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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 4. TEST RESULTS

The results from the thermal and cyclic loading are presented in this chapter. The prewetting and curing procedures adopted in this study prevented shrinkage cracking and debonding during and after construction of the connections. The specimens were kept inside the laboratory throughout the testing program, with each specimen first being subjected to the thermal cycling followed by the cyclic structural loading.

EFFECTS FROM THERMAL LOADING

The specimens were thermally loaded to create a temperature gradient between the top and bottom flanges of approximately 50 °F (28 °C). A total of 10 thermal cycles were applied to each test specimen except for the full-depth connection specimens, which only underwent 8 cycles. The thermal loading generated an upward deflection at the mid-span of between 0.425 and 0.570 inch (10.8 and 14.5 mm). The deflection versus temperature gradient curves for the conventionally grouted connections in the study are presented in figure 50, and the curves for the UHPC connections are shown in figure 51.

This graph shows the relationship between upward deflection and temperature gradient in beams with conventionally grouted connections. The x-axis shows temperature gradient and ranges from 0 to 60 °F (0 to 15.56 °C), and the y-axis shows the mid-span deflection and ranges from -0.10 to 0.50 inch (-2.54 to 12.70 mm). Two lines are shown in the graph: partial-depth grout and full-depth grout. Both lines show a positive relationship between temperature gradient and deflection. The partial-depth connection has a maximum temperature gradient of 55.3 °F (30.7 °C) and a maximum deflection of 0.425 inch (10.8 mm). The full-depth connection has a maximum temperature gradient of 56.5 °F (31.4 °C) and a maximum deflection of 0.442 inch (11.2 mm).

Source: FHWA.
1 inch = 25.4 mm.
1 °F = 0.556 °C.
Figure 50. Graph. Relationship between upward deflection and temperature gradient in beams with conventionally grouted connections.

This graph shows the relationship between upward deflection and temperature gradient in beams with ultra-high performance concrete (UHPC) connections. The x-axis shows temperature gradient and ranges from 0 to 80 °F (0 to 26.67 °C), and the y-axis shows the mid-span deflection and ranges from -0.10 to 0.60 inch (-2.54 to 15.24 mm). Two lines are shown in the graph: partial-depth UHPC and full-depth UHPC. Both lines show a positive relationship between the temperature gradient and deflection. The partial-depth connection has a maximum temperature gradient of 57.5 °F (31.9 °C) and a maximum deflection of 0.570 inch (14.5 mm). The full-depth connection has a maximum temperature gradient of 77.9 °F (43.3 °C) and a maximum deflection of 0.439 inch (11.2 mm).

Source: FHWA.
1 inch = 25.4 mm.
1 °F = 0.556 °C.
Figure 51. Graph. Relationship between upward deflection and temperature gradient in beams with UHPC connections.

Table 10 summarizes the thermal loading and unloading data. The behavior of the beams used in the tests was generally the same. All of the tests had approximately the same deflection rate due to the thermal stress. The only exception was for the full-depth UHPC connection, which had a somewhat lower deflection rate. Despite reaching a gradient that was 20 °F (11 °C) higher than the other tests, the deflection was similar. The partial-depth UHPC connection had the greatest deflection, likely due to the largest heating rate. A visual inspection was conducted after the thermal loading. Only minor, non-structural cracking was observed in the partial-depth conventional grouted connection; the most severe is shown in figure 52. No debonding was caused by thermal loading for any of the connections.

Table 10. Data summary of the thermal tests.
Connection
Type
Maximum
Deflection
(inches)
Maximum
Gradient
(°F)
Heating
Rate
(inch/°F)
Cooling
Rate
(inch/°F)
Average
Rate
(inch/°F)
Mean
Deviation
(inch/°F)
Partial-depth grout 0.425 55.3 7.68 × 10−3 7.97 × 10−3 7.82 × 10−3 0.28 × 10−3
Full-depth grout 0.442 56.5 7.34 × 10−3 7.63 × 10−3 7.48 × 10−3 0.24 × 10−3
Partial-depth UHPC 0.570 57.5 8.11 × 10−3 6.88 × 10−3 7.50 × 10−3 0.66 × 10−3
Full-depth UHPC 0.439 77.9 6.01 × 10−3 6.13 × 10−3 6.07 × 10−3 0.44 × 10−3

1 inch = 25.4 mm.

1 °F = 0.556 °C.

1 inch/°F = 45.72 mm/°C.

This photo shows some of the cracking that occurred to the partial-depth conventionally grouted connection in the process of thermal loading. A 1-ft (0.305-m) length is shown as comparison to the cracks. Seven cracks are visible. The cracks occurred mainly at the interface between the grout and box beams and are between about 0.5 and 2 inches (12.7 and 50.8 mm). The average length is 1.2 inch (30.7 mm).

Source: FHWA.
1 ft = 0.305 m.
Figure 52. Photo. Representative cracking observed in the partial-depth conventional grout connection after thermal loading.

EFFECTS FROM CYCLIC STRUCTURAL LOADING

The partial-depth conventional grout connection was first tested in this study, followed by the full-depth conventional grout connection, then the partial- and full-depth UHPC connections. The boundary conditions, loading range, and loading cycles used on each connection are presented in table 4 through table 7.

To effectively evaluate the connection performance and efficiency under different conditions, this study adopted three parameters to measure the performance of the connection. The first two are the proportion of moment factor for the loaded beam and longitudinal strains in the beams, respectively. These demonstrate the ability of the connection to transfer loads between beams. The third is Δδ, which provides an early indication of degradation of the connection. To be consistent between all tests, the longitudinal strain reported in graphs and used for proportion of moment are those from the embedded bottom strain gauges. The deflection measurements for proportion of moment are the average of both the vertical LVDTs on the beams, while Δδ is calculated using the method defined in chapter 3.

Proportion of Moment and Δδ Between the Beams

The proportion of moment carried by each beam and Δδ between the two beams was also assessed for each of the four connection details.

Partial-Depth Conventional Grout Connection

The full 100-kip (445-kN) transverse PT force was applied at each PT point 7 d after casting the shear key, generating PT distribution of 8 kip/ft (117 kN/m). The beams were then thermally loaded. The thermal loading did not initiate any local or global distress in the connection. Before the cyclic structural loading, the connection was checked, and only minor non-structural cracks were observed.

The beams were first tested in the unstiffened configuration. Loading ranges started at 18 kip (80 kN) and increased to 36, 54, 72, and 90 kip (160, 240, 320, and 400 kN). In total, 3 million cycles were performed; the existing cracks were not observed to propagate in the connection, and no new cracks formed. The transverse PT was then reduced from 8 to 6, 4, 2, and 0.8 kip/ft (117 to 87, 58, 29, and 12 kN/m). At each of these reduced transverse PT levels, the beams were cyclically loaded with the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. An additional 3.9 million cycles were completed with no new cracks forming or existing cracks propagating. The longitudinal tensile strain at the mid-span, the loaded beam proportion of moment, and Δδ in these loading configurations are presented in figure 53 through figure 55, respectively. The tensile strain data were only available for the 90-kip (400-kN) loading range under the 8-kip/ft (117-kN/m) PT level.

