Strand Debonding for Pretensioned Girders (2017)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

11 2.1 Research Approach A multiple component analytical study was carried out with the objective of demonstrating the effects of strand debonding on prestressed girder design and behavior. An initial analysis of present AASHTO limits to strand debonding based on two previously reported experimental programs was conducted (Section 2.2). Following this analysis, a parametric design study (Section 2.3) was undertaken in which preliminary designs of 1,392 girders were performed, of which 522 cases were selected for more detailed evaluation based on AASHTO LRFD Bridge Design Specifications provisions. The parameters considered in this study included (1) girder shape, (2) strand diameter, and (3) concrete strength. For each case, four amounts of total prestressing were considered: 100% of strands that may be located in the bulb or lower flange (Nmax) and approximately 75%, 50%, and 25% of this value. The results of this parametric study provided information for the decisions and selections made as the analytic and experimental programs progressed. An extensive FEM modeling program (Section 2.4) was developed with the goal of developing an analytical platform from which a deeper understanding of the local and global behaviors of prestressed girders containing partially debonded strands could be established. The result- ing 3D FEM platform significantly extended the parametric scope of the experimental study. Forty-four prototype girders (and some additional variations on these) were modeled, and their performance was evaluated. The FEM platform was validated using experimental data available in the literature, and its efficacy was further confirmed by accurately modeling the experimental behaviors observed in this study (Chapter 3). In the process of executing the analytical research, a number of additional questions arose. Issues associated with the transverse behavior of the bulb were addressed through an extensive STM-based study (Section 2.5), which included 9,408 design cases. The results of the STM study were used to refine detailing recommendations for prestressed concrete girders irrespective of strand debonding (Chapter 3). Finally, a question raised during the research regarding debonding of girders with highly skewed ends was addressed (Section 2.6) using techniques of fundamental mechanics and validated using the FEM platform developed for the research program. 2.2 Evaluation of Current AASHTO Limits on Strand Debonding The results from two previous studies are used to further understand the influence of strand debonding. These studies are presented in the following sections. C h a p t e r 2 Analytical Research Approach and Findings

12 Strand Debonding for pretensioned Girders 2.2.1 Shahawy et al. (1993) The recommended 25% debonding limit in the current AASHTO LRFD Bridge Design Specifi- cations is attributed to an experimental study by Shahawy et al. (1993). In this study, 32 full-scale prestressed girders were tested, including 8 girders with debonded strands: 4 having a debonding ratio, dr = 0.25 and 4 having dr = 0.50. Both the north and south ends of each girder were tested; thus, a total of 16 tests examined debonded conditions [although only 14 data points (7 girders) were reported]. Table 2.1 summarizes the failure loads observed for each test of a girder having debonded strands and the corresponding “control” girders having no debonding. The data indicate no clear trend, especially between the girders having dr = 0.25 and those having dr = 0.50; each failed at very similar loads. Shahawy et al. (1993) based their recommendation for limiting debonding to 25% on the failure modes of the 50% debonded girders, which were described as being less ductile. The Shahawy et al. test girders were designed based on the AASHTO Standard Specifications for Highway Bridges (1989), which did not require a check for longitudinal tension as is now required by AASHTO LRFD Article 5.8.3.5. After publication of the results of their tests for the fully bonded girders [Shahawy and Batchelor (1996)], Collins and Mitchell (1997) pointed out in a discussion that the girders did not meet the longitudinal reinforcement requirements implied by the modified compression field theory; these requirements were later adopted as AASHTO LRFD Article 5.8.3.5. A review of Shahawy et al. (1993) confirmed that the debonded girders did not meet the longitu- dinal reinforcement requirement of AASHTO LRFD Article 5.8.3.5. Thus, it is possible that the undesirable failure mode reported was the result of failing to meet the longitudinal tension steel requirements, which would most likely be accentuated by debonding strands in some girders. It is believed that the failure mode may have been different had additional, nonprestressed longi- tudinal reinforcement, as required by the current AASHTO LRFD Specifications, been provided. The effects of the specimens not meeting the longitudinal reinforcement requirements were evaluated, as follows: 1. The girder parameters (area of bonded prestressing steel; concrete strength; girder depth, h; shear depth, dv; etc.) were determined from Shahawy et al. (1993). The distance to the critical section, dc, was taken as dv from the center of bearing consistent with the 2016 version of the AASHTO LRFD Bridge Design Specifications. 2. The total shear (Vtotal) and moment (Mtotal) at the critical section, dc, were determined as the sum of the effects of the experimentally applied concentrated load (P) and the girder self-weight. 3. Using Vtotal and Mtotal at dc, the corresponding values of es, q, and b were calculated based on the current version of AASHTO LRFD Article 5.8.3.4.2. These values were used to calculate Vc. 4. The total shear resistance, Vn = Vc + Vs, was found and compared to the value of Vtotal. The value of P was iterated upon (Steps 2 and 3) until Vtotal = Vn. This value is the predicted shear capacity of the girder, Vn. 5. The longitudinal tension at the critical section was checked according to AASHTO LRFD Eq. 5.8.3.5-1, i.e., ≥ φ + φ −    0.5A f M d V Vps ps total v f total v s cot q (in these tests Nu and Vp were zero). The value of P was again iterated upon (and es, q, and b changed accordingly since q affects Vs) Test Series dr = 0 dr = 0.25 dr = 0.50North end South end North end South end North end South end A0-XX-R 313 276 281 173 not reported A2-XX-3R 257 312 253 170 200 160 C0-XX-R 176 180 237 123 233 127 C1-XX-R 177 196 164 143 158 133 Table 2.1. Failure load (kips) for Shahawy et al. (1993) tests.

analytical research approach and Findings 13 until the two sides of the equation are made equal. This new value of Vtotal is the predicted girder capacity if the failure is due to insufficient longitudinal steel at the critical section, VT@dc. 6. Finally, the longitudinal tension at the face of the support was checked according to AASHTO LRFD Eq. 5.8.3.5-2, i.e., ≥ φ −    0.5A f V Vps ps total v s cot q. Once again, the value of P was iterated upon until the two sides of the equation were made equal. This final value of Vtotal is the predicted girder capacity if the failure is due to insufficient longitudinal steel at the face of the support, VT@support. The three predicted values of shear to cause failure (Vshear, VT@dc, and VT@support) were compared to the experimentally reported shear values at failure, Vexp, at each section considered (dc and face of the support) for each girder reported by Shahawy et al. (1993). Figure 2.1 shows plots of the calculated and observed capacities for all three scenarios. Data falling “above” the 1:1 line indicate that the observed failure shear was lower than the calculated shear capacity; values falling below the 1:1 line indicate that the observed capacity exceeded the calculated capacity. Data for all girders for which data were available are shown; girders having debonded strands are shown with solid data points. The following observations are made: 1. Fifty-two of the 64 specimens tested did not achieve the shear strength capacity (Vn) predicted by AASHTO LRFD Bridge Design Specifications (2016) (Figure 2.1a). 2. The experimentally observed strength of the girders is best predicted by the available longitu- dinal steel tensile capacity of the girder at the critical section (VT@dc, shown in Figure 2.1b). This conclusion is consistent with the observations of Collins and Mitchell (1997). These girders were designed based on the Standard Specifications for which there was no requirement for minimum longitudinal steel. 3. The predicted capacity based on longitudinal tension at the face of the support (VT@support) is seen to be very conservative (Figure 2.1c). This observation is not unexpected. This provision (a) shear capacity (Vn) calculated using AASHTO LRFD Eq. 5.8.3.4.2 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450 Ca lc ul at ed S he ar C ap ac ity (k ips ) Observed Shear Capacity (kips) 25% debonding 50% debonding calculated capacity underestimates observed capacity calculated capacity overestimates observed capacity Calculated Observed = 1.31 Figure 2.1. Experimental and predicted shear capacities of Shahawy et al. (1993) girders. (continued on next page)

14 Strand Debonding for pretensioned Girders (c) shear capacity at face of support (VT@support) calculated using AASHTO LRFD Eq. 5.8.3.5-2 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450 )spik( ecaf tr opp us @ T n o desab yticapaC raehS detal uclaC Observed Shear Capacity (kips) 25% debonding 50% debonding calculated capacity underestimates observed capacity calculated capacity overestimates observed capacity Calculated Observed = 0.46 girders having '2-point loading' (b) shear capacity at critical section (VT@dc) calculated using AASHTO LRFD Eq. 5.8.3.5-1 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450 Observed Shear Capacity (kips) 25% debonding 50% debonding calculated capacity underestimates observed capacity calculated capacity overestimates observed capacity Calculated Observed = 0.81 d @ T n o desab yticapaC raehS detal uclaC cr it (ki ps ) Figure 2.1. (Continued). of the AASHTO LRFD Bridge Design Specifications assumes a linear bond relationship over the strand transfer length of 60db. This transfer length is known to be conservative resulting in an under-prediction of the tensile resistance provided in situ. 4. The predicted VT@dc and VT@support capacities (Figures 2.1b and c) of girders having debonded strands are lower than comparable girders reflecting the reduced Aps term in AASHTO LRFD Eqs. 5.8.3.5-1 and 5.8.3.5-2 due to the debonded strands. The fact that the experimentally observed capacity remains essentially unchanged, as shown in Table 2.1, further demonstrates

analytical research approach and Findings 15 that the debonding itself had little effect on girder capacity provided that the remaining bonded steel is adequate to resist the tension demand. 5. The data are inconclusive. It is not possible to conclude that debonding had no effect on the shear strength; however, it is also not possible to conclude that debonding was the only cause of premature shear failure. 2.2.2 Russell et al. (2003) As part of this study, both ends of three 72-in. deep bulb-tee girders were tested. Each beam had 24 strands with 6 strands debonded at the ends, resulting in 25% debonding. Confinement reinforcement in the bottom flange at the ends consisted of No. 3 bars at 6 in. spacing. One speci- men (BT6) was designed using the AASHTO Standard Specifications for Highway Bridges (1996). As such, no additional longitudinal reinforcement at the ends was included. The other two girders (BT7 and BT8) were designed using the AASHTO LRFD Bridge Design Specifications through the 2000 Interim Provisions, which required the addition of 8 No. 6 longitudinal bars at the ends. For specimen BT6, the load capacity was limited by strand slip. One end of girders BT7 and BT8 could not be tested to failure because the capacity of the test apparatus was reached. Up to the maximum load that could be applied, BT7 exhibited some slippage whereas BT8 did not. Testing to failure of the other end indicated no slippage in BT8 and some slippage in BT7. Both girders failed at the web-to-bottom flange interface with web crushing/spalling and horizontal shear. Russell et al. (2003) confirmed that if there is not sufficient longitudinal reinforcement, the strands will slip. This slippage results in a shear-bond failure not a shear failure. A number of the specimens (with 25% or 50% debonding) tested by Shahawy et al. (1993) also exhibited shear-bond failures. Shear-bond failures are not deemed to be a rational basis for limiting strand debonding provided the longitudinal reinforcement is adequate. 2.3 Design Case Studies In order to better understand the effects of debonding across a range of girder types and capacities, a parametric design study was undertaken. The parameters considered in the study (Table 2.2) included (1) girder shape, (2) strand diameter (db), and (3) concrete strength ( f c′). Composite slab thickness (t) and girder spacing (S) were constant for each girder type. For each case, four amounts of total prestressing were considered: 100% of strands that may be located in the bulb or lower flange (Nmax) and approximately 75%, 50%, and 25% of this value. All analyses were carried out considering the same loading in which permanent loads, DC, were taken as the girder self-weight, slab weight, and an additional 300 lb/ft to account for barrier wall loads (two 750 lb/ft barriers distributed over five girders). DW was taken as 35 psf (3-in. thick asphalt overlay). HL-93 live loading was assumed and the maximum moment calculated at midspan.1 Distribution factors were calculated for interior girders having two or more lanes loaded. 2.3.1 Determination of Maximum Girder Span The intent of this study was to evaluate large debonding requirements with girders being “stretched” to their maximum span lengths and capacities. The maximum girder span length for each section was taken as the greatest length satisfying AASHTO LRFD STRENGTH I, SERVICE I, 1 It is acknowledged that the maximum live load moment does not occur at the midspan; however, this assumption simplifies the calculations, and is a very close estimate of the maximum live load moment, especially for longer spans.

