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Federal Highway Administration
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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
REPORT |
This report is an archived publication and may contain dated technical, contact, and link information |
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Publication Number: FHWA-HRT-17-042 Date: November 2017 |
Publication Number: FHWA-HRT-17-042 Date: November 2017 |
This chapter presents the data from the five loading scenarios that were explored. For every loading scenario, the same data plots are shown in the same order as a means to provide easy context for how things change from one loading scenario to another. Additionally, every data plot shows a side-by-side output of the current and new design methods, with the size of the web splice plate being the identifying difference. For each scenario, contour plots are presented for the step that achieves the factored design forces, and, for a later step, that was either the last step or the step where the analysis could no longer converge to a solution. To assist in decoding the contour outputs, the following list defines the six types of stress/strain/force contours that are presented:
0 shows the moment versus rotation plot for the left support. The current design method results are plotted with circle data points, and the new design method results plotted with square data points. The overall response of the two models does not differ much between the two methods other than a slight reduction in moment strength after yielding. Contour plots present the results for the step with approximately Mu = 8,016 kip-ft applied (see 0 through 0) and for the last step in each analysis (see 0 through 0).
Source: FHWA
Figure 15. Graph. Moment versus rotation of the left support under pure positive moment for the splice designed using the current and new methods.
Source: FHWA
Figure 16. Illustration. Mises stresses at pure positive Mu (deck not shown for clarity).
Source: FHWA
Figure 17. Illustration. Mises stresses at pure positive Mu (splice plates and deck not shown for clarity).
Source: FHWA
Figure 18. Illustration. Longitudinal stresses at pure positive Mu (deck not shown for clarity).
Source: FHWA
Figure 19. Illustration. Longitudinal stresses at pure positive Mu (splice plates and deck not shown for clarity).
Source: FHWA
Figure 22. Illustration. Mises stresses at last step of pure positive moment (deck not shown for clarity).
Source: FHWA
Figure 23. Illustration. Mises stresses at last step of pure positive moment (splice plates and deck not shown for clarity).
Source: FHWA
Figure 24. Illustration. Longitudinal stresses at last step of pure positive moment (deck not shown for clarity).
Source: FHWA
Figure 25. Illustration. Longitudinal stresses at last step of pure positive moment (splice plates and deck not shown for clarity).
Source: FHWA
Figure 26. Illustration. PEEQ at last step of pure positive moment (deck not shown for clarity).
Source: FHWA
Figure 27. Illustration. PEEQ at last step of pure positive moment (splice plates and deck not shown for clarity).
Source: FHWA
Figure 28. Illustration. Resultant forces on bolt shear planes at last step of pure positive moment.
At the design moment, the results in terms of Mises and longitudinal stresses (see 0 though 0) do not differ much between the two methods. The only noticeable difference is that the splice designed by the new method had fewer bolts in the web, which resulted in a higher demand over the splice designed by the current method. However, the shear forces were well within the limits of the bolts (see 0 and 0).
Analysis of the plots from the last step show that the rounding over of the moment/rotation curve presented in 0 was due to plastic hinging of the left girder section. At 0.01 radians of rotation, about half the depth of the left girder has yielded at this point (see 0 through 0). The larger web splice in the splice designed by the current method also transferred more moment than the web splice designed by the new method, as is evident from the increased yielding in the left girder section (see 0). The PEEQ also shows that the splice designed by the current method attracted more plasticity into the web splice, although the splice designed by the new method led to flange splices with a higher demand (see 0 and 0). However, the web bolt demands were also higher for splice designed by the new method (see 0 and 0), with the largest bolt force being 41.5 kip. It is likely that any additional moment would effectively start fracturing bolts in the splice designed by the new method. However, the limit state of bolt fracture occurred at three times the design moment, and this would not have controlled the design. The vector plots in 0 show the web’s participation in transferring moment because the vectors are horizontal (i.e., no shear in web) with a linear variation in magnitude increasing toward the tension flange.