This graph shows the longitudinal tensile strain measured at the mid-span in unstiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 4.90 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 180 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 4.9 million cycles with post-tensioning (PT) levels of 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges except for the 8-kip/ft (117 kN/m) PT level, which only has the 90-kip (400-kN) loading range. Two rows of bars appear at the top of the graph, with the top indicating the three loading ranges and the bottom indicating the five PT levels. Solid vertical lines divide the graph between different PT levels, and dashed vertical lines divide the graph between different loading ranges. Solid lines occur at 1.00 × 10 superscript 6, 2.50 × 10 superscript 6, 3.30 × 10 superscript 6, and 4.10 × 10 superscript 6 cycles, which begin the PT levels of 6, 4, 2, and 0.8 kip/ft (87, 58, 29, and 12 kN/m), respectively. Dashed lines occur at 1.50 × 10 superscript 6, 2.00 × 10 superscript 6, 2.65 × 10 superscript 6, 2.80 × 10 superscript 6, 3.45 × 10 superscript 6, 3.60 × 10 superscript 6, 4.25 × 10 superscript 6, and 4.40 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72- and 90-kip (320- and 400-kN) for all PT ranges except for 8 kip/ft (117 kN/m), which only has a loading range of 90 kip (400 kN). Therefore, the dashed lines at 1.50 × 10 superscript 6, 2.65 × 10 superscript 6, 3.45 × 10 superscript 6, and 4.25 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 2.00 × 10 superscript 6, 2.80 × 10 superscript 6, 3.60 × 10 superscript 6, and 4.40 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 6-, 4-, 2-, and 0.8-kip/ft (87-, 58-, 29-, and 12-kN/m) PT levels, respectively. Strain levels do not change noticeably under the PT levels. Strains in the unloaded (beam B) and loaded (beam A) beams in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 97 and 103 microstrain, 121 and 130 microstrain, and 150 and 160 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 53. Graph. Longitudinal tensile strain measured at the mid-span in unstiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the calculated proportion of moment based on the mid-span strain and deflection for unstiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 4.90 × 10 superscript 6 cycles, and the y-axis shows the proportion of moment carried by beam A and ranges from 40 to 60 percent. Two lines are shown: deflection-based and strain-based. The graph shows 4.9 million cycles with post-tensioning (PT) levels of 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges except for the 8-kip/ft (117-kN/m) PT level, which only has the 90-kip (400-kN) loading range. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the five PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 1.00 × 10 superscript 6, 2.50 × 10 superscript 6, 3.30 × 10 superscript 6, and 4.10 × 10 superscript 6 cycles, which begin at PT levels of 6, 4, 2, and 0.8 kip/ft (87, 58, 29, and 12 kN/m), respectively. Dashed lines occur at 1.50 × 10 superscript 6, 2.00 × 10 superscript 6, 2.65 × 10 superscript 6, 2.80 × 10 superscript 6, 3.45 × 10 superscript 6, 3.60 × 10 superscript 6, 4.25 × 10 superscript 6, and 4.40 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges except the 8-kip/ft (117-kN/m) range, which only has a loading range of 90 kip (400 kN). Therefore, the dashed lines at 1.50 × 10 superscript 6, 2.65 × 10 superscript 6, 3.45 × 10 superscript 6, and 4.25 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 2.00 × 10 superscript 6, 2.80 × 10 superscript 6, 3.60 × 10 superscript 6, and 4.40 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 6-, 4-, 2-, and 0.8-kip/ft (87-, 58-, 29-, and 12-kN/m) PT levels, respectively. The proportion of the moment carried by beam A remains at approximately 52 percent for both the strain-based response and the deflection-based response throughout the entirety of the test.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 54. Graph. Proportion of moment based on the mid-span strain and deflection for unstiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in unstiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows number of cycles and ranges from 0.50 to 6.90 × 10 superscript 6 cycles, and the y-axis shows differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). Only one line is shown that represents the differential deflection. The graph shows 6.9 million cycles with post-tensioning (PT) levels of 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges except for the 8-kip/ft (117-kN/m) PT level, which also includes a 36-kip (160-kN) loading range. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the five PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 3.00 × 10 superscript 6, 4.50 × 10 superscript 6, 5.30 × 10 superscript 6, and 6.10 × 10 superscript 6 cycles, which begin at PT levels of 6, 4, 2, and 0.8 kip/ft (87, 58, 29, and 12 kN/m), respectively. Dashed lines occur at 1.00 × 10 superscript 6, 1.50 × 10 superscript 6, 2.00 × 10 superscript 6, 3.50 × 10 superscript 6, 40 × 10 superscript 6, 4.65 × 10 superscript 6, 4.80 × 10 superscript 6, 5.45 × 10 superscript 6, 5.60 × 10 superscript 6, 6.25 × 10 superscript 6, and 6.40 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges except the 8-kip/ft (117-kN/m) range, which also includes a 36-kip (160-kN) loading range. Therefore, the dashed lines at 1.50 × 10 superscript 6, 3.50 × 10 superscript 6, 4.65 × 10 superscript 6, 5.45 × 10 superscript 6, and 6.25 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 2.00 × 10 superscript 6, 40 × 10 superscript 6, 4.80 × 10 superscript 6, 5.60 × 10 superscript 6, and 6.40 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 6-, 4-, 2-, and 0.8-kip/ft (117-, 87-, 58-, 29-, and 12-kN/m) PT levels, respectively. The dashed line at 1.00 × 10 superscript 6 cycles indicates the start of the 54-kip (240-kN) loading range for the 8-kip/ft (117-kN/m) PT level. The differential deflection stayed between 0.001 and 0.003 inch (0.025 and 0.076 mm) through most PT levels and loading ranges with slight fluctuations.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
1 inch = 25.4 mm.
† = 54-kip loading range.
‡ = 72-kip loading range.
Note: Data for the first 500,000 cycles were not collected properly and therefore were not included.
Figure 55. Graph. Δδ measured at the mid-span in unstiffened beams with a partial-depth uncracked conventionally grouted connection.

The level of the three variables remained nearly constant within a particular loading range regardless of the level of transverse PT applied. Specifically, the longitudinal strain while in the 90-kip (400-kN) loading range remained 160 and 145 με for the loaded and unloaded beams, respectively. The proportion of moment on the loaded beam was consistently around 52 percent regardless of the loading range or the level of PT applied. Δδ was about 0.0025 inch (0.064 mm) in the largest loading range regardless of level of PT. These results indicate that the amount of transverse PT did not seem to have an effect on system performance when the connection was intact without any apparent cracking or debonding. Further discussion of the effect of transverse PT is provided in the Transverse PT section in chapter 5.

The specimen was stiffened using the two methods previously discussed, and 1.6 and 1.75 million cycles were performed with the partially and fully stiffened connections, respectively. The results for the partially stiffened boundary condition are shown in figure 56 through figure 58. Increasing the stiffness was found to decrease the longitudinal strain in the beams. When less PT force was used, strains were found to be lower, a more even load distribution was calculated, and lower Δδ was recorded. An error in an LVDT resulted in the deflection-based proportion of moment to be based solely on the exterior LVDT for the unloaded beam in this configuration.

This graph shows the longitudinal tensile strain measured at the mid-span in partially stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 1.60 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 180 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 1.6 million cycles with post-tensioning (PT) levels of 2 and 0.8 kip/ft (29 and 12 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. A solid vertical line at 0.80 × 10 superscript 6 cycles divides the graph between the two PT levels, and dashed vertical lines divide the graph between the three loading ranges within each PT level. The dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.95 × 10 superscript 6, and 1.10 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.95 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading ranges, and the dashed lines at 0.30 × 10 superscript 6 and 1.10 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading ranges for the 2- and 0.8-kip/ft (29- and 12-kN/m) PT levels, respectively. The strains for the 2-kip/ft (29-kN/m) PT level in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 65 and 75 microstrain, 90 and 100 microstrain, and 110 and 125 microstrain, respectively. The strains for the 0.8-kip/ft (12-kN/m) PT level in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 60 and 64 microstrain, 80 and 78 microstrain, and 100 and 100 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 56. Graph. Longitudinal tensile strain measured at the mid-span in partially stiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the calculated loaded proportion of moment based on the mid-span strain and deflection for partially stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 1.60 × 10 superscript 6 cycles, and the y-axis shows the proportion of moment carried by beam A and ranges from 40 to 60 percent. Two lines are shown: deflection-based and strain-based. The graph shows 1.6 million cycles with post-tensioning (PT) levels of 2 and 0.8 kip/ft (29 and 12 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the three loading ranges and the bottom indicating the two PT levels. A solid vertical line at 0.80 × 10 superscript 6 cycles divides the graph between the two PT levels, and dashed vertical lines divide the graph between different loading ranges. The dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.95 × 10 superscript 6, and 1.10 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.95 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading ranges, and the dashed lines at 0.30 × 10 superscript 6 and 1.10 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading ranges for the 2- and 0.8-kip/ft (29- and 12-kN/m) PT levels, respectively. The deflection-based moment distribution line was consistently between 51 and 52 percent for all PT levels and loading ranges. The strain-based moment distribution line was between 52 and 54 percent during the 2-kip/ft (29-kN/m) PT level and between 49 and 52 percent for the 0.8-kip/ft (12-kN/m) PT level.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 57. Graph. Loaded proportion of moment based on the mid-span strain and deflection for partially stiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in partially stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 1.60 × 10 superscript 6 cycles, and the y-axis shows differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 1.6 million cycles with post-tensioning (PT) levels of 2 and 0.8 kip/ft (29 and 12 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. A solid vertical line at 0.80 × 10 superscript 6 cycles divides the graph between the two PT levels, and dashed vertical lines at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.95 × 10 superscript 6, and 1.10 × 10 superscript 6 cycles divide the graph between the three loading ranges. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.95 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading ranges, and the dashed lines at 0.30 × 10 superscript 6 and 1.10 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading ranges for the 2- and 0.8-kip/ft (29- and 12-kN/m) PT levels, respectively. The 2-kip/ft (29-kN/m) PT level has no data due to an instrument error. The differential deflection for the 0.8-kip/ft (12-kN/m) PT level in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 0.004, 0.002, and -0.001 inch (0.102, 0.05, and -0.025 mm), respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
1 inch = 25.4 mm.
Figure 58. Graph. Δδ measured at the mid-span in partially stiffened beams with a partial-depth uncracked conventionally grouted connection.

After the partially stiffened cycles were completed, the fully stiffened configuration was tested. The results for the fully stiffened boundary condition are shown in figure 59 and figure 60. The values reported were the strain range and deflection, as calculated from figure 41. For the final 360,000 cycles, the transverse PT force was eliminated. The fully stiffened boundary condition further lowered the longitudinal tensile strain experienced by the beams. Δδ was also lower—about 0.001 inch (0.025 mm)—compared to the simply supported case. The thermal cracks observed were not seen to propagate in the connection, indicating that the transverse PT force had a minimal impact on system performance as long as the connection remained in good condition.

This graph shows the longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 1.75 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 80 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 1.75 million cycles with post-tensioning (PT) levels of 2, 0.8, and 0 kip/ft (29, 12, and 0 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the three PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 0.80 × 10 superscript 6 and 1.40 × 10 superscript 6 cycles, which separate the 2-, 0.8-, and 0-kip/ft (29-, 2-, and 0-kN/m) PT ranges respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.90 × 10 superscript 6, 0.93 × 10 superscript 6, 1.43 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. The dashed lines at 0.15 × 10 superscript 6 and 1.43 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.93 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 2-, 0.8-, and 0-kip/ft (29-, 12-, and 0-kN/m) PT levels, respectively. The 0.8-kip/ft (12-kN/m) PT level has two cycles of increases from 54 to 90 kip (240 to 400 kN). The dashed line at 0.90 × 10 superscript 6 cycles indicates the start of the second of the 54- to 72-kip (240- 320-kN) loading range increase. The strain range does not noticeably change under the different PT levels. The strain ranges in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 31 and 39 microstrain, 37 and 48 microstrain, and 45 and 55 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
§ = 15,000 cycles at both the 54- and 72-kip loading ranges.
◊ = 90-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 59. Graph. Longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in fully stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis show the number of cycles and ranges from 0 to 1.75 × 10 superscript 6 cycles, and the y-axis shows the differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 1.75 million cycles with post-tensioning (PT) levels of 2, 0.8, and 0 kip/ft (29, 12, and 0 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the three PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 0.80 × 10 superscript 6 and 1.40 × 10 superscript 6 cycles, which separate the 2-, 0.8-, and 0-kip/ft (29-, 2-, and 0-kN/m) PT ranges, respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.90 × 10 superscript 6, 0.93 × 10 superscript 6, 1.43 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. The dashed lines at 0.15 × 10 superscript 6 and 1.43 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range for the 2- and 0-kip/ft (29- and 0-kN/m) PT levels, respectively, and the dashed lines at 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.93 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 2-, 0.8-, and 0-kip/ft (29-, 12-, and 0-kN/m) PT levels, respectively. The 0.8-kip/ft (12-kN/m) PT level has two cycles of increases from 54 to 90 kip (240 to 400 kN). The dashed line at 0.90 × 10 superscript 6 cycles indicates the start of the second of the 54- to 72-kip (240- to 320-kN) loading range increase. The differential deflection for all PT levels and loading ranges is between 0.0005 and 0.0015 inch (0.013 and 0.038 mm).

