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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Connection of Simple-Span Precast Concrete Girders for Continuity. Washington, DC: The National Academies Press. doi: 10.17226/13746.
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4CHAPTER 2 FINDINGS This chapter summarizes the results of the surveys, the literature search, the analytical work, and the experimental program. SUMMARY OF THE SURVEYS Task 1 required the authors to assess the current state of the practice for continuous-for-live-load bridges. As part of this task, two surveys were conducted of state DOTs, contractors, fabricators, and designers. The first survey assessed the gen- eral use of continuous-for-live-load bridges and the use of various connection details. The second survey addressed con- structability issues. The purpose of the first survey was to determine typical parameters for the connections between precast girders that are made continuous for live load. This survey was sent to all 50 state DOTs and to selected designers and fabricators. Answering the survey were 39 state DOTs, 4 designers, and 8 fabricators for a total of 51 responses. Of the 51 respondents, 35 indicated that they used, designed, or fabricated continuous- for-live-load precast/prestressed bridges. The following assessments apply only to those respondents who indicated that they used continuous-for-live-load bridges. In all but one case, negative moment continuity was estab- lished by using a reinforced deck over the diaphragm. One respondent used a mechanical splice between the top flanges of the girders. All those who designed for continuous live load used a positive moment connection. It was clear from the outset of the project that the positive moment connection was of greater concern than was the neg- ative moment connection, so most of the questions focused on the positive moment connection. The significant findings were as follows. Type of Connection When asked to identify the type of positive moment con- nection used, 17 respondents used a bent-bar connection, 4 used straight bars, 24 used bent strands, 3 used a welded-bar detail, and 3 used mechanical strand connectors (the responses add up to more than 35 as some respondents used more than one type of connection). It appears the bent-bar and bent-strand connections are the favored connections, with approximately equal usage. Of the respondents, 75% (26 total) overlap (mesh) the bar or strand in the diaphragm area. Seventeen respon- dents (50%) indicated that they provided transverse rein- forcing through the beam into the diaphragm. Type of Girder Used The positive moment connection is used most frequently with I girders and bulb-T girders, although a number of respon- dents also used it for box girders and shapes specific to a given state. Embedment Seven respondents indicated that they did not embed the girder ends in the diaphragm. The remainder embedded the girder ends in the diaphragm anywhere from 2 to 12 in. There was no clear preference for embedment depth: 10 respon- dents indicated embeddings less than 2 in., 4 respondents embedded 2 to 4 in., 3 embedded 4 to 6 in., 6 embedded 6 to 8 in., 6 embedded 8 to 10 in., 11 embedded 10 to 12 in., and 12 embedded the girder ends more than 12 in. (responses total more than 35 as multiple responses were allowed). Concrete Strength Girder concrete compressive strength ranged from 3,500 to 7,000 psi at release and 4,000 to 9,000 psi at 28 days for normal mixes. Normal strength deck/diaphragm concrete was 3,000 to 5,000 psi at 28 days. Some respondents (19) indi- cated that high-performance mixes were occasionally used. For girders, these mixes ranged from 4,000 to 9,000 psi at release and 6,500 to 10,000 psi at 28 days, while the deck/ diaphragm concrete ranged from 3,000 to 7,000 psi. Support Conditions More than 80% of the respondents indicated that the bear- ings were placed under the girder ends. Approximately 10% used no bearings, leaving the girder and diaphragm to sit directly on the bearing surface. The remaining 10% either placed the bearings under the diaphragm or under both the girder and diaphragm.

5Construction Sequence Twenty-eight respondents (80%) indicated that the dia- phragm and deck were cast at the same time. Fourteen respon- dents (40%) cast the diaphragm, or some part of the dia- phragm, first. Again, the total responses exceed 100% because some respondents did both. Only 12 respondents indicated specifying a minimum age for the girders before the dia- phragm and deck are cast. The minimum ages varied from 28 to 90 days with no two respondents having the same age requirement. Some respondents indicated multiple age require- ments. The initial survey also asked questions about con- structability and connection performance. More detailed ques- tions were asked in a second survey. The results of this second survey showed that the most common concerns were conges- tion in the diaphragm area and the possibility that the concrete could not be adequately consolidated in this area. Fabrication problems included a difficulty in installing bars pre-bent (due to form interference), difficulties in bend- ing bars or strands after the girders were fabricated, and that an extended bar or strand were sometimes cut off or broken off during fabrication or while being transported. If a bar or strand was accidentally cut or broken, the solution was to drill and epoxy a new bar or strand in place. The respondents were asked to rate the significance of identified problems in terms of increased cost, increased con- struction time, decreased quality, or a combination thereof. In the overwhelming majority of responses, the problems were rated as being of only minor significance. The respondents were also asked to provide costs for pro- viding the connections. Many did not respond, and the responses that were received were difficult to interpret. In some cases, the respondents indicated that the cost of the con- nection could not be easily separated. In other cases, the cost depended largely on the detail used and the fabricator’s meth- ods. However, it appeared that the maximum cost of provid- ing the positive moment connection was $200 per girder. This was insignificant compared with the overall girder cost. LITERATURE REVIEW A search was made for literature that had been published since the publication of NCHRP Report 322 in 1989 (11) or that had not been included in that report. The most signifi- cant findings were a series of reports done for the Missouri Highway and Transportation Department (now the Missouri DOT) (8–10). These reports cover experimental work done on bent-strand types of connections. In the early 1970s, the Missouri Cooperative Highway Research Program commissioned a study on the feasibility of using extensions of the prestressing strand to develop posi- tive moment continuity of prestressed I-beam members. The first phase of the research dealt with an investigation of the bonding characteristics of untensioned prestressing strand (8), which could be used in the continuity connection. A relation- ship between the maximum force and embedment length of the untensioned prestressing strand in a stress field similar to that in the diaphragm of a highway bridge was developed. In all, 69 pull-out specimens were tested with three strand con- figurations: straight, frayed, and a 90° bent. From the inves- tigation, the modulus of slip for each of the strand configu- rations was determined, and equations relating steel stress to the embedment length were developed. It was found that bent strand provided the best anchorage, having half the slip of the straight or frayed strand. Straight strand was found to per- form marginally better than frayed strand. The other vari- ables included in the testing program were strand diameter, concrete strength, and containment reinforcing, but they were found to be of little consequence. The second phase was to verify and apply the expressions developed in the first phase to an actual I-beam end connec- tion (9). Six full-scale bent-strand connections were tested: three specimens consisting of two short, 6-ft 3-in. stub beams, a 30-in. diaphragm, and a 6.5-in. slab; and three specimens made only of the beams and diaphragms (no slab). As with the PCA tests (4,6), the specimens were tested for positive moment as simple spans, but only monotonic static loads were applied. The stub girders were embedded 17.5 in. into the dia- phragm and 3/4-in.-diameter coil tie rods were used to trans- mit the force from the end of the beams to the diaphragm. From the results of Phases I and II, a design method was proposed for positive moment connections using bent strand. The required area of extended, 90o bent strand (Aps req’d) is given by: where M = positive moment; As fy = area and yield stress of the diaphragm coil tie rod; d = depth from extreme compression fiber to centroid of diaphragm coil tie; dps = depth from extreme compression fiber to centroid of strand; jdps = internal moment arm; fps = (Le − 8.25 in.)/0.228 < 150 ksi; and Le = embedment length (in.). After determining the required area of steel and embedment length, the section is checked for ultimate strength by: fpu = (Le − 8.25 in.)/0.163; a = (Aps fpu − As fy )/0.85fc′b; Mu = N[Aps fpu(dps − a/2) + As fy(d − a/2)]; b = width of compression face (rectangular section assumed); A M A f jd d d f jdps s y ps ps ps ps ( ’ )req d = − + −( )

6fc′ = compressive strength of concrete; and N = understrength factor. The results of the two phases are given in two interim reports (8, 9) and a summary appears in the final report (10). Another study was conducted in 1980 (13). In this study, the fatigue resistance of the untensioned, bonded prestress- ing strand, consistent with the bent-strand configuration for a precast I-beam bridge, was examined. Eighteen single-type specimens, consisting of overlapping, opposing bent strand cast into a single block of concrete, and twenty-three double- type specimens, consisting of U-shaped strand with a con- crete block cast on each end, were tested in cyclic tension. This study recommended that the stress in the strand be lim- ited to 15% of the ultimate strength of the strand to prevent fatigue failure. It was further recommended that the dia- phragm be cast before the slab. In addition to the Missouri studies, five other studies on continuous span bridges were found. Abdalla, Ramirez, and Lee (14) tested three continuous Type I girders and a 27-in. box girder, all with debonded strands. In each case, the gird- ers were assembled into a single beam line of a two-span bridge with 24-ft 4-in. spans and an 18-in. diaphragm (except for the first I girder specimen, which had 24-ft spans and a 30-in. diaphragm). The ends of the girders were embedded 6-in. into the diaphragm (except for the first Type I specimen, which had an 8.5-in. embedment). A total of 12 strands were used in each I girder, while the box girders had 20 strands. The number of debonded strands was 0%, 50%, 67%, or 83% for the I girders and was 50% for the boxes. Note that the AASHTO Standard Specifications for Highway Bridges (15) does not limit the number of debonded strands, but this level of debonding would not be permitted under the AASHTO LRFD Specifications (12). Continuity for negative moment was achieved by using eight No. 6 bars in the 4-ft × 4-in. deck slab. For positive moment continuity, four strands were bent at 90o angles and embedded in the diaphragm. The significant conclusions of these studies were as follows. 1. Time-dependent moments were measured at the connection by evaluating the change in center sup- port reactions. These moments were compared with the predictions from the PCA method (7 ) and the method suggested in NCHRP Report 322 (11) (called the “CTL method” [Construction Technology Labora- tories method] in Reference 14 ). When using the CTL method, the time-dependent moments were evaluated both with and without the effect of restraint from the deck reinforcing steel. It was found that the method given in NCHRP Report 322 did a better job of pre- dicting time-dependent moments if the effect of the deck steel was accounted for; however, there were still some significant differences between measured and pre- dicted values. 2. The girders were loaded to produce negative moment over the support: the debonded girders exhibited flexural shear cracking where the fully bonded gird- ers did not. Deflection behavior was the same for both bonded and debonded girders until the flexural shear cracks occurred, at which point the debonded girders showed more deflection. 3. The negative moment behavior was evaluated by two models: the PCA model and the CTL model. The PCA model considers center supports to be a single sup- port and the connection to be zero width and infinitely rigid (i.e., the beam is modeled as two spans). In the CTL model, the center support is modeled as two supports and the connection is considered to be of finite width and flexible (i.e., the beam is modeled as three spans with the center span being the finite length connection/ diaphragm). The results show the CTL method pro- vides reasonable and conservative estimates of conti- nuity moments and negative moment capacity and that the PCA method was not conservative. 4. Flexural shear cracks in the I girder specimens occurred earlier than predicted by the PCA and CTL methods. For the CTL method, analysis was done using both uncracked and cracked transformed sec- tions. The PCA method and the CTL method using the uncracked sections overpredicted the flexural shear cracking load by 35% for the specimens with 50% debonding, by 52% for specimens with 67% debond- ing, and by 82% percent for specimens with 83% debonding. When evaluated with the CTL method, but using the cracked section, the overprediction dropped to 19%, 33%, and 49%, respectively. The cracks opened prematurely in the debonded regions, and moment redis- tribution was noted. 5. The equations for web shear cracking given in the AASHTO Standard Specifications for Bridge Design (15), coupled with the PCA and CTL methods, pro- vided conservative estimates of shear strength for the I girders. For the debonded girders, the measured load was 25 to 60% greater than predicted. The mea- sured load was 10 to 30% greater than predicted for the fully bonded girders. The web shear cracking for the box girders was slightly underpredicted, with the mea- sured load being 80% of the predicted load for the debonded girders and 93% of the predicted load for the fully bonded girders. In another series of studies, Ramirez and Peterman (16, 17) studied continuous, topped deck panels. However, since these studies were on panels, not girder and deck bridges, they were not seen as germane to this research. Tadros et al. (18) and Ma et al. (19) explored continuity in Nebraska NU-type girders. The first phase of the research was a parametric study to examine the effect of construction sequence on the development of time-dependent moments. It

