Details of the Study on the Use of 0.7-in Diameter Strands in Precast Pretensioned Girders (2022)

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1 Appendix A Design Procedure Used for Parametric Study The cross-sectional properties and geometry of the selected sections are provided in Table A.1 and Figure A.1, respectively. Table A.1 Cross-sectional properties Girder Depth (in.) A (in. 2) I (in. 4) yb (in.) tweb (in.) Single web girders AASHTO-PCI BT-54 54 659 268,077 27.6 6 AASHTO-PCI BT-63 63 713 392,638 32.1 AASHTO-PCI BT-72 72 767 545,894 36.6 AASHTO Type VI 72 1,085 733,320 36.4 8 Florida FIB-96 96 1,267 1,515,000 42.8 7 Nebraska NU-900 35.4 648 110,262 16.1 5.9 Nebraska NU-1100 43.3 695 182,279 19.6 Nebraska NU-1600 63.0 811 458,482 28.4 Nebraska NU-2000 78.7 904 790,592 35.7 Ohio WF-36 36 878 145,592 18.2 8 Ohio WF-54 54 1,022 412,056 27.0 Ohio WF-72 72 1,166 844,069 35.8 Washington WF74G 74 924 734,356 35.7 6-1/8 Washington WF100G 100 1,083 1,524,912 48.3 Double web girders AASHTO BIV-48 48 843 203,088 20.8 5 NEXT 40D 40 1,859 258,217 26.6 tapered 13 - 15 Texas U-40 40 980 183,108 16.3 5 Texas U-54 54 1,120 403,020 22.4 Washington U54G5 54 1,111 314,382 19.8 7 Washington UF60G5 60 1,280 519,561 24.7 Washington UF72G 72 1,449 844,135 30.3

2 Figure A.1 Cross-sections of girders in design case study

3 Figure A.1 Cross-sections of girders in design case study (cont.) The design procedure programmed into the Excel spreadsheet is summarized in the flow chart shown in Figure A.2. This figure and steps below describe the procedure followed: 1. The girder is filled with as many straight strands as geometrically possible, and the span is increased until either SERVICE I or SERVICE III limits are reached at the midspan or the STRENGTH I limit is met; from this the maximum achievable span is determined. Four top strands providing a total of 60-kip compressive force are used for all the cases. The four top strands are not included in STRENGTH I limit state calculations as is customary for prestressing strand on the compression side of a girder.

4 2. The tensile and compressive stress limits at prestress transfer and the SERVICE I and SERVICE III limits near the end of the girder are checked. If these stress limits are not exceeded, the design is complete based on Step 1. Otherwise, the design progresses to Step 3. If the stress limits at transfer are exceeded, the value of concrete strength at prestress transfer that would satisfy these limits, f’ci = ηf’c, is determined. This “side check” is akin to permitting the girder to cure further prior to prestress transfer in order to mitigate excessive stresses. The values used for design were f’ci = 0.8f’c for f’c ≤10 ksi or f’ci = 0.6 f’c for f’c >10 ksi. A value of η greater than 1.0 indicates that the design is controlled by concrete strength at release and f’c must be increased (or the span shortened). A value of η between 0.8 (or 0.6) and 1.0 indicates that the stress limits could be met by delaying release in order to increase concrete strength at transfer. Regardless of the outcome of this “side check”, all designs progressed using the values of f’ci = 0.8f’c or 0.6 f’c. 3. Using the design values for f’ci, debonding is attempted to remedy the Step 2 stress check(s) that is not satisfied while limiting the total debonding ratio, dr, to 25% and 40% in any single layer. If the stress checks are satisfied by this debonding, the design is complete. 4. If a successful design is not possible using debonding (Step 3), all strands are assumed to be bonded and harping is attempted to satisfy the Step 2 stress limits. Regardless of girder length, harp points are assumed to be 15 ft to either side of the girder center line. If more than eight strands had to be harped, second harp points are selected 19 ft to either side of the girder center line. If the stress checks are satisfied by harping, the design is complete. 5. If harping alone (Step 4) is not sufficient, a combination of harping and debonding is used to bring the Step 2 stresses within limits. Once again, the total debonding and debonding in a single layer are limited to 25% and 40%, respectively. The number of harped strands is kept as low as possible. If the stress checks are satisfied by a combination of harping and debonding, the design is complete. Strands in Texas U girders are not permitted to have harped strands. Hence, debonding strands up to the current limits was the only available method for keeping release stresses below the AASHTO limits for this girder type. 6. If the methods of mitigating stresses considered in Steps 3, 4, or 5 remain insufficient to satisfy the Step 2 stress limits, the span is shortened, and the process repeated with the shorter span until a design satisfying all stress limits is achieved. 7. Once an acceptable span is obtained, the required transverse reinforcement is determined. 8. A final design constraint is based on satisfying AASHTO LRFD Articles 5.9.4.4.1 and 5.9.4.4.2 dealing with splitting reinforcement and confinement near the ends of girders, and longitudinal reinforcement in AASHTO LRFD Article 5.7.3.5. The designs were based on limiting splitting reinforcement near the ends of the girders to No. 5 reinforcement with spacing not less than 2 in. While implemented, this step is not shown in Figure A.2since there are other possible means of mitigating this constraint.