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
§ = 15,000 cycles at both the 54- and 72-kip loading ranges.
◊ = 90-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 60. Graph. Δδ measured at the mid-span in fully stiffened beams with a partial-depth uncracked conventionally grouted connection.

More than 10 million cycles of structural loading were applied to the beams with a partial-depth conventional grout connection. At its most severe, the structural loading applied an Mequivalent of 478 kip-ft (646 kN-m) transferred through the connection. No distress was observed.

The connection was then mechanically cracked by applying a direct tensile force on top of the connection, as shown in figure 61. Cracks at the interface between the grout and box beam concrete were initiated and extended about 32 ft (9.8 m). The extent to which the cracks extended into the connection was checked by ponding water on the connection. Water was observed to penetrate the connection, indicating the connection had debonded along the length of the observed cracking.

This photo shows the setup used to induce cracking in the connection. There are two small hydraulic jacks spanning the connection pushing against two metal brackets. These metal brackets are secured to the top of each box beam with post-tensioning rods and a hydraulic jack.

Source: FHWA.
A. Cracking setup.

This photo shows a 2-ft (0.61-m) length of the connection showing a crack at the interface between the box beam and the connection extending the entire length of the insert.

Source: FHWA.
B. Cracked connection.

Figure 61. Photos. Mechanical cracking of the partial-depth conventionally grouted connection, including the cracking setup and the cracked connection.

The beams were again cyclically loaded using the fully stiffened boundary condition. Transverse PT forces ranging from 8 to 0 kip/ft (117 to 0 kN/m) were tested, and 830,000 cycles were completed. The cracks were found to propagate along the connection regardless of the transverse PT force applied but propagated more quickly under lower levels of PT. After the 8- and 4-kip/ft (117- and 87-kN/m) PT cycles, the end of the crack was seen to extend about 9 inches (230 mm), and additional cracks propagated within the already cracked connection. The most extensive cracking occurred after the 0.8- and 0-kip/ft (12- and 0-kN/m) levels of PT cycles. After the 0.8-kip/ft (12-kN/m) cycles, the crack extended 4 ft (1.2 m) to a total cracked length of 37 ft (11.3 m). The cycles with no PT further extended the crack to 40 ft (12.2 m). The crack propagation can be seen in figure 62. Red marker indicates the extent of the mechanical cracking, while green, blue, and orange markers show propagation after the 4-, 0.8-, and 1-kip/ft (87-, 12-, and 0-kN/m) PT levels, respectively.

This figure shows the top of the two girders and the connection from the 2- to 10-ft (0.61 to 3.05-m) mark. Various marker lines are present on the connection grout and the interface between the beams and the connection. Red marker is visible throughout the entire connection, which indicates the extent of the mechanical cracking.

Source: FHWA.
A. Connection from the 2- to 10-ft (0.61- to 3.05-m) mark.

This figure shows the top of the two girders and the connection from the 10- to 20-ft (3.05- to 6.10-m) mark. Various marker lines are present on the connection grout and the interface between the beams and the connection. Red marker is visible throughout the entire connection, which indicates the extent of the mechanical cracking.

Source: FHWA.
B. Connection from the 10- to 20-ft (3.05- to 6.10-m) mark.

This figure shows the top of the two girders and the connection from the 28- to 36-ft (8.53- to 10.97-m) mark. Various marker lines are present on the connection grout and the interface between the beams and the connection. Red marker is visible from 28 to 34 ft (28 to 10.4 m), which indicates the extent of the mechanical cracking. A green line extends from the 34-ft (10.4-m) mark to the 35-ft (10.7-m) mark, which indicates the extent of crack propagation at the 4-kip/ft (87-kN/m) post-tensioning (PT) level. A blue line extends from the 35-ft (10.7-m) mark to the end of this figure, which indicates the extent of crack propagation at the 0.8-kip/ft (12-kN/m) PT level.

Source: FHWA.
C. Connection from the 28- to 36-ft (8.53- to 10.97-m) mark.

This figure shows the top of the two girders and the connection from the 36- to 46-ft (10.97- to 14.02-m) mark. Various marker lines are present on the connection grout and the interface between the beams and the connection. An orange line extends from the 39-ft (11.9-m) mark to the 41-ft (12.5-m) mark, which indicates the extent of crack propagation at the 0-kip/ft (0-kN/m) post-tensioning (PT) level. A blue line extends from 36 to 39 ft (10.7 to 11.9 m), which indicates the extent of crack propagation at the 0.8-kip/ft (12-kN/m) PT level, with a few small extensions within the precracked section.

Source: FHWA.
D. Connection from the 36- to 46-ft (10.97- to 14.02-m) mark.
Note: Numbers in the photos reflect distance from the west end in feet where 1 ft = 0.305 m.
Figure 62. Photos. Propagation of the end of the connection crack induced by cyclic structural loading.

The longitudinal tensile strain range and Δδ between the two adjacent beams at the mid-span for the partially cracked connections are presented in figure 63 and figure 64. The partially cracked connection could still effectively transfer the load from one beam to the other, likely through friction between the grout and the box beam concrete; however, a slightly larger Δδ was observed. A jump can be seen during the 90-kip (400-kN) range of the cycles without PT around 800,000 cycles. This may correspond to the propagation of the crack seen in figure 62.

This graph shows the longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a partial-depth partially cracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 0.83 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 80 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 830,000 cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 0.17 × 10 superscript 6, 0.49 × 10 superscript 6, and 0.66 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.02 × 10 superscript 6, 0.19 × 10 superscript 6, 0.51 × 10 superscript 6, and 0.68 × 10 superscript 6 cycles. Each PT level begins with 10,000 cycles in each of the 54- and 72- kip (240- and 320-kN) loading ranges and then increases to 90 kip (400 kN) for all PT ranges. Therefore, the dashed lines at 0.02 × 10 superscript 6, 0.19 × 10 superscript 6, 0.51 × 10 superscript 6, and 0.68 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The strain range does not noticeably change under the PT levels. The strains in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 30 and 39 microstrain, 35 and 47 microstrain, and 42 and 56 microstrain, respectively. There is a clear jump of 2 microstrain in both beams around 800,000 cycles.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
§ = 10,000 cycles at both the 54- and 72-kip loading ranges.
Figure 63. Graph. Longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a partial-depth partially cracked conventionally grouted connection.

This graph shows the differential deflection measured at the mid-span in fully stiffened beams with a partial-depth partially cracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 0.83 × 10 superscript 6 cycles, and the y-axis shows the differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 830,000 cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 0.17 × 10 superscript 6, 0.49 × 10 superscript 6, and 0.66 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.02 × 10 superscript 6, 0.19 × 10 superscript 6, 0.51 × 10 superscript 6, and 0.68 × 10 superscript 6 cycles. Each PT level begins with 10,000 cycles in each of the 54- and 72-kip (240- and 320-kN) loading ranges, which then increase to 90 kip (400 kN) for all PT ranges. Therefore, the dashed lines at 0.02 × 10 superscript 6, 0.19 × 10 superscript 6, 0.51 × 10 superscript 6, and 0.68 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The differential deflection increases gradually through each test. In the 90-kip (400-kN) loading range, the differential deflection for the 8- and 4-kip/ft (117- and 58-kN/m) PT levels is around 0.0020 inch (0.051 mm). In the 0.8-kip/ft (12 kN/m) PT level, the differential deflection increases to 0.0025 inch (0.064 mm). With no PT, the differential deflection is around 0.0033 inch (0.084 mm) before 800,000 cycles where it jumps to 0.0056 inch (0.142 mm).

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
1 inch = 25.4 mm.
§ = 10,000 cycles at both the 54- and 72-kip loading ranges.
Figure 64. Graph. Δδ measured at the mid-span in fully stiffened beams with a partial-depth partially cracked conventionally grouted connection.

The connection was then mechanically cracked so the full length of the connection was cracked. The beams were then subjected to further cyclic loading with the stiffest boundary condition. A total of 200,000 cycles were performed with the transverse PT forces ranging from 8 to 0 kip/ft (117 to 0 kN/m).

The longitudinal tensile strain range and Δδ between the two adjacent beams at the mid-span for the fully-cracked connection are presented in figure 65 and figure 66. Larger Δδ and longitudinal strains were observed in the fully cracked connection.