16 Strand Debonding for pretensioned Girders and SERVICE III requirements; that is, L = min[LSTRENGTH I, LSERVICE I, LSERVICE III] ≥ Lmin, in which each length is defined in the following sections. In the following equations, compressive stresses are taken as positive. 2.3.1.1 STRENGTH I The design capacity (fMn) of all girder sections was determined using plane section analysis software RESPONSE 2000 (Bentz 2000). From this, the maximum permissible span length of the girder (LSTRENGTH I) was determined as the greatest value of span length satisfying fMn/Mu ≥ 1.0 for the STRENGTH I load combination. 2.3.1.2 SERVICE I (AASHTO LRFD Articles 3.4.1 and 5.9.4.2.1) Under SERVICE I loading, compression stresses are limited to 0.45f c′ for the effects of the sum of effective prestress and permanent loads and to 0.60fc′ for the effects of the sum of effective prestress, permanent loads, and transient loads. The compressive stresses were computed as follows (Eqs. 2.1–2.2): Girder: −     + + + + ≤ ′ 1 0.45 Eq. 2.1a , ,NA f A e S M M S M M S fp pLT girder girder top of girder girder slab top of girder WS barrier wall top of girder composite c girder −     + + + + + ≤ ′ 1 0.60 Eq. 2.1b , ,NA f A e S M M S M M M S fp pLT girder girder top of girder girder slab top of girder WS barrier wall LL top of girder composite c girder Deck slab: + ≤ ′0.45 Eq. 2.2a , , M M S f WS barrier wall top of slab composite c slab Parameter Range of Values I girders Bulb-tees Adjacent and Spread Boxes U-girders Girder type Type II, IV and VI; WF36-49, WF54-49, WF72- 49, NU-900, NU- 1350, NU-1800 BT-54 BT-63 BT-72 BI-36, BII-36, BIV-36 BI-48, BII-49, BIV-48 T-U40 T-U54 W-U54G4 W-U66G4 W-U78G4 Total number of strands in section Nmax, 0.75Nmax, 0.50Nmax and 0.25Nmax S: Girder spacing 8 ft 8 ft 8 ft (spread) 4 ft (adjacent) 14 ft t: Cast-in-place slab thickness 8 in. 8 in. 8 in. (spread) 3 in. (adjacent) 8 in. L: Simple span length Minimum practical to the maximum possible value (Section 2.3.1) dr: Debond ratio (Section 2.3.2) 0 to 0.76 0 to 0.77 0 to 0.77 0 to 0.78 Concrete material properties f’c = compressive strength of concrete = 6, 8, 12, 15 ksi f’ci = concrete compressive strength at prestress transfer = 0.6f’c f’c (deck) = compressive strength of composite cast-in-place deck concrete = 5 ksi c = unit weight of all concrete = 0.15 kcf Strand db = 0.5-, 0.6-, 0.7-in. diameter low-relaxation strand fpu = ultimate strength of prestressing strand = 270 ksi and Eps = 28500 ksi strands are initially stressed to 0.75fpu = 202.5 ksi fpi = initial prestress at transfer = (0.9)0.75fpu = 182 ksi (10% loss at transfer) Long-term effective stress in the prestressing strand = 0.56fpu = 151 ksi Table 2.2. Range of values of parameters considered.

analytical research approach and Findings 17 + + ≤ ′0.60 Eq. 2.2b , , M M M S f WS barrier wall LL top of girder composite c slab The subscript “girder” refers to the properties of the precast girder alone whereas the subscript “composite” refers to the full composite section. From the calculations required for Eqs. 2.1 and 2.2, a maximum girder span length (LSERVICE I) was determined for the SERVICE I load combination. 2.3.1.3 SERVICE III (AASHTO LRFD Articles 3.4.1 and 5.9.4.2.2) Under SERVICE III loading, tension stresses in precompressed tension zones having bonded reinforcement, calculated by Eq. 2.3, are limited to 0.19√f c′. +  − − + ≥ − ′ 1 0.19 Eq. 2.3 , ,NA f A e S M S M M S fp pLT girder girder bottom of girder DC bottom of girder DW LL bottom of girder composite c girder Equation 2.3 was used to determine a maximum girder span length (LSERVICE III) for the SERVICE III load combination. 2.3.1.4 Minimum Girder Span Length At prestress transfer, the use of Nmax (particularly with 0.7-in. diameter strands) results in large compressive stresses in the bottom flange. In order to meet AASHTO specified compressive stress limits, a minimum girder span length (Lmin) is required so that the tensile stresses from the girder dead load (Mgirder) counteract these compressive stresses. However, the girder span length is also limited by STRENGTH I, SERVICE I, and SERVICE III requirements. A workable case cannot be identified if the span length from strength and service requirements is less than that required to decompress the heavily prestressed flange. This scenario occurred for many of the cases considered. 2.3.2 Debonding Ratio Having established the maximum girder span length, L = min [LSTRENGTH I, LSERVICE I, LSERVICE III] ≥ Lmin, the debonding requirement for each case may be determined. The maximum number of strands (Nt) that may be placed in the section and continue to satisfy the 0.24√f ′ci concrete tensile stress limit at prestress transfer at the location of the transfer length (Lt) is determined from (Eq. 2.4): −   ≥ − ′ 1 0.24 Eq. 2.4N A f A e S ft p pi girder girder bottom of girder ci The use of the 0.24√f ′ci limit requires the addition of nonprestressed steel to resist cracking. Significantly more debonding will be required if the lower tensile limit (requiring no additional steel) of 0.0948√f ′ci ≤ 0.2 ksi is adopted. Nt is a “property” of the section geometry and concrete strength at prestress transfer only. The concrete compression limit (Eq. 2.5) at prestress transfer of 0.6f ′ci was also checked at the transfer length (Lt) and, as expected, found not to control in any case. The required strand-debonding ratio in each case is, therefore, dr = 1 - Nt/N where N is the number of strands provided. Required debonding ratios were determined ranged up to greater than 75%. +  ≤ ′ 1 0.60 Eq. 2.5N A f A e S ft p pi girder girder bottom of girder ci

18 Strand Debonding for pretensioned Girders The concrete compression limit of 0.6f ′ci and tension limit of 0.24√f ′ci were also checked at midspan at the time of prestress transfer. In this calculation, the total number of strands in the section, N, was considered and the self-weight of the girder was included. The compressive and tensile stresses at midspan were determined from Eqs. 2.6 and 2.7, where the moment at midspan, Mgirder, is that resulting from the self-weight of the girder only (i.e., Mg = AgrcL2/8; where rc is the density of concrete). −   + ≥ − ′ 1 0.24 Eq. 2.6NA f A e S M S fp pi girder girder top of girder girder top of girder ci +  − ≤ ′ 1 0.60 Eq. 2.7NA f A e S M S fp pi girder girder bottom of girder girder bottom of girder ci For a number of cases with the largest number of strands (Nmax) and lowest concrete strength ( f ′c = 6 ksi), the top tensile stress at the midspan exceeded the AASHTO limit. These cases were not considered further. 2.3.3 Summary of Design Parameter Study Initially, 1,392 cases were considered based on combinations of the parameters shown in Table 2.2. From these, 522 cases (171 I girders, 218 box girders, and 133 U-girders) were identi- fied for further analyses using a series of MATLAB scripts written specifically for this project. The complete summary of analysis results is provided in Appendix B. Figure 2.2 summarizes the reinforcement ratio (r = Aps /Ag; where Aps is the total area of strands in the sections, bonded and unbonded, and Ag is the girder gross cross-sectional area) of these cases in terms of debonding ratio (dr) and span length normalized with respect to the girder depth (L/h). As expected, a larger amount of debonding is required for cases with a large value of r that correspond to those girders having a larger L/h ratio; i.e., girders for which flexure dominate the response. All of the selected cases required partial strand debonding, ranging between 3% and 77%. (The cases that satisfied the prestress transfer stress limits without partial debonding were not included in the analyses.) Debonding lengths were chosen to satisfy stress limits, and a 3-ft debonding increment was used. Additional nonprestressed reinforcement was added as required to satisfy the longitudinal reinforcement requirements of AASHTO LRFD Article 5.8.3.5. As a first attempt, No. 4 Gr. 60 reinforcing bars were considered. If No. 4 bars did not provide sufficient increase in the tensile strength, larger Gr. 60 bars (No. 5 and No. 6) were evaluated. The development lengths were checked and found to be adequate. It should be noted that it would not be possible to add additional steel for cases with 100% of strands in the bulb or lower flange, i.e., those with N equal to Nmax. In Figure 2.3, the ratio of available longitudinal resistance to tensile demand (Aps fps /T) is plotted against the debonding ratio (dr) and span normalized with respect to the girder depth (L/h). The following observations are made: 1. As expected, the value of Aps fps /T decreases as the level of debonding ratio (dr) increases. 2. The lowest values of Aps fps /T are for cases with the smaller values of L/h. This trend is also expected because the influence of shear, which increases the tensile demand (T), becomes more pronounced as L/h decreases. 3. Cases with the larger debonding ratios (dr) correspond to those with the smaller L/h. For example, based on the best linear fit through the results of all I girders, dr = 0.25 and 0.70

analytical research approach and Findings 19 (a) I girders and bulb-tees (b) box girders (c) U-girders Figure 2.2. Reinforcement ratio versus debonding ratio and normalized span length.

20 Strand Debonding for pretensioned Girders (a) I girders and bulb-tees (b) Box girders (c) U-girders Figure 2.3. Variation of Apsfps/T as a function of debonding ratio and normalized span length. (No nonprestressed reinforcement).

analytical research approach and Findings 21 approximately correspond to L/h = 23.2 and 10, respectively (Figure 2.4). This trend is attributed to the fact that longer girders have larger dead loads that counteract the effects of the prestressing force; hence, a short, heavily prestressed girder requires a higher degree of debonding. 4. The largest and smallest values of Aps fps /T are for box and U-girders, respectively. 5. There are no major differences between similar girder types. 6. Relatively few numbers of reinforcing bars were found to be necessary to remedy the tensile strength deficiency resulting from partially debonded strands. The maximum number of bars required for each girder type is as follows: a. I girders and bulb-tees: 9 No. 4 Gr. 60 for Type IV (L = 120 ft, f ′c = 15 ksi, dr = 0.72, 0.6-in. diameter stands, N ≈ 0.75Nmax) b. Box girders: 5 No. 4 Gr. 60 for BI-36 spread box (L = 45 ft, f ′c = 6 ksi, dr = 0.33, 0.7-in. diameter stands, N ≈ 0.25Nmax) c. U-girders: 10 No. 6 Gr. 60 Texas U40 (L = 95 ft, f ′c = 12 ksi, dr = 0.68, 0.7-in. diameter strands, N ≈ 0.50Nmax) 7. The box girders required the fewest amount of additional nonprestressed reinforcement; 25 cases, which correspond to 11% of the total number of box girders, required nonprestressed reinforcement. In the case of I girders and U-girders, nearly the same percentage of the total cases required some additional nonprestressed reinforcement: 32% (55 cases) for I girders and 33% (44 cases) for U-girders. While No. 4 Gr. 60 reinforcing bars sufficiently augmented the tensile capacity of I girders with partially debonded strands, No. 6 Gr. 60 reinforcement had to be provided for a number of U-girders. 2.4 Finite Element Method Modeling An extensive FEM modeling program was developed in this study with the goal of developing an analytical platform from which a deeper understanding of the local and global behaviors of prestressed girders containing partially debonded strands could be established. The resulting 3D FEM platform significantly extended the parametric scope of the experimental study, which was limited by time, financial resources, and specimen size. (No nonprestressed reinforcement) Figure 2.4. Interrelationship between Apsfps/T, dr, and L/h. (I girders with no nonprestressed reinforcement shown).

