5-1T East 23.89 25.12 West 23.43 26.59 RD6-5-2T East 25.53 19.93 West 24.67 23.71 RD8-5-1 East 21.16 20.89 West 19.13 19.41 RD8-5-2 East 16.79 21.43 West 10.54 13.17 20.94 6.05 8,570 13,490 RD8-5-1T East 35.63 29.78 West 15.94 26.34 RD8-5-2T East 20.87 21.99 West 18.99 23.01 RD10-5-1 East 23.48 16.16 West 28.59 17.54 RD10-5-2 East 13.95 19.33 18.36 West 15.74 17.12 3.72 9,711 14,470 RD10-5-1T East 21.76 16.22 West 21.1 17.4 RD10-5-2T East 16.36 15.25 West 17.13 16.58 (a) Excessive movement of the beams during flame cutting, Lt observed as 50.43 in. (b) Excessive movement of the beams during flame cutting, Lt observed as 47.48 in. (c) Excessive movement of the beams during flame cutting, Lt observed as 48.98 in. length measurements over time were made using the strand Figure 3.24 illustrates the transfer length measurements at end slip method. release plotted against the concrete strengths at 1 day of age for Strands A/B. (Although Strand A and Strand B represent two different sources of strand, their NASP Bond Test values 3.4.4 Discussion of Transfer Length were very similar; therefore, the data from the two strands are Measurements treated as part of one data set.) Two regression curves are The discussion on transfer lengths focuses on two essential shown in Figure 3.24; one shows the best fit for data derived elements: (1) what effects, if any, concrete strength has on from the DEMEC gage, and the other shows the best fit for transfer length and (2) whether the NASP Bond Test provides the data derived from strand end slip measurements. Both re- an indicator regarding transfer length. Another objective of gression curves in Figure 3.24 show that transfer lengths this discussion is to present to the industry a reasonable code shorten as concrete strengths increase. equation to adequately predict the transfer lengths of preten- Figure 3.25 shows the transfer length measurements at re- sioned strands. lease plotted against the concrete strengths at 1-day of age for

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45 Table 3.12. Summary of transfer lengths at release for Strand D in top locations. X S f ci f c (56d ) Beam Number Location North South (kips) (kips) (psi) (psi) RD6-5-1T East 27.91 21.46 23.76 West 27.52 20.26 3.03 6,183 8,500 RD6-5-2T East 23.7 20.2 West 23.61 25.43 RD8-5-1T East 22.06 16.45 22.64 West 17.61 18.84 4.68 8,570 13,490 RD8-5-2T East 27.82 23.71 West 28.67 25.94 RD10-5-1T East 16.79 15.56 15.93 West 17.27 16.32 2.22 9,711 14,470 RD10-5-2T East 18.98 15.02 West 16.19 11.29 Table 3.13. Summary of transfer lengths at release for I-shaped beams--bottom Strands B and D (0.5 in.) and Strand A6 (0.6 in.). X S f ci f c (56d ) Beam Number Location North South (kips) (kips) (psi) (psi) IB6-5-1 East 16.12 6.42 10.77 West 17.82 2.9 5.43 5,810 9,350 Cent. 10.93 9.45 Midd. 16 6.48 IB10-5-1 East 11.14 12.45 10.59 West 10.03 5.8 2.15 7,615 13,490 Cent. 11.6 12.45 Midd. 11.31 9.9 ID6-5-1 East 24.47 12.23 18.49 West 23.47 2.56 9.88 5,492 9,840 Cent. 26.69 (a) Midd. 28.96 11.04 ID10-5-1 East 19.03 19.03 20.82 West 20.34 23.61 2.8 8,225 14,160 Cent. 15.99 21.13 Midd 23.51 23.94 IA6-6-1 East 18.36 16.33 21.17 4.68 West 29.83 22.21 Cent. 20.15 20.15 4,381 8,990 IA6-6-2 East 9.62 14.18 16.04 4.49 West 15.48 19.47 Cent. 22.58 14.92 IA10-6-1 East 9.4 21.15 13.29 5.91 West 14.35 5.81 10,480 14,990 Cent. 10.19 18.85 IA10-6-2 East 17.94 10.64 14.72 3.46 West 13.85 10.76 10,590 14,930 Cent. 17.83 17.32 (a) Spalling of concrete surface during flame cutting

