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Publication Number:  FHWA-HRT-17-093    Date:  February 2018
Publication Number: FHWA-HRT-17-093
Date: February 2018

 

Adjacent Box Beam Connections: Performance and Optimization

CHAPTER 5. DISCUSSION

This chapter discusses the effect of certain connection parameters, including the depth of the connection, condition of the connection, the level of transverse PT applied, and the material used in the connection. The data are presented using bar graphs of the average values, with the error bars indicating the minimum and maximum values observed. The average, minimum, and maximum values are based on a five-point moving average of the recorded values.

PARTIAL- VERSUS FULL-DEPTH CONNECTION

Because tests on partial- and full-depth conventional grouted connections were not performed with the same level of cracking and boundary conditions, a meaningful analysis isolating the effect of the connection depth was not possible. Therefore, this section focuses on the comparison between the partial- and full-depth UHPC connections only.

The effect on the longitudinal strains in the bottom flange of the beams is shown in figure 91. When the partially stiffened end condition was used, little effect can be seen as the strains in the loaded and unloaded beams were virtually identical between the partial- and full-depth connections. However, when the fully stiffened boundary condition was employed, the range of strains in each of the full-depth beams decreased around 10 με. This may have been caused by a higher EI due to a larger area of material in the connection. The larger drop in strain between the full- and partial-depth connections in the fully stiffened boundary configuration could be caused by the full-depth connection limiting transverse bending through the connection. This could lead to increased deflection and, therefore, increased longitudinal strain.

This graph gives a comparison of longitudinal strains in the beams with partial- and full-depth ultra-high performance concrete (UHPC) connections under the partially and fully stiffened boundary conditions. The x-axis shows six conditions: partially stiffened 54 kip (240 kN), partially stiffened 72 kip (320 kN), partially stiffened 90 kip (400 kN), fully stiffened 54 kip (240 kN), fully stiffened 72 kip (320 kN), and fully stiffened 90 kip (400 kN). The y-axis shows strain range and ranges from 0 to 120 microstrain. For each category on the x-axis, there are two stacked bars: beam B partial depth with beam A partial depth stacked above as well as beam B full depth with beam A full depth stacked above. The strains in the beams with a full-depth connection are lower than in ones with a partial-depth connection, between 3 to 5 microstrain lower for the loaded beams with partially stiffened boundaries, and about 10 microstrain for loaded beams with fully stiffened boundaries.

Source: FHWA.
1 kip = 4.448 kN.
*Fully stiffened strain is reported as the strain range.
Figure 91. Graph. Comparison of the longitudinal strain ranges for the partial- and full-depth UHPC connections.

The loaded beam proportion of moment for the two connection depths under the partially stiffened boundary condition can be seen in figure 92. The moment was well distributed with both the partial- and full-depth connections, with more equitable distribution occurring when a full-depth shear key was used. This could be caused by increased torsional stiffness provided with a full-depth connection. This increased stiffness allows the beams to deflect more evenly and results in more uniform Δδ and strains in the two beams. This is shown in both the deflection- and strain-based measures of proportion of moment.

This graph shows a comparison between the proportion of moment carried by the loaded beam for the beams with partial- and full-depth ultra-high performance concrete (UHPC) connections under the partially stiffened boundary condition. The x-axis shows three conditions: partially stiffened 54 kip (240 kN), partially stiffened 72 kip (320 kN), and partially stiffened 90 kip (400 kN). The y-axis shows the proportion of moment carried by beam A and ranges from 40 to 60 percent. For each category on the x-axis, there are four bars, specifically strain full depth stacked on top of deflection full depth and strain partial depth stacked on top of deflection partial depth. The proportion of moment carried by the full-depth beam as assessed by both the strain and deflection measurements is consistently 1 percent lower than the partial-depth beam except for the strain-based proportion for partial-depth beam in the 72-kip (320-kN) loading range where they are equal.

Source: FHWA.
1 kip = 4.448 kN.
Figure 92. Graph. Comparison of the loaded beam proportion of moment between the partial- and full-depth UHPC connections.

As with the performance with longitudinal strains, both connection depths were able to minimize Δδ between the beams, limiting the differential movement to 0.004 inch (0.102 mm) in both cases. The full-depth connection again performed slightly better, limiting observed values between the beams to within 0.002 inch (0.051 mm). A plot showing the Δδ for the two connection depths is shown in figure 93.