22 Strand Debonding for pretensioned Girders Commercial software was used to conduct all 3D FEM analyses. The software is focused on reinforced concrete structures and is widely used for both design and research. A summary of the FEM platform features is described in the following sections. A detailed description of the modeling technique and validation studies conducted is provided in Appendix C. 2.4.1 Development and Validation of 3D-FEM Model 2.4.1.1 Material Models A fracture-plastic model was employed to describe the behavior of concrete. The model— consisting of a fracture model based on a smeared crack formulation and crack band concept, and a plasticity model residing on a plastic failure surface—is intended to accurately capture concrete behavior in tension (fracture) and compression (crushing). By combining fracture and plasticity models, tensile strength reduction after concrete crushing and compressive strength reduction after concrete cracking are both taken into account. Additionally, the shear strength of cracked concrete was calculated based on the modified compression field theory (Vecchio and Collins 1986). Tension stiffening, based on the CEB-FIP model (1990), was also considered in the constitutive model used. Concrete modeling parameters were based on default values or values obtained from AASHTO-prescribed formulas. The only free parameter in the modeling conducted was the compressive strength of concrete. For nonprestressed reinforcement, the classical elasto-plastic material model was employed. Additionally, a rigid connection was assumed between concrete and reinforcement (i.e., “perfect bond” condition). For prestressing strands, a more accurate representation of the strand response, based on a Ramberg-Osgood model, was used to describe the nonlinear stress-strain relation. For strands, perfect bond is not realistic; indeed, bond slip can initiate immediately upon prestress transfer. A bond stress-slip model following the formulation of the CEB-FIP model (1990) was used to describe the mechanical interaction at the concrete-strand interface. The bond model was scaled such that it would result in prescribed transfer lengths of either a “realistic” value of 30db or the AASHTO-prescribed value of 60db (shown in Figure 2.5). The bond model calibrations were Figure 2.5. Representative example of pattern of bonded strands and longitudinal distribution in AASHTO Type IV girder—Case 1 shown.

analytical research approach and Findings 23 validated and a mesh-sensitivity study conducted using experimental data from Burgueño and Sun (2011), as described in Appendix C. 2.4.1.2 Structural Modeling In each model, the concrete of the girder was meshed with 3D hexahedral elements, while the reinforcement and prestressing strands were modeled with 3D truss elements. Their interaction is captured by the bond-slip model based on the relative displacement between the steel truss element and the surrounding hexahedral concrete element. The prestress of the strands was modeled in a manner similar to the practice of pre-tensioning. An external force required to generate the desired prestress was applied to each strand. After concrete was “cast” (concrete modeled with properties corresponding to those at prestress transfer), the external force was deactivated to simulate the prestress transfer. The construction of the slab was modeled similarly. Initially, the top slab was “deactivated” during girder construc- tion so that it would have no effect at prestress transfer. Following this step and an increase in the underlying girder concrete strength, the top slab load was first applied and then the slab was “activated” to work together with the girder to resist the simulated AASHTO-prescribed STRENGTH I and SERVICE I and III loadings. In this manner, the critical loading stages for the prestressed girder were modeled in a realistic manner. In addition to output files, the commercial software provides a post-processing interface to graphically illustrate the simulation results. The stress and strain in concrete and strands can be graphically demonstrated on the model, as well as the cracks shown. The software permits a threshold level of damage to be illustrated; that is, only damage (crack widths) greater than this threshold is shown in output graphics. This feature of the analysis software was used extensively in this report. Two FEM models of previous laboratory-tested girders (Hawkins and Kuchma 2007) were used to validate the FEM model. All FEM material properties and geometries were consistent with those reported, and the actual transfer length of 38db, determined from elastic shortening measurements, was used. In order to accurately capture the girder construction process, the analysis was divided into four loading phases: (1) casting girder (analysis step 1), (2) prestressing strand release (steps 2–7), (3) cast top slabs (step 8), and (4) external loading as described in Hawkins and Kuchma (steps 9–26). Details of the experimental girders and FEM modeling are provided in Appendix C. As shown in Appendix C, ultimate capacity and failure mode, load-deflection behavior at various locations along the spans, and crack patterns all indicated excellent agreement between the FEM-predicted and experimental behavior. In particular, the FEM model was able to capture the splitting failure associated with partial debonding of one girder. 2.4.2 FEM Parametric Study A parametric FEM study, aimed at accumulating the following information important to structural analysis and safety evaluation of prestressed girders with partially debonded strands, was conducted: 1. Crack patterns and stress distribution at the critical loading stages of prestress transfer, service conditions, and at ultimate load; 2. Effects of partial debonding on crack patterns and failure modes; and 3. The impact of local effects such as the debonding details and bond interface properties. A matrix of 44 3D models, shown in Table 2.3, was selected based on the outcome of the larger parametric design study described in Section 2.3 and Appendix B. Five girder shapes: AASHTO

24 Strand Debonding for pretensioned Girders Type IV, Nebraska NU-900, AASHTO BIV-48 (in adjacent box arrangement), Texas U-54, and BT-72 girders were considered. The effects of span, extent of partial debonding, concrete strength, and strand size on the structural performance of the girders were explored. For each girder, three critical loading phases were studied: prestress transfer, service (AASHTO SERVICE I and III), and ultimate (STRENGTH I) limit states. SERVICE and STRENGTH limit states considered live load arrangement intended to maximize either flexure or shear. Additionally, each model was “loaded to failure” (in both flexure and shear) to assess its ultimate capac- ity. A summary of key stress checks made in this study is presented in Table 2.4. A summary of the results of each analysis is presented in single-page summary matrices provided in Appendix D. 2.4.2.1 Modeling Parameters For consistency, a number of parameters and details are kept constant or consistent across all analyses. These parameters are described as follows: 2.4.2.1.1 Concrete Strength. Concrete strength, f ′c, is given in Table 2.3 for each model. In all cases, the concrete strength at prestress transfer was taken as fci = 0.6 f ′c, a conservative lower bound. The slab strength in every case is taken as f ′c,slab = 5 ksi, a value representative of in situ slab strength. 2.4.2.1.2 Prestressing Strand. Strand diameter, db, is given in Table 2.3 for each model. In all cases, 270-ksi low-relaxation strand was used. Initial prestress was taken as 0.75fpu = 202.5 ksi in every case. Long-term prestress accounting for all losses (but not bond slip, which is accounted f’c (ksi) AASHTO Type IV Nebraska NU-900 Case Strands dr L (ft) Case Strands dr L (ft) 6 - - - 8 9 14-0.6 14-0.7 0.14 0.43 55 65 8 1 34-0.5 0.59 85 10 11 12 30-0.5 14-0.6 14-0.7 0.33 0.00 0.29 70 55 65 12 2 3 4 66-0.5 50-0.5 34-0.5 0.73 0.64 0.47 115 100 85 13 14 15 60-0.5 44-0.5 30-0.5 0.53 0.36 0.07 100 85 70 15 5 6 7 66-0.5 50-0.5 34-0.5 0.70 0.60 0.41 115 105 85 16 17 18 19 60-0.5 44-0.5 30-0.5 60-0.6 0.47 0.27 0.00 0.67 100 85 70 115 AASHTO BIV-48 adjacent Texas U-54 6 20 21 22 46-0.5 34-0.5 23-0.5 0.57 0.41 0.13 120 105 85 33 42-0.5 0.45 80 8 23 24 25 46-0.5 34-0.5 46-0.6 0.52 0.36 0.65 120 105 140 34 35 63-0.5 42-0.5 0.57 0.36 95 80 12 26 27 28 29 46-0.5 34-0.5 46-0.6 46-0.7 0.35 0.12 0.57 0.70 120 105 145 165 36 37 38 85-0.5 63-0.5 42-0.5 0.60 0.46 0.19 110 95 85 15 30 31 32 46-0.5 46-0.6 46-0.7 0.22 0.52 0.65 120 145 165 39 40 41 42 85-0.5 63-0.5 42-0.5 85-0.6 0.53 0.37 0.05 0.71 115 95 85 135 AASHTO BT-72 15 43 44 38-0.7 28-0.7 0.63 0.50 135 115 dr = debonding ratio Table 2.3. Cases for 3D FEM analytical study.

analytical research approach and Findings 25 for directly in the model) was taken as 0.56fpu = 151.2 ksi in all cases. Strand bond parameters were calibrated such that the transfer length would be 60db. 2.4.2.1.3 Partial Debonding. The maximum partial dr for each model is given in Table 2.3. This value is the dr at the girder end. Partially debonded strands were introduced (bonded) into the cross section in three approximately equal increments of 3 ft each. Thus, at a location 9 ft into the span, all strands in the section were bonded. Figure 2.5 shows an example for Case 1, an 85-ft long Type IV girder having 34 strands, 20 of which are partially debonded (dr = 0.59). The debonding pattern used in each analysis is summarized in the respective summary matrix (Appendix D) and is generally consistent (except in cases with very large debonding ratios) with the proposed detailing guidelines (Chapter 4). The overall girder behavior was not significantly affected by the strand debonding pattern used; strand debonding patterns primarily affected local transverse stresses in the bulb as discussed in Section 2.5. 2.4.2.1.4 Shear Reinforcement. Shear reinforcement was modeled as discrete bars in all cases and included both vertical web reinforcement (extending into the slab) and bulb or flange confinement reinforcing appropriate for the girder shape. All shear reinforcement was assumed to have a yield strength of fy = 60 ksi. Shear reinforcement details are given in each summary matrix (Appendix D). 2.4.2.1.5 Boundary Conditions. All girders were modeled as simply supported beams having a full-width 12-in. long rigid bearing supported by a pin at one end and a roller at the other. Full width is understood to mean the full width of the bottom flange less a distance accounting for the chamfer, typically 2 in. on both sides. This arrangement allowed realistic rota- tion at the girder end during prestress transfer and reasonably mimics neoprene-bearing pads, once the girder would be placed in service. The entire cross section of all girders, except BIV-48, was modeled. A half section of BIV-48 was modeled having boundary conditions along the line of symmetry that enforce the assumed plane sections behavior of the box section. 2.4.2.1.6 Applied Loads. In all the analyses, permanent loads (DC) included girder self- weight, slab weight, and an additional 300 lb/ft to account for barrier wall loads (two 750 lb/ft Location Along Girder Length Criteria At Prestress Transfer STRENGTH I SERVICE I and III Near support (At support face, dv/2 and dv) Concrete tension ft 0.24 f’ci 1 Not checked Not checked Prestressing steel Not checked T Apsfps HL-93 loading for shear strand is not developed at this location; thus, fps < fpu OK if satisfied for STRENGTH I At midspan Concrete tension ft 0.24 f’ci 1 Not checked At SERVICE III ft 0.19 f’c HL-93 loading for flexure Concrete compression fc 0.60f’ci Not checked At SERVICE I fc 0.45 f’c permanent load fc 0.60 f’c HL-93 loading for flexure Prestressing steel OK if satisfied for STRENGTH I T Apsfpu HL-93 loading for flexure OK if satisfied for STRENGTH I 1It will be additionally noted if ft ≤ 0.0948 f’ci ≤ 0.2 ksi. Table 2.4. Stress criteria checked in 3D FEM models.