5 Figure A.2 Design flow chart The aforementioned design steps were used to first design a girder for the maximum possible span at the minimum considered spacing of S = 6 ft (12 ft for double web girders), using 0.6-in. strands. New girders were designed using the same concrete strength, concrete density, and strand diameter while increasing the girder spacing by 2-ft increments until reaching the maximum spacing of 12 ft (16 ft for double web girders). The process was then repeated with 0.7-in. strands. The calculations shown assume the ability to safely harp 0.7-in. strands. The number of 0.7-in. harped strands was limited to one-half of the total straight strands (i.e., limited to one-third of the strands provided in the section). A similar practice is used in some states for 0.5-in. and 0.6-in. strands. Assuming multiple hold downs are not used, a limit is placed on the slope of harped strands to control the force to be resisted by hold-down devices. In some states (e.g., Washington), 1-on-6 and 1-on-8 are used as the limits for 0.5-in. and 0.6-in. harped strands, respectively. The difference is intended to account for the larger prestressing force, and therefore hold-down force, of 0.6-in. strands. Using this approach, a limit of 1-on-11 is obtained for 0.7-in. strands. All the girders meet the limits of 1-on-8 and 1-on-11 with the exception of: (a) BT-54, 10 ksi NWC, S=12 ft, 0.7 in.; (b) BT-63, 10 ksi LWC, S=12 ft, 0.7 in.; (c) BT-72, 10 ksi LWC, S=12 ft, 0.7 in.; (d) U54G5, 10 ksi LWC, S=16 ft, 0.6 in.; (e) U54G5, 10 ksi LWC, S=16 ft, 0.7 in.; and (f) WF100G, 18 ksi NWC, S=12 ft, 0.7 in. For either 0.6-in. or 0.7-in. strands, the bridge using U54G girders spaced at 16 ft had the shortest span, and the harped strands had a slope of 1-on-5. YES Determine maximum simple span, L, that can be achieved considering only: SERVICE I at midspan: fc < 0.45fc’ and 0.40 fc’; fps ≤ 0.8fpy SERVICE III at midspan: ft ≤ 0.19√fc’ STRENGTH I: fps ≤ fpu Straight 0.7 in. strands 4 top strands @ 15 kips each Check stresses near girder ends: SERVICE I: fc < 0.45fc’ and 0.40 fc’; fps ≤ 0.8fpy SERVICE III: ft ≤ 0.19√fc’ Design complete; all limits satisfied NO NO ASIDE: Calculate and report ηfc’ required to satisfy ft ≤ 0.24√fci Determine straight strand debonding ratio, dr, required to satisfy all the stress limits Stagger strand cut-offs = transfer length Check §5.7.3.5 can be satisfied dr < 0.25 Design complete; all limits satisfied, debonding required dr > 0.25 With no debonding Harp 0.7 in. strands to satisfy all the stress limits Harp points 15 ft from midspan 2 in. strand pattern maintained Satisfy the stress limits Design complete; all limits satisfied, harping required YES NO Combine harping and debonding (dr < 0.25) to satisfy all the stress limits Design complete; all limits satisfied, requiring combination of harping and debonding NO Shorten span length, L Satisfy the stress limits YES YES Check stresses near girder ends at prestress transfer: Tension: ft ≤ 0.24√fci Compression: fc ≤ 0.65fci fci = 0.8fc’ for fc’ ≤ 10 ksi; 0.6fc’ for fc’ > 10 ksi NO AND