This graph shows a comparison of the differential deflections (uppercase delta subscript lowercase delta) recorded for the beams with partial- and full-depth ultra-high performance concrete (UHPC) connections under the partially stiffened boundary condition. The x-axis shows six groupings of bars: partially stiffened 54 kip (240 kN), partially stiffened 72 kip (320 kN), partially stiffened 90 kip (400 kN), fully stiffened 54 kip (240 kN), filly stiffened 72 kip (320 kN), and fully stiffened 90 kip (400 kN). The y-axis shows differential deflection and ranges from -0.004 to 0.010 inch (-0.102 to 0.254 mm). Each grouping has two bars: one for partial depth and another for full depth. In the partially stiffened case, the partial-depth connection has differential deflections of 0.0028- 0.0028- and 0.0025-inch (0.071-, 0.071-, and 0.064-mm) for the 54-, 72-, and 90-kip (240-, 320, and 400-kN) loading ranges, respectively, while for the full-depth connection, they were 0.0002-, 0.0005-, and -0.0015-inch (0.005-, 0.013-, and -0.038-mm) for the same ranges, respectively. Differential deflection under the full-depth connection were approximately 0.0005- 0.0006- and 0.0005-inch (0.013-, 0.015-, and 0.013-mm) for the 54-, 72-, and 90-kip (240-, 320, and 400-kN) loading ranges, respectively, while for the full-depth connection, they were 0.0008-, 0.0010-, and -0.0004-inch (0.020-, 0.025-, and -0.010-mm) for the same ranges, respectively.

Source: FHWA.
1 inch = 25.4 mm.
1 kip = 4.448 kN.
Figure 93. Graph. Comparison of Δδ of the partial- and full-depth UHPC connections.

Figure 94 shows the transverse strains in the connection at the mid-span as well as 6 ft (1.8 m) to the east side of the mid-span. This graph shows that the transverse strains in the connection were lower for the full-depth connection. Transverse strains were generated in the connection as it transferred the moment acting like a transverse beam. The full-depth connection was 2.5 times deeper than the partial-depth connection. This resulted in lower transverse strains in the extreme fibers of the full-depth connection.

This graph shows a comparison of the top transverse strain in the beams with partial- and full-depth ultra-high performance concrete (UHPC) connections under the partially stiffened boundary condition. The x-axis shows six conditions: partially stiffened 54 kip (240 kN), partially stiffened 72 kip (320 kN), partially stiffened 90 kip (400 kN), fully stiffened 54 kip (240 kN), fully stiffened 72 kip (320 kN), and fully stiffened 90 kip (400 kN). The y-axis shows strain range and ranges from 0 to 40 microstrain. For each category on the x-axis, there are two stacked bars: east partial depth with mid-span partial depth stacked above it as well as east full depth with mid-span full depth stacked above it. The strains in the beams with a full-depth connection are lower than in ones with a partial-depth connection, between 5 to 15 microstrain lower for the loaded beams and between 5 to 10 microstrain lower for the unloaded beams with partially stiffened boundaries. With the fully stiffened boundary, loaded beams with full-depth connections have a strain range between 7 and 10 microstrain lower than partial-depth connections, for the unloaded beams this difference is between 5 to 10 microstrain.

Source: FHWA.
1 kip = 4.448 kN.
Figure 94. Graph. Comparison of the top transverse strain ranges in the partial- and full-depth UHPC connections.

The performance of both the partial- and full-depth connections was satisfactory within the context of the metrics discussed here. The increased depth of the full-depth connection resulted in somewhat better load sharing and more uniform deformations; however, increasing the depth of the connection increases construction costs, especially if a more expensive material such as UHPC is being utilized in the connection.

CONDITION OF THE CONNECTION

This section discusses the performance of the partial-depth conventional grout connection with respect to the condition of the connection. This was the only configuration that was run in uncracked, partially cracked, and fully cracked connections. The responses of the beams are shown in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges for the 0.8- and 0-kip/ft (12- and 0-kN/m) PT levels.

The beams exhibited a nearly identical strain response to the loading cycles regardless of the condition of the connection, as can be seen in the comparison in figure 95. The cracked connections could still effectively transfer the load from one beam to the other when a level of PT was utilized likely through friction between the grout and the box beam concrete. Ranges of strain in the loaded beam were only about 2 με higher for beams with a cracked connection. When no PT was used, the strains on the unloaded beam remained the same regardless of crack condition, while strains on the loaded beam were seen to increase, especially on the beam with the fully cracked connection.