7was concluded that the construction sequence greatly affects the development of positive moments. It was recommended that if the diaphragm is cast first (without the slab), the slab should be cast within 230 days to prevent cracking. It was also recommended that if the diaphragm is cast first, negative moment connections be supplied between the beams to pre- vent cracking and spalling at the joint between the diaphragm and deck. The study further recommends that when the dia- phragm and deck are cast together, an unbonded joint be used between the diaphragm and beam to allow the beam to rotate under the deck weight. Tadros et al. (18) and Ma et al. (19) also explored the use of negative moment connections between the tops of the pre- cast beams. Providing this connection has two advantages. This connection allows the beams to take some of the nega- tive moment rather than relying on the deck to take all of the negative moment. The other advantage occurs when the diaphragm is cast before the slab. When the slab weight is added, the end of the beam will attempt to rotate and this will put tension into the negative moment connection. This tension is balanced by compressing the bottom of the diaphragm, and this precompression will mitigate the tensile force caused by time-dependent positive moments. Two negative moment connections were tested. The first used threaded rods embedded in the top of an NU 1100 girder. The rods were passed through a connection plate and held with nuts. The second connection used strand that projected from the top flange of the beams. The strands of adjacent beams were connected by a strand connector. Both connection types were tested and found to perform well. GIRDER CRACKING IN ALABAMA A number of bridges constructed in Alabama with pre- stressed concrete girders made continuous have experienced significant cracking at interior supports. This experience has been widely discussed and was even reported in the national media (20). As a result, the authors were asked to investigate and discuss this experience. The focus of the Alabama experience of bridges with pre- stressed concrete girders made continuous is the I-565 viaduct in Huntsville, where cracking was observed in the continuity diaphragms and in girders near the continuity diaphragms. A summary of information on the viaduct and the cracking observed in the prestressed girders and continuity diaphragms follows. The data were gathered from several sources, includ- ing a report on the cracked girder investigations prepared by the Alabama DOT for these bridges (21). Details of the Viaduct The viaduct is composed of dual 12,200-ft-long bridges with a combination of steel and prestressed concrete spans. The majority of the prestressed concrete girders in the bridge were PCI BT-54 or BT-63 girders. A limited number of other AASHTO girders were also used. The girders were composite with a 6.5-in. composite deck, and the decks were formed using steel stay-in-place forms or removable plywood formwork. The ends of the prestressed girders were embedded 3 in. into continuity diaphragms. Mild reinforcement was extended from the ends of the girders into the continuity diaphragms to provide a positive moment connection. The positive moment connection reinforcement was hooked in the continuity dia- phragm and was embedded into the end of the girder. The total thickness of the continuity diaphragm was 16 in.; this is significantly greater than the typical continuity diaphragm used in Alabama at that time, which was 8 or 10 in. thick. The bridge was opened to traffic in 1991. Details of the Observed Cracks Limited cracking in girders as described below was observed during the first inspections in Spring 1992. Cracks had opened significantly by the next inspection in March 1994, which prompted the thorough inspection of all girders on the bridge. Three types of cracks were observed: 1. Spalling in the face of the continuity diaphragm was caused as the embedded girders pulled out of the diaphragm. 2. Vertical or inclined cracks in the girders near continu- ity diaphragms at interior supports were observed. In some cases, the girder cracking initiated at or near the ends of the embedment of the positive moment rein- forcement, which were all terminated at one location. The positive moment reinforcement terminated within the debonded length of some of the strands. 3. Vertical cracks in the end faces of the continuity dia- phragms were also observed. All three types of cracking can be attributed to the effects of positive moment at the interior support. In no cases were all girders in the bridge cross section cracked. Girders exhibiting cracking tended to be grouped in the cross section. Cracked girders were reported in 2-, 3-, and 4-span units. Cracking beyond the end region was not reported for any girders where cracking of any type was reported near an interior support. Cracks large enough to be repaired were injected with epoxy in September 1994. In some cases, new cracks reap- peared after repair although it was reported that repair spec- ifications were not closely followed. In 1995, inspections of the approximately 2,000 girders in the project indicated that 74 girders were cracked and the continuity diaphragm was cracked from girder pull-out at the ends of 200 to 250 girders. Girder Characteristics and Testing Detailed monitoring and load tests were conducted on two continuous units where a number of girders were cracked.

8about the same time in Alabama have not exhibited the extent and type of cracking observed on the I-565 bridge. In conclusion, several points can be made: 1. The effects of the thermal gradient across the depth of the superstructure may be significant in the design of bridges with precast concrete girders made continuous. 2. The Alabama bridges continued to perform as designed even with significant cracking at the ends of some gird- ers in the cross section. 3. Very few bridges with precast concrete girders made continuous have experienced significant cracking of the type observed on the I-565 and US 280 bridges in Ala- bama. In general, performance of this type of bridge has been very satisfactory. 4. The thickness of the continuity diaphragm and the embedment of the girders into the diaphragms may have been a significant factor in causing the observed crack- ing in the girders. INITIAL ANALYTICAL STUDIES Using the information gained in the literature search and from the survey, the next task was to propose specimen con- figurations for the experimental work. To accomplish this task, an analytical model was created. This model, a modernized ver- sion of BRIDGERM (11), was named RESTRAINT and works within a standard spreadsheet program (see Appendix A). The program models a two-span continuous structure. The support conditions assume that there is a support at each end of the girder (see Figure 3) because this was the most common support condition identified in the survey. This is also consis- tent with the support condition used in analysis program BRIDGERM given in NCHRP Report 322 (11). RESTRAINT used flexibility-based analysis by discretizing the span and the diaphragm into several elements. Prior to using the restraint program, moment curvature relationships are developed for the cross section. Any convenient method of determining the moment-curvature relationship (e.g., hand calculations, com- puter program, finite element analysis, or experimental data) can be used. For this study, the RESPONSE Program (22) was used to find the moment-curvature relationship. These data are then input into the spreadsheet. The time the diaphragm and deck are cast as input into RESTRAINT, assuming that release of the pretensioning force is time = 0 (this can be a different time based on the age of girder; however, the reference is made to the time after the release of post-tensioning). Because some states cast the dia- phragm first, the program allows the time the diaphragm and deck are cast to be different. Basic material properties are also input. With the basic information available, the program calcu- lates the internal moments that would result from creep of the prestressed girder and shrinkage of the girder and deck. Creep and shrinkage strains are found from the relationships given One of the units was instrumented and subjected to load tests. Characteristics of the girders and results from the unit tested are summarized below: • The girders in the subject span on the main line struc- ture were PCI BT-54 girders. There were nine girders in the cross section, spaced at 8 ft. The pier-to-pier dis- tance was 100 ft, with a design span of 98.5 ft between bearings. • The girders were manufactured in December 1988 and January 1989. The deck was cast in late April and early May 1989. • Cracks in the girders were monitored during load test- ing of the bridge. The maximum crack opening reported from the effect of two load-testing vehicles was reported to be about 0.0055 in. A maximum crack opening of about 0.030 in. was reported during the course of a day as the sun heated the deck slab. • The camber at midspan was observed to be about 0.41 in. due to the solar effect. • ALDOT concluded that the cracking was caused by pos- itive moments that developed as a result of the thermal gradient across the section. • Measured deflections from two load-testing vehicles placed on the bridge were only about 75% of the deflec- tion computed using a finite element model; therefore, it was concluded that the presence of the cracks did not significantly affect the structural behavior of the bridge. As a result of the experience of cracking with this and other bridges, ALDOT no longer allows the use of prestressed con- crete girders made continuous. Subsequent to the investigation of the I-565 bridge in Huntsville, another bridge was found with cracking in the gird- ers near the continuity diaphragms. This bridge was located on US 280 in Lee County, Alabama. The bridge was con- structed using AASHTO Type II girders with mild reinforce- ment extending into the continuity diaphragms to make a pos- itive moment connection. The girders were also embedded several inches into the continuity diaphragm. The behavior of this bridge was investigated by monitoring crack widths and performing a load test. The investigation produced the same results regarding the cause of cracking and the remaining capacity of the bridge as for the previous bridge. Conclusions Drawn from ALDOT Bridge Cracking The cracking observed in the girders and continuity dia- phragms of the Alabama bridges was significant and defi- nitely a matter of concern. However, similar situations with widespread cracking of this type have not been reported in the United States for bridges with prestressed concrete gird- ers made continuous. In fact, similar bridges constructed at

in the American Concrete Institute Report 209 (23). The pro- gram also accounts for loss of prestressing force using the method given in the Precast/Prestressed Concrete Institute Handbook (24). In the span, shrinkage of the deck and girder is assumed to be uniform, while creep caused by dead load plus prestressing force is assumed to be parabolic. At the dia- phragm there is no prestressing, so the creep is 0. Since the slab and diaphragm are usually cast together, the differential shrinkage between them is assumed to be 0. Once the internal moments are known, the program adds the dead-load moments. If desired, a live load, consisting of a point load at midspan, can be included and the moment from this force is also added. The program then divides each span into 10 or more elements (defined by the user). A single element is used for the diaphragm. With the moments known, the program can determine the curvature of each element from the moment-curvature relationship. The program then 9 performs a consistent deflection analysis. The center reac- tions are removed to make the system statically determinate. Using the curvatures, the deflection at the center supports can be found. The required reactions needed to restore the center support deflection to 0 are found. The other reactions are found from equilibrium and are used to calculate the conti- nuity moments. The continuity moments are then added to the other moments, and the entire analysis is repeated until the answer converges. To verify this program, the 1/2-scale I girders used in the original PCA tests were modeled (6). The results showed a reasonable agreement with the experiment (see Figure 4), although the effect of differential shrinkage (the first peak in the curve) was overestimated. A parametric study was conducted on a two-span bridge consisting of AASHTO Type III girders. The spans were 65 ft, and the girder spacing was 8 ft. A 2-ft-wide diaphragm was Figure 3. RESTRAINT Model. Figure 4. Comparison of RESTRAINT (Present Study) with PCA data. -1 -0.5 0 0.5 1 1.5 2 2.5 0 150 300 450 600 750 Time from Removal of Deck Formwork (Days) R ea ct io n at C en te r S up po rt (k ips ) -4.5 -2.5 -0.5 1.5 3.5 5.5 7.5 9.5 R ea ct io n at C en te r S up po rt (k N) PCA Tests Present Study Predicted Cracking of Diaphragm Observed Cracking of Diaphragm5