This graph shows the longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a partial-depth fully cracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 0.200 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 80 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 200,000 cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles that run in the 18-, 36-, 54-, 72-, and 90-kip (80-, 160-, 240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, and dashed vertical lines divide the graph between the five loading ranges. Solid lines occur at 0.050 × 10 superscript 6, 0.100 × 10 superscript 6, and 0.150 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.010 × 10 superscript 6, 0.020 × 10 superscript 6, 0.030 × 10 superscript 6, 0.040 × 10 superscript 6, 0.060 × 10 superscript 6, 0.070 × 10 superscript 6, 0.080 × 10 superscript 6, 0.090 × 10 superscript 6, 0.110 × 10 superscript 6, 0.120 × 10 superscript 6, 0.130 × 10 superscript 6, 0.140 × 10 superscript 6, 0.160 × 10 superscript 6, 0.170 × 10 superscript 6, 0.180 × 10 superscript 6, and 0.190 × 10 superscript 6 cycles. Each PT level begins with the 18-kip (80-kN) loading range and increases through the 36-, 54-, 72- , and 90-kip (160-, 240-, 320-, and 400-kN) loading ranges, respectively. Therefore, the dashed lines at 0.010 × 10 superscript 6, 0.060 × 10 superscript 6, 0.110 × 10 superscript 6, and 0.160 × 10 superscript 6 cycles indicate the start of the 36-kip (160-kN) loading range, the dashed lines at 0.020 × 10 superscript 6, 0.070 × 10 superscript 6, 0.120 × 10 superscript 6, and 0.170 × 10 superscript 6 cycles indicate the start of the 54-kip (240-kN) loading range, the dashed lines at 0.030 × 10 superscript 6, 0.080 × 10 superscript 6, 0.130 × 10 superscript 6, and 0.180 × 10 superscript 6 cycles indicate the start of the 72-kip (320-kN) loading range, and the dashed lines at 0.040 × 10 superscript 6, 0.090 × 10 superscript 6, 0.140 × 10 superscript 6, and 0.190 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The strain ranges do not change noticeably under the PT levels. The strains in beams B and A in the 18-, 36-, 54-, 72-, and 90-kip (80-, 160-, 240-, 320-, and 400-kN) loading ranges are approximately 16 and 21 microstrain, 21 and 32 microstrain, 28 and 41 microstrain, 36 and 48 microstrain, and 43 and 59 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
△ = 18-kip loading range.
⌂ = 36-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
◊ = 90-kip loading range.
Figure 65. Graph. Longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a partial-depth fully cracked conventionally grouted connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in fully stiffened beams with a partial-depth fully cracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 0.200 × 10 superscript 6 cycles, and the y-axis shows differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 200,000 cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles run in the 18-, 36-, 54-, 72-, and 90-kip (80-, 160-, 240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, and dashed vertical lines divide the graph between the five loading ranges. Solid lines occur at 0.050 × 10 superscript 6, 0.100 × 10 superscript 6, and 0.150 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.010 × 10 superscript 6, 0.020 × 10 superscript 6, 0.030 × 10 superscript 6, 0.040 × 10 superscript 6, 0.060 × 10 superscript 6, 0.070 × 10 superscript 6, 0.080 × 10 superscript 6, 0.090 × 10 superscript 6, 0.110 × 10 superscript 6, 0.120 × 10 superscript 6, 0.130 × 10 superscript 6, 0.140 × 10 superscript 6, 0.160 × 10 superscript 6, 0.170 × 10 superscript 6, 0.180 × 10 superscript 6, and 0.190 × 10 superscript 6 cycles. Each PT level begins with the 18-kip (80-kN) loading range and increases through the 36-, 54-, 72- , and 90-kip (160-, 240-, 320-, and 400-kN) loading ranges, respectively. Therefore, the dashed lines at 0.010 × 10 superscript 6, 0.060 × 10 superscript 6, 0.110 × 10 superscript 6, and 0.160 × 10 superscript 6 cycles indicate the start of the 36-kip (160-kN) loading range, the dashed lines at 0.020 × 10 superscript 6, 0.070 × 10 superscript 6, 0.120 × 10 superscript 6, and 0.170 × 10 superscript 6 cycles indicate the start of the 54-kip (240 kN) loading range, the dashed lines at 0.030 × 10 superscript 6, 0.080 × 10 superscript 6, 0.130 × 10 superscript 6, and 0.180 × 10 superscript 6 cycles indicate the start of the 72-kip (320-kN) loading range, and the dashed lines at 0.040 × 10 superscript 6, 0.090 × 10 superscript 6, 0.140 × 10 superscript 6, and 0.190 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The differential deflection does not noticeably change under the 8- and 4-kip/ft (117- and 58-kN/m) PT levels. The differential deflection in the 18-, 36-, 54-, 72-, and 90-kip (80-, 160-, 240-, 320-, and 400-kN) loading ranges are approximately 0.0005, 0.0018, 0.0034, 0.0045, and 0.0051 inch (0.013, 0.046, 0.086, 0.114, and 0.130 mm), respectively. These values increase to 0.0013, 0.0045, 0.0057, 0.0062, and 0.0066 inch (0.033, 0.114, 0.145, 0.157, and 0.168 mm), respectively, under the 0.8-kip/ft (12-kN/m) PT level and to 0.0046, 0.0090, 0.0104, 0.0116, and 0.0121 inch (0.117, 0.229, 0.264, 0.295, and 0.307 mm), respectively, with no PT.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
△ = 18-kip loading range.
⌂ = 36-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
◊ = 90-kip loading range.
Figure 66. Graph. Δδ measured at the mid-span in fully stiffened beams with a partial-depth fully cracked conventionally grouted connection.

The transverse PT force did not have much effect on the longitudinal strain at the mid-span. The transverse PT force varied from 8 to 0 kip/ft (117 to 0 kN/m) in the partially and fully cracked connections. The transverse PT affected Δδ. When it was removed from the fully cracked connection, Δδ was noted to increase within the 50,000 cycles conducted in this study.

Full-Depth Conventional Grout Connection

The same construction procedure used for partial-depth conventionally grouted connection was adopted for the full-depth conventionally grouted connection. Approximately two-thirds of the length of the connection cracked when the wrench-tight PT force was removed. The transverse curvature (i.e., sweep) of the beams with the full-depth connection may have varied enough to cause cracking to develop, as illustrated in figure 67. When the PT forces were applied, the beams aligned from the applied force. After the grout was cast and the transverse force was removed, the beams tried to return to their original shape. This introduced a tensile force across the connection and could lead to connection cracking if the bond strength between the grout and the box beams were not sufficiently large. This would imply that the differential transverse curvature on the beams with the full-depth shear keys was larger than that on the beams with the partial-depth shear keys. This caused the full-depth shear key to crack upon release of the PT force, while the partial-depth shear key did not.

This illustration shows how the full-depth conventionally grouted connection could have cracked when the post-tensioning (PT) force was released. The top part of the figure shows two curved box beams aligned. The gap in the center is much smaller than the gap at the ends, as the beams curve away from each other. The bottom part of the figure shows two straight beams with force arrows indicating the PT.

Source: FHWA.
Figure 67. Illustration. Exaggerated transverse curve in box beams.

Cyclic loading was applied to the specimen with the partially cracked connection using the unstiffened configuration and varying levels of transverse PT. A total of 2.25 million cycles were completed, and the existing cracking in the connection was observed to propagate. However, the crack did not extend the entire length of the beam. The connection was further cracked with the same method used for the partial-depth connection so that the connection interface cracks extended the entire length of the specimen. The beams were then loaded for another 150,000 cycles. The longitudinal tensile strain at the mid-span and the proportion of moment carried by the loaded beam are presented in figure 68 and figure 69, respectively. Δδ between the two beams is presented in figure 70. With transverse PT forces of 8, 4, and 0.8 kip/ft (117, 58, and 12 kN/m), the partially cracked connection could still effectively transfer the moment, having a proportion of moment factor of about 54 percent. When the transverse PT was removed, the proportion of moment factor remained about 54 percent under the 54-kip (240-kN) loading range but increased to over 57 percent when the loading range increased to 72 and 90 kip (320 and 400 kN).

Similar observations were noted with Δδ. As shown in figure 70, Δδ was constantly within 0.001 inch (0.025 mm) for all loading ranges while having any level of transverse PT. It jumped to around 0.015 inch (0.381 mm) for the partially cracked connection under the 72-kip (320-kN) loading range. Both the partially and fully cracked connections had Δδ of around 0.018 inch (0.457 mm) in the 90-kip (400-kN) loading range.

This graph shows tensile strain at the mid-span showing full-depth connection, conventional grout, unstiffened boundary, and partially and fully cracked conditions. The x-axis shows the number of cycles and ranges from 0 to 2.40 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 160 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load. The graph shows 2.4 million cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Three rows of bars appear at the top of the graph, with the top indicating the crack condition of the connection, the middle indicating the loading ranges, and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, dashed vertical lines divide the graph between the three loading ranges, and a bold solid line divides the partially and fully cracked connection condition. Solid lines occur at 0.60 × 10 superscript 6, 1.20 × 10 superscript 6, and 1.80 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, 0.90 × 10 superscript 6, 1.35 × 10 superscript 6, 1.50 × 10 superscript 6, 1.95 × 10 superscript 6, and 2.10 × 10 superscript 6 cycles. Each PT level begins with the 54-kip (240-kN) loading range and increases to the 72- and 90-kip (320- and 400-kN) loading ranges for all PT ranges. Therefore, the dashed lines at 0.15 × 10 superscript 6, 0.75 × 10 superscript 6, 1.35 × 10 superscript 6, and 1.95 × 10 superscript 6 cycles indicate the start of the 72-kip (320-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6, 0.90 × 10 superscript 6, 1.50 × 10 superscript 6, and 2.10 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The bold line is located at 2.25 × 10 superscript 6 cycles, indicating the transition of the connection from the partially cracked to fully cracked state. The levels of strain do not change noticeably under the 8-, 4-, and 0.8-kip/ft (117-, 58-, and 12-kN/m) PT levels in the partially cracked connection. The strains in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 63 and 73 microstrain, 87 and 99 microstrain, and 103 and 120 microstrain, respectively. The strains in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges with a partially cracked connection and no PT are approximately 61 and 66 microstrain, 77 and 104 microstrain, and 103 and 133 microstrain, respectively. The strains in beams B and A with a fully cracked connection are approximately 95 and 128 microstrain, respectively, in the 90-kip (400-kN) loading range.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 68. Graph. Tensile strain at the mid-span showing full-depth connection, conventional grout, unstiffened boundary, and partially and fully cracked conditions.