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46 Table 3.14. Summary of transfer lengths at release for top strands in I-shaped beams. X S f ci f c (56d ) Beam Number Location North South (kips) (kips) (psi) (psi) IA6-6-1 Top 22.84 9.36 4,381 8,990 18.57 6.23 IA6-6-2 Top 20.22 21.84 IA10-6-1 Top 3.82 2.87 1.35 10,480 14,990 1.91 IA10-6-2 Top 9.3 9.17 0.18 10,590 14,930 9.04 IB6-5-1 Top 21.43 13.80 10.80 5,810 9,350 6.16 ID6-5-1 Top 36.25 33.12 4.4 5,492 9,840 29.99 ID10-5-1 Top (a) 16.86 - 8,225 14,160 16.86 (a) End clamp loosened during detensioning Table 3.15. Transfer length at release measured by DEMEC gage and strand end slip for 0.5-in. Strands A/B. Strand End Slips DEMEC Beam North (in.) South (in.) North (in.) South (in.) RB4-5-1 18.4 18.5 24.2 27.1 RB4-5-2 21.1 22.5 RA6A-5-1 17.7 17.7 16.0 17.5 RA6A-5-2 24.5 22.0 RA6-5-1 19.2 18.2 RA6-5-2 16.5 15.0 RA6-5-1-T 20.3 19.8 RA6-5-2-T 19.4 16.6 RA8-5-1 13.3 13.5 14.3 12.0 RA8-5-2 14.9 12.1 RA8-5-1-T 12.1 14.7 12.0 15.6 RA8-5-2-T 16.4 15.1 RA10-5-1 24.3 9.7 24.3 14.4 RA10-5-2 12.8 15.0 RA10-5-1-T 14.7 12.4 12.5 11.7 RA10-5-2-T 12.4 12.1 IB6-5-1 12.2 Not available 15.2 IB10-5-1 11.1 Not available 11.0 measurements were not taken.

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47 Table 3.16. Transfer length at release measured by DEMEC gage and strand end slip for 0.5-in. Strand D. Strand End Slips DEMEC Beam North (in.) South (in.) North (in.) South (in.) RD4-5-1 32.8 31.0 25.6 24.8 RD4-5-2 36.9 Not available RD6A-5-1 35.4 29.1 39.0 26.4 RD6A-5-2 20.5 20.1 RD6-5-1 30.2 28.1 RD6-5-2 25.6 29.2 RD6-5-1-T 27.7 20.9 RD6-5-2-T 23.7 22.8 RD8-5-1 20.2 20.2 11.3 18.5 RD8-5-2 13.7 17.3 RD8-5-1-T 19.8 17.6 12.4 12.0 RD8-5-2-T 28.2 24.8 RD10-5-1 26.0 16.9 23.4 19.4 RD10-5-2 14.8 18.2 RD10-5-1-T 17.0 15.9 16.1 15.7 RD10-5-2-T 17.6 13.2 ID6-5-1 25.2 Not available 25.9 ID10-5-1 17.5 Not available 19.7 measurements were not taken. Table 3.17. Transfer Length at release measured by DEMEC gage and strand end slip for 0.6-in. Strand A6. Strand End Slips DEMEC Beam North (in.) South (in.) North (in.) South (in.) RA4-6-1 33.4 25.0 31.4 30.3 RA4-6-2 30.2 29.3 RA6-6-1 29.7 28.2 22.4 21.1 RA6-6-2 31.7 30.1 RA6-6-3 25.8 33.6 RA8-6-1 28.2 29.2 19.5 22.0 RA8-6-2 28.2 25.7 RA8-6-3 22.8 28.3 RA10-6-1 20.0 21.9 16.6 15.0 RA10-6-2 15.6 21.8 RA10-6-3 16.3 22.7 IA6-6-2 24.3 26.1 15.9 16.2 IA10-6-1 18.0 Not available 11.3 IA10-6-2 16.0 Not available 16.5 measurements were not taken.