This graph shows a comparison of the longitudinal strain ranges in the partial-depth conventionally grouted connections based on the crack condition of the connection. The x-axis shows six categories: 0.8-kip/ft (12-kN/m) post-tensioning (PT) with 54-kip (240-kN) load, 0.8-kip/ft (12-kN/m) PT with 72-kip (320-kN) load, 0.8-kip/ft (12-kN/m) PT with 90-kip (400-kN) load, 0-kip/ft (0-kN/m) PT with 54-kip (240-kN) load, 0-kip/ft (0-kN/m) PT with 72-kip (320-kN) load, and 0-kip/ft (0-kN/m) PT with 90-kip (400-kN) load. The y-axis shows strain range and ranges from 0 to 70 microstrain. For each category on the x-axis, there are three stacked bar graphs: beam B uncracked with beam A uncracked stacked above it, beam B partially cracked with beam A partially cracked stacked above it, and beam B fully cracked with beam A fully cracked stacked above it. Strain levels in both beams are comparable in the condition that utilizes PT. But when no PT was used, the strains on the unloaded beam remained the same while strains on the loaded beam were seen to increase in connections with longer cracks.

Source: FHWA.
1 kip = 4.448 kN.
Figure 95. Graph. Comparison of longitudinal strain ranges based on the extent of cracking in the connection.

As shown in figure 96, Δδ was affected by the condition of the connection. The uncracked section was able to maintain a Δδ below 0.001 inch (0.025 mm). With the introduction of cracks in the connection, Δδ increased to between 0.002 and 0.004 inch (0.051 and 0.102 mm) for the partially cracked connection. When the connection was entirely debonded, Δδ of over 0.012 inch (0.305 mm) was observed in the 90-kip (400-kN) loading cycle. This demonstrates that the connection condition has the potential to have a significant impact on Δδ between adjacent beams.

This graph shows a comparison of the differential deflection (uppercase delta subscript lowercase delta) in the partial-depth conventionally grouted connections based on the crack condition of the connection. The x-axis shows six categories: 0.8-kip/ft (12-kN/m) post-tensioning (PT) with 54-kip (240-kN) load, 0.8-kip/ft (12-kN/m) PT with 72-kip (320-kN) load, 0.8-kip/ft (12-kN/m) PT with 90-kip (400-kN) load, 0-kip/ft (0-kN/m) PT with 54-kip (240-kN) load, 0-kip/ft (0-kN/m) PT with 72-kip (320-kN) load, and 0-kip/ft (0-kN/m) PT with 90-kip (400-kN) load. The y-axis shows differential deflection and ranges from 0 to 0.020 inch (0 to 0.508 mm). For each category on the x-axis, there are three bars: uncracked, partially cracked, and fully cracked. Regardless of loading range and level of PT, the average differential deflection for the uncracked and partially cracked connections were less than 0.001 inch (0.025 mm) and between 0.002 and 0.004 inch (0.051 and 0.102 mm), respectively. The fully cracked connection had average deflections between 0.005 and 0.007 inch (0.127 and 0.178 mm) with some PT and between 0.010 and 0.013 inch (0.254 and 0.330 mm) with no PT.

Source: FHWA.
1 inch = 25.4 mm.
1 kip/ft = 14.59 kN/m.
1 kip = 4.448 kN.
Figure 96. Graph. Comparison of Δδ between the beams based on the extent of cracking in the connection.

Figure 97 and figure 98 show a comparison of transverse strains in the connection and in the beams, respectively, based on the condition of the connection. Overall, there was not a large difference between the transverse strains in the connection. As for the internal transverse strains in the beams, the strains in the loaded beams were found to increase, while the strains in the unloaded beams were found to decrease. This is intuitive because when the connection is not intact, it cannot transfer loads as effectively.

This graph compares the top transverse strain range for the transverse strain gauge on the connection at the mid-span based on the crack condition of the connection. The x-axis shows six categories: 0.8-kip/ft (12-kN/m) post-tensioning (PT) with 54-kip (240-kN) load, 0.8-kip/ft (12-kN/m) PT with 72-kip (320-kN) load, 0.8-kip/ft (12-kN/m) PT with 90-kip (400-kN) load, 0-kip/ft (0-kN/m) PT with 54-kip (240-kN) load, 0-kip/ft (0-kN/m) PT with 72-kip (320-kN) load, and 0-kip/ft (0-kN/m) PT with 90-kip (400-kN) load. The y-axis shows strain range and ranges from 0 to 30 microstrain. For each category on the x-axis, there are three bars: uncracked, partially cracked, and fully cracked. There was no discernable difference between the transverse strain in the connection based on crack condition.