This graph shows the calculated proportion of moment carried by the loaded beam based on the mid-span strain and deflection for the full-depth partially and fully cracked conventionally grouted connections. The x-axis shows the number of cycles and ranges from 0 to 2.40 × 10 superscript 6 cycles, and the y-axis shows the proportion of moment carried by beam A and ranges from 40 to 70 percent. Two lines are shown: deflection-based and strain-based. The graph shows 2.4 million cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Three rows of bars appear at the top of the graph, with the top indicating crack condition of the connection, the middle indicating the loading ranges, and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, dashed vertical lines divide the graph between the three loading ranges, and a bold solid line divides the partially and fully cracked connection condition. Solid lines occur at 0.60 × 10 superscript 6, 1.20 × 10 superscript 6, and 1.80 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, 0.90 × 10 superscript 6, 1.35 × 10 superscript 6, 1.50 × 10 superscript 6, 1.95 × 10 superscript 6, and 2.10 × 10 superscript 6 cycles. Each PT level begins with the 54-kip (240-kN) loading range and increases to the 72 and 90 kip (320 and 400 kN) loading ranges for all PT ranges. Therefore, the dashed lines at 0.15 × 10 superscript 6, 0.75 × 10 superscript 6, 1.35 × 10 superscript 6, and 1.95 × 10 superscript 6 cycles indicate the start of the 72-kip (320 kN) loading range, and the dashed lines at 0.30 × 10 superscript 6, 0.90 × 10 superscript 6, 1.50 × 10 superscript 6, and 2.10 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The solid bold line is located at 2.25 × 10 superscript 6 cycles, indicating the transition of the connection from the partially cracked to fully cracked state. The proportion of moment does not noticeably change under the 8-, 4-, and 0.8-kip/ft (117-, 58-, and 12-kN/m) PT levels in the partially cracked connection, with the strain-based line at approximately 53 to 54 percent and the deflection-based line at approximately 58 to 62 percent. The proportion of moment carried by beam A increases after the 54-kip (240-kN) loading range with no PT to about 57 percent for the strain-based line and to about 65 percent for the deflection-based line. When the connection is fully cracked, the deflection-based line becomes nearly 70 percent, while the strain-based line remains at 57 percent.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
Figure 69. Graph. Proportion of moment carried by the loaded beam based on the mid-span strain and deflection for the full-depth partially and fully cracked conventionally grouted connections.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in the full-depth partially and fully cracked conventionally grouted connections. The x-axis shows the number of cycles and ranges from 0 to 2.40 × 10 superscript 6 cycles, and the y-axis shows the differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 2.4 million cycles with post-tensioning (PT) levels of 8, 4, 0.8, and 0 kip/ft (117, 58, 12, and 0 kN/m). Each PT level has cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Three rows of bars appear at the top of the graph, with the top indicating crack condition of the connection, the middle indicating the loading ranges, and the bottom indicating the PT levels. Solid vertical lines divide the graph between the four PT levels, dashed vertical lines divide the graph between the three loading ranges, and a bold solid line divides the partially and fully cracked connection conditions. Solid lines occur at 0.60 × 10 superscript 6, 1.20 × 10 superscript 6, and 1.80 × 10 superscript 6 cycles, which separate the graph into 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, 0.90 × 10 superscript 6, 1.35 × 10 superscript 6, 1.50 × 10 superscript 6, 1.95 × 10 superscript 6, and 2.10 × 10 superscript 6 cycles. Each PT level begins with the 54-kip (240-kN) loading range and increases to the 72- and 90-kip (320- and 400-kN) loading ranges for all PT ranges. Therefore, the dashed lines at 0.15 × 10 superscript 6, 0.75 × 10 superscript 6, 1.35 × 10 superscript 6, and 1.95 × 10 superscript 6 cycles indicate the start of the 72-kip (320-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6, 0.90 × 10 superscript 6, 1.50 × 10 superscript 6, and 2.10 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 8-, 4-, 0.8-, and 0-kip/ft (117-, 58-, 12-, and 0-kN/m) PT levels, respectively. The bold line is located at 2.25 × 10 superscript 6 cycles, indicating the transition of the connection from the partially cracked to fully cracked state. The differential deflection is around 0 inch (0 mm) for the 8-, 4-, and 0.8-kip/ft (117-, 58-, and 12-kN/m) PT levels as well as for the 54-kip (240-kN) loading range without PT. With no PT, the differential deflection increases to 0.011 inch (0.28 mm) in the partially cracked 72-kip (320-kN) loading range and increases as high as 0.021 inch (0.53 mm) in the 90-kip (400-kN) loading range. When the connection is fully cracked, the differential deflection is 0.017 inch (0.43 mm).

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
1 inch = 25.4 mm.
Figure 70. Graph. Δδ measured at the mid-span in the full-depth partially and fully cracked conventionally grouted connections.

Partial-Depth UHPC Connection

After the conventional grout connections were tested, the pair of beams were separated and repositioned to construct the UHPC connections. Both UHPC connections were constructed successfully, and no cracks were observed before the cyclic structural loading.

The beams with the partial-depth UHPC connection were loaded with the partially stiffened and fully stiffened boundary conditions. A total of 1.55 million cycles were performed, and no cracking was observed in the specimen. The longitudinal tensile strain at the mid-span for beams with partial-depth UHPC connection is presented in figure 71. Values for the tensile strain for the fully stiffened portion of the plot are the range of longitudinal strains. Proportion of moment on the loaded beam for the partially stiffened connection is presented in figure 72. Δδ for the connection is presented in figure 73. Under the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges, the loaded beam had a proportion of moment around 50 percent with the partially stiffened boundary, and Δδ was limited to within 0.005 inch (0.127 mm).

This graph shows the longitudinal tensile strain measured at the mid-span in partially and fully stiffened beams with a partial-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 1.55 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 180 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 1.55 million cycles. Both the partially stiffened and fully stiffened conditions have cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the boundary conditions (i.e., partially and fully stiffened). A solid vertical line at 0.60 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. The dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, and 0.90 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.75 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6 and 0.90 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The strains in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges under the partially stiffened boundary condition are approximately 61 and 65 microstrain, 80 and 83 microstrain, and 102 and 108 microstrain, respectively. The strain in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges under the fully stiffened boundary condition are 32 and 39 microstrain, 40 and 49 microstrain, and 48 and 60 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
Figure 71. Graph. Longitudinal tensile strain measured at the mid-span in partially and fully stiffened beams with a partial-depth UHPC connection.

This graph shows the calculated proportion of moment carried by the loaded beam based on the mid-span strain and deflection for partially stiffened beams with a partial-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 0.60 × 10 superscript 6 cycles, and the y-axis shows the proportion of moment carried by beam A and ranges from 40 to 60 percent. Two lines are shown: displacement-based and strain-based. The graph shows 600,000 cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two dashed vertical lines at 0.15 × 10 superscript 6 and 0.30 × 10 superscript 6 cycles separate the graph into three regions to represent the three loading ranges. The deflection-based proportion of moment is between 51 and 52 percent for all cycles. The strain-based proportion of moment is between 50 and 53 percent for all cycles.

Source: FHWA.
1 kip = 4.448 kN.
Figure 72. Graph. Proportion of moment carried by the loaded beam based on the mid-span strain and deflection for partially stiffened beams with a partial-depth UHPC connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in partially and fully stiffened beams with a partial-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 1.55 × 10 superscript 6 cycles, and the y-axis shows the differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 1.55 million cycles. Both the partially and fully stiffened conditions have cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, with the top indicating the boundary condition (i.e., partially or fully stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.60 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between three loading ranges. The dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, and 0.90 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.75 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6 and 0.90 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The differential deflection in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges is between 0.0016 and 0.0037 inch (0.041 and 0.094 mm) for the partially stiffened boundary condition. The differential deflection for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges is 0.002, 0.003 and 0.004 inch (0.051, 0.076, and 0.102 mm), respectively, for the fully stiffened boundary condition.

Source: FHWA.
1 inch = 25.4 mm.
1 kip = 4.448 kN.
Figure 73. Graph. Δδ measured at the mid-span in partially and fully stiffened beams with a partial-depth UHPC connection.

An attempt to induce cracking in the connection with the same method as the conventional grout specimens was performed. When the transverse tensile force was applied across the connection, cracks developed in the box beam rather than in the UHPC or the connection interface, as shown in figure 74. This suggests that the interface bond strength between the UHPC and EA interface concrete was similar to or greater than the tensile strength of the box beam concrete. This behavior demonstrates that UHPC can create a connection whose behavior is comparable to or exceeds the tensile cracking strength of monolithically cast concrete box beams due to the tensile strength, interface bond strength, and reinforcement development ability of the UHPC.

This photo shows the ultra-high performance concrete (UHPC) connection after trying to mechanically crack the connection using the same method used with the conventionally grouted connection, wherein a static actuator applies force to transversely push apart the beams. Rather than a crack developing on the connection interface, one instead developed in one of the box beams about 8 inches (203 mm) from the connection.

Source: FHWA.
Figure 74. Photo. Crack development in the box beam during an attempt to mechanically induce a crack in the UHPC connection.

Full-Depth UHPC Connection

The partial-depth UHPC connection exhibited performance that could be expected to be comparable to a monolithic bridge system. Given the similarities between the partial- and full-depth UHPC connections, it was anticipated that the full-depth UHPC connection would exhibit similar performance.

The longitudinal tensile strain for the unstiffened and partially stiffened cases is presented in figure 75, the loaded beam proportion of moment for these cases is given in figure 76, and Δδ is presented in figure 77. The partially stiffened boundary condition caused the strains measured at mid-span to decrease. The proportion of moment on the loaded beam stayed constant around 51 percent. Δδ between the beams were minor, between -0.002 and 0.001 inch (-0.051 and 0.025 mm), across both boundary conditions and all loading ranges.

This graph shows the longitudinal tensile strain measured at the mid-span in unstiffened and partially stiffened beams with a full-depth UHPC connection. The x-axis shows the number of cycles and ranges from 0 to 0.60 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 180 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). Two rows of bars appear at the top of the graph, with the top indicating the two boundary conditions (i.e., unstiffened and partially stiffened) and the bottom indicating the loading ranges (i.e., 54, 72, and 90 kip (240, 320, and 400 kN)). The graph shows 600,000 cycles. Both the partially and fully stiffened conditions have cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. A solid vertical line at 0.15 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. The dashed lines occur at 0.05 × 10 superscript 6, 0.10 × 10 superscript 6, 0.30 × 10 superscript 6, and 0.45 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.05 × 10 superscript 6 and 0.30 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.10 × 10 superscript 6 and 0.45 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The strains in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 73 and 75 microstrain, 98 and 100 microstrain, and 121 and 123 microstrain, respectively for the unstiffened boundary condition. The strains in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are 58 and 60 microstrain, 80 and 82 microstrain, and 103 and 106 microstrain, respectively, for the partially stiffened boundary condition.