26 Strand Debonding for pretensioned Girders walls distributed over five girders). An additional wearing surface load (DW) is taken as 35 psf (3-in. thick asphalt overlay). HL-93 live loading (LL), considering appropriate distribution factors and vehicle placement for moment or shear, was used in all analyses. AASHTO impact loads (IM) were included in all the appropriate cases. 2.4.2.1.7 Modeling Steps. As described previously, modeling followed the typical order of prestressed concrete construction. Six primary steps are summarized in Table 2.5. Release of tendons and application of loads were introduced over a number of substeps to permit load redistribution. No inertial properties were modeled; therefore, tendon release was assumed to be “slow,” having no impact or dynamic effects. Application of vehicle loads in Steps 5 and 6 were repeated with the vehicle located on the span to maximize the effects for either flexure or shear, consistent with AASHTO design requirements. In both cases, Step 6 incrementally increased the HL-93 axle loading above the STRENGTH I limit state condition (Step 5) until girder failure. Therefore, the value of a shown in Table 2.5 was greater than 1.75 (the STRENGTH I limit state). Due to the complexity of modeling the loads, the lane portion of the HL-93 was not increased above the STRENGTH I limit state (i.e., the lane load was “constant” having an applied load factor of 1.75). 2.4.2.1.8 Model Conventions. All FEM models simulated the entire girder span, the appropriate effective slab width, and were symmetric about midspan. The origin was defined at the midspan soffit. Thus, in all figures showing only half the span, the axis labels indicate the midspan of the girder. All vehicle loads were applied such that the left end (as shown in figures) of each girder is critical. When half spans are shown, it is the west end of the girder and the longitudinal profiles are not to scale: the vertical dimension was stretched to enhance clarity. Figure 2.6 illustrates the details of representative commercial software models for each girder shape considered. 2.4.2.2 Simulation Summary Detailed model information, stress distributions, crack patterns, and local responses of each girder model are provided as single-page summary matrices in Appendix D. A summary of all checks (described in Table 2.4) is provided in Table 2.6. Values shown in bold text indicate that the value fails the check; otherwise, all stresses and ratios presented pass the AASHTO-prescribed stress checks. The stress checks summarized in Table 2.6 are as follows. 2.4.2.2.1 Prestress Transfer. The tension (T) check verifies that at no location along the girder does the concrete tensile stress exceed the AASHTO-prescribed limit, that is, ft ≤ 0.24√ f ′ci [in this case, ft ≤ 0.24√(0.6 f ′c)]. This limit is usually associated with cracking at the top surface of the Step Description Applied Loads Concrete Strength External Prestress Internal Prestress 1 “Cast” concrete None N.A. 0.75fpu N.A. 2 Release tendons Girder only fci = 0.6f’c 0 0.9(0.75fpu)1 3 Place slab Girder and slab f’c 0 0.56fpu 4 SERVICE I SERVICE III DC+DW+(LL+IM) DC+DW+0.8(LL+IM) f’c 0 0.56fpu 5 STRENGTH I 1.25DC+1.50DW+1.75(LL+IM) Flexure and shear f’c 0 0.56fpu 6 Failure 1.25DC+1.50DW+ 1.75(LLlane) + (LLtruck+IM) Flexure and shear f’c 0 0.56fpu 1Losses upon transfer were determined within FEM model based on the provided bond slip model; in general, losses were approximately 10% of the initial prestress force. Table 2.5. FEM modeling steps.

analytical research approach and Findings 27 (a) Type IV girder (b) NU-900 girder (c) BIV-48 girder (half-section model) (d) U-54 girder (e) BT-72 girder Figure 2.6. Representative ATENA models showing complete girder (left) and west half span and section (right).

Model Parameters (See Table 2.3) Stress Checks (See Table 2.4) Ultimate CapacityAt Prestress Transfer SERVICE STRENGTH I T C I III Flexure Cracking Shear Flexure Shear Case f’c db N L dr S ft fc ft fc Cracking Aps fps/T at section: ksi in. no. ft - ft ksi ksi ksi ksi Support dv/2 dv See App. D AASHTO Type IV girders 1 8 0.5 34 85 0.59 8 0.28 2.16 0.21 1.50 minor none 0.79 1.01 1.12 3.15 4.75 2 12 0.5 66 115 0.73 0.39 4.00 0.35 2.83 none none 0.74 1.02 1.09 3.75 4.75 3 12 0.5 50 100 0.64 0.38 3.38 0.33 2.30 none none 0.70 1.01 1.11 3.05 5.55 4 12 0.5 34 85 0.47 0.43 2.45 0.26 1.53 minor none 0.74 1.04 1.15 2.95 5.35 5 15 0.5 66 115 0.70 0.42 4.17 0.36 2.87 none none 0.71 1.02 1.10 3.45 5.15 6 15 0.5 50 105 0.60 0.47 3.34 0.31 2.27 minor none 0.70 1.03 1.11 3.05 4.75 7 15 0.5 34 85 0.41 0.53 2.51 0.30 1.62 minor none 0.73 1.05 1.14 3.00 5.35 Nebraska DOT NU-900 girders 8 6 0.6 14 55 0.14 8 0.33 1.56 0.17 1.12 some minor 0.63 0.89 0.99 2.75 3.15 8A Case 8 with additional As = 0.88 in.2 0.31 1.58 0.17 1.12 some minor 0.69 0.98 1.08 2.75 3.20 9 6 0.7 14 65 0.43 0.23 1.94 0.15 1.01 some minor 0.62 0.82 0.96 1.95 3.75 9A Case 9 with additional As = 1.32 in.2 0.23 1.99 0.15 1.01 some minor 0.71 0.99 1.10 2.00 3.80 10 8 0.5 30 70 0.33 0.26 2.16 0.28 1.31 some none 0.77 1.02 1.04 2.55 3.35 11 8 0.6 14 55 0.00 0.28 1.85 0.21 1.31 some minor 0.65 0.93 1.01 2.15 3.35 11A Case 11 with additional As = 0.62 in.2 0.30 1.78 0.21 1.31 some minor 0.69 0.99 1.07 2.15 3.45 12 8 0.7 14 65 0.29 0.32 2.03 0.18 1.26 some minor 0.64 0.81 0.96 2.55 3.75 12A Case 12 with additional As = 1.32 in.2 0.31 2.08 0.18 1.26 some minor 0.74 1.01 1.10 2.55 3.75 13 12 0.5 60 100 0.53 0.31 3.73 0.58 2.40 some some 0.74 1.00 1.02 2.55 3.35 13B Case 13 with all debonded strands introduced at one 0.26 3.90 SERVICE and STRENGTH load cases not run location (6 ft) 14 12 0.5 44 85 0.36 0.33 3.01 0.43 1.90 some none 0.70 1.01 1.05 2.15 3.55 15 12 0.5 30 70 0.07 0.35 2.34 0.31 1.82 some none 0.69 1.02 1.06 2.15 3.55 16 15 0.5 60 100 0.47 0.36 3.81 0.72 2.45 some none 0.70 1.02 1.03 2.15 4.15 17 15 0.5 44 85 0.27 0.39 3.06 0.45 2.08 some none 0.69 1.02 1.04 2.15 3.75 18 15 0.5 30 70 0.00 0.38 2.86 0.33 2.00 some none 0.62 1.03 1.07 2.15 3.15 19 15 0.6 60 115 0.67 0.36 5.07 0.51 4.80 minor minor 0.75 1.03 1.09 2.35 3.85 AASHTO BIV-48 adjacent box girders 20 6 0.5 46 120 0.57 4 0.16 2.67 0.08 2.22 none none 0.72 1.02 1.05 3.55 6.15 21 6 0.5 34 105 0.41 0.17 2.03 0.09 1.77 none none 0.72 1.01 1.09 3.95 6.55 22 6 0.5 23 85 0.13 0.19 1.82 0.14 1.52 none none 0.70 1.00 1.12 3.15 4.35 23 8 0.5 46 120 0.52 0.26 2.80 0.10 2.23 none none 0.72 1.01 1.06 4.75 5.75 24 8 0.5 34 105 0.36 0.23 2.10 0.12 1.70 none none 0.72 1.02 1.10 3.75 7.35 25 8 0.6 46 140 0.65 0.22 3.70 0.14 2.30 none none 0.79 0.99 1.01 4.95 7.15 26 12 0.5 46 120 0.35 0.33 2.89 0.15 2.26 none none 0.71 1.02 1.09 3.75 8.75 27 12 0.5 34 105 0.12 0.32 2.27 0.18 1.89 none none 0.70 1.02 1.14 3.15 6.15 28 12 0.6 46 145 0.57 0.30 3.93 0.13 3.24 none none 0.65 0.98 1.00 4.55 8.75 29 12 0.7 46 165 0.70 0.30 5.24 0.21 3.48 none none 0.68 0.90 0.95 5.15 7.35 29A Case 29 with additional As = 1.32 in.2 0.22 5.24 0.21 3.48 none none 0.75 1.01 1.05 5.20 7.35 30 15 0.5 46 120 0.22 0.38 2.91 0.20 2.52 none none 0.71 1.03 1.13 3.55 7.15 31 15 0.6 46 145 0.52 0.42 4.04 0.18 3.26 none none 0.76 0.98 1.04 4.15 6.55 31A Case 31 with additional As = 0.44 in.2 0.30 4.20 0.18 3.26 none none 0.78 1.00 1.07 4.15 6.55 32 15 0.7 46 165 0.65 0.35 5.25 0.19 3.54 none none 0.64 0.89 0.97 5.55 8.35 32A Case 32 with additional As = 0.26 5.48 0.19 3.54 none none 0.70 1.00 1.07 5.50 8.35 1.32 in.2 Texas DOT U-54 girders 33 6 0.5 42 80 0.45 14 0.26 1.85 0.14 2.36 some minor 0.69 1.00 1.12 2.55 4.75 34 8 0.5 63 95 0.57 0.29 2.67 0.20 3.19 some none 0.67 1.01 1.14 3.35 5.00 35 8 0.5 42 80 0.38 0.29 1.89 0.17 2.31 some minor 0.71 1.00 1.13 2.75 4.75 36 12 0.5 85 110 0.60 0.32 3.68 0.19 4.00 minor none 0.73 1.01 1.14 3.35 5.60 37 12 0.5 63 95 0.46 0.35 2.69 0.31 3.16 some none 0.76 1.01 1.13 2.35 4.75 38 12 0.5 42 85 0.19 0.36 2.01 0.51 2.48 some some 0.73 1.01 1.16 1.75 3.35 39 15 0.5 85 115 0.53 0.46 3.73 0.21 4.27 some none 0.75 1.01 1.15 2.95 5.35 40 15 0.5 63 95 0.37 0.41 2.71 0.23 3.18 minor none 0.72 1.01 1.13 3.15 5.55 41 15 0.5 42 85 0.05 0.41 2.30 0.62 2.89 some some 0.70 1.01 1.18 1.95 2.75 42 15 0.6 85 135 0.71 0.42 4.98 0.23 6.09 minor none 0.69 1.00 1.00 2.75 5.55 BT-72 girders 43 15 0.7 38 135 0.63 8 0.32 5.38 0.26 4.43 minor minor 0.69 1.05 1.14 5.45 7.50 44 15 0.7 28 115 0.50 0.35 4.92 0.29 3.18 some minor 0.67 1.03 1.12 5.50 8.80 Table 2.6. Summary of FEM simulation stress checks and predicted ultimate capacity.