used and the deck thickness was taken as 8 in. Complete details of this study can be found in the literature (25). The conclusions of the parametric study were as follows: 1. The age of the girders at the time continuity is estab- lished was the single most important factor in behav- ior, as expected. If continuity is established when the girders are young, creep of the girders dominates the behavior leading to the formation of large positive restraint moments. If the girders are older, the dominant effect is differential shrinkage between the girder and the deck. This causes the formation of an initial negative moment. Depending on the relative age and properties of the girder and deck, this initial negative moment may be larger than the positive restraint moments cause by girder creep, leading to a net negative moment at the connection. 2. The amount of positive moment reinforcement at the diaphragm had a significant effect on performance. If no positive moment connection was used, the system cracked and the system behaved as simple rather the continuous spans. As the amount of positive moment reinforcement at the connection was increased, there was an increase in continuity—that is, the midspan positive moment due to live load decreased and the negative moment over the pier due to live load in- creased. Greater amounts of positive moment rein- forcement also reduced the cracking at the connections; however, greater amounts of positive moment reinforc- ing increased the positive restraint moment. The effect of the positive restraint moment must be added to the positive moments caused by dead and live loads. For the limited number of cases studied, the net positive moment at the midspan is essentially independent of amount of reinforcement used in the positive moment connection at the diaphragm. This conclusion was sim- ilar to that drawn by NCHRP Report 322 (11). 3. Some designers and owners recommend that the positive moment connection at the diaphragm have a capacity of no greater than 1.2 Mcr,where Mcr is the positive cracking moment calculated using the nontrans- formed composite cross section and the concrete strength of the diaphragm (it assumes that failure will occur in the diaphragm, but in the shape of the composite cross section). The results of the parametric study showed that using connection details with capacities above 1.2 Mcr did not significantly improve the behavior of the struc- ture. Thus, limiting the positive moment reinforcement such that the capacity does not exceed 1.2 Mcr seems reasonable from a practical standpoint because addi- tional reinforcement is not beneficial and it increases diaphragm congestion. 4. Using RESTRAINT, a continuity index was defined as the ratio of the calculated live-load moment divided by the live-load moment that would occur if the sys- 10 tem were linear elastic and continuous. A continuity index of 1 indicates full continuity. For the midspan, the continuity index will be 1 or greater and the conti- nuity will be 1 or less at the supports. The parametric study indicated that, due to cracking, the system will never be 100% continuous and the maximum continu- ity will be about 80%. 5. The program did not show any significant effect of diaphragm width. In this study, diaphragm width is perpendicular to the span. The diaphragm dimension parallel to the span is referred to as the thickness. Ini- tially, the diaphragm was modeled as a rectangular sec- tion with a width equal to the effective width of the com- posite girder flange. The diaphragm was also modeled as a T beam with a flange width equal to the effective width of the composite girder flange and a web width equal to the bottom flange of the girder. There was no significant difference in the results. An additional parametric study was performed on a two-span bridge using AASHTO Type V girders with 100-ft spans to see whether girder size and span altered results; however, the results showed that the conclusions of the original study remained valid. EXPERIMENTAL STUDIES Positive Moment Connection Capacities— Stub Specimens The survey results showed a wide variety in positive moment connection details used by the various states. One of the issues the experimental program attempted to address was the capacity of different details for the positive moment connections. To test positive moment connection capacities, a series of six short, or stub, specimens were tested. The spec- imens consisted of two 16-ft-long Type II AASHTO I gird- ers joined by a diaphragm (see Figure 5). They were intended to represent the length between live-load inflection points at a connection in a multispan bridge consisting of equal 50-ft spans. The distance between the ends of the girders in the connection was always 10 in., but the dimension of the dia- phragm varied with the connection being tested. The six connections consisted of different combinations of connection type (bent bar or bent strand) and diaphragm widths. Table 1 details the connections and Figure 6 shows typical details. Specimens 1 and 2 tested basic bent-strand or bent-bar connections. Since some states embed the girder ends into the diaphragm, Specimens 3 and 4 had the stub girders embedded into the diaphragm. Specimen 5 examined whether adding stirrups in the diaphragm just outside of girders would strengthen the connection. Some states place horizontal bars through the webs, flanges, or both of the girder to strengthen the connection. This was tested in Specimen 6.

The analytical study had suggested that, to counteract the time-dependent effects, it was not efficient to have a con- nection where the capacity exceeded 1.2 times the cracking moment (1.2 Mcr), so the bent-strand or bent-bar connections were detailed to have a capacity of 1.2 Mcr. The usual design assumption is that cracking will occur at the interface of the beam and the diaphragm, but that the failure will occur in the diaphragm concrete. Therefore, the cracking moment, Mcr is usually based on the composite cross section, but assuming the entire section is made of diaphragm concrete. All bent bar connections were detailed using hooked No. 5 bars meeting the provisions for hooked bars in the AASHTO LRFD Specifications (see Figure 6). It was necessary to off- set bars so that they would mesh without interference, result- ing in an asymmetrical connection. As will be discussed later, this asymmetry seems to have affected the connection behavior. For the bent strand, the number of strand and the length of the strand to be embedded in the diaphragm were determined based on the equations suggested by Salmons and others (8–10, 13), which are given in the previous section on the literature search. The number of strands was chosen arbitrarily as six because this number used the entire bottom row of strands. The 11 equations are then used to determine the required length of strand to be embedded in the diaphragm. Salmons and his coau- thors suggest that the length of strand be determined based both on a working stress and an ultimate strength and on the largest of the two chosen. For these details, the connection was assumed to have a working strength of Mcr and an ultimate strength of 1.2 Mcr. The length of strand embedded into the diaphragm was calculated to be 26 in., consisting of an 8-in. projection into the diaphragm before the bend and an 18-in. tail after the bend. Detailed calculations are given in Appendix B. The specimens were tested as cantilever beams (see Fig- ure 7). The specimen sat on a center support and was tem- porarily supported at both ends. Loading mechanisms were placed at each end (see Figure 8). During testing, one end was lifted off its support and the support was removed, cre- ating a cantilever beam. The free end was then subjected to the required loading regime. Complete details of the experi- mental set-up are in Appendix B. On Specimens 1 and 2, the deck was not cast all the way to the end. This was done so that the stub girders could be reused. After testing the first connection, the diaphragm was cut out and the girders were turned end-for-end, placing the previously unused end of the stub at the diaphragm. The diaphragm and a portion of the slab could then be cast and new specimens created (Speci- mens 3 and 4). For consistency and to allow attachment of the loading mechanism, the ends of the slabs were cut off of the previously used girders when they were turned end-for- end (Specimens 3 and 4). Specimens 5 and 6 each used new girders, but the slabs were not cast all the way to the end. Again, this was for consistency and to allow attachment of the loading mechanism. To understand the loading regime, it is necessary to consider a multispan bridge. As the truck traverses the first two spans, the connection between the first two spans is subjected to the maximum negative live-load moment. As the truck enters the third span, this same connection is now subjected to the max- imum positive live-load moment. The value of the maximum negative live-load moment was determined by analyzing two-, three-, and four-span bridges, with each span being 50 ft. The maximum negative live-load moment was almost the same for all three bridges and was found to be approximately 365 k-ft. Analysis of three- and four-span bridges yielded the maxi- mum positive live-load moment, which was determined to be Figure 5. Connection capacity (stub girder) specimen. TABLE 1 Details of positive moment connections in the stub specimens Specimen Number Type of Specimen Diaphragm Width (in.) Girder End Embedment (in.) Special Feature Cycles to Failure 1 Bent strand 10 0 None 16,000 2 Bent bar 10 0 None 25,000 3 Bent strand 22 6 None 55,000 4 Bent bar 22 6 None 11,600 5 Bent bar 22 6 Extra stirrups in diaphragm 56,000 6 Bent bar 26 8 Web bars 13,3000

Figure 6. Details of the connections.

approximately 90 k-ft. All moment values were at the face of the diaphragm. The loading regime was designed to represent the worst case loading. In this case, it was assumed that creep, shrink- age, and/or temperature strains in the deck and girders would produce a positive moment equal to the nominal cracking moment, Mcr. It was also assumed that the cracking would occur at the beam-diaphragm interface and that the limiting factor would be properties of the diaphragm concrete. There- fore, the nominal cracking moment was calculated using the geometry of the composite beam, but the properties of dia- phragm concrete. The section is considered as reinforced but not prestressed. This is consistent with normal design prac- tice. The deck and diaphragm were assumed to have a nom- inal strength of 4,000 psi, and the nominal cracking moment is calculated as 245 k-ft. Since the connection was assumed to be loaded to Mcr by time-dependent and temperature effects, the live load would cycle the moment about Mcr. The loading regime is shown in Figure 9. The first three cycles are between the positive and negative live-load moments. This simulates loading the bridge without any time- dependent moments and provides initial stiffness data for the connection. Next, the connection is loaded three cycles to the cracking moment to simulate the assumed effect of the time dependent and temperature moments. 13 The connection was then loaded to the combination of the live-load moments and the assumed time-dependent and tem- perature moments: Mcr ± MLL. This is a very severe loading sequence, which is thought to represent a worst-case scenario. The first load cycle exceeded the nominal capacity of 1.2 Mcr, so there was a possibility that the connection would fail on the first load cycle. The connection would be cycled at Mcr ± MLL for 1,000,000 cycles or until the connection failed. General Observations on the Stub Specimens While each connection had its own unique characteristics, there were some characteristics that were common to all the specimens. Figures 10 and 11 show the actual load versus the end deflection of Specimen 5 and a set of best-fit linear curves. The linear curve fitting was done automatically in a standard spreadsheet program. These results are representative of all specimens. The initial stiffness of the system is consistent with theoretical results (see following section on finite ele- ment modeling analysis). The section retains this stiffness until it is loaded to the cracking moment, Mcr. After this, the specimen shows a bilinear response. This is the result of the loading system (see Appendix B), which loads the specimen as a cantilevered beam. When the applied load is 0, the con- nection is being compressed by the dead-load moment, which is approximately 100 k-ft. At an applied load of 7 kips, the dead load is relieved and the crack begins to open. Until the compressive stress from the dead load is relieved, the connec- tion maintains a stiffness equal to the initial stiffness. After the compressive stress is relieved, the connection stiffness drops markedly. There is a slight reduction in stiffness with addi- tional cycles, but the change is small. However, during the cyclic loading, there is still load transfer across the joint. Even- tually the positive moment connection fails, either by pull out of the strand or fracture of the bars. The resulting load ver- sus deflection graph shows the resistance, and eventual fail- ure, of the slab alone (see Figure 10). At this point, the con- nection behaves like a hinge. It was noted that the cracking behavior is quite different than that assumed in theoretical models. These models assume the concrete is monolithic and when cracking occurs, the resulting cracked section shows the cracks going all the way into the slab (see Figure 12). In reality, there are cold (con- struction) joints at the beam-diaphragm interface and at the beam-slab interface. Because the joint at the beam-diaphragm interface is based on a weak chemical bond, which is not as strong as the tensile strength of monolithic concrete, cracks may form before the calculated cracking moment is reached. However, at the top of the crack, the joint at the beam-slab interface tends to act as a crack arrestor. It was noted that the crack would form at the bottom of the joint, propagate to the top of the beam, and stop. The cracks did not propagate into the slab until just before the connection failed (see Figure 13). In fact, it was found that formation of cracks in slab was usu- ally a sign of impending failure. Figure 7. Test set-up for the stub girder specimens.