Source: FHWA.
1 kip/ft = 14.59 kN/m.
1 kip = 4.448 kN.
Figure 97. Graph. Comparison of the top transverse strain ranges at the mid-span in the connection based on the extent of cracking in the connection.

This graph compares the top transverse strain range for the transverse strain gauges in the loaded and unloaded beams at the mid-span based on the crack condition of the connection. The x-axis shows six categories: 0.8-kip/ft (12-kN/m) post-tensioning (PT) with 54-kip (240-kN) load, 0.8-kip/ft (12-kN/m) PT with 72-kip (320-kN) load, 0.8-kip/ft (12-kN/m) PT with 90-kip (400-kN) load, 0-kip/ft (0-kN/m) PT with 54-kip (240-kN) load, 0-kip/ft (0-kN/m) PT with 72-kip (320-kN) load, and 0-kip/ft (0-kN/m) PT with 90-kip (400-kN) load. The y-axis shows strain range and ranges from 0 to 25 microstrain. For each category on the x-axis, there are three stacked bars: beam B uncracked with beam A uncracked stacked above it, beam B partially cracked with beam A partially cracked stacked above it, and beam B fully cracked with beam A fully cracked stacked above it. The strains in beam A were found to increase, while the strains in beam B were found to decrease as the load range increased regardless of the level of PT.

Source: FHWA.
1 kip/ft = 14.59 kN/m.
1 kip = 4.448 kN.
Figure 98. Graph. Comparison of the top transverse strain ranges in the beams based on the extent of cracking in the connection.

The condition of the connection was found to have an impact on the performance of the connection, particularly when the PT force was removed. Loaded beam longitudinal and transverse strains and Δδ were seen to increase, while unloaded beam transverse strains were found to decrease. This shows that the condition of the connection plays an important role in force transfer.

TRANSVERSE PT

This section investigates the effect of transverse PT, which was evaluated using the loaded beam proportion of moment and Δδ between the two beams under different levels of transverse PT force.

Figure 99 and figure 100 show the measured longitudinal tensile strains at the mid-span and the calculated proportion of moment carried by the loaded beam, respectively, for the beams with an unstiffened partial-depth conventionally grouted connection. The two beams were loaded under different levels of transverse PT force distribution from 8 to 0.8 kip/ft (117 to 12 kN/m). The measured tensile strains in the two beams did not noticeably change under different levels of transverse PT applied. The calculated proportion of moment on the loaded beam were consistently between about 51 and 52 percent throughout all the PT levels.

This graph compares the longitudinal strain for the unloaded and loaded beams with unstiffened uncracked partial-depth conventional connections based on the level of post-tensioning (PT). The x-axis shows five PT conditions: 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12-kN/m). The y-axis shows strain range and ranges from 0 to 180 microstrain. For each category on the x-axis, there are three stacked bars: 54-kip (240-kN) load for beam B with beam A stacked above, 72-kip (320-kN) load for beam B with beam A stacked above, and 90-kip (400-kN) load for beam B with beam A stacked above. There was no discernable difference between the longitudinal strain in either beam regardless of the PT level.

Source: FHWA.
1 kip/ft = 14.59 kN/m.
1 kip = 4.448 kN.
Figure 99. Comparison of the longitudinal strain ranges for the unloaded and loaded beams with unstiffened uncracked partial-depth conventional connections based on the level of PT.

This graph compares the proportion of moment carried by the loaded beam for the beams with unstiffened uncracked partial-depth conventional connections based on the level of post-tensioning (PT). The x-axis shows five PT conditions: 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12 kN/m). The y-axis shows the proportion of moment carried by beam A and ranges from 45 to 55 percent. There are three stacked bars (strain at 54 kip (240 kN) with deflection at 54 kip (240 kN) stacked above it, strain at 72 kip (320 kN) with deflection at 72 kip (320 kN) stacked above it, and strain at 90 kip (400 kN) with deflection at 90 kip (400 kN) stacked above it) except for 8 kip/ft (117 kN/m), which only shows the 90-kip (400-kN) condition. There was no discernable difference between the proportion of moment in either beam regardless of the PT level.

Source: FHWA.
1 kip/ft = 14.59 kN/m.
1 kip = 4.448 kN.
Figure 100. Graph. Comparison of the loaded beam proportion of moment in the beams with unstiffened uncracked partial-depth connections based on the level of PT force.