analytical research approach and Findings 29 girder near the girder end, as is clearly shown in the crack patterns at prestress transfer shown in Appendix D. For all cases considered (except 20 and 21) 0.0948√ f ′ci < ft ≤ 0.24√ f ′ci; therefore, nonprestressed reinforcement satisfying the requirements of AASHTO LRFD Table 5.9.4.1.2-1 is required in the region of tensile stress. All cases shown in Table 2.6 satisfy the ft ≤ 0.24√f ′ci limit; indeed the drs were selected to ensure this requirement would be met. It is noted that the required additional tensile steel needed to control cracking was not provided in the models since the intent of this study was to assess the effectiveness of the debonding alone to mitigate these tension stresses. The compression (C) check verifies that at no location along the girder does the concrete com- pressive stress exceed the AASHTO-prescribed limit, that is, fc ≤ 0.60f ′ci (in this case, fc ≤ 0.36 f ′c). As indicated in Table 2.6 by bold entries, a few BIV girders fail this check; these cases would likely be considered impractical spans, but were included in this study in order to capture the full range of potential behavior. In each case that failed this check, considering a higher concrete strength at prestress transfer would result in the stress limit being satisfied. For example, Case 23 ( fc = 2.80 ksi ≤ 0.60 f ′ci; where f ′ci = 3.6 ksi) closely replicates Case 20 ( fc = 2.67 ksi > 0.60 f ′ci; where f ′ci = 4.8 ksi) but with a higher concrete strength; the compressive stress check passes in the latter case. Images of the cracking at prestress transfer are shown in the individual simulation summaries in Appendix D. A crack threshold of 0.000 in. is used to illustrate cracking; therefore, any predicted cracking, regardless of size, is indicated. The maximum crack size observed is also noted. 2.4.2.2.2 SERVICE I Limit State. The SERVICE I check verifies that at no location along the girder do the concrete tensile stresses exceed the AASHTO-prescribed limit, that is, ft ≤ 0.19√ f ′c. The SERVICE III check verifies that at no location along the girder do the concrete compressive stresses exceed the AASHTO-prescribed limits, that is, fc ≤ 0.45f ′c under the effects of permanent load and fc ≤ 0.60 f ′c under the effects of HL-93 loading for flexure. All girders performed adequately under SERVICE I and SERVICE III loading. 2.4.2.2.3 STRENGTH I Limit State. The primary consideration at the STRENGTH I limit state is the performance of the strands. Since the girder spans were selected based on satisfying moment capacity of the section, all sections perform adequately at the section under maximum moment. Similarly, since the spans were intentionally stretched in this study to maximize the utilization of a section, shear capacity is also adequate. The focus of this study was to evaluate the ability of the strands to develop the required tensile forces near the girder supports. The criterion, in this case, is that the tensile force, T, developed in the strands exceeds that available: Aps fps. Near the supports, debonded strands are not included in the Aps term and strands that have not been fully developed may only contribute a strand force fps that is less than fpu. In Table 2.6, this check has been expressed as the calculated ratio Aps fps/T. A value exceeding unity indicates that the check is satisfied. This check is made at three sections: the face of the support, and at distances of dv/2 and dv from the face of the support, where dv is the shear depth of the member. The distance dv from the face of the support is considered the critical section for shear (AASHTO LRFD Article 5.8.3.5). As indicated in Table 2.6 by bold entries, all girders fail this check at the face of the support although most satisfy this requirement at a distance of dv/2 from the support face. In the FEM analyses conducted, which captured the effects of strand slip, this behavior indicates that while there may be localized strand slip in the strand transfer length, adequate residual bond remains to develop the strand further along its length. That is, the effect of the strand bond capacity being exceeded at the face of the support does not lead to failure of the girder; indeed most girders demonstrated significant reserve shear capacity beyond the STRENGTH I limit state as described below.

30 Strand Debonding for pretensioned Girders Some BIV and NU-900 sections also fail to meet the Aps fps/T ≥ 1.0 criterion at dv/2 and dv. Despite not meeting the criterion, redistribution is adequate such that significant reserve capacity is still available. Most girders meet the strand tension requirement at dv. Since the girder details were selected to maximize capacity while still generally meeting strand tension limits, the results are a vindication of the design approach used to maximize the girder spans in the first place. For those BIV girders in which Aps fps /T < 1.0, the debonding ratios are all quite high: dr = 0.52, 0.57, 0.65 (two cases), or 0.70. For the NU girders that fail this check, however, the debonding ratios are generally lower, some respecting current AASHTO limits (dr < 0.25): dr = 0.00, 0.14, 0.29, 0.43, or 0.67. In the FEM study, the support lengths were taken as only 12 in. and no overhang behind the support (allowing a longer transfer length) was provided. Methods of mitigating the low tensile capacity at the support face include providing supplemental nonprestressed reinforcing steel (As fy in AASHTO LRFD Eq. 5.8.3.5-2) or providing additional anchorage for the strand in either an overhang or by embedding it in an integral abutment or diaphragm (effectively increasing fps). 2.4.2.2.4 Ultimate Capacity. Following the STRENGTH I limit state, the HL-93 axle loads were increased. The value of a shown in Table 2.6 corresponds to the live load factor to cause girder failure, i.e., 1.25DC + 1.50DW + 1.75(LLlane) + a(LLtruck + IM). The values for critical flexure and shear are provided for all cases. Since girder span length was stretched, it should be expected that all girders are “flexure critical,” that is, the value of a causing failure is lower for flexure than for shear. The predicted ultimate behavior for all girders subjected to flexural-critical loading is an expected flexural mode of failure. Most analyses indicate prestressing strand strains in excess of 1%. Crushing of the slab is evident primarily in girders having lower concrete strength (the lower girder modulus leads to greater top flange compression strains and, therefore, crushing of the lower-strength composite slab). Ten of the 44 girders demonstrated flexure-shear failures in which, typically near girder ends, shear distress accompanies the dominantly flexural tension failure. Girders that exhibited flexure-shear failures generally had higher debonding ratios (0.14, 0.29, 0.33, 0.43, 0.53 [twice], 0.60, 0.67, 0.70, or 0.71); thus, the strand tension capacity, T, likely played a role in the shear component of the predicted flexure-shear failure. Considering the NU girders, all of those that failed the Aps fps /T ≥ 1.0 check at the STRENGTH I limit state also demonstrated flexure-shear failures. None of the BIV girders, however, demonstrated significant shear distress in their ultimate behavior, perhaps due to the proportionally larger web area of such sections (especially compared to the thin-webbed NU section). The ultimate behavior under shear loading is more informative and appears to identify a few trends. As shown in Figure 2.7, four primary modes of failure were observed (top down in Figure 2.7b and c): (1) single dominant shear band or strut associated with an axle load (19 cases), (2) distributed shear cracking (10 cases), (3) flexure-shear behavior (6 cases), and (4) flexural tension or strand yield (9 cases). As seen in Figure 2.7b, shear failures are dominant in girders having greater debonding ratios. Additionally, higher debonding ratios tended toward the formation of single crack bands. Shear failure corresponds to a failure of the Aps fps /T ≥ 1.0 criterion at the critical section for shear. Nonetheless, one must be careful with this conclusion because girders having higher debonding ratios are naturally those with a higher prestress reinforcing ratio (r = NAps/Ac) (Figure 2.7a). Such girders are “over-reinforced” for flexure and, therefore, are expected to have a shear-dominated behavior. The corollary of this observation is that those girders having a low prestress reinforcing ratio (and therefore lower debonding requirements) tend to fail in a flexural mode of behavior. These trends are exhibited graphically between Figures 2.7a and b.

analytical research approach and Findings 31 2.4.2.2.5 Performance of Different Girder Cross Sections. Little difference was observed in the overall behavior of AASHTO Type IV and NU-900 girders. Generally, NU girders when “stretched” to their longest practical spans exhibited lower concrete stresses at prestress transfer—indicating less need for debonding. NU girders also had proportionally lower ulti- mate capacities and therefore exhibited greater cracking at the STRENGTH I limit state. These comparisons reflect the “more efficient” section of the NU family of girders as compared to the AASHTO type girders. The NU-900 girders that failed the Apsfps/T ≥ 1.0 criteria had few larger diameter strands near their support. The larger strands have longer transfer lengths and, hence, the fps term is developed more gradually along the girder span. In each of the cases, the Aps term is also relatively low near the support. Both Type IV and NU-900 girders exhibited limited evidence of longitudinal web cracking at the girder ends resulting from prestress transfer. Such cracking is occasionally observed in the field and is associated with large prestress forces (Kannel et al. 1997). The BIV-48 girders behaved well—illustrating no cracking exceeding 0.016 in. at the STRENGTH I limit state and proportionally larger ultimate capacities. Due to the greater com- bined web dimension, ultimate shear capacity was quite high. Stresses at prestress transfer for the BIV-48 girders were consistent with all other girders considered. The BIV-48 girders that failed the Aps fps /T ≥ 1.0 criteria did so for a very different reason than the NU-900 girders. The BIV girders that failed were all very long (between 140 and 165 ft) resulting in relatively large flexural demands. Due to their length, the shear load case results in minimal flexural demand; the shear capacity is, therefore, quite high, driving up the strand tension demand, T. The BIV-48 girders that failed the Aps fps/T ≥ 1.0 criteria all had very high ultimate shear capacities in which the value of a exceeded 7. 2.5 Strut-and-Tie Modeling of End Regions It is important to note that although the issue of longitudinal splitting described was identified and initially associated with a case of strand debonding (Section 2.5.1), the issue is not restricted to girders having debonded strands. Rather, the contents of this section must be interpreted to apply to the pattern of bonded strands at a girder end, irrespective of the presence of debonded strands. (a) Greater prestress reinforcing ratio results in greater debonding ratio (b) Debonding ratio and failure mode (c) Representative failure modes (horizontal and vertical scales vary) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.00 0.01 0.02 Prestress reinforcing ratio, 0.0 0.2 0.4 0.6 0.8 Debonding ratio, dr Flexural tension Flexure-shear Distributed shear Single shear band Case 42 Case 13 Case 37 Case 38 D eb on di ng ra tio , d r ρ = Aps/Ag Figure 2.7. Qualitative relationship between prestress reinforcing ratio, dr, and ultimate failure modes for cases having no additional nonprestressed reinforcement (i.e., no cases labeled A in Table 2.6).

32 Strand Debonding for pretensioned Girders 2.5.1 Motivating Example Partial debonding of strands is required to reduce concrete stresses and mitigate cracking in girder end regions. Nonetheless, the details associated with partial debonding can, in fact, cause local cracking and potentially lead to early and abrupt ultimate-limit-state failure, particularly at girder ends (Ross et al. 2013). This effect was illustrated in one test specimen reported by Hamilton (2009) in a study focusing on enhancing the shear performance of existing girders using fiber-reinforced polymer (FRP) materials. Although the Hamilton study is beyond the scope of the reported research, a critical serviceability issue was identified. Hamilton (2009) considered specimens designed to replicate in-service Type IV girders. Of interest is the fact that the partial debonding provided violated Article 5.11.4.3 of the AASHTO LRFD Bridge Design Specifications (2012) by having 57% of all strands debonded, as seen in Figure 2.8b. Additionally, the debonded strands were all in the middle of the section and the 18-in.-wide bearing pad did not extend beneath the remaining bonded strands (Figure 2.8). As a result, the compressive strut resulting from the application of a shear load was required to spread from the web to engage the outermost bonded strands and “return” back inward to be reacted at the bearing pad. This transfer necessitates the formation of a transverse tie as shown schematically in Figure 2.8c. As can be seen in Figure 2.8a, the presence of this tie resulted in vertical cracks through the bulb. Additionally, the compressive thrust appears to have “cracked out” or “pushed off” the cover concrete on the left side of the bulb (Figure 2.8a). 2.5.2 STM of Prestressed Girder End Region Ross et al. (2013) proposed an STM approach, as an alternative to extant prescriptive detail requirements, for designing bulb confinement reinforcement to mitigate lateral splitting failures at the ultimate limit state. The STM proposed by Ross et al.(2013) is similar in geometry to that proposed here but with significantly greater simplification that makes the investigation of the effects of strand pattern not feasible. In the present work, no such simplification is made; in fact, the analyses conducted for this project uses what Ross et al. (2013) ultimately recommended: “. . . the strut angle must be calculated directly.” An STM provides a simple yet effective tool to investigate the local effects of the pattern of bonded strands (and, by extension, debonding pattern) on cracking at the ends of girders. The following assumptions are typical of the STM approach and permit the 3D STM at the end of the girder (Figure 2.8c) to be modeled as a two-dimensional STM as shown: 1. All sections and STMs are symmetric about the vertical centerline of the girder cross section. 2. The horizontal strands are sufficient to anchor the inclined strut in the longitudinal direction of the girder. With this assumption, the angle of this strut does not affect the 2D (cross sectional) STM from capturing the section behavior. (a) Details and cracking (b) Partially debonded strands (c) STM Figure 2.8. Lower bulb of Type IV girder (photos: Hamilton 2009).

analytical research approach and Findings 33 3. Struts and ties are anchored at nodes corresponding to centroids of groups of bonded pre- stressing strand. This assumption implies that all bonded strands resist the generated tie force equally, which is consistent with the Bernoulli beam assumption (i.e., plane sections remain plane). Extending this assumption to the cross section STM, each strut will be anchored at a node corresponding to the centroid of a strand group and the corresponding strut force is proportional to the number of bonded strands represented by the node. 4. Girders are not skewed at their ends. The proposed STM adopted in the present study is shown in Figure 2.9. In Figure 2.9, the following nomenclature is used: B2, B3, D5, and D6 are girder dimensions (PCI 2011). Vu = total reaction (shear) at support. Nw = total number of bonded strands at section. nf = number of bonded strands in one side of the outer portion of bulb. The outer portion of bulb is defined as that extending beyond projection of web width, B3. Strands aligned with the edge of web are assumed to fall in the outer portion of bulb. xp = horizontal distance to girder centerline of centroid of nf strands in outer portion of bulb. yp = vertical distance to girder soffit of centroid of nf strands in outer portion of bulb. cb is calculated to ensure uniform bearing pressure across width of bearing pad, bb, i.e., Eq. 2.8: ( )( )= −2 1 Eq. 2.8c b n Nb b f w Although a uniform distribution is used here, the calculation of cb may be refined to reflect any distribution of bearing stress across the bearing pad such as would be the case where the bearing was treated as a Winkler beam. The tension in the horizontal tie, t, located at yp from the soffit may be calculated (Eq. 2.9): [ ]( ) ( ) ( )= α φ = − + − φ Eq. 2.9t V n N x h y x c y Vu f w p b p p b p u The tie force is written as a fraction, a, of the reaction force. This equation is essentially iden- tical to the Ross et al. (2013) equation but with cb, xp, and yp calculated based on strand pattern Figure 2.9. STM (shown on BT girder bulb).