Stub Specimen 1: Bent Strand Specimen 1 was a bent-strand connection where the girder ends were not embedded in the diaphragm (see Figure 14). This specimen proved rather easy to construct. The strand was bent by the fabricator using a small hand-pumped hydraulic device, which had been designed by one of the maintenance 14 workers. This device provided sharp, clean, 90° bends. How- ever, it was noted that this device kinks the strand with a bend radius of about 0.5 in. and did break individual wires on some of the bent strands. It was not difficult to place the girders end-to-end because the strand is very flexible and could be easily moved. How- ever, the strands touched each other on the sides (see Fig- Figure 8. Loading device.

ure 14), so concrete could not completely surround the strand. This would lead to interaction effects. It was also found that when the concrete was placed and vibrated, the strand ends moved from side to side with the placement and vibration, so the actual final position of the strand tails was not known. Unfortunately, there were a few problems with testing this first specimen. After the assembly of the specimen, the 15 hydraulic system suffered a break down and was not opera- tional for about 4 months. During this time, the specimen was subjected to thermal deformations. By the time the test had started, it was noted that hairline cracks had formed at the girder-diaphragm interface. A second problem occurred when the specimen was loaded to Mcr. Using the loading system described in Appendix B, -500 -400 -300 -200 -100 0 100 200 300 400 M om en t ( k-f t) 3 cycles between - MLL and + MLL 3 cycles to Mcr with same span Fatigue cycles between Mcr + MLL and Mcr - MLL to Failure Figure 9. Loading of the stub girder specimens. Figure 10. Load versus end deflection for Specimen 5. Specimen #5 End Deflection -30 -20 -10 0 10 20 30 40 -0.5 0 0.5 1 1.5 2 2.5 Deflection (in) Lo ad (k ips ) Mcr 25000 cycles 50000 cycles Failure

16 the load applied to the system had to be calculated taking dead-load effects into account. The load at the end supports was read from the load cells. It was assumed that all the load was dead load; however, subsequent calculations revealed that thermal effects had caused the specimen to camber up and the end reactions had increased. This thermal effect was inadvertently added to the applied load, and the specimen was overloaded in the positive moment direction by approx- imately 35% on the first few load cycles. After the error was discovered, the specimen was loaded correctly for subsequent load cycles. However, it is possible that the overload may have damaged the connection and shortened the cyclic load life span. The specimen survived for 16,000 cycles before failing. Failure occurred when the concrete on the bottom of the diaphragm split and popped off (see Figure 15). Usually a splitting type of failure is a sign of slipping and pull-out of the strand. There was noticeable spread, or “bird-caging,” of the strand. The strands were not broken, although some indi- vidual wires were broken. Stub Specimen 2: Bent Bar Specimen 2 used a bent-bar configuration (see Figures 1 and 16). The girder ends were not embedded in the diaphragm. This specimen was more difficult to construct. An unsym- metrical bar pattern must be used to avoid interference when the connection is assembled. It was also found that the bars cannot be installed pre-bent. As shown in Figure 6, the bent bars extend above the top of the bottom flange of the speci- men. If the bars are installed pre-bent, the metal beam forms cannot be closed. As a result, straight bars were cast into the Figure 11. Best-fit load versus end deflection for Specimen 5. Best Fit Load End Deflection Specimen 5 0 5 10 15 20 25 30 35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Deflection (in) Lo ad (k ) Initial Test Mcr 50000 cycles 25000 cycles Figure 12. Theoretical and observed cracked sections. Figure 13. Typical slab cracking.

end of the girder and the bars were field bent. In the field- bending operation, it was difficult to bend the bars consis- tently to the same length and radius. The lack of consistency in the bends made it hard to install the corner bar in the bends (see Figure 16). Once assembled, the specimen was tested in the same man- ner as Specimen 1 (see Appendix B for details). This specimen lasted for 25,000 cycles before failure. At failure, there were diagonal cracks that formed in the faces of the diaphragm and part of the diaphragm spalled off (see Figures 17 and 18). These cracks are similar to those found in actual bridges (see Figure 19). The bars were found to have fractured (see Fig- ure 20). A visual examination of the bars by a metallurgist showed the bars had failed in fatigue. An observation was made with respect to crack opening: in Specimen 1, crack openings on either side of the stub beam were the same, but this was not true of Specimen 2. As shown in Figures 6 and 16, the bars in the stub beam are closer to one side of the bottom flange than to the other. The crack openings on the side of the flange where the bar was closer were smaller than those on the opposite side. 17 Stub Specimen 3: Bent Strand, Beam Ends Embedded Specimen 3 was identical to Specimen 1 except that the diaphragm width was increased to 22 in. (560 mm) and the stub girder ends were embedded 6 in. into the diaphragm. This specimen lasted for 55,000 cycles before failing. The mode of failure was quite different from the nonembedded specimen: while both specimens showed extensive spalling of the concrete on the bottom of the diaphragm, the embed- ded specimen also exhibited cracking and spalling on the face of the diaphragm (see Figure 21). Stub Specimen 4: Bent Bar, Beam Ends Embedded Specimen 4 was identical to Specimen 2 except that the gird- ers were embedded 6 in. into the diaphragm. This specimen Figure 14. Bent strand, Specimen 1. Figure 15. Failure of Specimen 1, bent strand. Figure 16. Bent bar, Specimen 2.

Figure 18. Spalling of the diaphragm. Figure 19. Diagonal cracking and spalling in a bridge in Tennessee. Figure 20. Fractured bars. Figure 21. Diaphragm spalling, Specimen 3. Figure 17. Diaphragm diagonal cracking.

only lasted for 11,600 cycles. Examination of the data showed no particular or peculiar behavior that might account for this unexpected failure. As explained in Appendix B, the cyclic loading was stopped at certain intervals and static load tests were performed. The static load test at 10,000 cycles showed that the cracks on one side of the diaphragm were opening much wider than those on the other side (0.05 in. on one side, 0.025 in. on the other). These crack openings were not unusu- ally large compared with those for other specimens. Approx- imately 1,000 cycles later, the specimen failed. The bars frac- tured and diagonal cracks occurred in the diaphragm. The cause of this early failure is uncertain, but the most probable explanation is uneven stresses in the bars. Bent-bar connections are difficult to construct because the bars must be installed straight and then field bent. As a result, the bar bends are inconsistent (see Figure 16). This inconsistency in the bends may have caused some bars to take more load than others, leading to a premature failure. Bonded strain gages had been installed on some of the bars; but only one survived beyond 5,000 cycles, so comparisons of bar strains are not possible. Stub Specimen 5: Bent Bar, Beam Ends Embedded, Additional Stirrups in Diaphragm Specimen 5 was identical to Specimen 4 except that addi- tional stirrups were placed in the diaphragm, close to the out- side edge of the bottom flange (see Figures 6 and 22). This test was to see if these additional stirrups would strengthen the connection. If these stirrups strengthen the connection, they could be used in place of some of the bars extended from the end of the girder, lessening the congestion in the dia- phragm area. This specimen took 56,400 cycles before failure, and the failure was similar to that of Specimen 4. It did not appear that the additional stirrups added any strength to the connec- tion. However, the stirrups did preserve the strength after the main bars had fractured. After fracture of the bars in Speci- men 4, the largest load that could be applied was 26 kips and the end deflection was 4 in. Specimen 5 was able to hold the test load of 32 kips with an end deflection of 2 inches. Visual observation of the failure area showed that the additional stir- 19 rups were spanning the crack and preventing failure (see Fig- ure 23). This detail may be useful in seismic zones to provide additional ductility. Stub Specimen 6: Bent Bar, Beam Ends Embedded, Web Bars Added Specimen 6 used the same bent-bar configuration as Spec- imens 2, 4, and 5, but this connection used horizontal bars passed through the web of the beam (see Figures 6 and 24). The survey results showed details similar to this are used by some states. Since the stub beams were fabricated before it was decided to use this type of specimen, no holes were cast in the web for these bars. As a result, the holes had to be drilled. The vertical beam stirrups were located with a mag- netometer, and a hammer drill was used to make the holes. No. 5 reinforcing bars were then passed through the holes and encased in stirrups (see Figures 6 and 24). In order to accom- modate these web bars, the diaphragm had to be enlarged to 26 in. Figure 22. Additional diaphragm stirrups, Specimen 5. Figure 23. Failure of Specimen 5, stirrups span the crack. Figure 24. Web bars, Specimen 6.

This detail significantly improved the behavior of the con- nection. The connection lasted for 133,000 cycles before fail- ing. This connection was also stiffer than the others tested (see the finite element modeling analysis section, this chap- ter). After the bars in the positive moment area fractured, the specimen was still able to hold the applied load of 32 kips with an end deflection of 1.2 in. Failure was due to fracture of the bars in the positive moment connection and by the girders pulling out of the diaphragm. At failure, there was significant spalling of the dia- phragm concrete. After the test was complete, the spalled diaphragm concrete was broken out so the beams could be inspected. Cracking was found in the webs (see Figure 25), so while this connection performed better than any other, the cracking in the beams at failure might be an undesirable result. The Effect of Embedment Four of the six specimens had the girder end embedded into the diaphragm. For the bent-strand connection, embedment seemed beneficial. The number of cycles to failure increased by a factor of three. A change in failure mode was observed. In the nonembedded bent-strand specimen, the girders sepa- rated from the face of the diaphragm, but there was no dam- age to the face of the diaphragm. In the embedded specimen, diagonal cracks indicating a pull-out type of failure were observed. For the bent-bar specimens, the results were less conclu- sive. The embedded bent-bar specimen (Specimen 4) failed at less than half the cycles of the nonembedded specimen (Specimen 2), but another embedded bent-bar specimen (Specimen 5) failed at twice the number of cycles as the non- embedded specimen. Bonded strain gages were placed on four of the bent bars in each specimen, but the survival rate 20 of these gages was low. Often, only one or two gages sur- vived to failure. However, the gages that did survive suggest that bar strains were lower in the embedded specimens than in the nonembedded specimen. FULL-SIZE SPECIMENS Description of the Specimens The full-size specimens were constructed of two 50-ft Type III AASHTO I girders joined with a 10-in. diaphragm. An 8-ft-wide × 7.5-in. thick composite concrete deck slab was cast on top (see Figures 26 and 27). As with the stub specimens, the slab was not cast all the way to the end (see Figure 26). The girders were to be reused by turning them end-for-end and creating a new specimen. The last 12 ft of the deck slab was not cast to create the second specimen without having to remove any of the deck slab. For reference, the cardinal compass directions are shown in Figure 26. The girders are designated as “east” and “west.” The girder faces are “north” and “south.” A discussion of the experimental set up and instrumentation is included in Appendix B. Each end of the girder specimens was cast with both bent bar and extended strands so that either end could be used for either type of connection (see Figure 28). Unlike the Type II girders used for the stub specimens, it was possible to install some of the bars pre-bent and still close the forms; however, some of the bars had to be installed straight and then field bent later. A constructability issue arose during the fabrication of the girders. When the strands were detensioned, some or all of the wires in some strands unwrapped and deformed, creating a “bird cage” effect, as is visible on most strands shown in Figure 28. The strands were rewrapped, but some of the bird- caging remained. This occurred approximately 6 to 8 inches from the face of the girders, just about at the point where the strand would be bent. Since there is a possibility that this sit- uation might occur in real field applications, it was decided to proceed with using these strands to see whether there was an effect on connection strength. Figure 25. Cracking of the girder in Specimen 6. Girder Diaphragm E W N S Figure 26. Full-size specimen.