0 shows the moment versus rotation plot for the left support with the current method results plotted with circular data points and the new method results plotted with square data points. The overall responses of the two models are nearly equal, and it is obvious that negative moment controlled the design of this connection because the connection did not have a tremendous reserve in strength beyond the design negative moment. Contour plots are presented for the step with approximately Mu = 15,185 kip-ft applied (see 0 through 0) and for the last step in each analysis (see 0 through 0).
Source: FHWA
Figure 30. Graph. Moment versus rotation of the left support under pure negative moment for the splice designed using the current and new methods.
Source: FHWA
Figure 32. Illustration. Mises stresses at pure negative Mu (splice plates not shown for clarity).
Source: FHWA
Figure 34. Illustration. Longitudinal stresses at pure negative Mu (splice plates not shown for clarity).
Source: FHWA
Figure 36. Illustration. PEEQ at pure negative Mu (splice plates not shown for clarity).
Source: FHWA
Figure 40. Illustration. Mises stresses at last step of pure negative moment (splice plates not shown for clarity).
Source: FHWA
Figure 42. Illustration. Longitudinal stresses at last step of pure negative moment (splice plates not shown for clarity).
Source: FHWA
Figure 44. Illustration. PEEQ at last step of pure negative moment (splice plates not shown for clarity).
Source: FHWA
Figure 45. Illustration. Resultant forces on bolt shear planes at last step of pure negative moment.
At the design moment, the Mises stresses show that the flanges of the left girder have just yielded along with the flange splice plates (see 0 and 0). The same can be said for the longitudinal stresses (see 0 and 0), which indicate, not surprisingly, that these stresses dominated the Mises failure criterion. The PEEQ plot in 0 shows that the splice designed by the new method had a slightly higher demand on the flange splice plates than the splice designed by the current method. Though the demands on the flange bolts were nearly the same between the two methods, there was an expected higher demand on the web bolts in the splice designed with the new method (see 0 and 0).
Analysis of the plots from the last step shows that the rounding over of the moment/rotation curve presented in 0 was from plastic hinging of the left girder section (see 0 and 0). At 0.015 radians of rotation, nearly the entire depth of the left girder had yielded. The stress contours between the two scenarios only differed in regards to the splice designed by the current method, which transferred more stress across the web splice than the splice designed by the new method. There was more yielding in the girder webs and web splice in the splice designed by the current method. However, the demands on the flange splices in the splice designed by the new method were higher (mostly evident on the PEEQ plot in 0). This resulted in higher demands on the bolts in the flange splices designed by the new method (with the highest shear forces being 39.4 kip) approaching their fracture strength (see 0 and 0). The vector plots in 0 show the web’s participation in transferring moment as the vectors were horizontal (i.e., no shear in web) with a linear variation in magnitude increasing away from the girder centroid.
0 shows a force versus displacement plot for the left support with the circular data points indicating the results from the current method and the square data points indicating the results from the new method. The plots are identical, which is the first indication that the design method is insensitive to shear loading. The plateau response of each of the curves in 0 is primarily from hinging in the left girder section at the interface between the elastic and inelastic elements.
Source: FHWA
Figure 47. Graph. Force versus displacement at the left support under high shear loading for the splice designed using the current and new methods.
Contour plots are presented for the step with Vu = 1,312 kip (see 0 through 0). The system is still elastic (see 0 and 0), although the shear stresses were at about 80 percent of their yield value (see 0 and 0). The bolt demands were low; the bolts were only at about one-third of their design capacity although slightly higher in the splice designed by the new method (see 0 and 0).
Source: FHWA
Figure 51. Illustration. Longitudinal stresses at Vu (splice plates not shown for clarity).
Step 26 was chosen as the second interrogation level because it began just after yielding had started. Contour plots are shown in 0 through 0. The subsequent steps resulted in excessive straining at the plastic hinge in the left girder, not within the spliced region. In both models, the majority of both webs were yielding, and the middle portion of the web splice plates was also approaching yield (see 0 and 0). Not surprisingly, the yielding response was dominated by the shear stresses as the contour plot showed most of the web at or approaching 29 ksi (see 0 and 0). The most telling plots were the PEEQ contours in 0 and 0, which were each plotted with a maximum strain of 0.015. The differences were minor between the splices created via the two design methods; each showed a nearly equal level of plastic straining, which indicates that the design method was insensitive to shear response. The resultant bolt forces (0 and 0) were uniform under shear (though expectedly larger in the splice designed via the new method because of lesser bolts) but still well within their design limits. The vectors in 0 were mostly vertical under this scenario of primarily shear loading; however, the corner bolts were slightly rotated, which indicates that some effect of moment was being taken by those bolts.