Figure 101 shows Δδ for the beams connected with an unstiffened partial-depth conventionally grouted connection. Δδ also showed little variance, maintaining a value of approximately 0.002 inch (0. 051 mm). For comparison, the Precast Prestressed Concrete Bridge Design Manual includes a discussion that the acceptable amount of Δδ between adjacent box beams is 0.020 inch (0.508 mm) for spans up to 100 ft (30.5 m).(3)

This graph compares the differential deflection (uppercase delta subscript lowercase delta) for the beams with unstiffened uncracked partial-depth conventional connections based on the level of post-tensioning (PT). The x-axis shows five PT conditions: 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12 kN/m). The y-axis shows differential displacement and ranges from -0.002 to 0.010 inch (-0.051 to 0.254 mm). For each category on the x-axis, there are three bars representing three loading ranges: 54, 72, and 90 kip (240, 320, and 400 kN). There was no discernable difference between the differential displacements regardless of the PT level.

Source: FHWA.
1 inch = 25.4 mm.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 101. Graph. Comparison of Δδ in the beams with unstiffened uncracked partial-depth connections based on the level of PT force.

The beams with the partial-depth conventional grout connection were loaded with the stiffest boundary condition, with uncracked, partially cracked, and fully cracked connections. The partially and fully cracked conventionally grouted connections were loaded under transverse PT forces ranging from 8 to 0 kip/ft (117 to 0 kN/m). The results of the longitudinal tensile strain and Δδ are presented in figure 102 and figure 103, respectively. The intact connection did not see a notable effect on the longitudinal strain ranges between different levels of transverse PT. Similar observations were made for the partially and fully cracked connections. Δδ in the partially and fully cracked connection, however, was affected by the level of PT used in the beams. It can be seen that the uncracked connection maintained a Δδ of around 0.001 inch (0.025 mm) regardless of the level of PT force. The partially cracked connection had a Δδ under 0.0025 inch (0.064 mm) for PT levels less than 2 kip/ft (29 kN/m) and over 0.006 inch (0.152 mm) with the PT force removed. The difference was even more dramatic with the fully cracked connection, with Δδ doubling from 0.006 to 0.012 inch (0.152 to 0.305 mm) when the PT force was removed.

This graph compares the longitudinal strain ranges for the beams with fully stiffened uncracked partial-depth conventional connections based on the level of post-tensioning (PT) force and crack condition in the 90-kip (400-kN) loading range. The x-axis shows five PT conditions: 8, 4, 2, 0.8, and 0 kip/ft (117, 58, 29, 12, and 0 kN/m). The y-axis shows strain range and ranges from 0 to 70 microstrain. There are three stacked bars (beam B uncracked with beam A uncracked stacked above it, beam B partially cracked with beam A partially cracked stacked above it, and beam B fully cracked with beam A fully cracked above it) for each category on the x-axis except for 8 and 4 kip/ft (117 and 58 kN/m), which do not show bars for the uncracked condition, and 2 kip/ft (29 kN/m), which does not show bars for partially or fully cracked conditions. There was no discernable difference between the longitudinal strain range-based PT level and PT level.

Source: FHWA.
1 kip/ft = 14.59 kN/m.
Figure 102. Graph. Comparison of longitudinal strain ranges in beams with fully stiffened partial-depth connections based on the level of PT force.

This graph shows a comparison of the differential deflection (uppercase delta subscript lowercase delta) in partial-depth conventionally grouted connections based on the level of post-tensioning (PT) and crack condition of the connection. The x-axis shows five PT conditions: 8, 4, 2, 0.8, and 0 kip/ft (117, 58, 29, 12, and 0 kN/m). The y-axis shows differential deflection and ranges from 0 to 0.020 inch (0 to 0.508 mm). There are three bars (uncracked, partially cracked, and fully cracked) for each category on the x-axis except for 8 and 4 kip/ft (117 and 58 kN/m), which do not show bars for the uncracked condition, and 2 kip/ft (29 kN/m), which does not show bars for partially or fully cracked conditions. Regardless of level of PT, the average differential deflection for the uncracked and partially cracked connections were less than 0.002 inch (0.051 mm) and between 0.002 and 0.003 inch (0.051 and 0.076 mm), respectively. The fully cracked connection had average deflection of 0.005 inch (0.127 mm) with PT greater than 2 kip/ft (29 kN/m), 0.0065 inch (0.165 mm) with 0.8 kip/ft (12 kN/m) of PT, and 0.012 inch (0.305 mm) with no PT.