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48 40.00 35.00 Transfer Length from DEMEC (in) 30.00 R2 = 0.5768 25.00 0.5" A Strand 0.5" B Strand 20.00 0.5" D Strand 15.00 0.6" A6 Strand Perfect Fit 10.00 Linear (All Strands) 5.00 0.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 Transfer Length from End Slips (in) Figure 3.23. Transfer lengths measured by DEMEC gage versus transfer lengths measured by strand end slip. Table 3.18. Change in transfer lengths over time for bottom 0.5 in. diameter Strands A/B in two-strand rectangular beams. Transfer Length at Release from Strand End Transfer Length after 60 Transfer Length after 90 Transfer Length from 240 Slips Days from Strand End Slips Days from Strand End Slips Days from Strand End Slips Beam (in.) (in.) (in.) (in.) Number North South North South North South North South Average W & E Average W & E Average W & E Average W & E RB4-5-1 18.42 18.48 RB4-5-2 21.11 22.46 RA6-5-1 19.17 18.20 33.07 28.86 33.07 29.55 33.69 30.03 RA6-5-2 16.53 15.01 26.57 20.82 26.56 23.38 27.95 23.52 RA6A-5-1 17.74 17.68 25.23 26.62 26.33 28.14 26.54 28.55 RA6A-5-2 24.50 22.02 28.92 27.72 31.41 29.03 31.75 29.38 RA8-5-1 13.30 13.50 15.59 21.13 17.68 21.46 24.91 22.54 RA8-5-2 14.92 12.08 22.07 19.24 23.69 19.71 35.23 19.98 RA10-5-1 24.27 9.69 23.92 9.83 24.13 12.11 24.34 13.14 RA10-5-2 12.75 15.02 16.47 16.67 18.05 17.23 19.15 17.30

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49 Table 3.19. Change in transfer lengths over time for bottom 0.5-in. diameter Strand D in two-strand rectangular beams. Transfer Length at Release from Strand End Transfer Length after 60 Transfer Length after 90 Transfer Length from 240 Slips Days from Strand End Slips Days from Strand End Slips Days from Strand End Slips Beam (in.) (in.) (in.) (in.) Number North South North South North South North South Average W & E Average W & E Average W & E Average W & E RD4-5-1 32.78 31.02 RD4-5-2 42.19 49.70 RD6-5-1 30.24 28.07 43.00 38.57 46.82 44.37 49.75 45.26 RD6-5-2 25.60 29.22 36.79 39.87 41.99 44.72 44.24 48.27 RD6A-5-1 35.40 29.10 37.39 34.47 39.40 36.41 39.94 37.16 RD6A-5-2 20.48 20.08 26.26 35.24 30.73 39.37 32.39 40.07 RD8-5-1 20.15 20.15 28.34 26.55 32.66 30.33 39.08 34.54 RD8-5-2 13.66 17.30 34.14 46.08 36.82 47.73 37.38 50.41 RD10-5-1 26.03 16.85 26.31 25.27 26.45 26.51 30.24 27.14 RD10-5-2 14.85 18.23 17.47 20.16 18.71 22.30 22.30 22.03 Table 3.20. Change in transfer lengths over time for 0.6-in. Strand A6 in two-strand rectangular beams. Transfer Length at Release from Strand End Transfer Length after 60 Transfer Length after 90 Transfer Length from 240 Slips Days from Strand End Slips Days from Strand End Slips Days from Strand End Slips Beam (in.) (in.) (in.) (in.) Number North South North South North South North South Average W & E Average W & E Average W & E Average W & E RA4-6-1 33.42 24.98 RA4-6-2 30.24 29.35 RA6-6-1 29.73 28.19 36.87 41.73 39.00 44.45 40.85 55.13 RA6-6-2 31.65 30.10 47.03 46.36 49.24 48.20 52.18 49.37 RA6-6-3 25.83 33.63 39.73 44.60 44.08 44.82 44.96 45.93 RA8-6-1 28.21 29.17 42.46 41.87 43.87 43.26 45.48 43.41 RA8-6-2 28.20 25.70 42.68 38.55 46.28 42.35 46.35 42.37 RA8-6-3 22.80 28.26 36.85 44.00 41.17 46.93 43.00 49.22 RA10-6-1 20.03 21.92 25.69 25.77 28.08 28.82 29.98 32.15 RA10-6-2 15.62 21.78 20.99 25.99 26.14 29.47 26.79 30.70 RA10-6-3 16.34 22.73 24.46 28.82 26.13 32.30 27.73 33.32