Source: FHWA
Figure 57. Illustration. Mises stresses at step 26 (splice plates not shown for clarity).
Source: FHWA
Figure 59. Illustration. Longitudinal stresses at step 26 (splice plates not shown for clarity).
Source: FHWA
Figure 61. Illustration. Shear stresses at step 26 (splice plates not shown for clarity).
Source: FHWA
Figure 64. Illustration. PEEQ at step 26 (plotted with maximum of 0.015; splice plates not shown for clarity).
0 shows a force versus displacement plot for the left support. Circular data points indicate the results from the current method, and square data points indicate the results from the new method. In this scenario, the load was applied to a cantilever beam, so the plateau response demonstrated in each of the methods was not representative of behavior in the bolted connection. The response was due to hinging at the interface between the elastic and inelastic elements in the right girder. However, throughout the loading, the responses were identical. Results in 0 through 0 are presented for step 20, in which Vu = 1,312 kip, while results in 0 through 0 are presented for step 34 just before the plastic hinge formed in the right girder.
Source: FHWA
Figure 67. Graph. Force versus displacement at left support under proportional positive moment for the splice designed using the current and new methods.
Source: FHWA
Figure 68. Illustration. Mises stresses at proportional positive moment loading at Vu (deck not shown for clarity).
Source: FHWA
Figure 69. Illustration. Mises stresses at proportional positive moment loading at Vu (splice plates and deck not shown for clarity).
Source: FHWA
Figure 70. Illustration. Longitudinal stresses at proportional positive moment loading at Vu (deck not shown for clarity).
Source: FHWA
Figure 71. Illustration. Longitudinal stresses at proportional positive moment loading at Vu (splice plates and deck not shown for clarity).
Source: FHWA
Figure 72. Illustration. Shear stresses at proportional positive moment loading at Vu (deck not shown for clarity).
Source: FHWA
Figure 73. Illustration. Shear stresses at proportional positive moment loading at Vu (splice plates and deck not shown for clarity).
Source: FHWA
Figure 74. Illustration. Resultant forces on bolt shear planes at proportional positive moment loading at Vu.
Source: FHWA
Figure 75. Graph. Web splice bolt shear vectors at proportional positive moment loading at Vu.
Source: FHWA
Figure 77. Illustration. Mises stresses at step 34 (splice plates and deck not shown for clarity).
Source: FHWA
Figure 78. Illustration. Longitudinal stresses at step 34 (deck not shown for clarity).
Source: FHWA
Figure 79. Illustration. Longitudinal stresses at step 34 (splice plates and deck not shown for clarity).
Source: FHWA
Figure 81. Illustration. Shear stresses at step 34 (splice plates and deck not shown for clarity).
Source: FHWA
Figure 83. Illustration. PEEQ at step 34 (splice plates and deck not shown for clarity).
At the design force level, the system was elastic (see 0 and 0). Bolt forces were slightly higher for the splice designed using the new method but were well within their design limits (see 0 and 0).
At step 34, the applied shear was 2,230 kip, which was 70 percent higher than the design shear. The Mises stresses showed yielding in the upper portion of the left girder and yielding over nearly the full depth at the interface between the elastic and inelastic elements on the right girder (see 0 and 0). It may seem odd to see the left girder yield near the top flange in a positive proportional moment scenario; however, as seen in 0, in this scenario, a negative moment had to be applied at the left support to attain a positive design moment at the bolted splice. Further analysis of the longitudinal and shear stress plots showed that the yielding was dominated by the shear stresses as they were closest to their yielding limit (see 0 and 0). The PEEQ plots in 0 and 0 showed similar response in the web, although slightly higher demands existed on the flange splice plates in the splice designed using the new design methodology. The bolt forces shown in 0 were within their design limits, although the forces were expectedly larger in the splice designed using the new method. The bolt force vectors in 0 were primarily vertical, indicating that the shear in the girder was dominating the force in the bolts. However, the vectors for bolts closest to the flanges had horizontal components, and there was a characteristic rotation of all the vectors around a point near the girder neutral axis, indicating that the web splice did carry some moment.
