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

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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 Figure 5. Connection capacity (stub girder) the required loading regime. Complete details of the experi- specimen. 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 The analytical study had suggested that, to counteract the connection, the diaphragm was cut out and the girders were time-dependent effects, it was not efficient to have a con- turned end-for-end, placing the previously unused end of the nection where the capacity exceeded 1.2 times the cracking stub at the diaphragm. The diaphragm and a portion of the moment (1.2 Mcr), so the bent-strand or bent-bar connections slab could then be cast and new specimens created (Speci- were detailed to have a capacity of 1.2 Mcr. The usual design mens 3 and 4). For consistency and to allow attachment of assumption is that cracking will occur at the interface of the the loading mechanism, the ends of the slabs were cut off of beam and the diaphragm, but that the failure will occur in the the previously used girders when they were turned end-for- diaphragm concrete. Therefore, the cracking moment, Mcr is end (Specimens 3 and 4). Specimens 5 and 6 each used new usually based on the composite cross section, but assuming girders, but the slabs were not cast all the way to the end. the entire section is made of diaphragm concrete. Again, this was for consistency and to allow attachment of All bent bar connections were detailed using hooked No. 5 the loading mechanism. bars meeting the provisions for hooked bars in the AASHTO To understand the loading regime, it is necessary to consider LRFD Specifications (see Figure 6). It was necessary to off- a multispan bridge. As the truck traverses the first two spans, set bars so that they would mesh without interference, result- the connection between the first two spans is subjected to the ing in an asymmetrical connection. As will be discussed maximum negative live-load moment. As the truck enters the later, this asymmetry seems to have affected the connection third span, this same connection is now subjected to the max- behavior. imum positive live-load moment. The value of the maximum For the bent strand, the number of strand and the length of negative live-load moment was determined by analyzing two-, the strand to be embedded in the diaphragm were determined three-, and four-span bridges, with each span being 50 ft. The based on the equations suggested by Salmons and others (810, maximum negative live-load moment was almost the same for 13), which are given in the previous section on the literature all three bridges and was found to be approximately 365 k-ft. search. The number of strands was chosen arbitrarily as six Analysis of three- and four-span bridges yielded the maxi- because this number used the entire bottom row of strands. The mum positive live-load moment, which was determined to be TABLE 1 Details of positive moment connections in the stub specimens Specimen Type Diaphragm Girder End Special Cycles Number of Width Embedment Feature to Specimen (in.) (in.) 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 56,000 in diaphragm 6 Bent bar 26 8 Web bars 13,3000

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Figure 6. Details of the connections.

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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 Figure 7. Test set-up for the stub girder specimens. 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 approximately 90 k-ft. All moment values were at the face of markedly. There is a slight reduction in stiffness with addi- the diaphragm. tional cycles, but the change is small. However, during the The loading regime was designed to represent the worst cyclic loading, there is still load transfer across the joint. Even- case loading. In this case, it was assumed that creep, shrink- tually the positive moment connection fails, either by pull out age, and/or temperature strains in the deck and girders would of the strand or fracture of the bars. The resulting load ver- produce a positive moment equal to the nominal cracking sus deflection graph shows the resistance, and eventual fail- moment, Mcr. It was also assumed that the cracking would ure, of the slab alone (see Figure 10). At this point, the con- occur at the beam-diaphragm interface and that the limiting nection behaves like a hinge. factor would be properties of the diaphragm concrete. There- It was noted that the cracking behavior is quite different fore, the nominal cracking moment was calculated using the than that assumed in theoretical models. These models assume geometry of the composite beam, but the properties of dia- the concrete is monolithic and when cracking occurs, the phragm concrete. The section is considered as reinforced but resulting cracked section shows the cracks going all the way not prestressed. This is consistent with normal design prac- into the slab (see Figure 12). In reality, there are cold (con- tice. The deck and diaphragm were assumed to have a nom- struction) joints at the beam-diaphragm interface and at the inal strength of 4,000 psi, and the nominal cracking moment beam-slab interface. Because the joint at the beam-diaphragm is calculated as 245 k-ft. Since the connection was assumed interface is based on a weak chemical bond, which is not as to be loaded to Mcr by time-dependent and temperature effects, strong as the tensile strength of monolithic concrete, cracks the live load would cycle the moment about Mcr. may form before the calculated cracking moment is reached. The loading regime is shown in Figure 9. The first three However, at the top of the crack, the joint at the beam-slab cycles are between the positive and negative live-load interface tends to act as a crack arrestor. It was noted that the moments. This simulates loading the bridge without any time- crack would form at the bottom of the joint, propagate to the dependent moments and provides initial stiffness data for the top of the beam, and stop. The cracks did not propagate into connection. Next, the connection is loaded three cycles to the the slab until just before the connection failed (see Figure 13). cracking moment to simulate the assumed effect of the time In fact, it was found that formation of cracks in slab was usu- dependent and temperature moments. ally a sign of impending failure.

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

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

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

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17 Figure 15. Failure of Specimen 1, bent strand. 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 Figure 14. Bent strand, Specimen 1. face of the diaphragm (see Figure 21). Stub Specimen 4: Bent Bar, Beam Ends Embedded end of the girder and the bars were field bent. In the field- bending operation, it was difficult to bend the bars consis- Specimen 4 was identical to Specimen 2 except that the gird- tently to the same length and radius. The lack of consistency ers were embedded 6 in. into the diaphragm. This specimen 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. Figure 16. Bent bar, Specimen 2.

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

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19 only lasted for 11,600 cycles. Examination of the data showed rups were spanning the crack and preventing failure (see Fig- no particular or peculiar behavior that might account for this ure 23). This detail may be useful in seismic zones to provide unexpected failure. As explained in Appendix B, the cyclic additional ductility. 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 Stub Specimen 6: Bent Bar, Beam Ends much wider than those on the other side (0.05 in. on one side, Embedded, Web Bars Added 0.025 in. on the other). These crack openings were not unusu- ally large compared with those for other specimens. Approx- Specimen 6 used the same bent-bar configuration as Spec- imately 1,000 cycles later, the specimen failed. The bars frac- imens 2, 4, and 5, but this connection used horizontal bars tured and diagonal cracks occurred in the diaphragm. passed through the web of the beam (see Figures 6 and 24). The cause of this early failure is uncertain, but the most The survey results showed details similar to this are used by probable explanation is uneven stresses in the bars. Bent-bar some states. Since the stub beams were fabricated before it connections are difficult to construct because the bars must be was decided to use this type of specimen, no holes were cast installed straight and then field bent. As a result, the bar bends in the web for these bars. As a result, the holes had to be are inconsistent (see Figure 16). This inconsistency in the bends drilled. The vertical beam stirrups were located with a mag- may have caused some bars to take more load than others, leading to a premature failure. Bonded strain gages had been netometer, and a hammer drill was used to make the holes. installed on some of the bars; but only one survived beyond No. 5 reinforcing bars were then passed through the holes and 5,000 cycles, so comparisons of bar strains are not possible. 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. 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 Figure 23. Failure of Specimen 5, stirrups span the crack. 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- Figure 22. Additional diaphragm stirrups, Specimen 5. Figure 24. Web bars, Specimen 6.