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50 Table 3.21. Change in transfer length over time for 0.5-in. Strand A in four-strand rectangular beams. Transfer Length at Transfer Length after 60 Transfer Length after 90 Transfer Length after 240 Release from Strand Days from Strand End Days from Strand End Days from Strand End Beam Number and End Slips (in.) Slips (in.) Slips (in.) Slips (in.) Location North South North South North South North South Average W & E Average W & E Average W & E Average W & E RA8-5-1-T (Top) 12.06 14.65 24.27 24.67 24.96 26.18 25.16 27.21 (Bottom) 3.37 13.61 11.59 21.29 11.66 25.11 12.80 27.27 RA8-5-2-T (Top) 16.37 15.13 27.30 27.30 28.20 28.68 28.96 29.44 (Bottom) 13.54 14.48 22.03 24.25 23.31 25.40 24.05 25.33 RA6-5-1-T (Top) 20.25 19.84 33.01 32.69 34.46 34.96 34.60 34.89 (Bottom) 20.00 18.82 31.92 26.29 34.06 28.36 34.06 28.56 RA6-5-2-T (Top) 19.44 16.61 37.07 35.15 39.33 37.28 40.64 37.49 (Bottom) 18.89 17.55 45.33 35.77 47.82 42.71 49.55 43.34 RA10-5-1-T (Top) 14.73 12.41 21.59 18.79 22.16 19.43 22.16 19.70 (Bottom) 17.95 11.69 19.00 14.40 19.07 15.30 19.62 15.93 RA10-5-2-T (Top) 12.37 12.10 14.29 22.15 15.42 22.22 15.63 22.36 (Bottom) 11.83 13.16 16.28 16.01 16.56 16.29 17.33 16.43 Table 3.22. Change in transfer length over time for 0.5-in. Strand D in four-strand rectangular beams. Transfer Length at Transfer Length after 60 Transfer Length after 90 Transfer Length from 240 Release from Strand Days from Strand End Days from Strand End Days from Strand End Beam Number and End Slips (in.) Slips (in.) Slips (in.) Slips (in.) Location North South North South North South North South Average W & E Average W & E Average W & E Average W & E RD8-5-1-T (Top) 19.84 17.64 35.57 35.90 40.15 39.59 41.18 42.47 (Bottom) 25.78 28.06 23.98 38.41 30.63 41.05 27.73 44.59 RD8-5-2-T (Top) 28.25 24.82 65.51 67.04 67.56 68.62 68.52 68.62 (Bottom) 19.93 22.50 49.52 32.36 50.91 33.26 52.86 35.00 RD6-5-1-T (Top) 27.71 20.86 53.89 56.65 57.32 59.03 58.79 60.29 (Bottom) 23.66 25.85 38.10 38.09 40.76 42.20 42.89 45.27 RD6-5-2-T (Top) 23.66 22.81 49.07 48.64 57.90 53.33 63.27 54.49 (Bottom) 25.10 21.82 65.45 39.67 69.56 44.05 RD10-5-1-T (Top) 17.03 15.94 26.10 24.12 27.87 26.36 30.19 27.11 (Bottom) 21.43 16.81 23.51 19.77 23.51 21.63 23.77 RD10-5-2-T (Top) 17.58 13.15 24.81 23.58 26.30 24.95 26.58 26.99 (Bottom) 16.74 15.92 24.05 23.01 25.98 23.01 28.18 23.01

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51 40 35 30 From DEMEC Transfer Lengths (in.) 2 R = 0.4215 25 20 From Strand End Slips 2 15 R = 0.6429 10 5 0 0 2000 4000 6000 8000 10000 12000 Concrete Strengths (psi) Strand End Slip DEMEC Omitted Data Figure 3.24. Transfer length versus fci for Strands A/B in rectangular beams. 40 35 From Strand End Slips R2 = 0.6556 30 Transfer Lengths (in.) 25 From DEMEC 20 R2 = 0.3195 15 10 5 0 0 2000 4000 6000 8000 10000 12000 Concrete Strengths (psi) Strand End Slip DEMEC Omitted Data Figure 3.25. Transfer length versus fci for Strand D in rectangular beams. Strand D. Again, it is clear that the transfer length decreases Bond Test value and the square root of concrete strength. The with increasing concrete strength. coefficient of determination in those comparisons is a very Finally, Figure 3.26 illustrates the transfer length measure- robust 0.8. If the NASP Bond Test value, which is a direct ments taken on beams made with the 0.6 in. diameter strand, measure of bond between the strand and concrete, varies with Strand A6. Again, the data clearly show the inverse relation- the square root of concrete strength, then it is logical that ship between transfer lengths and concrete strength. The data the transfer length would also vary with the square root of from all three of the strand sources are illustrated in Figure concrete strength. 3.27, where the transfer lengths for each strand are plotted Figure 3.28 plots the same data as Figure 3.27, but does a against the concrete strengths at release. best-fit curve from power regressions. The coefficients of Figures 3.24 through 3.27 show the relation between trans- determination for these power curves are nearly as good as fer length data and linear regression models. Linear regression the coefficients of determination for the linear regressions. is often used because the methodology is less abstract than Furthermore, the best-fit regressions provide an exponent in others and perhaps more easily understood. However, there is the equation of -0.56, -0.83 and -0.56. As a reminder, the a direct relationship between the NASP Bond Test values in inverse of the square root would be an exponent of -0.50. concrete and the square root of concrete strengths. Figures Figure 3.29 plots the transfer lengths for Strands A/B at re- 3.12 and 3.13 show a strong correlation between the NASP lease and at 240 days after release. The data are fitted to a

