Proposed Modification to AASHTO Cross-Frame Analysis and Design (2021) / Chapter Skim
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From page 60... ...
60 Findings and Applications As noted in Chapters 1 and 2, the five major objectives of NCHRP Project 12-113 are addressed with both experimental and analytical studies. The experimental portions included the instrumentation and monitoring of three bridges, while the analytical studies included four independent studies (Fatigue Loading Study, R-Factor Study, Commercial Design Software Study, and Stability Study)
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From page 61... ...
Findings and Applications 61 Given the distinct differences in the two experimental tests, this section of the report is divided into two major subsections. Section 3.1.1 highlights key findings from the controlled live load tests, and Section 3.1.2 summarizes the measured rainflow-counting data considering one month of measured traffic data on the instrumented components of the bridges.
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From page 62... ...
62 Proposed Modification to AASHTO Cross-Frame Analysis and Design the figures presented in this section, both the static and moving-load cases, are based on instrumented cross-frames in Bridge 1 unless noted otherwise. The full set of field data related to all three bridges can be found in Appendix E
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From page 63... ...
Findings and Applications 63 stress cycle when the truck traverses along the left-hand side of the panel but experiences a compressive stress cycle when the truck transverses along the right-hand side. • The influence of longitudinal load position is localized, as demonstrated by the fact that the measured axial stresses are nearly zero when the truck is positioned beyond 50 feet from the panel of interest, regardless of the lane position.
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64 Proposed Modification to AASHTO Cross-Frame Analysis and Design load was not purely static. For example, a small spike was recorded at the beginning of plateau B in Figure 3-3.
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Findings and Applications 65 • Interestingly, all but two instrumented cross-frame members experienced a net tensile stress under the applied load. This behavior seems to indicate that the simplified postprocessing methods commonly utilized in 2D analysis programs as outlined in Section 2.5, do not accurately represent realistic conditions.
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66 Proposed Modification to AASHTO Cross-Frame Analysis and Design It is also important to note that in general terms, a user can manipulate a model in many ways to achieve the target solution; however, those changes may not be a good representation of the actual structural system. The team was interested in achieving good agreement between measurements and FEA predictions but not at the expense of using unreasonable assumptions.
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From page 67... ...
Findings and Applications 67 is noticeably higher than what is observed for girder stresses or deflections. Even for the most sophisticated full-shell, 3D FEA model and a relatively simple bridge geometry, the errors associated with the critical cross-frame forces still ranged from 0 to 60%.
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68 Proposed Modification to AASHTO Cross-Frame Analysis and Design The primary goal for obtaining these data was to establish effective and maximum stress range metrics by which the computational studies and current AASHTO fatigue criteria could be assessed. Effective stress ranges are related to finite-life behavior (Fatigue II limit state)
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Findings and Applications 69 Similar histograms were produced for girder flanges as well. Figure 3-6 presents a sideby-side comparison of the stress range spectra measured for a cross-frame member (D1-2 in Figure 3-2)
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70 Proposed Modification to AASHTO Cross-Frame Analysis and Design two bridges. These results imply that the cross-frames in this skewed system, especially with a contiguous layout, generally experience slightly higher stress ranges than the normal and horizontally curved systems.
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Findings and Applications 71 fatigue load factors for cross-frame design. Section 3.2.3 reviews the WIM data and explores the frequency at which a "double truck" case (i.e., a loading condition that maximizes the force reversal in a cross-frame member)
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72 Proposed Modification to AASHTO Cross-Frame Analysis and Design the compiled design force ranges for all top strut members evaluated near the maximum positive dead load moment region (edge bay) of straight and normal bridges.
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Findings and Applications 73 lane can be evaluated. By examining the results independently for bridge types, the impacts of support skewness and bridge curvature can also be assessed.
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74 Proposed Modification to AASHTO Cross-Frame Analysis and Design manually developing a spreadsheet to evaluate each cross-frame due to AASHTO fatigue loading criteria is possible. 3.2.1.2 Governing Lane Passage Where Section 3.2.1.1 evaluated which cross-frame members govern load-induced fatigue design, the section herein addresses the lane position corresponding to those critically loaded members.
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From page 75... ...
Findings and Applications 75 To clarify the intent of the figure, the straight, normal data set is considered as an example. For all 312 straight and normal bridges evaluated, the governing cross-frame was located in an interior bay near the maximum positive dead load moment region on 204 occasions (65%)
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76 Proposed Modification to AASHTO Cross-Frame Analysis and Design and diagonals in these areas. As such, loads that maximize the induced torque on the bridge cross-section are often critical.
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Findings and Applications 77 straight bridge, the resulting force range from the passing truck increases 10% when a 1,500-ft radius is introduced and an additional 9% when the radius is halved to 750 feet. The general response of the cross-frame is the same, except for the magnitudes.