Full-Size Specimen 1 Behavior During Construction The first specimen used a bent-bar configuration in the positive moment connection. As with the stubs, the connec- tion was designed to provide a capacity of 1.2 Mcr. This required eight No. 5 hooked bars (see Figures 27 and 29). Since the stub specimen tests indicated that asymmetrical connections were undesirable, the bars in the connection were 21 placed as symmetrically as possible, but still allowed for mesh- ing of the bars. This configuration was still slightly asym- metrical and resulted in a very congested diaphragm area. Tolerances in bending rebar result in bends that do not line up (see Figure 30). This creates problems in inserting corner bars as detailed in Figure 29. A similar problem occurred with the bent-bar stub specimens as shown in Figure 16. The first specimen used a partial diaphragm pour (see Fig- ure 29). This configuration is used by several states. In this connection, the bottom of the diaphragm is poured well before the deck slab is added. The idea of the partial dia- phragm is that the weight of the deck slab concrete will rotate the end of the girder into the partial diaphragm and compress the concrete. Then, any tension caused by positive moments will simply reduce the compression rather than cause tensile cracking. The partial diaphragm was poured when the gird- ers were 28 days old. According to the survey, the depth of the diaphragm pour is usually one-third to one-half of the diaphragm depth. In this case, the diaphragm was poured to depth of 19 in. This was determined as the minimum depth that would allow the tails of the bent bars to be completely covered with the initial pour. Figure 31 shows the variation of the east-end reaction with time. The west-end reaction data are almost identical. From the time the partial diaphragm is cast to the time the slab is added 28 days later, the end reactions increase approx- imately 3 kips, creating a positive moment at the diaphragm of 150 k-ft. This positive moment is caused by a combination Figure 27. Cross section of full-size specimen. Figure 28. End of the girders for the full-size specimens. Strand that has been rewrapped Strand that has not been rewrapped

of creep, shrinkage, and average temperature effects in the girders. The effect of daily temperature variation is seen as the waves in the graph. Prior to adding the slab, this effect of daily temperature variation is approximately ±1k. The deck slab was added 28 days later. Figure 32 shows the results of a vibrating wire strain gage placed at the level of the positive moment connection bar, in the middle of the diaphragm (see Figure 29). The graph shows the time period when the deck slab was cast to a few days after. During the time from casting the partial diaphragm to adding the deck 22 slab, tensile strains ranging from 60 to 90 microstrain develop in the diaphragm. The variation seen is due to temperature. After the deck slab is added, this strain gage at the bottom of the diaphragm shows an immediate increase in compres- sive strain of 40 microstrain, which would correspond to a stress of approximately 160 psi. Vibrating wire strain gages placed 6 in. from ends of the girders (at the level of the bot- tom row of strand) show an increased compressive strain of 50 microstrain, which corresponds to a stress of approximately 250 psi. Therefore, some compressive stress develops at the joint. It is important to remember that the stresses cited are the instantaneous stressed caused by pouring the deck slab. At the time the deck slab was cast, the diaphragm was in ten- sion because of creep, shrinkage, and temperature effects in the girders. The compressive stresses created when the deck slab was poured were not enough to overcome this tension, and the diaphragm still shows a net tension even after the deck slab is added. After the deck slab is poured, the instruments show an unex- pected response. A few hours after the pour, the strain in the diaphragm increases (becomes more tensile) then decreases (becomes more compressive) over the next 2 days. After 2 days, the net strain is compressive. This is caused by thermal effects. In Figure 32, the second curve shows the temperature in the deck slab. The strains in the diaphragm are constant for a few hours, and then they follow the deck slab temperature curve. A similar response is seen in the reactions. Figure 33 shows the east-end reaction at the time the deck slab is cast until Figure 29. Bent bar specimen with partial diaphragm. Figure 30. Misaligned bars due to field bending.

2 days after. There is an immediate increase in load of about 10 kips when the deck slab is poured. This is consistent with the girders still behaving as simple spans, so the partial dia- phragm does not provide continuity. Over the next 8 h, the end loads increase an additional 4 kips. The peak load corre- sponds to peak concrete temperature in the deck slab. During the next 2 days, the end supports lose almost all the load gained during the deck slab pour. The loss of load mimics the deck slab temperature graph. These responses are caused by the heat of hydration in the deck slab. After the concrete is poured, the deck slab con- crete begins to heat up as the chemical reaction progresses. This will also heat up the top flange of the girder, causing an 23 expansion. The data show the girders camber upward 0.01 in. Since the partial diaphragm provides some connectivity, the entire system appears to deflect upward with the girders. This causes the tension at the diaphragm and the increase in the end reactions. The final set of the concrete—the point at which there are measurable mechanical properties in the concrete—is usu- ally taken as just before the point at which the heat of hydra- tion graph peaks. At this point, the hardened deck slab begins to influence the system. When the deck slab begins to cool, it will contract. Since the concrete and the reinforcing steel have almost the same coefficient of thermal expansion, the reinforcing steel expands and contracts with the concrete and 0 5000 10000 15000 20000 25000 30000 35000 0 20 40 60 80 100 120 140 160 180 200 Time - Days from beam fabrication R ea ct io n (p ou nd s) Pour Diaphragm Pour Slab All Forms Removed -100 -80 -60 -40 -20 0 20 40 60 80 100 56 57 58 59 60 Time - Days from beam fabrication M ic ro st ra in 0 5 10 15 20 25 30 35 40 45 50 Te m pe ra tu re D eg re e C Cast Slab Diaphragm Strain Slab Temperature Figure 31. Variation of east end reaction with time. Figure 32. Variation of strain at bottom of diaphragm with time.

offers little resistance to the thermal movements. Thus, the cooling of the deck slab results in a contraction of the deck slab, which mimics the effect of deck slab shrinkage. The models predict that contraction of the deck slab will cause a decrease in the end reactions, compression at the bottom of the diaphragm, and a downward deflection of the girders. All of these responses are seen in the data. Figure 34 shows the placement of vibrating wire strain gages in the cross section. All gages shown in Figure 34 are placed at midspan of the girders. Figures 35 and 36 show the strains in the top and bottom flanges of one of the girders. The initial values are the compressive strains due to prestress- ing and any creep or shrinkage that has occurred. The graph also shows the temperature measured in the deck slab and in the top or bottom flange of the girder. When the deck slab weight is added, there is a positive (i.e., tensile) change in the 24 strain in the bottom flange and a negative (i.e., compressive) strain in the top flange, as expected. Both the top and bottom flange strains stay reasonably constant until just before the peak in the deck slab temperature, which is approximately the time of the final set for the concrete. The strains then approx- imately follow the temperature curve. It therefore appears that at this point, the deck slab has hardened sufficiently to begin affecting the girder behavior. The peak strains in the flanges occur slightly before either the peak deck slab temperatures or the peak girder temperature. There is slightly better agree- ment with the gradient (slab temperature − bottom flange tem- perature), but the strain still peaks earlier. The reason for this is not apparent. Clearly, the girder is subject to a complex series of interactions involving the thermal contraction of the slab and thermal strains in the girder. Completely understand- ing this behavior would require complex computer analysis beyond the scope of this project. Figure 37 shows the strain in the slab. The strain is taken as 0 at the point of final set, as determined from Figures 35 and 36. The deck slab strain follows the slab temperature. Tem- perature decreases cause tension as the deck slab attempts to contract but is restrained by the girder. Increases in temper- ature cause compression as the deck slab expands but is restrained by the girder. Again, this is the expected behavior. Monitoring after Construction The deck slab was wet cured for 7 days, and the forms were removed during the next 14 days. Form removal took some time because of the specimen geometry. In order to duplicate field conditions as clearly as possible, the specimen was supported by three load cells placed under each girder (see Appendix B). Thus, all the support was near the center- line of the specimen and there was a possibility that the spec- Figure 33. East end reaction after deck slab pour. 15000 20000 25000 30000 35000 40000 56 56.5 57 57.5 58 58.5 59 Time - Days from beam fabrication R ea ct io n (p ou nd s) 0 5 10 15 20 25 30 35 40 45 50 Sl ab T em p (d eg re e C ) Cast Slab Slab Concrete Temp. End Reaction R ea ct io n (p ou nd s) Sl ab T em p (d eg re e C ) Figure 34. Placement of vibrating wire strain gages in cross section at midspan.

imen might tip over unless stabilizers were installed (see Fig- ure 26) as the forms were removed. Until the stabilizers were installed, the specimen was kept stable by formwork under the diaphragm. As a result, it was not possible to accurately monitor the center reaction while the formwork was under the diaphragm. However, since the only formwork support was at the center, changes in the center reaction should result in changes to the end reactions—for example, if the center reaction increases, the end reactions should decrease by the same amount. Thus, during the form removal period, devel- opment of moments due to time-dependent effects can be determined from the end reactions. 25 During the form removal period, the end reactions showed daily variation due to temperature, but the average reaction did not change. This was unexpected because it was thought that these reactions would continue to decrease due to shrink- age of the deck slab. A shrinkage specimen was made when the deck slab was cast. It was water cured for 7 days (the same as the deck slab) and then allowed to shrink. The specimen was kept in a trailer near the beam. Shrinkage was measured through an embedded vibrating wire gage. During the period of form removal, a shrinkage of approximately 350 micro- strain was measured. A similar shrinkage specimen had been made for the girder; and, during the same period, the girder -775 -750 -725 -700 57 57.5 58 58.5 59 Time - Days from beam fabrication B ot to m F la ng e St ra in - M ic ro st ra in 0 7 14 21 28 35 42 Te m pe ra tu re - De gr ee C Bottom Flange Strain Pour Slab Temperature Gradient Slab Temperature Figure 35. Bottom flange strain after deck slab pour. Figure 36. Top flange strain after deck slab pour. -300 -250 -200 -150 -100 -50 0 57 57.5 58 58.5 59 Time - Days from beam fabrication To p Fl an ge S tra in - m ic ro st ra in 0 7 14 21 28 35 42 Te m pe ra tu re d eg re e C Slab Temperature Top Flange Strain Temperature Gradient Pour Slab

concrete shrank only 45 microstrain. With a differential shrink- age of almost 300 microstrain, some development of nega- tive moment should have been seen through a decrease in the end reactions. After all the forms were removed, the system was moni- tored for 4 months. The most striking observation was the daily change in the reactions due to temperature (see Fig- ure 31). The end reactions vary by approximately +5 kips per day. This is a daily variation equal to approximately 20% of the reaction. For this variation in reaction, the moment at the 26 diaphragm would vary +250 k-ft per day. Given that the nominal cracking moment at the diaphragm was calculated as 420 k-ft and the positive moment connection capacity was 504 k-ft, this daily variation is significant. During the monitoring period, the average end reaction increases about 5 kips while the center reaction drops by 10 kips, and there are not large differences in the girder-slab strains. Figure 38 shows that after the slab is cast, the deck slab and top flange strains decrease the same amount (200 micro- strain) while the bottom flange strain decreases slightly more Figure 37. Deck slab strain after deck slab pour. -20 0 20 40 60 80 100 120 57 57.5 58 58.5 59 Time - Days from beam fabrication Sl ab S tra in - m ic ro st ra in 0 5 10 15 20 25 30 35 40 45 Te m pe ra tu re d eg re e C Slab Temperature Slab Strain Pour Slab Final Set of Slab Figure 38. Change in girder/deck slab strain with time. -1200 -1000 -800 -600 -400 -200 0 200 0 50 100 150 200 250 Time - Days from beam fabrication m ic ro st ra in Bottom Flange Strain Top Flange Strain Deck Slab Strain Pour Slab Strain at prestress transfer Bottom flange = -548 Top flange = 0 Pour Partial Diaphragm