Source: FHWA.
1 inch = 25.4 mm.
1 kip/ft = 14.59 kN/m.
Figure 103. Graph. Comparison of Δδ in beams with fully stiffened partial-depth connections based on the level of PT force.

Figure 104 through figure 106 show the longitudinal strain, proportion of moment, and Δδ for the partially cracked full-depth conventionally grouted connection, respectively. It can still effectively transfer the loads between adjacent beams and limit Δδ as long as PT is present. Once the PT force was removed, changes were seen in all three measured variables. Longitudinal strain in the loaded beam increased by over 10 με, while the unloaded beam decreased by 5 με. This led to a 3 percent increase in the strain-based proportion of moment carried by the loaded beam. The deflection-based proportion of moment was also seen to increase by nearly 4.5 percent. Δδ increased from 0.0005 inch (0.013 mm) at 0.8 kip/ft (12 kN/m) of PT force to 0.019 inch (0.483 mm) with no PT applied.

This graph compares the longitudinal strains for beams with partially cracked unstiffened full-depth conventional connections based on the level of post-tensioning (PT). The x-axis shows four PT conditions: 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). The y-axis shows strain range and ranges from 0 to 160 microstrain. For each of the categories on the x-axis, there are three stacked bars: beam B at 54 kip (240 kN) with beam A at 54 kip (240 kN) stacked above it, beam B at 72 kip (320 kip) with beam A at 72 kip (320 kip) stacked above it, and beam B at 90 kip (400 kN) with beam A at 90 kip (400 kN) stacked above it. No difference was seen in the beams that utilized PT. When no PT was used, strains in the loaded beam (i.e., beam A) were seen to increase, and the unloaded beam (i.e., beam B) strains decreased in the 72- and 90-kip (320- and 400-kN) loading ranges by about 8 and 11 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 104. Graph. Comparison of longitudinal strain ranges in beams with partially cracked unstiffened full-depth conventional connections based on the level of PT force.

This graph compares the proportion of moment carried by the loaded beam for beams with partially cracked unstiffened full-depth conventional connections based on the level of post-tensioning (PT). The x-axis shows four PT conditions: 8, 40, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). The y-axis shows the proportion of moment carried by beam A and ranges from 40 to 70 percent. For each of the categories on the x-axis, there are three stacked bars: strain at 54 kip (240 kN) with deflection at 54 kip (240 kN) stacked above it, strain at 72 kip (320 kip) with deflection at 72 kip (320 kip) stacked above it, and strain at 90 kip (400 kN) with deflection at 90 kip (400 kN) stacked above it. When no PT was used, both measures of proportion of moment were seen to increase in the 72- and 90-kip (320- and 400-kN) loading ranges by about 3 percent.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 105. Graph. Comparison of loaded beam proportion of moment in beams with partially cracked unstiffened full-depth conventional connections based on the level of PT force.

This graph compares the differential deflection (uppercase delta subscript lowercase delta) for the beams with partially cracked unstiffened full-depth conventional connections based on the level of post-tensioning (PT). The x-axis shows four PT conditions: 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). The y-axis shows differential deflection and ranges from -0.0050 to 0.0250 inch (-0.127 to 0.635 mm). For each PT condition, three bars are shown for the following load ranges: 54, 72, and 90 kip (240, 320, and 400 kN). Differential deflection when PT was used was always around 0 inch (0 mm). When no PT was used, differential displacement in the 54-kip (240-kN) loading range remained near 0 inch (0 mm), while it increased in the 72- and 90-kip (320- and 400-kN) loading ranges to around 0.012 and 0.019 inch (0.305 and 0.483 mm), respectively.

Source: FHWA.
1 inch = 25.4 mm.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 106. Comparison of Δδ in beams with partially cracked unstiffened full-depth conventional connections based on the level of PT force.

The AASHTO LRFD Bridge Design Specifications recommends installation of transverse PT to develop a minimum of 0.25 ksi (1.7 MPa) compression at connection.(6) The Precast Prestressed Concrete Bridge Design Manual recommends PT forces ranging from 6 to 16 kip/ft (88 to 233 kN/m).(3) In general practice, the transverse PT force is commonly applied at the beam ends and at diaphragm locations. This limits the benefits of the PT effects to only the areas immediately surrounding these locations. Because of the discrete PT application points, the transverse PT force is not uniform along the connections, reducing its ability to mitigate tensile deformations in the connections and thus allowing cracks to initiate and propagate. If the transverse PT force can be more evenly distributed along the span, the system performance could improve from the increase in keyway shear strength due to the confinement force spread along the bridge length.(40) The induced compression can also compensate for some of the transverse tensile strain from structural loading, shrinkage, and thermal effects. In this study, the transverse PT force was applied at the beam ends and at the two in-span diaphragms along the 48-ft (14.6-m) span. (Refer to figure 22 for overall testing configuration.) High-strength PT bars were used at each PT location, reacting against 7- by 7- by 2-inch (178- by 178- by 51-mm) bearing plates. The bar was located mid-height in the shear key, about 9 inches (229 mm) from the top surface.