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78 Proposed Modification to AASHTO Cross-Frame Analysis and Design q = largest skew angle on bridge relative to the axis normal to the longitudinal girders, Ls = span length at the bridge centerline, R = minimum radius of the horizontal curvature, ncf = number of intermediate cross-frames in the span, and m = constant, taken as 1 for simple-span bridges and 2 for continuous-span bridges. As the equations show, the skew index increases for shorter, wider spans with larger skew angles.
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Findings and Applications 79 in skew index generally resulted in a 25% increase in the critical cross-frame force demand. In general, these observations are consistent with the field experimental data outlined in Section 3.1.
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80 Proposed Modification to AASHTO Cross-Frame Analysis and Design analytical and experimental results of instrumented Bridges 1, 2, and 3, a few key observations are established. First, the governing design stress ranges for Bridges 1 and 2 are close to the mean response (2.35 ksi)
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Findings and Applications 81 whereas ratios exceeding unity represent designs in violation of AASHTO LRFD. As outlined previously, it is assumed that the design of all intermediate cross-frame members is governed by the critical, maximum case.
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82 Proposed Modification to AASHTO Cross-Frame Analysis and Design economies are possible in cross-frame design, while still providing adequate structural safety. The absence of observed load-induced fatigue failures does not necessarily imply the current AASHTO LRFD design criteria are overly conservative and wasteful from a cost perspective.
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Findings and Applications 83 As noted previously, fatigue resistance is beyond the scope of the project and is not discussed further. Instead, the research team narrowed its efforts to examining the modeling approach (stiffness modification and simplified analysis techniques)
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84 Proposed Modification to AASHTO Cross-Frame Analysis and Design distribution of all stress ranges produced by the 18 WIM site records)
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Findings and Applications 85 of variation associated with this value is 0.23. This load factor is less than the current Fatigue I load factor of 1.75, which indicates a potential source of conservatism in the design load criteria for cross-frame fatigue.
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86 Proposed Modification to AASHTO Cross-Frame Analysis and Design factor for Fatigue II. This suggests that the 0.8 load factor may be conservative for characterizing the response of cross-frames to the U.S.
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Findings and Applications 87 In order to obtain reliability indices close to the assumed target reliability of unity, adjustments are required to either the load or resistance factors. As an alternative to altering the resistance factors [or the associated changes in constant amplitude fatigue thresholds, (F)
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88 Proposed Modification to AASHTO Cross-Frame Analysis and Design Detail Category Reliability Index Fatigue I Fatigue II A 1.32 1.74 B 1.22 1.70 B′ 1.49 2.39 C 1.29 1.79 C′ 1.30 1.77 D 1.82 2.81 E 1.08 1.87 E′ 1.77 2.25 Table 3-9. Reliability of cross-frames for Fatigue I and II limit states using adjustment factor of 0.65 to existing load factors.
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Findings and Applications 89 First, the Fatigue II load factors inherently built into the force demands (i.e., the numerator of the D/C ratio) are reduced from 0.80 to 0.52 based on the findings outlined above.
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90 Proposed Modification to AASHTO Cross-Frame Analysis and Design As discussed in Section 2.3.3.5, a cluster analysis was performed on the multi-lane WIM data to consider if a bridge may be loaded with other truck traffic during a primary drive lane load event (i.e., passage of one or more axles of a vehicle)
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Findings and Applications 91 how often (for the year of data considered) any truck was within a certain window of the drive lane truck, relative to the total volume of traffic in the drive lane for each specific site.
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92 Proposed Modification to AASHTO Cross-Frame Analysis and Design longitudinal direction, it is apparent that, for cross-frames, the largest frequency of occurrence for passing vehicles occurring simultaneously is appreciably low (i.e., larger headway distances generally do not result in superimposed cross-frame forces)
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Findings and Applications 93 variable to pinpoint which cross-frames are critical without some refined, influence-surface analysis (i.e., to examine all possible truck positions and cross-frame force effects)
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94 Proposed Modification to AASHTO Cross-Frame Analysis and Design 3.3 R-Factor Study (3D Analysis) This section summarizes the results related to the R-Factor Study, which focuses on addressing Objective (c)
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Findings and Applications 95 From Figure 3-21, the following observations can be made with respect to the panel-level study: • In general, the parameters of the single-angle section (thickness, leg width) and the aspect ratio of the panel (girder spacing, panel height)
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96 Proposed Modification to AASHTO Cross-Frame Analysis and Design Battistini et al.