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52 40 35 From Strand End Slips Transfer Lengths (in.) 30 R2 = 0.6399 25 20 15 From DEMEC 10 R2 = 0.687 5 0 0 2000 4000 6000 8000 10000 12000 Concrete Strengths (psi) Strand End Slip DEMEC Figure 3.26. Transfer length versus fci for Strand A6 (0.6 in) in rectangular beams. 45 40 Strand D R2 = 0.6556 Transfer Length (in.) 35 30 Strand A6 (0.6 in.) R2 = 0.6399 25 20 15 Strands A/B 10 R2 = 0.6429 5 0 0 2 4 6 8 10 12 14 Concrete Strength (ksi) Strands A/B Strand D Strand A6 (0.6 in.) . Figure 3.27. Linear regression for transfer lengths and fci 70 Strand D 60 R2 = 0.5815 Transfer Length (in.) 50 Strand A6 (0.6 in.) R2 = 0.6526 40 30 20 Strand A/B R2 = 0.6112 10 0 0 2 4 6 8 10 12 14 Concrete Strength (ksi) Strand A/B Strand D Strand A6 (0.6 in.) . Figure 3.28. Power regression for transfer lengths and fci

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53 60 Transfer Length at Release (in.) 50 40 y = 149.93x-0.8913 30 R2 = 0.3886 20 y = 44.79x-0.56 10 R2= 0.72 0 0 2 4 6 8 10 12 14 Concrete Strength at Release (ksi) Figure 3.29. Transfer lengths versus concrete strengths for 0.5-in. Strands A/B at release and at 240 days. power regression curve. The best-fit equations are also shown for Strand D are considerably longer than those for Strands in Figure 3.29. In Figures 3.29 through 3.32, transfer length A/B. Recall that Strand D had a NASP Bond Test value of data obtained immediately after release are represented by 6,890 lb, whereas both Strands A and B had NASP Bond Test diamond-shaped data points and the solid regression curve. values in excess of 20,000 lb (see Table 3.3). These data would Transfer lengths measured at 240 days are represented by support the idea that higher NASP Bond Test values will triangular-shaped data points and the dashed regression curve. result in shorter transfer lengths. Figure 3.30 plots the transfer lengths for Strand D at both Figure 3.31 plots the same data but for the 0.6 in. diameter release and at 240 days after release. Again, these data are fit- strand, Strand A6. Again, the data clearly show that transfer ted to a power regression curve. Note that the transfer lengths lengths decrease with increasing concrete strength. 60 Transfer Length at Release (in.) 50 y = 432.02x-1.19 40 R2 = 0.63 30 y = 115.53x-0.83 20 R2 = 0.71 10 0 0 2 4 6 8 10 12 14 Concrete Strength at Release (ksi) Figure 3.30. Transfer lengths versus concrete strengths for 0.5-in. Strand D at release and at 240 days. 60 Transfer Length at Release (in.) 50 y = 156.73x-0.75 40 R2 = 0.87 30 y = 68.78x-0.56 R2 = 0.68 20 10 0 0 2 4 6 8 10 12 Concrete Strength at Release (ksi) Figure 3.31. Transfer lengths versus concrete strengths for 0.6-in. Strand A6 at release and at 240 days.