(250 microstrain). It was expected that the center reaction would increase and that there would be large differences between the strains due to differential shrinkage of the deck slab. Most analyses of this type of system show that if the girders are older than 60 days when the deck slabs are placed, a large increase in the center reaction and development of large negative moment occurs. The PCA tests (7 ) found an increase in center reaction with time. The results of the current study are consistent with recent field studies of bridges. FHWA sponsored a program to build high-performance concrete highway bridges in several states. The results are compiled on CD-ROM (26). Strain gages were placed in girders in three states: Louisiana, South Dakota, and Washington. In these projects, the girders were rather old when the deck slabs were placed (approximately 60 days for Louisiana, 200 days for Washington, and 300 days for South Dakota), so the effects of the differential shrinkage should have been noticeable through large strain changes and down- ward cambers of the girders. However, the strains in the gird- ers remained almost constant (except for daily temperature variation), and there was little change in the cambers. Thus, it does not appear that large negative moments develop. This is also consistent with anecdotal field evidence that negative moment distress has not been observed in these bridges. The results found in the present study seem to agree with the studies by Ramirez et al. (14), which showed that the models overpredict formation of negative moment due to dif- ferential shrinkage. The reasons why bridges do not show the predicted negative moment development is not entirely clear; however, some possibilities can be offered. The actual deck shrinkage potential may be overestimated. Analytical shrinkage values are usually based an assumed rel- ative humidity. Real decks may be exposed to much higher humidity, especially at early ages when shrinkage potentials are greatest. In the case of the specimen reported here, the specimen was monitored over the summer at a facility near the Ohio River. The daily relative humidity frequently exceeded 90%. Decks are also subject to frequent rewetting from rain and snow. The models base negative moment development on dif- ferential shrinkage, but usually use the free shrinkage values. These are usually obtained from equations given in the AASHTO Codes or ACI 209 (12, 23). In reality, the deck is not free to shrink. Decks are usually heavily reinforced, and this reinforcement will restrain the shrinkage. Because the deck shrinkage is restrained by the steel, the shrinkage strain in the deck will not be the unrestrained shrink- age, but rather an effective shrinkage strain. The effective shrinkage strain in the deck can be found from εeffective = εsh(Ac /Atr) where εsh = unrestrained shrinkage strain for deck concrete; Ac = gross area of concrete deck slab; 27 Atr = area of concrete deck slab with transformed longitu- dinal deck reinforcement, Ac + As (n − 1); As = total area of longitudinal deck reinforcement; n = modular ratio = Es /Ec; Es = modulus of elasticity of the steel; and Ec = modulus of elasticity of the concrete. If the concrete modulus is low (as at early ages), the mod- ular ratio increases and the effective shrinkage decreases. Thus, at early ages when the incremental shrinkage is high, the effect of bar restraint is also high. At later ages, the con- crete modulus increases and the effect of bar restraint is less pronounced, but the incremental shrinkages are also lower. BRIDGERM and RESTRAINT (the program developed for this study) both incorporate an equation developed by Dischinger (11). According to NCHRP Report 322, this equa- tion is used to account for the restraining effect of the bar in the slab; what the equation actually does is attempt to correct for the fact that the modular ratio of the slab changes with time because the concrete modulus changes with time. How- ever, even with corrections for relative humidity and rein- forcement, RESTRAINT still predicts that a negative moment due to differential shrinkage should form. Clearly, more work is needed on this aspect of the model. As previously noted, the end reactions did not decrease due to differential shrinkage as was expected, but rather increased. The cause of increase in end reaction is due to two effects. One was a slight settlement at the center support. In order to duplicate field conditions, bearing pads had been placed under the load cells. These pads seemed to have creeped slightly, and the center support showed a settlement of 0.06 in. An analysis was run and it was determined that this settlement would cause an increase in the end reactions of 1.8 k, about one-third of the observed change. The remaining change is a combination of temperature effects and creep/shrinkage effects; however, it is very diffi- cult to separate the individual contributions. What is clear is that over the monitoring period, the girder bottom flanges at midspan showed an average of 80 microstrain more compres- sion than did the top flanges (see Figure 38). This strain gradi- ent would have caused the girders to camber up and increase the end reactions. During the monitoring period, the center deflection decreased by 0.02 in.; but, when the effect of the center support movement is removed, the girder actually cambered up 0.02 in. During the monitoring period, cracks were observed at the girder-diaphragm interface. During the monitoring period, these cracks opened an average of 0.015 in. when measured 3 in. from the bottom of the specimens, but there was varia- tion. The average crack openings were 0.007 in. on the south- west joint, 0.015 in. on the northeast and northwest joints, and 0.020 in. on the southeast joints (see Figure 26 for direc- tion). Note that cracks on the east side of the diaphragm

opened more than did those on the west side of the diaphragm and that the cracks on opposite sides of the same girder did not open the same amount. The reason the cracks on oppo- site sides of the girder do not open the same is because of the bar placement (see Figure 27). Although it was desirable to place the bars in a symmetric pattern, this cannot be done and still allow for the bars to mesh. As a result, the bars had to be offset about 3/4 in. This places the bars closest to the northeast and southwest faces, which had less crack opening than did 28 those on the opposite faces where the bars were further from girder faces. Figures 39 and 40 show the variation of crack opening with time for cracks at the bottom of west girder. The crack openings appear to show some softening of the connection during the monitoring period as the crack opening amplitude increases with subsequent cycles. No similar trend is seen with the reactions as the amplitude of the daily change remains fairly constant over the monitoring period (see Figure 31). -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0 20 40 60 80 100 120 140 160 180 Time - Days from beam fabrication Cr ac k O pe ni ng (in ) Pour Diaphragm Pour Slab Remove All Forms Figure 39. Opening of the crack at the bottom flange of the girder, northwest joint. Figure 40. Opening of the crack at the bottom flange of the girder, southwest joint. -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0 20 40 60 80 100 120 140 160 180 Time - Days From beam fabrication Cr ac k O pe ni ng (in ) Cast Diaphragm Cast Slab All Forms Removed

During the monitoring period, there was virtually no opening at the top of the joint. Testing after Monitoring After the monitoring period was over, the girders were tested to determine continuity. It is thought that cracking at the diaphragm will result in a partial or complete loss of con- tinuity. By loading the specimen one span at a time, the conti- nuity of the structure could be determined. Load was applied to the specimens with a pair of hydraulic cylinders (see Fig- ure 41) placed in each span at 22 ft from the face of the dia- phragm. Analysis showed that this was the most efficient posi- tioning of the loads. The specimen was loaded as follows to create a negative moment at the center support: 1. Span 1 was loaded with a downward load, 2. Span 2 was loaded with a downward load, 3. Span 1 was unloaded, and 4. Span 2 was unloaded. The loads were such that when both spans were loaded, the applied moment was equal to the negative live-load moment. This is consistent with design procedures where the maximum negative moment occurs when the design truck has at least one axle on either side of the support. This loading also allowed for checking the requirements of the current AASHTO LRFD Specifications Art. 5.14.1.2.7c (12), which states: If the calculated stress at the bottom of the joint for the com- bination of superimposed permanent loads, settlement, creep, shrinkage, 50% live load and temperature gradient, if applica- ble, is compressive, the joint may be considered fully effective. When one span is loaded, the applied negative moment is 50% of the negative live-load moment. 29 Continuity was determined by the change in reactions and the changes in girder strains. If the girder is continuous, load- ing one span will have a known effect on the reactions and strains in the other span. In a simple-span case, loading one span will have no effect on the other. If there is partial con- tinuity, the strains and reactions will be between the simple and continuous cases. Figures 42 and 43 show the results of loading the speci- men after the monitoring was complete. The test consisted of one load cycle to establish a baseline. The east girder was loaded first, and then the west girder was loaded. The x axis is time, and horizontal lines on the graphs show the anticipated reactions and strains for both the continuous and simple spans cases. The reactions and strains are consistent with continu- ity, even though cracking exists at the connection. After the initial testing, the cracks at the diaphragm were opened by simulating the positive moment that would develop from creep and shrinkage of the girders if continuity was established at an early age. To do this, a post-tensioning bar was placed through the bottom flange of the girder, and a post-tensioning force was applied (see Figures 44 and 45). This would cause the girders to camber up—simulating the formation of additional positive moment. Note that the post- tensioning (called “PT” in the figures) bars only went through the girders and did not go through the diaphragm (i.e., the bar was dead-headed at the end of the girder where the girder was attached to the diaphragm). The bar was a 1.375-in.-diameter Dywidag bar. It was tensioned to the maximum allowable force of 160 kips. This increased each end reaction by 8 kips, resulting in an additional positive moment of 400 k-ft or 0.96 Mcr. The cracks at the bottom of the joint opened as follows: southeast—0.01 in., northwest—0.008 in., and southwest—0.004 in. The instrument on the northeast joint malfunctioned, so no data are available. The post-tensioning load was applied in four stages. After each stage of post-tensioning, vertical loads were applied to the specimen. Downward loads were applied to the specimen as mentioned above to obtain the negative live-load moment. After the negative moment was applied and removed, posi- tive (upward) loads of 10 kips were applied in sequence in each span. This upward load placed the maximum positive live-load moment on the connection when both spans were loaded. Figures 46 and 47 show the crack opening at the bot- tom of the specimen for two cracks: northwest and southeast. The northwest crack appears to close under the initial load, even though the crack opening does not return to zero. This is not unusual with cracks in concrete—the surfaces tend to be rough and the rough cracks will often not close all the way back. The southwest crack does not appear to close under ini- tial load. By the time all the post-tensioning is applied, both cracks are opening and staying open on loading. However, the data from subsequent loading still show that the connec- tion remains effective because the girders act as if continu- ous (see Figure 48). Figure 41. Loading device.

30 -20 0 20 40 60 80 0 4 8 12 16 Time (min) B ot to m F la ng e St ra in (m icr os tra in) East Beam West Beam Strain if Simple Spans Strain - Loaded Span - if Continuous - One Span Loaded Strain if Continuous - Both Spans Loaded Strain - Unloaded Span - if Continuous - One Span Loaded East Beam Loaded West Beam Loaded Both Beams Loaded Figure 43. Change in bottom flange strain: loading to negative LL moment before post-tensioning. -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 4 8 12 16 Time (min) Ch an ge in R ea ct io ns (p ou nd s) East End West End End Reaction if Simple Spans End Reaction - Loaded Span - Continuous - One Span Loaded End Reaction Continuous - Both Spans Loaded End Reaction - Unloaded Span - Continuous - One Span Loaded East Beam Loaded West Beam Loaded Both Beams Loaded Figure 42. Change in end reactions: loading to negative LL moment before post-tensioning.

Since the girders remained continuous after the post- tensioning, the girders were loaded by increasing the positive load (creating positive moment) to determine the load at which, if any, the continuity was lost. Figures 49 and 50 show the end reactions and bottom flange strains for a loading to the maximum negative moment (−38 kips at each point) fol- lowed by loading up to +40 kips at the east point and +42 kips at the west point. This positive load would cause an addi- tional positive moment of 395 k-ft. Added to the 400 k-ft caused by the post-tensioning, the total positive moment was 795 k-ft or 1.90 Mcr. This exceeded the nominal design capacity of 1.2 Mcr, but that capacity was calculated using nominal properties. The nominal bar yield was 60 ksi, but the 31 actual bar yield was 83 ksi. The nominal concrete strength was 4 ksi, but the actual strength was 6.7 ksi. Using the actual properties, the capacity becomes 828 k-ft or 2.0 Mcr. There was no indication that the bars had yielded, nor was cracking observed in the diaphragm. It appears from Figures 49 and 50 that the girders main- tained continuity as the values of the reactions and strains at each load increment are those expected for a continuous sys- tem. It should be noted that when the west load was increased to 42 kips, the structure began to lift off the center supports, so the test was stopped at this point. Crack openings at the max- imum load were as follows: southeast—0.035 in., northwest— 0.029 in., northeast—0.025 in., and southwest—0.015 in. Figure 44. Position of post-tensioning duct. Figure 45. Post-tensioning device. Load Cell JackNut and Spacer PT Bar -80 -60 -40 -20 0 20 40 0 0.005 0.01 0.015 0.02 0.025 0.03 Crack Opening (in) To ta l a pp lie d lo ad (k ) Load Before PT Load After Each PT Increment Figure 46. Crack opening at bottom of girder load during post-tensioning, northwest joint.