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Findings and Applications 97 but neglected in the figures for clarity. For more information regarding the pertinent parameters of the superstructure, refer to Appendix F
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98 Proposed Modification to AASHTO Cross-Frame Analysis and Design bending stiffness of the plate increases. The reason for this is that the eccentricity is a linear function while the bending stiffness changes as a cubic function.
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Findings and Applications 99 The figure only presents the results related to the bridges analyzed with 1⁄2-inch-thick gusset plates. However, bridges with 1-inch-thick gusset plates were evaluated, and the results are subsequently provided in Appendix F
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100 Proposed Modification to AASHTO Cross-Frame Analysis and Design is to be expected when compared to the shell-element modeling approach. With that said, assigning a single R-factor for all cross-frame members, regardless of connection details, bridge geometry, and loading conditions, is a viable option.
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From page 101... ...
Findings and Applications 101 For each cross-frame response, several different results are presented, including the shellelement model (which serves as the control) , the truss-element model range (i.e., R = 0.5 and R = 1.0)
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From page 102... ...
102 Proposed Modification to AASHTO Cross-Frame Analysis and Design data points are close to the mean of the eccentric-beam data set (box-and-whiskers) shown in Figure 3-23 (i.e., a Fsimplified/Fshell ratio of 0.94 compared to 0.96 in Figure 3-23)
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From page 103... ...
Findings and Applications 103 3.3.3 Major Outcomes Based on the results of the R-Factor Study presented in the preceding subsections, there are three major conclusions that can be drawn with respect to simplified 3D analysis methods for cross-frame design: • The appropriate R-factor to be assigned in truss-element models is largely a function of bridge geometry, cross-frame details, and uncertain loading conditions. Consequently, considerable scatter was observed in all phases of the analytical studies.
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104 Proposed Modification to AASHTO Cross-Frame Analysis and Design data are first shown in Sections 3.4.1 and 3.4.2. These sections address different aspects of the results.
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Findings and Applications 105 to capture the torsional response of the bridge and the complex load paths through the structure in each case. These geometric effects are addressed in subsequent sections.
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106 Proposed Modification to AASHTO Cross-Frame Analysis and Design Case 2 (top strut near the maximum positive dead load moment region) : • Similar to Case 1, the 3D commercial design software model generally produces excellent results when compared to the validated 3D FEA model in Abaqus.
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Findings and Applications 107 • 2D PEB model of a composite system utilizing the Timoshenko beam approach for equivalent cross-frame beam properties and the equivalent torsion constant (Jeq) for girder beam properties (top left quadrant)
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108 Proposed Modification to AASHTO Cross-Frame Analysis and Design For each figure, there are three metrics by which the results can be compared, as listed below: 1. The total shear force acting on the cross-frame panel relative to the shear force in the concrete deck: This value provides an indication of how accurate the equivalent beam properties in the 2D model are.
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From page 109... ...
Findings and Applications 109 Assuming equal shear force distribution in the postprocessing phase of 2D PEB models generally leads to poor results for cross-frame diagonals. With that in mind, evaluating the "true" shear force distribution from the 3D models provides an indication of how significant the effects illustrated in Figure 3-27 are.
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From page 110... ...
110 Proposed Modification to AASHTO Cross-Frame Analysis and Design Given that 2D PEB models generally produce reasonably accurate estimates for bottom strut force effects, especially for simple bridge geometries, it is important to note when these limitations and shortcomings become critical. If a bottom strut cross-frame member maximizes load-induced force effects and governs fatigue design, then this simplified analysis and postprocessing procedure likely produces reasonable estimates of the governing design forces.
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Findings and Applications 111 -1 0 1 2 3 4 5 3D (Control) 2D PEB; Timoshenko Beam 2D PEB; Flexural-Analogy Model; Equivalent Beam Case 1 Case 2 Case 2 (100 k)
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112 Proposed Modification to AASHTO Cross-Frame Analysis and Design • In Figure 3-30, the shear force acting on the top node (Vtop) and the bottom node (Vbot)
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Findings and Applications 113 effective concrete area with the corresponding modular ratio. Assuming an elastic stress distribution, the PTS/PBS ratio is related to beam curvature and is simplified as yTS/yBS, where yTS and yBS are the distances measured from the centroid of the respective strut to the computed neutral axis.
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114 Proposed Modification to AASHTO Cross-Frame Analysis and Design idealized curve is apparent in the realistic data, but the deviation from that curve is due to the fact that the "true" deformation patterns are not identical to the idealized one. With general observations established about the validity of common analysis and postprocessing procedures, the next step is to compare the predicted force effects between 3D and 2D models.