0 shows a force versus displacement plot for the left support. Circular data points indicate the results from the current method, and square data points indicate the results from the new method. Elastically, the behaviors were similar, although once inelasticity started, the splice designed using the new method demonstrated slightly lower strength. There was also a difference in where the analysis terminated. For the splice designed by the current method, the analysis was terminated after step 36 because the strength was not appreciably increasing. However, for the splice designed by the new method, the analysis could not converge to a solution beyond step 32, which was a result of some bolts reaching their capacity.
Source: FHWA
Figure 86. Graph. Force versus displacement at the left support under proportional negative moment for the splice designed using the current and new methods.
Contour plot data are presented in 0 through 0 at the design loading (i.e., step 27 in 0). The splice plates, a small portion of the right girder web near the top and bottom of the web splice, and the web splice had started to yield in the splice designed with both methods (see 0 and 0). The longitudinal stress plot indicates that most of the yielding was dominated by the longitudinal stresses generated from the moment (see 0 and 0). The PEEQ plots show that any significant yielding was primarily isolated to just the flange splice plates and was slightly greater in the splice designed using the new method (see 0 and 0). The resultant bolt forces show that the lead bolts on the flange splices had shear forces in the low 30-kip range in the splices designed by each method. The corner web bolts in the splice designed using the new method had bolt forces in the upper 30-kip range (see 0) versus the mid-20 kip for the current design method. This is more easily seen in 0 where the corner bolts on the right girder section were the most highly loaded, and the bolt forces were obviously lower in the splice designed using the current method because twice as many bolts were provided. The bolt vectors were primarily horizontal, indicating that the moment in the girders was controlling the forces in the bolts.
Source: FHWA
Figure 88. Illustration. Mises stresses at proportional negative moment at Vu (splice plates not shown for clarity).
Source: FHWA
Figure 90. Illustration. Longitudinal stresses at proportional negative moment at Vu (splice plates not shown for clarity).
Source: FHWA
Figure 92. Illustration. Shear stresses at proportional negative moment at Vu (splice plates not shown for clarity).
Source: FHWA
Figure 94. Illustration. PEEQ at proportional negative moment at Vu (splice plates not shown for clarity).
Source: FHWA
Figure 95. Illustration. Resultant forces on bolt shear planes at proportional negative moment at Vu.
At the higher level of interrogation, the response from step 32 was examined for each method, and contour plot data are presented in 0 through 0. At step 32, the shear in the girder was 1,574 kip. The Mises stress plots at this level show that yielding was primarily continuing in the right girder section only as a plastic hinge was developing, which was mainly driven by the longitudinal stresses (see 0 through 0). The PEEQ plots faintly show yielding in the right girder web, although most of the yielding was concentrated in the flange splice plate (see 0 and 0). There was also additional yielding in the web splice in the splice designed using the current method. The largest difference between the two methods can be seen in the bolt force results. In the splice designed using the new method, the force in the lead bolt in the flange splices varied from 38 to 40 kip depending on the bolt (see 0). This was reduced slightly in the splice designed using the current method, although the forces were in the mid-30 kip range. The web splice bolts were also loaded more heavily in the splice designed using the new method; in fact, the two corner bolts on the right girder section reached the 42-kip limit, which terminated the analysis. The force vectors in the web splice shown in 0 had large horizontal components in bolts closer to the flanges with a characteristic rotation of all vectors around the girder centroid, indicating that the web splice was contributing to moment transfer.
Source: FHWA
Figure 98. Illustration. Mises stresses at step 32 (splice plates not shown for clarity).
Source: FHWA
Figure 100. Illustration. Longitudinal stresses at step 32 (splice plates not shown for clarity).