32 Figure 48. Change in end reactions: Loading to negative LL moment after post-tensioning. -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 2 4 6 8 10 Time (min) Ch an ge in R ea ct io n (p ou nd s) East End West End End Reaction - Loaded Span - Continuous - One Span Loaded End Reaction if Simple Spans End Reaction - Continuous - Both Spans Loaded End Reaction - Unloaded Span - Continuous - One Span Loaded East Beam Loaded West Beam Loaded Both Beams Loaded Figure 47. Crack opening at bottom of girder load during post-tensioning, southeast joint. -80 -60 -40 -20 0 20 40 0 0.005 0.01 0.015 0.02 0.025 0.03 Crack Opening (in) To ta l L oa d (k) Load Before PT Load After Each Increment of PT

Figures 49 and 50 also show that continuity is maintained for negative moment after unloading. Full-Size Specimen 2 After completion of the first full-size test, the diaphragm and girders were cut apart. The second specimen was formed by turning the same girders end-for-end and forming a new diaphragm. When the slab was cast for the first specimen, the last 12 ft (3.7 m) of the slab was left off (see Figure 26). When the girders were turned around, there was room to cast 12 ft of slab on either side of the new diaphragm so that a complete joint was formed. The new slab was connected to the existing slab by bars extending from the existing slab. The slab section and diaphragm were poured as a single mono- lithic pour. The connection for the second full-size specimen was a bent-strand connection (see Figure 51). This connection was designed to a capacity of 1.2 Mcr, the same as full-size Spec- imen 1. The strand length was kept at 26 in., the same as Spec- imens 1 and 3. To get the proper capacity, a total of 10 bent strands were needed. The girder had a total of 20 strands, so only half of the strands were needed. The pattern for the 33 extended strands (see Figure 51) was chosen so that the strands were symmetrical and there was as much space as possible between adjacent strands. This minimizes interaction between the strands and maximizes bond strength. This specimen was tested at 21 days, after ensuring that deck slab-diaphragm concrete strength exceeded 4,000 psi. As with the first specimen, the loading mechanisms were placed 22.5 ft from the face of the diaphragm. The second full-size specimen was loaded as follows: 1. The east span was loaded to −38 kips. 2. The west span was loaded to −38 kips; at this point, the negative live-load moment was applied at the connection. 3. The east span was unloaded. 4. The west span was unloaded. 5. The east span was loaded to +20 kips; at this point, the positive live-load moment was applied at the connection. 6. The west span was loaded to +20 kips; at this point, twice the positive live-load moment was applied at the connection. 7. The east span was unloaded; at this point, the positive live-load moment was applied at the connection. 8. The west span was unloaded. Figure 49. Change in end reactions: application of additional positive moment. -20000 -15000 -10000 -5000 0 5000 10000 15000 20000 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Time (min) Ch an ge in R ea ct io ns (p ou nd s) East Reaction West Reaction East = -38k West = 0 East = 0 West = -38k East = -38k West = -38k East = 10k West = 0 East = 10k West = 10k East = 30k West = 10k East = 30k West = 30k East = 40k West = 30k East = 40k West = 40k East = 40k West = 42k East = 0 West = 40k East = -38k West = 0 East = 0 West = -38k East = -38k West = -38k Applied Loads Negative Load = Negative Moment Positive Load = Positive Moment

34 Figure 50. Change in bottom flange strain: application of additional positive moment. -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Time (m) Ch an ge in B ot to m F la ng e St ra in s (m icr os tra in) East Beam West Beam East = -38k West = 0 East = 0 West = -38k East = -38k West = -38k East = 10k West = 0 East = 10k West = 10k East = 30k West = 10k East = 30k West = 30k East = 40k West = 30k East = 40k West = 40k East = 40k West = 42k East = 0 West = 40k East = -38k West = 0 East = 0 West = -38k East = -38k West = -38k Applied Loads Negative Load = Negative Moment at joint Positive Load = Positive Moment at joint Figure 51. Full-size Specimen 2, bent strand.

Figures 52, 53, 54, and 55 show the results of the first load- ing. The load and bottom flange strains generally exceed those predicted by elastic analysis, especially when positive moment is applied and both spans are loaded. However, since there was no cracking observed at the diaphragm, the system should be continuous, so results of the load distribu- tion and the strains will be used as a baseline for comparison with other results. As with the first full-size specimen, the girders were post-tensioned in four increments to simulate creep and shrinkage. At the start of post-tensioning, the end reactions were 33 kips. The post-tensioning should have increased the end reactions by 8 kips. The first increment of post- tensioning increased the end reactions to 35 kips as expected; but, after the first increment of post-tensioning was applied, the pump for the post-tensioning ram broke and repairs took several days. When it was time to apply the last three incre- ments of post-tensioning, it was found that the end reac- tions had dropped 3 kips. This drop was mostly due to tem- perature changes, although there was also a slight movement of the west-end support (this support was monitored for the remainder of the test, and no further movement was found). As a result of this drop in the end reaction, the post- tensioning, when complete, increased the end reactions by 5 kips to a total of 38 kips rather than to the expected 41 kips. At this point, the applied positive moment was approximately 250 k-ft or 0.6 Mcr. As expected, no cracking was detected at the diaphragm. 35 In an effort to crack the joint, the specimen was loaded with a positive load in order to create additional positive moment at the joint. When a positive load of 20 k was applied at both points, the first cracks appeared at the diaphragm. The total applied positive moment at the joint was approximately 445 k-ft or 1.07 Mcr. Additional positive load up to 40 kips/point was applied. The moment at the diaphragm reached 640 k-ft or 1.54 Mcr. The average crack opening at the diaphragm was 0.011 in. As with the initial load, the data showed that the responses gen- erally exceeded that expected from elastic analysis. How- ever, when compared with the base line (see Figures 54 and 55), the responses indicated that continuity was maintained. Table 2 compares the end reactions and midspan bottom flange strains for both the uncracked section under a load of +20 kips/point and the cracked section under a load +40 kips/ point. Since the positive load is doubled, the ratio of the responses should be 2. As seen in Table 2, the average ratio of the end reactions is 1.97. This is a reasonable agreement. The average ratio of the strains is 2.13, higher than 2, but rea- sonable considering that in some cases small numbers are being compared. When additional positive load was applied, the specimen began to lift off the center supports, so it was no longer possible to apply positive moment to the connection through load. The research team had two choices: wait for the weather to warm up (which would increase the end reaction) or artifi- cially increase the end reaction. It was decided to increase the end reactions by jacking and shimming the end supports. -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 5 10 15 20 Time (min) Ch an ge in R ea ct io ns (p ou nd s) East Rxn West Rxn East Beam Loaded West Beam Loaded Both Beams Loaded End Reactions if Simple Span End Reaction - Loaded Span Continuous - One Span Loaded End Reaction - Continuous Both Spans Loaded End Reaction - Unloaded Span Continuous - One Span Loaded Figure 52. Change in end reactions: load to negative LL moment.

The west end was jacked and shimmed approximately 2.5 in., and then the east end was shimmed by a similar amount. With the combination of post-tensioning and shimming, the end reactions increased to 58 kips or 25 kips above the orig- inal reaction value, providing a total positive moment of 1,250 k-ft, which equals 3.0 Mcr or 2.5 times the nominal 36 capacity of 1.2 Mcr. The cracks at the bottom flange of the girder had opened to an average of 0.07 in. (see Figure 56). Unlike the bent-bar specimen, the crack openings were rea- sonably consistent on all four faces. Figure 57 shows the opening of one crack as a function of applied moment. There were cracks in the slab (see Figure 58) and at the bottom of -10000 -8000 -6000 -4000 -2000 0 2000 4000 0 5 10 15 20 25 Time (min) Ch an ge in R ea ct io n (po un ds ) East Beam West Beam End Reaction - Unloaded Span Continuous - One Span Loaded End Reaction - Continuous Both Spans Loaded End Reaction - Loaded Span Continuous - One Span Loaded End Reactions if Simple Span East Beam Loaded West Beam Loaded Both Beams Loaded Figure 54. Change in end reactions: load to positive LL moment. -20 0 20 40 60 80 0 5 10 15 20 Time (min) Ch an ge in B ot to m F la ng e St ra in (m icr os tra in) West Beam East Beam Strain if Simple Spans Strain - Loaded Span Continuous - One Span Loaded Strain - Unloaded Span Continuous - One Span Loaded Strain - Continuous - Both Spans LoadedEast Beam Loaded Both Beams Loaded West Beam Loaded Figure 53. Change in bottom flange strains: load to negative LL moment.

the diaphragm, and a small diagonal crack formed in the face of the diaphragm. This type of cracking was seen in the stub specimens and was usually a sign of impending failure. The jacking and shimming was done in increments, and the system was loaded to the negative live-load moment at various points during this process. Continuity, as measured by changes in the end reactions and strains in the girders, was 37 maintained until the last load cycle. In the last load cycle, the end reactions increased and strains increased significantly over the fully continuous case. Table 3 compares the end reactions and bottom flange strains of the baseline case for negative moment at the support (see Figures 52 and 53). The important ratio is the case in which both spans are loaded because this case represents the full live-load moment at the TABLE 2 Comparison of responses for positive moment: full-size Specimen 2 -60 -50 -40 -30 -20 -10 0 10 20 0 5 10 15 20 25 Time (min) Ch an ge in B ot to m F la ng e St ra in (m icr os tra in) West Beam East Beam Strain if Simple Spans Strain - Loaded Span Continuous - One Span Loaded Strain - Continuous - Both Spans Loaded Strain - Unloaded Span Continuous - One Span Loaded East Beam Loaded Both Beams Loaded West Beam Loaded Figure 55. Change in bottom flange strains: load to positive LL moment. Baseline Load = +20k Load = +40k Ratio End Reaction East/Load East (lb) –8,200 –16,500 2.01 End Reaction East/Load Both (lb) –6,800 –13,500 1.99 End Reaction East/Load West (lb) 1,150 2,700 2.35 End Reaction West/Load East (lb) 1,040 1,550 1.49 End Reaction West/Load Both (lb) –6,500 –13,500 2.08 End Reaction West/Load West (lb) –8,075 –15,250 1.89 Average 1.97 Strain East/Load East (microstrain) –34 –73 2.15 Strain East/Load Both (microstrain) –30 –63 2.10 Strain East/Load West (microstrain) 3 9 3.00 Strain West/Load East (microstrain) 5 7 1.40 Strain West/Load Both (microstrain) –26 –56 2.15 Strain West/Load West (microstrain) –32 –63 1.97 Average 2.13