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Findings and Applications 115 normal bridges. This is largely attributed to two ideas: (i)
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116 Proposed Modification to AASHTO Cross-Frame Analysis and Design member under a specific transverse lane passage maximized force effects, whereas the corresponding 2D model indicated that the force in the same member was maximized by a different lane passage. To maintain consistency, the governing lane position was established based on the control model (i.e., the 3D validated model in Abaqus)
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Findings and Applications 117 • The 2D PEB models (shear-analogy) consistently underpredict the governing design force range (-80% error on average)
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118 Proposed Modification to AASHTO Cross-Frame Analysis and Design It is evident from the results that 3D models offer increased repeatability and reliability in terms of cross-frame force effects. However, the biggest setback to simplified 2D analyses (particularly PEB models)
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From page 119... ...
Findings and Applications 119 3.4.5 Major Outcomes Based on the results of the Commercial Design Software Study presented, there are several conclusions that can be drawn with respect to simplified analysis methods for cross-frame design: • In general terms, designers must be cognizant of the potential trade-offs between sophisticated and simplified analysis (in terms of accuracy and ease of use)
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From page 120... ...
120 Proposed Modification to AASHTO Cross-Frame Analysis and Design develop than the 2D counterparts, these models offer solutions with improved accuracy, reliability, and repeatability. The traditional approach of connecting cross-frame members into a shared node along the web-to-flange juncture is also acceptable.
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From page 121... ...
Findings and Applications 121 section, several sample results are presented that demonstrate the benefits of a composite concrete deck on the buckling capacity of the steel girder section, even in the region around interior supports when shear studs may not be provided and the moments cause compression in the bottom flange. Figure 3-36 presents sample eigenvalue buckling results of a girder with an unbraced-lengthto-depth ratio (Lb/d)
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From page 122... ...
122 Proposed Modification to AASHTO Cross-Frame Analysis and Design in tension, Mcr exceeded My by approximately 50%. Thus, these unbraced segments would yield prior to reaching an instability, which in turn mitigates the bracing demands on the cross-frames in these regions.
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From page 123... ...
Findings and Applications 123 • Despite the nearly 70% reduction demonstrated in the right figure for the continuous lateral and torsional restraint condition, it is important to note that these results are presented in relative terms. In absolute terms, a 70% reduction in Mcr for this restraint condition still produces buckling capacities that exceed the lateral-only or no top flange restraint conditions.
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124 Proposed Modification to AASHTO Cross-Frame Analysis and Design Figure 3-38 also represents the results related to different girder cross-sections and bracing schemes. Girder Cross-sections 1, 2, and 3 are evaluated independently as denoted on the line graphs.
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From page 125... ...
Findings and Applications 125 From Figure 3-38, the following observations can be made with regards to brace strength requirements and uniformly distributed loading: • For these single-curvature bending cases, the brace moments ranged from 3% to 10% of the girder moment depending on the position of the load on the cross-section (load-height effects) and the specific cross-section.
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126 Proposed Modification to AASHTO Cross-Frame Analysis and Design The larger stiffness requirements produce much better agreement of the strength behavior with regards to Eq.
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Findings and Applications 127 Beams with Cross-section 1 properties were subjected to the reverse-curvature moment gradient outlined in Section 2.6. Five intermediate braces were incorporated to maximize the negative moment magnitude at the first intermediate cross-frame line.
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128 Proposed Modification to AASHTO Cross-Frame Analysis and Design • For these spot check conditions, it was generally observed that bracing demands are more critical for single-curvature bending conditions with less moment gradient (i.e., a smaller Cb factor) than reverse-curvature conditions with significant moment gradient.
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Findings and Applications 129 at midspan) for the following select parameters: a single-span, twin-girder system (ng = 2)
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130 Proposed Modification to AASHTO Cross-Frame Analysis and Design For clarity, these results are not included herein. However, the following items provide a cursory overview of the major observations: • The relative girder twist induced at critical buckling loads decreases as the brace stiffness increases.
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Findings and Applications 131 In general, the table shows that providing twice the ideal stiffness (2b i) typically results in load-induced girder twists exceeding the assumed twist in Eq.
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132 Proposed Modification to AASHTO Cross-Frame Analysis and Design construction. Given that cross-frames are generally not required as stability braces in the finished bridge, it is only necessary to evaluate stability-related force effects with other construction force effects, including dead loads (e.g., wet concrete, formwork, fit-up forces)
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Findings and Applications 133 3.5.5 Major Outcomes Based on the results of the Stability Study presented in the preceding subsections, there are several conclusions that can be drawn with respect to the bracing requirements for cross-frames and the LTB behavior of nonprismatic girders: • Given that a composite deck provides continuous restraint to the top flange and substantial restraint to the bottom flange, these bracing provisions are only necessary to evaluate during the construction stages. • In terms of implementation into AASHTO LRFD, it was determined that the general form of the torsional brace strength equations from the 14th Edition of AISC (2010)
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