34 Strand Debonding for pretensioned Girders and girder geometry, whereas Ross et al. (2013) made the following simplifications: yp = D6/2 and xp = cb= (B2 - B3)/3. An additional tension tie resisted at the level of the bearing pad is required when xp - cb is negative. Such cases only arise for small nf /Nw and, thus, are unlikely to result in large tension tie forces. It is assumed that the bearing itself will resist this tie. Based on sloped geometry of the Vu/f strut parallel to the beam span (Figure 2.8c), the tie force may be resisted by reinforcing steel located in the girder bulb above the bearing and extending approximately one-quarter the girder depth into the span. That is, tie reinforcement located within H/4 + Lbearing from the back of the bearing resists the tie force, where Lbearing is the length of the bearing. 2.5.3 Illustrative Examples For girder shapes having the same bulb geometry (e.g., BT and NU), the deepest such girder will be critical because deeper girders will have the greatest design shear (being the longest and heaviest girder). On this basis, BT-72, NU-1800, and AASHTO VI sections, all having the same nominal depth, d = 72 in., were selected for comparison. The approach taken to develop representative examples was as follows: 1. For each girder shape, three straight strand geometries (Nw) were selected as follows: a. Relatively lightly reinforced (strands occupying only lowest rows in the bulb), b. Moderately reinforced (strands populating nearly all rows in the bulb), and c. Heavily reinforced (at least five rows of strands extending into web). 2. For each BT-72 and AASHTO VI girder, a representative length (L) was selected using the pre- liminary design charts of Chapter 6 of the PCI Bridge Design Manual (2011). For NU-1800 girders, preliminary design charts provided in Hanna et al. (2010) were used. Values for girders with 0.6-in. diameter strands; f ′c = 12 ksi for BT-72 and AASHTO VI and 10 ksi for NU-1800; and girder spacings of 6 ft and 12 ft were used except as noted. 3. The design shear force, Vu/f, is calculated based on AASHTO LRFD Bridge Design Specifications (2014); the following basic assumptions were made: a. Girder self-weight is based on published values from the PCI Bridge Design Manual (2011) and Hanna et al. (2010). b. Slab self-weight is calculated using a unit weight of 0.15 kips/ft3. Slab depth was taken as 8 in. and 10 in. for the cases having girder spacing of 6 ft and 12 ft, respectively. c. An additional 0.3 kips/ft dead load is applied to each girder accounting for other bridge components (1.5 kips/ft on bridge distributed over five girders). d. AASHTO HL-93 live load arranged to maximize shear at the girder critical section for shear. e. Distribution factors for shear are calculated assuming interior girder having multiple lanes loaded (AASHTO LRFD Table 4.6.2.2.2.3a-1). f. STRENGTH I load combination including impact factor of 1.33. The cases considered are summarized in Table 2.7 and shown in Figure 2.10. All cases use straight 0.6-in. diameter strand, and a bearing width 2 in. less than the bulb soffit width (i.e., bb = B2 - 2 in.). Bearing length is taken as 12 in. in all cases. Changing these assumptions will have the following general effects: 1. Tie force varies minimally with strand diameter. For the same girder cross section, the change in moment capacity is approximately proportional to the change in strand area, Mn ≈ Apsfpudv, whereas the corresponding change in achievable girder length, L, varies approximately with √Mn; thus, the design shear (which is a function of L) and, therefore, tie force will be smaller for 0.5-in. diameter strands than for 0.6-in. diameter strands. 0.7-in. diameter strands will similarly increase the tie force but not proportionally as both moment and span length will

analytical research approach and Findings 35 Girder geometry Cases Range of debonding ratio Tie forces Cases satisfied by 60 ksi ties… Girder H S N at midspan L V/ tmax tdr = 0 No. 3 @ 6 in. No. 4 @ 6 in. in. ft ft kips kips kips having capacity… 83 kips 151 kips BT-72 82 12 24 @ 0.6 95 372 32 0 – 0.67 228 145 25% 62% BT-72 80 6 24 @ 0.6 135 297 32 0 – 0.67 182 116 31% 88% BT-72 82 12 38 @ 0.6 115 421 98 0 – 0.63 131 100 60% 100% BT-72 80 6 38 @ 0.6 138 326 98 0 – 0.63 101 77 88% 100% BT-72 82 12 48 @ 0.6 122 437 98 0 – 0.50 71 53 100% 100% BT-72 80 6 48 @ 0.6 163 339 98 0 – 0.50 55 41 100% 100% BT-72 82 12 38 @ 0.5 97 377 98 0 – 0.63 118 89 76% 100% BT-72 80 6 38 @ 0.5 130 290 98 0 – 0.63 91 69 96% 100% BT-54 64 12 38 @ 0.6 94 364 98 0 – 0.63 114 86 65%a 100%a BT-54 62 6 38 @ 0.6 130 281 98 0 – 0.63 88 67 88%a 100%a aFor BT-54, capacity of No. 3 ties at 6 in. = 71 kips and No. 4 ties at 6 in. = 130 kips. AASHTO VI 82 12 24 @ 0.6 90 379 21 0 – 0.58 58 49 100% 100% AASHTO VI 80 6 24 @ 0.6 131 318 21 0 – 0.58 49 41 100% 100% AASHTO VI 82 12 48 @ 0.6 128 478 156 0 – 0.63 81 77 100% 100% AASHTO VI 80 6 48 @ 0.6 165 376 156 0 – 0.63 63 60 100% 100% AASHTO VI 82 12 76 @ 0.6 145 521 633 0 – 0.55 63 63 100% 100% AASHTO VI 80 6 76 @ 0.6 180 401 633 0 – 0.55 49 48 100% 100% NU-1800 81 12 24 @ 0.6 88 360 36 0 – 0.67 327 120 28% 58% NU-1800 79 6 24 @ 0.6 120 282 36 0 – 0.67 256 94 36% 75% NU-1800 81 12 48 @ 0.6 136 478 583 0 – 0.67 390 220 13% 37% NU-1800 79 6 48 @ 0.6 167 355 583 0 – 0.67 289 164 22% 63% NU-1800 81 12 60 @ 0.6 153 519 1165 0 – 0.60 215 145 61% 96% NU-1800 79 6 60 @ 0.6 186 384 1165 0 – 0.60 159 107 77% 100% NU-1100 53 12 24 @ 0.6 73 313 36 0 – 0.67 283 104 19% 39% NU-1100 51 6 24 @ 0.6 90 224 36 0 – 0.67 203 75 31% 64% NU-1100 53 12 48 @ 0.6 105 392 583 0 – 0.67 319 181 11% 30% NU-1100 51 6 48 @ 0.6 128 281 583 0 – 0.67 229 129 19% 52% NU-1100 53 12 60 @ 0.6 115 415 1165 0 – 0.60 172 116 56% 87% NU-1100 51 6 60 @ 0.6 142 301 1165 0 – 0.60 125 84 72% 99% bFor NU-1100, capacity of No. 3 ties at 6 in. = 59 kips and No. 4 ties at 6 in. = 108 kips. Table 2.7. Summary of girder geometries considered and resulting tie requirements. also be limited by other design constraints (e.g., release stresses). Figure 2.11 illustrates a comparison of tie forces calculated for a BT-72 girder having 38 0.6- or 0.5-in. diameter strands. 2. Reducing the girder depth will reduce both the moment capacity and achievable span length. The design shear is approximately proportionally to span; thus, shallower girders, while hav- ing a greater shear to moment ratio, will, nonetheless, have a lower design shear and, hence, lower tie force. Figure 2.12 illustrates a comparison of tie forces calculated for BT-72 and BT-54 girders having 38 0.6-in. diameter strands. 3. Changing f ′c has no impact on the present calculations but would affect the maximum shear that may be resisted by a section, given by AASHTO LRFD Article 5.8.3.3 as Vn ≤ 0.25f ′c bvdv. This value would only be reached for heavily prestressed girders having impractically short spans. 4. Decreasing the bearing width, bb, increases the tie force considerably. Full width bearing is recommended for single-web bulbed girders. Full width is understood to mean the full width of the bottom flange less a distance accounting for the chamfer—typically 2 in. on both sides. Figure 2.13 illustrates the effect of reduced bearing width for BT-72 girders. 5. Bearing length has no impact on tie force but a shorter bearing length reduces the length of the region over which the resisting ties need to be placed (i.e., H/4 + Lbearing). A total of 9,408 cases were developed by investigating four girder shapes (BT-72, AASHTO VI, NU-1800, and NU-1100) in combination with two values of girder spacing (6 ft and 12 ft). For

36 Strand Debonding for pretensioned Girders BT-72 N = 24 BT-72 N = 38 BT-72 N = 48 (a) BT-72 6 in. 26 in. 24 in. 6 in. 26 in. 24 in. 6 in. 26 in. 24 in. -50 0 50 100 150 200 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Debonding ratio, dr compressive strut predicted fy = 60 ksi #3 ties @ 6 in. #4 ties @ 6 in. Ti e fo rc e, t (ki ps ) 10 .5 in . 72 in . + s la b 10 .5 in . 72 in . + s la b 10 .5 in . 72 in . + s la b Figure 2.10. Tie forces.

analytical research approach and Findings 37 AASHTO Type VI N = 24 AASHTO Type VI N = 48 AASHTO Type VI N = 76 (b) AASHTO Type VI 8 in. 28 in. 26 in. 8 in. 28 in. 26 in. 8 in. 28 in. 26 in. -50 -25 0 25 50 75 100 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Ti e fo rc e, t (ki ps ) Debonding ratio, dr compressive strut predicted fy = 60 ksi #3 ties @ 6 in. 18 in . 72 in . + s la b 18 in . 72 in . + s la b 18 in . 72 in . + s la b Figure 2.10. (Continued).