support. The ratio here is about 1.3, indicating a 30% drop in continuity. The system still shows some continuity, but it is clearly reduced. In the section on the analytical studies, it was found that after cracking, continuity was predicted to drop by 20% or more. This was not found in the experimental study until now, the point at which the connection was about to fail and the crack had propagated into the slab. Actually, this is the point where the experiment became consistent with the model. 38 As noted previously, the models predict that when positive moment cracks occur in the joint, the crack immediately prop- agates into the slab (see Figure 12). The experiments show this does not happen. The cracks start at the bottom of the joint and propagate upward under increasing load or under cyclic loading. When the crack finally penetrates the slab (as it did in this last case), the cracked section is now reasonably close to the cracked section used in the models and the expected drop in continuity is seen. Since the system was also to be tested for negative moment capacity, the positive moment testing was stopped at this point so that connection would not become excessively dam- aged. The ends of the girders were jacked up, and the shims were removed. The post-tensioning was also removed. The cracks closed back to openings of 0.005 in. Due to the tortu- ous nature of cracks in concrete, it is rare that the cracks close all the way back when load is removed. The end reactions also dropped to 25 kips because of the permanent deforma- tions at the joint and in the diaphragm (recall that the dia- phragm had also cracked). The system was subsequently reloaded with the negative live-load moment. Figures 59 and 60 show the end reactions and strains measured from the ini- tial loading sequence (before post-tensioning and jacking the ends) compared with this final loading sequence. The results show full continuity was restored. The tests show that the system maintains continuity even if positive moment cracking occurs at the joint. Loss of con- tinuity does not occur until the slab and diaphragm crack and the connection is near failure. Figure 56. Crack at bottom of girder after post- tensioning and shimming. -1000 -500 0 500 1000 1500 2000 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Crack Opening (inch) A pp lie d M om en t (ft -k) Initial (pt) Load/Unload after 1st Jacking West 2nd Jacking West 1st Jacking East 2nd Jacking East Load/Unload After 1st Jacking East Load/Unload after 2nd Jacking East Load/Unload After Remove PT and Shims 1.2 Mcr Nom Figure 57. Crack opening at northwest joint as a function of applied moment.

NEGATIVE MOMENT CAPACITY After the positive moment/continuity testing was com- plete, the specimen was tested for negative moment capac- ity. The deck was reinforced for negative load as required by the provision of the AASHTO LRFD Specifications (12). Figure 61 shows the deck reinforcing. Using the design concrete strength of 6,000 psi and assuming 60 ksi yield for the steel, the nominal moment capacity was calculated at 1,630 k-ft. This capacity increased to 2,200 k-ft when recal- culated using actual material properties of 11 ksi for the con- crete compressive strength and 80 ksi for yield of the steel. With the two-span configuration shown in Figure 26, the required applied load would have exceeded 200 kips/point. This would have required building a massive frame, and there were concerns that this much load would cause local failures. The solution was to test the girder as a cantilever and to allow the dead load to apply some of the negative moment. 39 The negative moment caused by the dead load can be calcu- lated accurately since the weight of the specimen is known from the measured reactions. Referring to Figure 26 for direc- tions, a downward load of 50 kips was applied to the east span to keep the system stable. Then, an upward load of 80 kips was applied in the west span. The combination of the two loads reduced the west-end reaction to about 7 kips. The west end was jacked up, and the west support was removed. The jack was released. At this point a negative moment of 545 k-ft was being applied. The west cylinder load was then reduced in increments of 5 kips. Cracking occurred at a moment of 880 k-ft. This was less than the cracking moment of 930 k-ft calculated using the design concrete compressive strength for the deck slab, which was 4 ksi. Using the measured material properties, the expected cracking moment increased to 1,580 k-ft. The reduction in strength was probably caused by the cracking that occurred in the deck slab during the positive moment testing. When the deck cracked, the cracks were always full depth (see Figure 62). As the negative moment increased, the deck continued to crack and the cracks propagated down into the girders (see Figure 63). The joint began to open from the top (see Fig- ure 64). Finally, the bottom of the girder crushed (see Fig- ure 65) at an applied moment of 2,250 k-ft, just 2% above the failure moment capacity predicted using actual material strengths. The cracking that occurred during the positive moment testing did not affect the negative moment capacity, although it did reduce the negative cracking moment. FINITE ELEMENT MODELING To evaluate the behavior of positive moment connections, a three-dimensional finite element model (FEM) was devel- oped, which included nonlinear effects of cracking and crush- ing of concrete as well as yielding of steel bars and strands. TABLE 3 Comparison of responses: cracked versus uncracked diaphragm Figure 58. Slab cracking in full-size Specimen 2. Baseline, Uncracked Baseline, Cracked Ratio Highest/Lowest End Reaction East/Load East (lb) 14,500 16,000 1.10 End Reaction East/Load Both (lb) 11,000 14,500 1.32 End Reaction East/Load West (lb) –3,300 –900 3.67 End Reaction West/Load East (lb) –2,500 –2,200 1.14 End Reaction West/Load Both (lb) 10,200 12,900 1.26 End Reaction West/Load West (lb) 13,300 14,900 1.12 Strain East/Load East (microstrain) 62 71 1.15 Strain East/Load Both (microstrain) 51 66 1.29 Strain East/Load West (microstrain) –10 –3 3.33 Strain West/Load East (microstrain) –10 –9 1.11 Strain West/Load Both (microstrain) 46 53 1.15 Strain West/Load West (microstrain) 60 62 1.03

Among the available finite element programs, ANSYS was chosen owing to its efficient element library and material models for the analysis of reinforced and prestressed con- crete members (27). The choice of three-dimensional model- ing was due to the fact that concrete element in ANSYS is three-dimensional and accurate analysis of the variable 40 width cross section of the composite section required three- dimensional analysis. Concrete is modeled using eight-noded SOLID65 elements with three degrees of freedoms at each node. The element is capable of simulating smeared cracking in three orthogonal directions, crushing, and plastic deformations. Steel reinforce- -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 2 4 6 8 10 12 14 16 18 20 Time (min) Ch an ge in E nd R ea ct io ns (p ou nd s) East Reaction Initial West Reaction Intial East Reaction Final West Reaction Final -20 0 20 40 60 80 0 2 4 6 8 10 12 14 16 18 20 Time (min) B ot to m F la ng e St ra in s (m icr os tra in) East Beam Initial East Beam Final West Beam Final West Beam Initial Figure 59. Comparison of change in end reactions: initial and final loading. Figure 60. Comparison of change in bottom flange strains: initial and final loading.

ment and prestressing strands are both modeled using the two- noded LINK-8 truss elements with three degrees of freedom at each node. The element is capable of simulating plasticity, stress stiffening, and large deflections. The equilibrium equa- tions are solved using the Adaptive Descent method; this method switches to a stiffer matrix if convergence difficul- ties are encountered and to the full tangent matrix as the solu- tion converges. Due to the softening behavior of concrete, a displacement control strategy is adopted. Information about the elements, convergence and solution methods can be found in the cited reference. One of the challenges in modeling this type of bridge is the construction sequence, in which the girders are first pre- stressed and then assembled together with the deck and dia- phragm concrete. Several methods were tried, but the approach adopted was to model the continuous bridge system. Since the main concern is on the behavior of the diaphragm and since the stiffness of the prestressed girder is considerably higher than that of the diaphragm, it was decided to model the prestressed girder as an equivalent reinforced concrete 41 girder with equal stiffness and cracking moment. This method was verified by comparing the behavior of a prestressed concrete girder modeled as an equivalent reinforced con- crete girder with the experiments of Elzanaty et al. (28) and fine element mesh (FEM) reported by Kotsovos and Pavlovic for the same experiment (29). A FEM was created of the stub specimen (see Figure 66). Because of the large size of the model, only one-quarter of the specimen was modeled. This model would simulate the original experimental plan of lifting both ends simultaneously. However, the actual experimental procedure was to fix one end and lift the other. It can be shown by simple structural analysis that this FEM will still provide accurate stresses, but the deformation of the free end will be half that measured. Therefore, when comparing FEM deflections with the exper- iments, the FEM deflections are doubled. Three FEMs were created: no connection, bent strand, and bent bar. In all cases, the girder ends were not embedded in the diaphragm. Figure 67 shows the predicted load versus deflection graphs compared with all six stub specimens (although the models do not account for embedment or web bars). The experimental Figure 61. Deck slab reinforcement. Slab Web Cracks Top Flange b cks Figure 62. Full-depth slab cracks negative moment capacity testing. Figure 63. Negative moment cracks in girder.

42 data shown are after 5,000 cycles. All of the specimen load vs. deflection lines are lower (less stiff) than the model, except for Specimen 6 (bent bar, embedded, web bars). All of the curves fall above the curve for no connection and below the curves for the bent bar and bent strand. The most probable reason for this is that the FEM did not account for the cold or construction joint at the beam-diaphragm interface. Such joints are much weaker than monolithic concrete. The experi- mental data end below the FEM data because failure in the FEM is based on rupture of the steel in monotonic loading while the experimental specimens failed by pull-out or fatigue. The FEM was not capable of simulating these failure modes. Figure 68 shows the moment versus curvature relation- ship for the bent-strand model and the two bent-strand spec- imens, Specimens 1 and 3. The moment-curvature relation- ship obtained from the RESPONSE program (22), which was used to obtain the moment versus curvature response for the RESTRAINT program, is also shown. Note that a similar behavior to the load-deflection graphs is observed. Specimen 1 exhibits some odd behavior, but recall that this specimen may have sustained some damage because of thermal load before testing (see previous section). The moment-curvature relationship for the bent-bar Specimen 2 is shown in Figure 69 and confirms the behavior shown in Figures 67 and 68. The FEMs show promise in predicting the behavior of the connections, but some improvements are needed. First, the joint between the girder and diaphragm should be modeled as a cold or construction joint. Second, the interface between the strands and the diaphragm concrete should be modeled appropriately to account for the slip observed in the experi- ments. Finally, the model must be able to account for pull- out and fatigue failures. Time and budget consideration pre- vented further FEM studies. Crushing at Bottom Girder Diaphragm Figure 65. Crushing at bottom of joint under negative moment. Figure 66. Finite element mesh for the stub specimens. Diaphragm Top Flange Crack hragm lange Figure 64. Separation at top of joint under negative moment.

43 (a) (b) 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 2 2.5 3 Deflection (inches) Lo ad (k ips ) Bent Strand FE Bent Bar FE No Positive Moment Connection FE o 0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Deflection (in) Lo ad (K ) Bent Strand FE Bent Bar FE No Positive Moment Connection FE 14 536 2 Figure 67. Stub specimen load versus deflection compared with FEM results.

44 0 500 1000 1500 2000 2500 0 0 .0005 0 .001 0.0015 Curvature M om en t ( kip -ft ) Response Program Present FE Analysis Bent Strand Specimen -400 -300 -200 -100 0 100 200 300 400 -0.0001 0 0.0001 0.0002 0.0003 0.0004 Curvature M om e n t ( ki p- ft ) Response Program Present FE Analysis Specimen 1 Specimen 3 Figure 68. Stub specimen moment versus curvature compared with FEM results bent strand.

45 0 150 300 450 600 750 0 0.0002 0.0004 0.0006 0.0008 0.001 Curvature M om en t ( kip -ft ) Response Program Present FE Analysis Bent Bar Specimen -450 -300 -150 0 150 300 450 -0.0002 -0.0001 0 0.0001 0.0002 Curvature M om e n t ( ki p- ft ) Response Program Specimen 2 West Side Present FE Analys is Figure 69. Stub specimen moment versus curvature compared with FEM results bent bar.

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 519: Connection of Simple-Span Precast Concrete Girders for Continuity includes recommended details and specifications for the design of continuity connections for precast concrete girders. Also included in the report are examples illustrating the design of four precast girder types made continuous for live load.

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