The transverse compression strain on the top surface of the shear key at 0, 4, and 10 ft (0, 1.2, and 3.0 m) away from the PT locations was measured before and after PT. It was found that the compression force dissipated quickly from the PT point. Figure 107 shows the distribution of compressive strains near the two middle PT points. When the bars had a PT of 100 kip (445 kN), the strain gauges located above the PT bar showed compressive strain readings between 150 and 250 με. Under the same PT, the strain gauges 4 and 10 ft (1.2 and 3.0 m) away from the PT bar recorded compressive strain readings of only 80 and 25 με, respectively. This strain corresponds to a compressive stress in the connection of about 800 psi (5.52 MPa) at the PT location. This is less than half of the 2,050-psi (14.1-MPa) compressive stress calculated to be present under the bearing plates of the PT rods. The stress decreased to only 300 psi (2.07 MPa) within 4 ft (1.2 m) of the PT location and only 100 psi (0.69 MPa) 10 ft away. This means that the PT force was not as effective at locations away from the application points. Similar results were observed by others for the full-depth conventional grout connections. A finite element model was developed by Sharpe to investigate the distribution of the transverse PT force.(44) The model indicated that PT forces dissipate quickly away from the PT locations. The system performance could be improved if the transverse PT force is well distributed along the span.

This bar graph compares the compressive strain measured along the connection and the post-tensioning (PT) force. The x-axis shows five conditions: east PT, 6 ft (1.8 m) east of the mid-span, mid-span, 6 ft (1.8 m) west of the mid-span, and west PT. The left y-axis shows compressive strain and ranges from 0 to 400 microstrain, and the right y-axis shows PT bar force and ranges from 0 to 120 kip (0 to 533.76 kN). The bars show connection compressive strain, and two red dots (one above east PT bar and one above west PT bar) represent the PT force. Strain at the PT locations are high at 150 and 250 microstrain, while 4 ft (1.2 m) away it drops to 85 microstrain and 10 ft (3.0 m) away it drops to 20 microstrain. There was 100-kip (444-kN) PT force at both the east and west PTs.

Source: FHWA.
1 kip = 4.448 kN.
1 ft = 0.305 m.
Figure 107. Graph. Connection compressive strain recorded during PT operation.

The level of PT was not found to affect the load carrying or Δδ in the beams as long as the connection was intact. For cracked connections with transverse PT applied, the connection could still effectively transfer the load, although Δδ increased. When the transverse PT force is removed, cracked connections can lose their ability to limit Δδ and their capacity to effectively transfer the moment. This results in increases in all of the measured factors, especially Δδ.

UHPC VERSUS CONVENTIONAL GROUT

This section compares the performance of the UHPC connections with the performance of the conventionally grouted connections. The full-depth conventionally grouted connection was included even though the connection could only be tested while the connection was cracked. The conventionally grouted values are taken from the series with 0.8 kip/ft (12 kN/m) of PT force, given that PT is a critical part of the detail.

Figure 108 and figure 109 show a comparison of longitudinal strain in beams with conventional and UHPC connections and partial- and full-depth connections, respectively. The partial-depth connection showed higher strain in both beams when a UHPC connection was used. The behavior of the full-depth connection was different, with the strain in the loaded beams about equal, while the strain in the unloaded UHPC beam was much greater than the strain in the unloaded conventionally grouted beam.

This graph shows a comparison of the longitudinal strain range in beams with partial-depth connections with the fully stiffened boundary condition. The x-axis shows three loading ranges: 54, 72, and 90 kip (240, 320, and 400 kN). The y-axis shows strain range and ranges from 0 to 70 microstrain. For each of the three loading ranges, there are two stacked bars: beam B conventional with beam A conventional stacked above it as well as beam B ultra-high performance concrete (UHPC) with beam A UHPC stacked above it. The UHPC connection showed higher strains in both the loaded and unloaded beams compared to the conventionally grouted connection.