38 Strand Debonding for pretensioned Girders NU-1800 N = 24 NU-1800 N = 48 NU-1800 N = 60 (c) NU-1800 10 .8 in . 5.9 in. 72 in . + sla b 38.4 in. 36.4 in. 10 .8 in . 5.9 in. 72 in . + sla b 38.4 in. 36.4 in. 10 .8 in . 5.9 in. 72 in . + sla b 38.4 in. 36.4 in. -50 0 50 100 150 200 250 300 350 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Debonding ratio, dr compressive strut predicted fy = 60 ksi #3 ties @ 6 in. #4 ties @ 3 in. #4 ties @ 6 in. Ti e fo rc e, t (ki ps ) Figure 2.10. (Continued).

analytical research approach and Findings 39 NU-1100 N = 24 NU-1100 N = 48 NU-1100 N = 60 (d) NU-1100 10 .8 in . 5.9 in. 72 in . + sla b 38.4 in. 36.4 in. 10 .8 in . 5.9 in. 72 in . + sla b 38.4 in. 36.4 in. 10 .8 in . 5.9 in. 72 in . + sla b 38.4 in. 36.4 in. -50 0 50 100 150 200 250 300 350 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Debonding ratio, dr compressive strut predicted fy = 60 ksi #3 ties @ 6 in. #4 ties @ 3 in. #4 ties @ 6 in. Ti e fo rc e, t (ki ps ) Figure 2.10. (Continued).

40 Strand Debonding for pretensioned Girders -50 0 50 100 150 200 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Debonding ratio, dr compressive strut predicted fy = 60 ksi #3 ties @ 6 in. #4 ties @ 6 in. Ti e fo rc e, t (ki ps ) Figure 2.11. Tie forces for BT-72 having N = 38 0.6- and 0.5-in. diameter strands and spans appropriate for girder spacing of 12 ft. -50 0 50 100 150 200 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Debonding ratio, dr compressive strut predicted fy = 60 ksi #4 ties @ 6 in. BT-72 BT-54 #3 ties @ 6 in. BT-72 BT-54Ti e fo rc e, t (ki ps ) Figure 2.12. Tie forces for BT-72 and BT-54 having N = 38 0.6-in. diameter strands and spans appropriate for girder spacing of 12 ft.

analytical research approach and Findings 41 each girder/spacing combination, all possible debonding patterns of strands in the outer portion of the bulb (i.e., varied nf) that satisfied the following criteria were considered: 1. Outermost strand in lowermost full-width rows remain bonded; 2. No more than 50% debonding in first (lowest) row; and 3. No strands in the plane of the web (i.e., the shaded region in Figure 2.9) were debonded. Figure 2.10 shows the calculated tie forces, t, for all cases plotted against the debonding ratio, dr. Due to the interaction of xp, yp, and cb associated with debonding patterns, there is no trend in tie force although more debonded cases tend to have tie forces less than those calculated for the fully bonded case (dr = 0) than greater. Also shown in Figure 2.10 is the tie capacity of 60 ksi No. 3 and No. 4 ties (i.e., two legs) having a spacing of 6 in. distributed over the length H/4 + Lbearing. Tie capacity may be proportionally increased using ties with strengths of 75 or 100 ksi, and capacities at other spacing may be similarly interpolated. Using “bundled” ties is also a means of increasing capacity. For example, two bundled No. 3 ties have 10% greater capacity than one No. 4 tie. Similarly, bundled ties at 6-in. spacing may be more practical to install and result in less congestion than single ties at 3-in. spacing, for instance. Additionally, embedded steel sole plates may contribute significantly to the available tie force. Bearings that are very stiff in plane (steel plate) may also contribute to the tie force through the force that may be transmitted through friction with the concrete soffit. Typical neoprene bearings are not believed to be sufficiently stiff to contribute to the tie force in a meaningful manner. Table 2.7 summarizes the maximum tie force observed for each beam detail, and the number of cases satisfied using each tie geometry by assuming the ties alone provide the required force. The following conclusions are drawn: 1. Tie force is dependent on the girder shape. Assuming a fixed value of bearing width, bb, tie force, t, is most affected by dimension xp as it defines the slope of strut A (Figure 2.9). As such, -50 0 50 100 150 200 250 10 12 14 16 18 20 22 24 26 Ti e fo rc e, t (ki ps ) Bearing width, bb (in.) #3 ties @ 6 in. #4 ties @ 6 in. compressive strut predicted fy = 60 ksi full-width bearing pad bb = 24 in. Figure 2.13. Effect of variation of bearing pad width, bb, on BT-72 girders having dr = 0.0.

42 Strand Debonding for pretensioned Girders tie forces are greater for wide flat bulbs (NU-1800) than for thinner deep bulbs (AASHTO Type VI). BT-72 falls between these extremes. A rectangular stem beam would have no tie force (that is, nf = 0). 2. Tie forces are reduced by maximizing the middle strut proportion of shear, i.e., (Vu/f) (1 - 2nf /Nw). The large AASHTO Type IV through VI girders accomplish this objective with a wider web resulting in four, rather than two, vertical columns of strands contributing to the middle strut. This observation additionally reinforces the guidance not to debond strands within the plane of the web. 3. No simple “rule of thumb” for detailing is identified. It is concluded that No. 3 ties at 6-in. spacing are adequate for AASHTO type girders. Similarly, No. 4 ties at 6-in. spacing are adequate for all but lightly prestressed BT-72 sections. 4. Due to their bulb width, deep NU girders have high tie forces and, therefore, require con- siderable more tie reinforcement (greater than No. 4 ties at 3 in. in many cases). To investigate the NU shape further, the analysis was repeated for a shallower NU-1100 section. The results are shown in Figure 2.10d and summarized in Table 2.7. Although the tie forces are reduced, the length over which the ties are provided, (H/4 + Lbearing), is also reduced; thus, tie reinforcement requirement is affected marginally. 2.5.4 Validation by Experimental Results The STM was applied to both the design and as-built experimental behavior of the single-web bulbed beams tested as part of this study. These results are presented in Section 3.5. The approach was also applied to the Type IV girder A2U1 tested by Hamilton (2009) that exhibited clear evidence of longitudinal splitting (Figure 2.8). The results are shown in Table 2.8. Although no details or photographs of the bulb confinement reinforcement are available, typically No. 3 ties at 6 in. would likely be provided, which is approximately one-half the reinforcement that would be required to resist the tension tie developing at the ultimate girder capacity. As shown in Figure 2.8, the girders were supported on neoprene bearings having a width of only 18 in. Little Variable A2U1 (Hamilton 2009) BT-7-Live (Russell et al. 2003) Girder 6 (Hawkins and Kuchma 2007) Type IV BT-72 BT-63 East West dr 0.57 0.25 0.00 0.38 H (in.) 62 80 73 N 15 18 42 26 nf 6 7 14 10 xp (in.) 8.3 7.9 6.3 6.4 yp (in.) 5.0 3.6 4.0 4.8 hb (in.) 17 10.5 10.5 bb (in.) 18 24 24 cb (in.) 5.4 7.3 8.0 7.4 0.512 0.502 0.179 0.353 Vdesign. (kips) not reported 478 582 536 t = Vdesign (kips) 240 104 189 ties required over H/4 + Lbearing No. 3 ties at 1.6 in. No. 3 ties at 3.8 in. No. 3 ties at 2.0 in. Vexp. (kips) 296 614 640 541 t = Vexp (kips) 152 308 115 191 ties required over H/4 + Lbearing No. 3 ties at 2.5 in. No. 3 ties at 1.3 in. No. 3 ties at 3.3 in. No. 3 ties at 1.9 in. ties provided over H/4 + Lbearing No. 3 ties at 6 in. No. 3 hairpins at 6 in. No. 3 ties at 5 in. Table 2.8. STM of girders tested by others.

analytical research approach and Findings 43 restraint would be expected from this bearing; thus, the observed splitting should be expected. Increasing the bearing to full width (24 in.) would reduce the tie force by 30% although the force would still have exceeded the capacity of No. 3 ties at 6 in. This trend is an indication that the debonding pattern in this girder drove the observed splitting behavior. Three BT-72 girders reported by Russell et al. (2003) investigated varying shear reinforcement designs. Each girder had the same strand and debonding pattern, and was reportedly provided with “No. 3 hairpins at 6 in.” as bulb confinement reinforcement. Girder BT-7-Live had the largest design load and experimental capacity; the STM analysis of this girder is reported in Table 2.8. Like A2U1, it appears that BT-7-Live had inadequate tie reinforcement required to resist the tension tie developing at the ultimate girder capacity. This girder was supported on a steel bearing plate that may be expected to provide some degree of tie restraint due to friction between the girder and transversely stiff plate. Such bearing restraint is not accounted for in the STM prediction. While no splitting is reported (this was not a concern of the test program and, therefore, may have simply been neglected), significant strand slip was reported for a single strand, which may indicate some internal transverse distress. Girder 6, reported by Hawkins and Kuchma (2007) and described in Appendix C was also modeled. The east end of this girder had 42 fully bonded straight strands while the west end had 16 of these strands debonded. Once again, the provided tie reinforcement appeared to be inadequate to resist the expected tie force developed at the ultimate limit state. However, it is not clear from the girder details whether some of the web shear reinforcement was anchored in such a way as to provide additional tie restraint. Additionally, like BT-7, steel bearing plates were used which would be expected to provide additional restraint. 2.5.5 Summary of End Region Behavior The current requirement for confinement reinforcement in AASHTO LRFD Article 5.10.10.2 (i.e., No. 3 ties having spacing not exceeding 6.0 in.) is apparently adequate to resist tension tie forces at the ultimate limit state for sections with a narrow bottom bulb (e.g., AASHTO I girders). However, this requirement is not sufficient for sections such as BT and NU girders that have a wider bulb. The proposed STM is a simple and effective method for assessing the demand on the confine- ment reinforcement in the bottom flange, and determining the required amount of reinforce- ment. In lieu of using the STM approach presented herein, No. 4 ties spaced at 3 in. provide adequate capacity for all cases except NU girders with fewer than 60 strands, which is the maxi- mum number of strands that can fit in the bottom bulb. For these cases, the STM formulation may be used or an embedded steel sole plate is recommended. It should be noted that the cur- rent Nebraska standard details require the use of such plates for NU girders [Jaber 2016; Bridge Office Policies and Procedures (BOPP) 2011]. 2.5.6 Extension of Bulbed Girder Results and Discussion of Other Girder Shapes The issues described in the previous sections are only applicable to single-web sections. In double-web sections such as box or U, shear is transmitted through the webs to the level of the bottom flange. Considering the idealized STM shown in Figure 2.14, there is no need for the web compressive strut to spread to find an anchoring node if the following two conditions are met: 1. Bearing is provided under at least the full dimension of each web (accounting for the chamfer—typically 2 in.); the full-width support allows the strut to be anchored in the same plane as it develops.

44 Strand Debonding for pretensioned Girders 2. The strands located in the planes of the webs are not debonded; this detail allows the necessary tension force also to be developed in the same plane as the compressive strut. As a result, partial debonding in box or U-sections should be restricted to the flange region outside the web width. Box or U-girders may also have end diaphragms to help to spread the web-delivered shear across the flange at the support. In such cases, small horizontal compressive struts, rather than tension tie demands will develop. 2.6 Evaluation of the Effects of Skewed Girder Ends Cracking at the flange-web interface of prestressed girders with skewed ends has been observed in practice. Figure 2.15 shows an example of such cracking. The effects of skewed ends were examined through a mechanistic model and nonlinear FEM. 2.6.1 Mechanistic Modeling A model was developed with reference to the generic bulbed girder shown in Figure 2.16, in which OB is the flange-web interface having a flange thickness of tf . OA is the section defining the triangular region of flange projecting beyond the web due to the skew angle q. Cracks Shrinkage cracks Figure 2.15. Example of cracking in skewed ends in W74G with 55-degree skew angle. Photo Courtesy of Washington State DOT. CL Figure 2.14. STM of box girder.

analytical research approach and Findings 45 The developed length of bonded strand i at OA is (Eq. 2.10): = θtan Eq. 2.10L yi i The force associated with each vertical group of ni bonded strands at location i developed at section OA is (Eq. 2.11): − = θtan Eq. 2.11P L l f n A y l f n Ai i t pi i ps t pi i ps ∑( )′ =The moment about due to the strands is Eq. 2.12 : Eq. 2.12OO M P yo i i ∑( ) =The shear along plane due to the strands is Eq. 2.13 : Eq. 2.13OB V Pi develops tensile stresses along the flange-web interface having a peak value at point and assumed to be triangularly distributed over length Eq. 2.14 : 1 Eq. 2.14 2 M f O L f P y t L x L O t t i i f ∑ ( ) ( ) = 6 −   V is resisted along the flange-web interface as a function of the anticipated shear lag across the flange dimension y. Struts having an angle a as shown may be used to approximate this behavior. In this manner, L may be defined by the choice of a, which may be reasonably estimated to be 26.6 degrees, i.e., L = 2 yi,max, which also corresponds approximately to that observed in Figure 2.15. ∑ =    The shear stress distribution along plane is (Eq. 2.15): 2 Eq. 2.15OB v P t L x L i f The interaction of and results in a principal tensile stress Eq. 2.16 : 2 4 Eq. 2.16 1 2 2f v f f vt t t( ) σ = + + Figure 2.16. Geometry and internal force distribution at the end of a skewed bulbed girder.