Source: FHWA.
1 kip = 4.448 kN.
Figure 75. Graph. Longitudinal tensile strain measured at the mid-span in unstiffened and partially stiffened beams with a full-depth UHPC connection.

This graph shows the proportion of the moment carried by the loaded beam based on the mid-span strain and deflection for unstiffened and partially stiffened beams with a full-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 0.60 × 10 superscript 6 cycles, and the y-axis shows the proportion of moment carried by beam A and ranges from 40 to 60 percent. Two lines are shown: displacement-based and strain-based. The graph shows 600,000 cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges for two boundary conditions (i.e., unstiffened and partially stiffened). Two rows of bars appear at the top of the graph, with the top indicating the boundary conditions and the bottom indicating the three loading ranges. A solid vertical line at 0.15 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. Dashed lines occur at 0.05 × 10 superscript 6, 0.10 × 10 superscript 6, 0.30 × 10 superscript 6, and 0.45 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.05 × 10 superscript 6 and 0.30 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.10 × 10 superscript 6 and 0.45 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the unstiffened and partially stiffened boundary conditions, respectively. Both the deflection-based and strain-based proportion of moment remain at 51 percent throughout all cycles in both the unstiffened and partially stiffened boundary conditions.

Source: FHWA.
1 kip = 4.448 kN.
Figure 76. Graph. Proportion of the moment carried by the loaded beam based on the mid-span strain and deflection for unstiffened and partially stiffened beams with a full-depth UHPC connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in unstiffened and partially stiffened beams with a full-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 0.60 × 10 superscript 6 cycles, and the y-axis shows the differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 600,000 cycles. Both the partially and fully stiffened conditions have cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. Two rows of bars appear at the top of the graph, the top indicating the boundary conditions (i.e., unstiffened and partially stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.15 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. Dashed lines occur at 0.05 × 10 superscript 6, 0.10 × 10 superscript 6, 0.30 × 10 superscript 6, and 0.45 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.05 × 10 superscript 6 and 0.30 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.10 × 10 superscript 6 and 0.45 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the unstiffened and partially stiffened boundary conditions, respectively. The differential deflection for the unstiffened boundary is consistently between 0 and -0.002 inch (0 and -0.051 mm). The differential deflection for the partially stiffened boundary is around 0 inch (0 mm) for the 54- and 72-kip (240- and 320-kN) loading ranges and decreases to around -0.002 inch (-0.051 mm) in the 90-kip (400-kN) loading range.

Source: FHWA.
1 kip = 4.448 kN.
1 inch = 25.4 mm.
Figure 77. Graph. Δδ measured at the mid-span in unstiffened and partially stiffened beams with a full-depth UHPC connection.

The longitudinal tensile strain range and Δδ for the uncracked full-depth UHPC connection with the fully stiffened boundary condition are presented in figure 78 and figure 79, respectively, and a total of 915,000 cycles were conducted. No cracks were initiated. The connection limited Δδ to within ±0.0015 inch (±0.038 mm).

This graph shows the longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a full-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 0.92 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 70 microstrain. Two lines are shown: beam A (which is considered loaded as it has both the 5-kip (22-kN) baseline load and the full loading range force) and beam B (which is considered unloaded as it only has the 5-kip (22-kN) baseline load). The graph shows 920,000 cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. A row of bars appears at the top of the graph indicating the three loading ranges. Dashed vertical lines divide the graph between those loading ranges. These lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.32 × 10 superscript 6, 0.37 × 10 superscript 6, and 0.42 × 10 superscript 6 cycles. The graph begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). This pattern occurs twice. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.37 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, the dashed lines at 0.30 × 10 superscript 6 and 0.42 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range, and the dashed line at 0.32 × 10 superscript 6 cycles indicates the start of the 54-kip (240-kN) loading range. The strain ranges in beams B and A in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges are approximately 26 and 32 microstrain, 33 and 41 microstrain, and 42 and 50 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
◊ = 90-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 78. Graph. Longitudinal tensile strain range measured at the mid-span in fully stiffened beams with a full-depth UHPC connection.

This graph shows the differential deflection (uppercase delta subscript lowercase delta) measured at the mid-span in fully stiffened beams with a full-depth ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 0.92 × 10 superscript 6 cycles, and the y-axis shows the differential deflection and ranges from -0.005 to 0.010 inch (-0.127 to 0.254 mm). One line is shown that represents the differential deflection. The graph shows 920,000 cycles that run in the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. A row of bars appears at the top of the graph indicating the three loading ranges. Dashed vertical lines divide the graph between those loading ranges. These lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.32 × 10 superscript 6, 0.37 × 10 superscript 6, and 0.42 × 10 superscript 6 cycles. The graph begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). This pattern occurs twice. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.37 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, the dashed lines at 0.30 × 10 superscript 6 and 0.42 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range, and the dashed line at 0.32 × 10 superscript 6 cycles indicates the start of the 54-kip (240 kN) loading range. The differential deflection is consistently between -0.0015 and 0.0005 inch (-0.038 and 0.013 mm) in all loading ranges for all cycles.

Source: FHWA.
1 kip = 4.448 kN.
1 inch = 25.4 mm.
◊ = 90-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 79. Graph. Δδ measured at the mid-span in fully stiffened beams with a full-depth UHPC connection.

Transverse Strain in the Beams

Connections mainly transfer a load from one beam to another through transverse shear, which drives adjacent beams to effectively have the same deflection. The connections also need to provide transverse flexural rigidity to resist transverse tensile forces due to eccentrically placed wheel loads and superimposed dead loads. The results of the transverse strain due to structural loading are presented here.

Figure 80 presents a reference for the transverse strain gauges used in this section. The simulated structural loading was intentionally placed 6 inches (152 mm) off the centerline of the beams (refer to figure 22 for the test setup) to increase the transverse tensile stress.

This illustration shows the locations of all transverse strain gauges that were installed on various beams in the study. The beams include (from left to right) the west support, west post-tensioning (PT), 6 ft (1.8 m) west of the mid-span, the mid-span, 6 ft (1.8 m) east of the mid-span, east PT, and east support. Not all gauges were present on all beams. There are 20 external gauges on top of the beam, 7 distributed along the connection, and 13 distributed within 6 ft (1.8 m) of either side of the mid-span. Six internal strain gauges are included in the top of the beams, and two are included at the bottom.

Source: FHWA.
1 ft = 0.305 m.
Figure 80. Illustration. Location of all possible transverse strain gauges in this study.

Figure 81 through figure 90 present the recorded transverse tensile strains for the uncracked partial-depth conventional grout and the partial- and full-depth UHPC connections. Specifically, figure 81 shows transverse strains measured by the embedded gauges for the simply supported partial-depth conventional grout connections. Some of the embedded strain gauges did not function properly during the tests; therefore, only those with valid data were reported. A transverse strain between 30 and 42 με was measured in beam A, while beam B had a transverse strain between 25 and 35 με in the 90-kip (400-kN) loading range. The beams were then loaded with the fully stiffened boundary condition. The transverse strain range is reported in figure 82 and figure 83. The stiffer boundary condition reduced the transverse tensile strain in the embedded strain gauges with values between 10 and 20 με in the 90-kip (400-kN) loading range. Surface tensile strain on the connection surface was similar to the embedded gauges in the beams.

This graph shows the top transverse strain recorded by internal strain gauges in two beams for unstiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 4.75 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 50 microstrain. Three lines are shown: beam A west (i.e., 6 ft (1.8 m) west of the mid-span), beam A mid-span (i.e., at the mid-span), and beam B east (i.e., 6 ft (1.8 m) east of the mid-span). The graph shows 4.75 million cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges with post-tensioning (PT) levels of 8, 6, 4, 2, and 0.8 kip/ft (117, 87, 58, 29, and 12 kN/m). Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the five PT levels and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 1.00 × 10 superscript 6, 2.50 × 10 superscript 6, 3.30 × 10 superscript 6, and 4.10 × 10 superscript 6 cycles, which begin the PT levels of 6, 4, 2, and 0.8 kip/ft (87, 58, 29, and 12 kN/m), respectively. Dashed lines occur at 1.50 × 10 superscript 6, 2.00 × 10 superscript 6, 2.65 × 10 superscript 6, 2.80 × 10 superscript 6, 3.45 × 10 superscript 6, 3.60 × 10 superscript 6, 4.25 × 10 superscript 6, and 4.40 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges except the 8-kip/ft (117-kN/m) loading range, which only has a loading range of 90 kip (400 kN). Therefore, the dashed lines at 1.50 × 10 superscript 6, 2.65 × 10 superscript 6, 3.45 × 10 superscript 6, and 4.25 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 2.00 × 10 superscript 6, 2.80 × 10 superscript 6, 3.60 × 10 superscript 6, and 4.40 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 6-, 4-, 2-, and 0.8-kip/ft (87-, 58-, 29,- and 12-kN/m) PT levels, respectively. The level of strain varies based on the loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 15 and 40 microstrain, and there is never more than a 10-microstrain difference between any two. The beam A west has the highest level of strain, followed by beam A mid-span and beam B east, which has the lowest strain.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 81. Graph. Top transverse strain ranges recorded by internal strain gauges in two beams for unstiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the top transverse strain range recorded at the mid-span for fully stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 1.76 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 40 microstrain. Two lines are shown: beam A internal (i.e., internal gauge in beam A) and grout external (i.e., external gauge on the grout). The graph shows 1.76 million cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges with post-tensioning (PT) levels of 2, 0.8, and 0 kip/ft (29, 12, and 0 kN/m). Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the three PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 0.80 × 10 superscript 6 and 1.40 × 10 superscript 6 cycles, which begin the 0.8- and 0-kip/ft (12- and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.90 × 10 superscript 6, 0.93 × 10 superscript 6, 1.43 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. The dashed lines at 0.15 × 10 superscript 6 and 1.43 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.93 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the 2-, 0.8-, 0.8-, and 0-kip/ft (29-, 12-, 12-, and 0-kN/m) PT levels, respectively. The 0.8-kip/ft (12-kN/m) PT level has two cycles of increases from 54 to 90 kip (240 to 400 kN). The dashed line at 0.90 × 10 superscript 6 cycles indicates the start of the second increase. The level of strain varies based on the loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 7 and 17 microstrain. In the 90-kip (400-kN) loading range, beam A has a strain range of 15 microstrain, and the grout external line shows 10 microstrain regardless of the level of PT. Under 2 kip/ft (29 kN/m) PT, only the beam A internal results are shown, with values starting at a strain range of 10 microstrain and increasing to 13 and 16 microstrain as the loading range increased.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
§ = 15,000 cycles at both the 54- and 72-kip loading ranges.
◊ = 90 kip loading range.
† = 54 kip loading range.
‡ = 72 kip loading range.
Figure 82. Graph. Top transverse strain ranges recorded at the mid-span for fully stiffened beams with a partial-depth uncracked conventionally grouted connection.