Source: FHWA.
1 kip = 4.448 kN.
Figure 108. Graph. Comparison of the longitudinal strain ranges in the fully stiffened beams with a partial-depth connection.

This graph shows a comparison of the longitudinal strains in beams with full-depth connections with the unstiffened boundary condition. The x-axis shows three loading ranges: 54, 72, and 90 kip (240, 320, and 400 kN). The y-axis shows strain range and ranges from 0 to 150 microstrain. For each of the three loading ranges, there are two stacked bars: beam B conventional with beam A conventional stacked above it as well as beam B ultra-high performance concrete (UHPC) with beam A UHPC stacked above it. Both connection types had approximately the same level of strain on the loaded beam, while the unloaded beam had between 5 and 15 microstrain more strain compared with the conventional connection.

Source: FHWA.
1 kip = 4.448 kN.
Figure 109. Graph. Comparison of the longitudinal strain ranges in the unstiffened beams with a full-depth connection.

This difference in performance in the full-depth connections becomes evident in the proportion of moment carried by the loaded beam as well. Figure 110 shows the proportion of moment in the full-depth unstiffened beams. The proportion of moment based on strain and Δδ for the UHPC connection were both about 50.5 percent, while the partially cracked conventionally grouted connection had a proportion of moment of about 53 percent based on strain and 60 percent based on deflection. The larger value for Δδ was due to the larger Δδ of the cracked connection.

This graph shows a comparison of the proportion of moment carried by the loaded beam in beams with partial-depth connections with the fully stiffened boundary condition. The x-axis shows three loading ranges: 54, 72, and 90 kip (240, 320, and 400 kN). The y-axis shows the proportion of moment carried by beam A and ranges from 40 to 70 percent. For each of the three loading ranges, there are two stacked bars: strain conventional with displacement conventional stacked above it as well as strain ultra-high performance concrete (UHPC) with displacement UHPC stacked above it. There is an exception for the 54-kip (240-kN) loading range, where displacement UHPC is below strain UHPC. The UHPC connection showed lower proportion of moment using both strain and displacement measures compared to the conventionally grouted connection.

Source: FHWA.
1 kip = 4.448 kN.
Figure 110. Graph. Comparison of the loaded beam proportion of moment in the unstiffened beams with a full-depth connection.

Both the UHPC connections and conventionally grouted connections were able to limit Δδ to within 0.004 inch (0.102 mm), as shown in figure 111 for the partial-depth connection and figure 112 for the full-depth connection.

This graph shows a comparison of the differential deflection (uppercase delta subscript lowercase delta) in beams with partial-depth connections with the fully stiffened boundary condition. The x-axis shows three loading ranges: 54, 72, and 90 kip (240, 320, and 400 kN). The y-axis shows differential deflection and ranges from 0 to 0.01 inch (0 to 0.254 mm). For each of the three loading ranges, there are two bars: conventional and ultra-high performance concrete (UHPC). The UHPC connection showed higher differential deflection in all of the loading ranges compared to the conventionally grouted connection.

Source: FHWA.
1 inch = 25.4 mm.
1 kip = 4.448 kN.
Figure 111. Graph. Comparison of Δδ of the fully stiffened beams with a partial-depth connection.

This graph shows a comparison of the differential deflection (uppercase delta subscript lowercase delta) in beams with full-depth connections with the unstiffened boundary condition. The x-axis shows three loading ranges: 54, 72, and 90 kip (240, 320, and 400 kN). The y-axis shows differential deflection and ranges from -0.005 to 0.01 inch (-0.127 to 0.254 mm). For each of the three loading ranges, there are two bars: conventional and ultra-high performance concrete (UHPC). There was no discernable difference between the two connection types as the differential deflections were all around 0 inch (0 mm).

Source: FHWA.
1 inch = 25.4 mm.
1 kip = 4.448 kN.
Figure 112. Graph. Comparison of Δδ of the unstiffened beams with a full-depth connection.

The performance of conventionally grouted connections is comparable to the performance of UHPC connections. The UHPC connection was found to be more robust than the conventionally grouted connection, however. The UHPC connection did not use PT; therefore, it did not run the risk of increasing Δδ and losing load distribution if the PT force was lost. It also reduced the likelihood of connection cracking, further reducing the possibility of increasing Δδ. As was described previously, if the conventional connection is cracked and PT forces are lost, the ability for the connection to limit Δδ and effectively transfer the load can be compromised.

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