46 Strand Debonding for pretensioned Girders This principal stress is oriented at an angle from Eq. 2.17 : tan 2 2 Eq. 2.17OA v ft ( )β β = For these calculations, all terms are defined in Figure 2.16 with the exception of: Aps = Area of one prestressing strand fpi = Initial prestress force lt = Strand transfer length ni = Total number of strands in group i of strands Based on the above equations and interdependence of the parameters selected, a number of conclusions can be made: 1. The strand forces in the triangular region of flange projecting beyond the web (Eq. 2.11) are proportional to the tangent of the skew angle, tan q. As a result, MO and V are also propor- tional to tan q. 2. The strand forces in the triangular region of flange projecting beyond the web (Eq. 2.11), and, therefore, MO and V are inversely proportional to transfer length of the strand. Thus, a shorter transfer length results in higher forces, the corollary of which is that the use of a longer assumed transfer length for design is unconservative in this case. 3. Debonding any strands in the triangular region of flange projecting beyond the web will reduce Pi and, thus, reduce the stresses along the web-flange interface. 4. Coupling Observations 1 and 3 suggests that some debonding is required in highly skewed bulbed girders in order to reduce web-flange interface stress. 2.6.2 Washington State Girder Examples The previously described approach and the observations stemming from it were evaluated with reference to girders G2 and G5 provided by Washington DOT. Both girders were W74G with end skews of 55 degrees. Each girder had 0.6-in. diameter Gr. 270 strands jacked to 43.9 kips, and had 6.0 ksi concrete. Girder G5 (details shown in Figure 2.17b) had 24 fully bonded straight strands in the flange, and exhibited cracking believed to be associated with the skew geometry (Figure 2.15). Girder G2 (Figure 2.17a), on the other hand, exhibited no such cracking. This girder had the same geometry as G5 but only eight straight strands and a detail in which the two strands at the acute corner were debonded a distance of 29 in. Key girder details are shown in Figure 2.17. The calculated principal stresses (Eq. 2.9) plotted in Figure 2.18 confirm that girder G5 is expected to crack but girder G2 is not. In these calculations, a realistic in situ transfer length of 30db was assumed. Using Girder G5, having 24 straight strands as a benchmark, the amount of debonding required to prevent cracking was calculated for different skew angles. The results shown in Table 2.9 indicate that for skew angles less than 19.5 degrees, no debonding of the 24 strands is required. For large skew angles greater than 55 degrees, all the strands in groups 1, 2, and 3 would have to be debonded to prevent the cracking observed (it is not recommended to debond the most exterior strands in a row). Table 2.9 also indicates that one-half of these strands will have to be debonded for skew angles greater than 25 degrees, and all of these strands will have to be debonded for skew angles greater than 55 degrees. 2.6.2.1 Nonlinear Finite Element Modeling of Girders G2 and G5 Nonlinear FEM (Section 2.4) was performed to evaluate the aforementioned observations, and further examine the effects of skewed ends. Using girders G2 and G5 (Figure 2.17) as a benchmark, five cases were examined, as summarized in Table 2.10. Cases G2-B and G5-A are

analytical research approach and Findings 47 (a) Girder G2 (note debonding of two strands at acute corner [left side]) (b) Girder G5 MARKED ENDMARKED END Figure 2.17. Details of girders G2 and G5. Drawings: Courtesy of Concrete Technology Corp., Tacoma, WA. 1 (ksi): G2 1 (ksi): G5 ft (ksi) (ks i) 0 0.5 1.0 1.5 2.0 2.5 x/L 0 0.2 0.4 0.6 0.8 1.0 Figure 2.18. Variation of principal tensile stresses. intended to replicate the field observations (hence, the use of a “realistic” transfer length of 30db, rather than the “design” transfer length of 60db). The remaining cases are intended to examine the following objectives: 1. The objective for G2-A was to assess whether the lack of cracking in G2-B was due to debonding of the acute side strands or the lower overall prestress force in this girder com- pared to that in G5-A. The acute side strands were left fully bonded in G2-A. 2. G5-B was used to assess whether the observed cracking is predicted when using the design transfer length of 60db. In other words, is the observed cracking a result of the developed

48 Strand Debonding for pretensioned Girders force at line OA shown in Figure 2.16 being greater in the “realistic” case than in the “design” case? 3. Based on the outcome of G5-A and G5-B, G5-C was designed to mitigate cracking, hence, demonstrating the hypothesis presented. The detail used for G5-C repeated the analysis of G5-A (30db) with six straight strands debonded as shown in Figure 2.19. A summary of predictions of cracking at the time of prestress release from skewed girder modeling is shown in Figure 2.20. Since minor cracking was observed in G5-A and not G5-B, the “difference” between realistic (30db) and design (60db) transfer length, alone, is apparently sufficient to account for cracking in this girder regardless of the large prestress force. For G5-C, the objective was to provide sufficient debonding to mitigate the observed cracking using the realistic 30db transfer length. It was found that debonding 6 strands (indicated in Figure 2.19) for a length of 29 in. was sufficient to mitigate observed cracking when using a transfer length of 30db. This observation was confirmed by also considering 4 strands debonded (cracking was observed) and 8 strands (no cracking); the latter cases are not shown. Based on the results summarized in Figure 2.20, the following observations are made: 1. The analyses confirm the research team’s hypothesis that no cracking would be observed in G2-A or B. Thus, no conclusion may be drawn on the effects of prestressing or transfer length. The transverse moment generated (Eq. 2.12) with only 8 strands in G2 is simply too small to result in cracking. Skew angle (deg.) Number of Bonded Strands in One-Half of the Bulb for Which No Cracking Is Predicted Total dr Group 1 Group 2 Group 3 Group 4 < 19.5 3 3 2 2 0.00 20 3 2 2 2 0.09 25 3 2 1 2 0.17 30 3 2 1 1 0.25 35 3 1 1 1 0.33 40 3 1 0 1 0.42 45 3 0 0 1 0.50 50 3 0 0 1 0.50 55 3 0 0 0 0.58 60 3 0 0 0 0.58 65 3 0 0 0 0.58 14 3 2 Table 2.9. Influence of skew angle on the required debonding for preventing cracking. Case G2-A G2-B G5-A G5-B G5-C Straight strands 8 8 24 24 24 Debonded strands None 2 at acute corner None None 6 strands debonded at 29 in. Transfer length used in FEM 30db 30db 30db 60db 30db Field observations N.A. No cracking Cracking (see Figure 2.15) N.A. N.A. FEM-predicted cracking No cracking at any threshold (Fig. 2.20a) No cracking predicted at any threshold (Fig. 2.20b) Minor cracking predicted at 0.008 in. threshold (Fig. 2.20c) No cracking predicted at 0.008 in. threshold (Fig. 2.20d) No cracking predicted at 0.008 in. threshold (Fig. 2.20e) Table 2.10. Summary of skewed girder FEM analyses.

analytical research approach and Findings 49 (a) Cross section (b) FEM Debonded strands Figure 2.19. Strand debonding in girder G5-C (debonded strands are circled). (a) Girder G2-A: 8 straight strands, no debonding, 30db transfer length. No cracking predicted (b) Girder G2-B: 8 straight strands, 2 debonded strands, 30db transfer length. No cracking predicted (c) Girder G5-A: 24 straight strands, no debonding, 30db transfer length. Cracking predicted (d) Girder G5-B: 24 straight strands, no debonding, 60db transfer length. No cracking predicted (e) Girder G5-C: 24 straight strands, 6 strands debonded, 30db transfer length. No cracking predicted Figure 2.20. Crack predictions at 0.008 in. threshold from skewed girder modeling (only predicted cracks greater than 0.008 in. are shown).

50 Strand Debonding for pretensioned Girders 2. G5-A exhibited cracking very similar to that seen in the field (Figure 2.15). 3. G5-B exhibited essentially no cracking. Hence, the “more gradual introduction of prestress force” resulting from longer “design” transfer length of 60db is sufficient to mitigate the crack- ing observed. That is, the individual strand forces, Pi (Eq. 2.11) and the transverse moment, MO (Eq. 2.12) is reduced, thereby lowering the concrete stress sufficiently to mitigate the observed cracking. 4. G5-C accomplishes the same objective as G5-B but through debonding in order to reduce the transverse moment, MO. The following conclusions are drawn: 1. The flange-web cracking shown in Figure 2.15 is attributable to transverse moment as described. Cracking is more significant with a greater moment present, and limiting this moment may mitigate cracking. 2. Reducing the nonuniform prestress force at a transverse section (i.e., OA in Figure 2.16) may mitigate the transverse moment in a skewed-ended girder. This goal may be accomplished by limiting the prestress force itself (compare G5-A to G2-A) or by providing debonding to minimize the moment at the root of the web at plane OO′ (compare G5-C to G5-A). 3. The use of more realistic transfer lengths (i.e., those shorter than the AASHTO-prescribed 60db) is more appropriate when evaluating the potential cracking of skewed ends. The longer design values result in lower stresses and are, therefore, non-conservative with respect to predicting the type of cracking shown in Figure 2.15. 2.7 Introduction of Debonded Strands at One Section The test specimens (Chapter 3) were detailed such that the debonded strands were gradually introduced along the girder length. This goal was achieved by meeting the following criterion stipulated in AASHTO LRFD Section 5.11.4.3: “Not more than 40 percent of the debonded strands, or four strands, whichever is greater, shall have the debonding terminated at any sections.” Similarly, the debonded strands in all the 44 cases described in Section 2.4.2 and Appendix D were rebonded at intervals of 3 ft. To investigate the case in which a large number of debonded strands are bonded at a single section, Case 13B was introduced. Case 13 (see Table 2.3) is an NU-900 having 28 fully bonded strands, 12 strands bonded at 3 ft, and 10 additional strands bonded at each of 6 ft and 9 ft, making a total number of strands N = 60 and maximum debonding ratio is dr = 0.53. Case 13B is otherwise identical to Case 13 except all 32 debonded strands are bonded at the same section at 6 ft. As shown in Table 2.6, this concentrated debonding pattern had little effect on the stresses at prestress release, resulting in a 4.5% increase in maximum compressive stress and 16% decrease in tensile stress. Figure 2.21 shows the stress distributions at prestress release. The effect of the sudden introduction of 32 strands at 6 ft (Case 13B), rather than being introduced in three increments over 9 ft (Case 13) is evident as a more abrupt transition of stress (marked with an arrow in Figure 2.21). While this stress raiser does not appear to result in any over-stresses, it should nonetheless be avoided by distributing the debonding curtailment in a uniform manner as presently required by AASHTO.

analytical research approach and Findings 51 Elevation - Longitudinal stress (Vertical dimension exaggerated 200%) Reverse plan (soffit) - Longitudinal stress (Transverse dimension exaggerated 200%) Reverse Plan (soffit) - Transverse stress (Transverse dimension exaggerated 200%) all stresses shown are compressive stress less than 0.15 ksi (a) Case 13 (b) Case 13B Bearing -3.91 ksi -2.61 ksi -3.26 ksi Bearing -3.91 ksi -2.61 ksi -3.26 ksi Figure 2.21. Effect of gradual versus concentrated introduction of debonded strands on stresses at prestress transfer. (Only the initial 25 ft of 100 ft long girder shown in all images.)