This graph shows the top transverse strain range recorded 6 ft (1.8 m) east of the mid-span for fully stiffened beams with a partial-depth uncracked conventionally grouted connection. The x-axis shows the number of cycles and ranges from 0 to 1.76 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 40 microstrain. Three lines are shown: beam A internal (i.e., internal gauge), grout exterior (i.e., external gauge on the grout), and beam B internal (i.e., internal gauge). The graph has 1.76 million cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges, with post-tensioning (PT) levels of 2, 0.8, and 0 kip/ft (29, 12, and 0 kN/m). Two rows of bars appear at the top of the graph, with the top indicating the loading ranges and the bottom indicating the PT levels. Solid vertical lines divide the graph between the three PT levels, and dashed vertical lines divide the graph between the three loading ranges. Solid lines occur at 0.80 × 10 superscript 6 and 1.40 × 10 superscript 6 cycles, which begin the 0.8- and 0-kip/ft (12- and 0-kN/m) PT levels, respectively. Dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.90 × 10 superscript 6, 0.93 × 10 superscript 6, 1.43 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles. Each PT level begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN) for all PT ranges. The dashed lines at 0.15 × 10 superscript 6 and 1.43 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading ranges, and the dashed lines at 0.30 × 10 superscript 6, 0.83 × 10 superscript 6, 0.93 × 10 superscript 6, and 1.46 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading ranges for the 2-, 0.8-, 0.8-, and 0-kip/ft (29-, 12-, 12-, and 0-kN/m) PT levels, respectively. The 0.8-kip/ft (12-kN/m) PT level has two cycles of increases from 54 to 90 kip (240 to 400 kN). The dashed line at 0.90 × 10 superscript 6 cycles indicates the start of the second of the 54- to 72-kip (240- to 320-kN) increase. The level of strain varies based on loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 9 and 18 microstrain. In the 90-kip (400-kN) loading range, beam A internal has a strain range of 17 microstrain, the grout external has a strain range of 15 microstrain, and beam B internal has a strain range of 13 microstrain regardless of the level of PT. The strain levels for the 72- and 54-kip (320- and 240-kN) loading ranges are generally 3 and 5 microstrain lower than the 90-kip (400-kN) loading range, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 kip/ft = 14.59 kN/m.
§ = 15,000 cycles at both the 54- and 72-kip loading ranges.
◊ = 90 kip loading range.
† = 54 kip loading range.
‡ = 72 kip loading range.
Figure 83. Graph. Top transverse strain ranges recorded 6 ft (1.8 m) east of the mid-span for fully stiffened beams with a partial-depth uncracked conventionally grouted connection.

For the partial-depth UHPC connections, surface strain gauges were installed on the connection and the box beam surfaces at the mid-span and 6 ft (1.8 m) from the mid-span. More surface strain gauges were installed on the connection at transverse PT locations. The transverse tensile strain in the UHPC was generally less than or equal to 20 με, which was the same as with the conventional grouted connection. The results are presented in figure 84 through figure 86.

This graph shows the top transverse strain range recorded at the mid-span for partially and fully stiffened beams with a partial-depth uncracked ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 1.55 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 50 microstrain. Two lines are shown: grout external (i.e., external gauge on the grout) and beam B internal (i.e., internal gauge in beam B). The graph shows 1.55 million cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges for both the partially and fully stiffened conditions. Two rows of bars appear at the top of the graph, with the top indicating the two boundary conditions (i.e., partially and fully stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.60 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. The dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, and 0.90 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.75 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6 and 0.90 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The level of strain varies based on loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 10 and 40 microstrain. In the 90-kip (400-kN) loading range in the partially stiffened condition, beam B internal has a strain range of 30 microstrain, and the grout external has a strain range of 37 microstrain. The strain levels for the 72- and 54-kip (320- and 240-kN) loading ranges in the partially stiffened condition are generally 7 and 15 microstrain lower than their 90-kip (400-kN) loading range counterparts, respectively. When fully stiffened, the strain range in the 90-kip (400-kN) loading range is 16 and 20 microstrain for beam B internal and grout external, respectively. The strain levels for the 72- and 54-kip (320- and 240-kN) loading for the fully stiffened condition are generally 4 and 6 microstrain lower than the 90-kip (400-kN), respectively.

Source: FHWA.
1 kip = 4.448 kN.
Figure 84. Graph. Top transverse strain ranges recorded at the mid-span for partially and fully stiffened beams with a partial-depth uncracked UHPC connection.

This graph shows the top transverse strain range recorded 6 ft (1.8 m) east of the mid-span for partially and fully stiffened beams with a partial-depth uncracked ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 1.55 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 50 microstrain. Three lines are shown: beam B internal (i.e., beam B internal gauge), grout external (i.e., external gauge on the grout), and beam A internal (i.e., beam A internal gauge). The graph has 1.55 million cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges for both the partially and fully stiffened conditions. Two rows of bars appear at the top of the graph, with the top indicating the two boundary conditions (i.e., partially and fully stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.60 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, and 0.90 × 10 superscript 6 cycles divide the graph between the three loading ranges. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.75 × 10 superscript 6 cycles indicate the start of the 72-kip (320-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6 and 0.90 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The strain range varies based on loading range, with higher strain ranges occurring under larger loading ranges. The strain ranges for all gauges are generally between 7 and 30 microstrain, but an increase to 50 microstrain in the gauge in beam B occurred in the 90-kip (400-kN) loading range for the partially stiffened condition. In the 90-kip (400-kN) loading range for the partially stiffened condition, the strain ranges are 37 microstrain for beam B, 23 microstrain for the external grout, and 27 microstrain for beam A. In the 72-kip (320-kN) loading range for the partially stiffened condition, the strain ranges for the three lines are 23, 14, 15 microstrain, respectively. In the 54-kip (240-kN) loading range for the partially stiffened condition, the strain ranges for the three lines are 20, 14, and 14 microstrain, respectively. When fully stiffened, the strain ranges in the 90-kip (400-kN) loading range for the three lines are 17, 15, and 13 microstrain, respectively. In the 72-kip (320-kN) loading range for the fully stiffened condition, the strain ranges for the three lines are 15, 13, and 10 microstrain, respectively. In the 54-kip (240-kN) loading range for the fully stiffened condition, the strain ranges for the three lines are 11, 10, and 8 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
Figure 85. Graph. Top transverse strain ranges recorded 6 ft (1.8 m) east of the mid-span for partially and fully stiffened beams with a partial-depth uncracked UHPC connection.

This graph shows the top transverse strain ranges recorded along the length of the connection for partially and fully stiffened beams with a partial-depth uncracked ultra-high performance concrete (UHPC) connection. The x-axis shows the number of cycles and ranges from 0 to 1.55 × 10 superscript 6 cycles, and the y-axis shows the strain range and ranges from 0 to 50 microstrain. Five lines are shown: the mid-span, 6 ft (1.8 m) west of the mid-span, 6 ft (1.8 m) east of the mid-span, east post-tensioning (PT) point, and west PT point. The graph has 1.55 million cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges for both the partially and fully stiffened conditions. Two rows of bars appear at the top of the graph, with the top indicating the two boundary conditions (i.e., partially and fully stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.60 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. The dashed lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.75 × 10 superscript 6, and 0.90 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.75 × 10 superscript 6 cycles indicate the start of the 72-kip (320-kN) loading range, and the dashed lines at 0.30 × 10 superscript 6 and 0.90 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The strain ranges vary based on loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 5 and 40 microstrain. In the 90-kip (400-kN) loading range for the partially stiffened condition, the mid-span gauge strain range is 36 microstrain, and the east and west PT strain ranges are 25 and 20 microstrain, respectively. In the 72-kip (320-kN) loading range for the partially stiffened condition, the mid-span gauge strain range is 28 microstrain, and the east and west PT strain ranges are both 15 microstrain. In the 54-kip (240-kN) loading range for the partially stiffened condition, the mid-span gauge strain range is 20 microstrain, and the east and west PT strain ranges are both 15 microstrain. When fully stiffened, the strain ranges in the 90-kip (400-kN) loading range are 20, 15, 17, 10, and 9 microstrain for the five lines, respectively. In the 72-kip (320-kN) loading range in the fully stiffened condition, the strain ranges for the five lines are 17, 12, 14, 9, and 7 microstrain, respectively. In the 54-kip (240-kN) fully stiffened condition, the strain ranges for the five lines are 14, 10, 11, 7, and 6 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
1 ft = 0.305 m.
Figure 86. Graph. Top transverse strain ranges recorded along the length of the connection for partially and fully stiffened beams with a partial-depth uncracked UHPC connection.

When the full-depth UHPC connection was tested, additional surface strain gauges were installed along the cross section at the same longitudinal locations on the beam. Not all of the strain gauges functioned properly; only those with valid data were reported in figure 87 through figure 90. The simply supported case showed the highest transverse tensile strain of all the cases studied. The strain gauges placed next to the connection usually had more transverse strain. The only exception was for the strain gauge located on the outside edge of the loaded beam 6 ft (1.8 m) from the mid-span, as shown in figure 88.

This graph shows the distribution of top transverse strain recorded along the top of the unstiffened and partially stiffened beams with a full-depth uncracked ultra-high performance concrete (UHPC) connection at the mid-span. The x-axis shows the number of cycles and ranges from 0 to 0.60 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 50 microstrain. Five lines are shown: beam A inside edge, beam B inside edge, beam B outside edge, connection, and beam A middle. The graph has 600,000 cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges in each boundary condition configuration. Two rows of bars appear at the top of the graph, with the top indicating the two boundary conditions (i.e., unstiffened and partially stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.15 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. Dashed lines occur at 0.05 × 10 superscript 6, 0.10 × 10 superscript 6, 0.30 × 10 superscript 6, and 0.45 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.05 × 10 superscript 6 and 0.30 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.10 × 10 superscript 6 and 0.45 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The level of strain varies based on loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 7 and 37 microstrain. In the 90-kip (400-kN) loading range for the unstiffened condition, the strain ranges for the five lines are 24, 17, 36, 33, and 29 microstrain, respectively. In the 72-kip (400-kN) loading range for the unstiffened condition, the strain ranges for the five lines are 18, 12, 30, 27, and 24 microstrain, respectively. In the 54-kip (240-kN) loading range for the unstiffened condition, the strain ranges for the five lines are 14, 8, 24, 20, and 17 microstrain, respectively. In the 90-kip (400-kN) loading range for the partially stiffened condition, the strain ranges of the five lines are 23, 16, 35, 30, and 27 microstrain, respectively. In the 72-kip (320-kN) loading range for the partially stiffened condition, the strain ranges of the five lines are 18, 12, 29, 25, and 22 microstrain, respectively. In the 54-kip (240-kN) loading range for the partially stiffened condition, the strain ranges of the five lines are 14, 8, 23, 19, and 16 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
Figure 87. Graph. Distribution of top transverse strain ranges recorded along the top of the unstiffened and partially stiffened beams with a full-depth uncracked UHPC connection at the mid-span.

This graph shows the distribution of top transverse strain recorded along the top of unstiffened and partially stiffened beams with a full-depth uncracked ultra-high performance concrete (UHPC) connection 6 ft (1.8 m) from the mid-span. The x-axis shows the number of cycles and ranges from 0 to 0.60 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 50 microstrain. Six lines are shown: beam A outside edge, beam A inside edge, B mid-span, beam B inside edge, beam B outside edge, and connection. The graph shows 600,000 cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges in each boundary condition configuration. Two rows of bars appear at the top of the graph, with the top indicating the two boundary conditions (i.e., unstiffened and partially stiffened) and the bottom indicating the loading ranges. A solid vertical line at 0.15 × 10 superscript 6 cycles divides the graph between the two boundary conditions, and dashed vertical lines divide the graph between the three loading ranges. Dashed lines occur at 0.05 × 10 superscript 6, 0.10 × 10 superscript 6, 0.30 × 10 superscript 6, and 0.45 × 10 superscript 6 cycles. Each boundary condition begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). Therefore, the dashed lines at 0.05 × 10 superscript 6 and 0.30 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, and the dashed lines at 0.10 × 10 superscript 6 and 0.45 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range for the partially and fully stiffened boundary conditions, respectively. The level of strain varies based on loading range, with higher strains occurring under larger loading ranges. The strains for all gauges are generally between 7 and 40 microstrain. In the 90-kip (400-kN) loading range for the unstiffened condition, the strain ranges for the five lines are 15, 24, 40, 35, and 21 microstrain, respectively. In the 72-kip (320-kN) loading range for the unstiffened condition, the strain ranges for the five lines are 11, 19, 34, 28, and 16 microstrain, respectively. In the 54-kip (240-kN) loading range for the unstiffened condition, the strain ranges for the five lines are 9, 14, 25, 22, and 12 microstrain, respectively. In the 90-kip (400-kN) loading range for the partially stiffened condition, the strain ranges of the five lines are 14, 21, 28, 30, 20, and 17 microstrain, respectively. In the 72-kip (320-kN) loading range for the partially stiffened condition, the strain ranges of the five lines are 10, 17, 23, 25, 17, and 15 microstrain, respectively. In the 54-kip (240-kN) loading range for the partially stiffened condition, the strain ranges of the five lines are 8, 13, 19, 20, 12, and 11 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
Figure 88. Graph. Top transverse strain ranges recorded along the top of unstiffened and partially stiffened beams with a full-depth uncracked UHPC connection 6 ft (1.8 m) from the mid-span.

This graph shows the distribution of top transverse strain range recorded along the top of fully stiffened beams with a full-depth uncracked ultra-high performance concrete (UHPC) connection at the mid-span. The x-axis shows the number of cycles and ranges from 0 to 0.92 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 40 microstrain. Five lines are shown: beam A inside edge, beam B inside edge, connection, beam A mid-line, and beam A outside edge. The graph shows 920,000 cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. A row of bars appears at the top of the graph indicating the loading ranges. Dashed vertical lines divide the graph between the three loading ranges, which each appear twice. These lines occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.32 × 10 superscript 6, 0.37 × 10 superscript 6, and 0.42 × 10 superscript 6 cycles. The graph begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). This pattern occurs twice. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.37 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, the dashed lines at 0.30 × 10 superscript 6 and 0.42 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range, and the dashed line at 0.32 × 10 superscript 6 cycles indicates the start of the 54-kip (240 kN) loading range in the second grouping. The strain range varies based on loading range, with higher ranges occurring under larger loading ranges. The strain ranges for all gauges are generally between 4 and 16 microstrain. In the 90-kip (400-kN) loading range, strain ranges for the five lines are 11, 16, 6, 8, and 14 microstrain, respectively. In the 72-kip (320-kN) loading range, strain ranges for the five lines are 9, 14, 5, 6, and 11 microstrain, respectively. In the 54-kip (240-kN) loading range, strain ranges for the five lines are 7, 10, 4, 4, and 9 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
◊ = 90-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 89. Graph. Top transverse strain ranges recorded along the top of fully stiffened beams with a full-depth uncracked UHPC connection at the mid-span.

This graph shows the distribution of top transverse strain ranges recorded along the top of fully stiffened beams with a full-depth uncracked ultra-high performance concrete (UHPC) connection 6 ft (1.8 m) east of the mid-span. The x-axis shows the number of cycles and ranges from 0 to 0.92 × 10 superscript 6 cycles, and the y-axis shows strain range and ranges from 0 to 70 microstrain. Six lines are shown: beam A outside edge, beam B outside edge, beam B mid-line, beam A inside edge, beam B inside edge, and connection. The graph shows 920,000 cycles and contains data for the 54-, 72-, and 90-kip (240-, 320-, and 400-kN) loading ranges. A row of bars appears at the top of the graph indicating the loading ranges. Dashed vertical lines divide the graph between the three loading ranges and occur at 0.15 × 10 superscript 6, 0.30 × 10 superscript 6, 0.32 × 10 superscript 6, 0.37 × 10 superscript 6, and 0.42 × 10 superscript 6 cycles. The graph begins with a loading range of 54 kip (240 kN), which increases to 72 and 90 kip (320 and 400 kN). This pattern occurs twice. Therefore, the dashed lines at 0.15 × 10 superscript 6 and 0.37 × 10 superscript 6 cycles indicate the start of the 72-kip (230-kN) loading range, the dashed lines at 0.30 × 10 superscript 6 and 0.42 × 10 superscript 6 cycles indicate the start of the 90-kip (400-kN) loading range, and the dashed line at 0.32 × 10 superscript 6 cycles indicates the start of the 54-kip (240-kN) loading range. The strain range varies based on loading range, with higher ranges occurring under larger loading ranges. The strain ranges for all gauges are generally between 2 and 35 microstrain. In the 90-kip (400-kN) loading range, strain ranges for the six lines are 6, 11, 5, 30, 8, and 33 microstrain, respectively. In the 72-kip (320-kN) loading range, strain ranges for the six lines are 5, 4, 4, 22, 7, and 29 microstrain, respectively. In the 54-kip (240-kN) loading range, strain ranges for the six lines are 4, 8, 3, 18, 6, and 19 microstrain, respectively.

Source: FHWA.
1 kip = 4.448 kN.
◊ = 90-kip loading range.
† = 54-kip loading range.
‡ = 72-kip loading range.
Figure 90. Graph. Top transverse strain ranges recorded along the top of fully stiffened beams with a full-depth uncracked UHPC connection 6 ft (1.8 m) east of the mid-span.

Independent of the connection design and boundary conditions, the transverse tensile strain generated by the structural loading was observed to be less than 40 με. If a maximum transverse tensile strain of 40 με in the box beam concrete close to the connection is assumed, the interface bond between the grout and box beam concrete should have enough strength to resist this strain. A 40-με deformation in a 6,000-psi (41-MPa) concrete produces a stress of approximately 150 psi (1 MPa).

Proper selection of a grout, a connection surface preparation technique, and curing methodology can mitigate interface cracking by ensuring that the tensile resistance of the connection is at least as strong as the precast concrete. It must be recognized that the early age dimensional stability of the grout is also important as shrinkage strains can be large, potentially resulting in cracking of the grout and interface debonding.

When a direct tensile force was applied to the UHPC connections, as demonstrated in figure 74, the box beam concrete cracked rather than the connection interface or the UHPC itself. This indicates that the interface bond between the UHPC and the box beam with an EA surface preparation and rebar in a non-contact lap splice is of similar or greater tensile strength as compared to the tensile strength of the box beam concrete. This was also observed in a study by De la Varga et al. where interface bond between different grout materials and concrete was investigated.(17) They found that, for connections with UHPC and EA, the failure primarily occurs in the concrete rather than at the interface or within UHPC itself. This is not true for conventional grout connections, as the interface often fails under the same conditions. Note that the discrete steel reinforcement that is distributed along the length of the UHPC connections provides further advantages in terms of increasing local shear and tensile strengths and limiting the crack width if any cracks should develop at the interface.

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