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64 · 0.90 for regions away from the towers, and The last column of the table lists the performance ratios for · 0.70 for regions close to the towers. the current 12t limited effective width provision in the code. Given that the example bridge has a girder spacing of 3.69 m (12 ft 11/4 in.), the proposed full-width adds approximately The above values are suitably conservative for the verifi- 1 m to the effective width of the slab specified by current cation case (Cooper River Bridge) as illustrated in Figure 73. For Cooper River as in Byers' bridges, there was high nor- AASHTO LRFD provisions, in both the positive and nega- malized effective width (close or equal to 1) in most regions tive moment regions. away from the towers and a bit lower (but still high--higher The effect of this increase in effective width can be assessed than 0.70) in regions close to the pylons. by comparing the last two columns of the table, which were The above values are recommended for use in cable-stayed both computed for the same trial steel section. Overall, the bridges with the characteristics of those analyzed in this comparison suggests that the effect of the increase in effec- work. This means that they address bridges with the follow- tive width for this example is minimal--safety margins are ing characteristics: increased, but only slightly. The example suggests that for such a girder spacing, it is likely that no designer would make any changes to flange and web plate sizes based on the liber- · Semi-harp cable pattern with two planes of cables; alized effective width. Interestingly, even the web bend- · Relatively thin concrete slab (approximate thickness 240 buckling performance ratio is not adversely affected in the to 250 mm, 9.5 to 10 in.); negative moment region. Evidently, the increase in the · Cable spacing approximately 10 percent of the back span moment of inertia I (which reduces the applied web stress length; and fcrw) more than offsets the increase in the depth of the com- · Floorbeam spacing approximately one-third of the cable pression portion of the web Dc (which reduces the web spacing. bend-buckling strength Fcrw). 3.6 IMPLEMENTATION EXAMPLE 3.7 SUMMARY Two worked examples of design calculations based on AASHTO LRFD provisions were prepared to illustrate use of The full width being proposed here for composite bridge the proposed new effective width criteria based on full width. members subject to the limits of the parametric study (S One of these was in the positive moment region of a continu- 4.8 m, L 60m, 60°) is in fact the most liberal of all effec- ous hybrid girder, while the other was in the negative moment tive width provisions in all known international codes. This region of a hybrid girder. Both examples are provided in proposal is based on an extensive and systematic investigation Appendix O. of bridge finite element models that are more sophisticated Table 12 summarizes flexural performance ratios associ- than the models upon which other codes are based, that are cor- ated with the limit state checks that are influenced by the roborated by experimental results both by others and by the effective width. By "flexural performance ratio" is meant the authors, and that explicitly investigate the negative moment ratio of applied bending stress (or moment) to resisting bend- region much more extensively than previous researchers ing stress (or moment) capacity, at applicable limit states. have done. TABLE 12 Flexural performance ratios in worked examples Limit State Region Component Proposed Current Top Flange 64.7% 69.1% Positive Bottom Flange 92.9% 93.8% Service II Top Flange 55.5% 58.6% Negative Bottom Flange 66.3% 67.7% Web-Bend-Buck 87.2% 89.0% Positive (Compact) 90.2% 91.3% Strength I Top Flange 92.3% 96.7% Negative Bottom Flange 95.8% 96.7%
OCR for page 65
65 In summary, the process that has been followed in arriv- · Designing a suite of bridges according to industry guide- ing at the proposed full width criteria has involved each of lines to support the parametric study; the following: · Performing a systematic parametric study of finite ele- ment models of these bridges that produced results from which effective widths according to the new definition · Formulating a new definition of effective width which could be methodically extracted; for the first time accounts for the variation of stresses · Formulating various candidate criteria for effective through the deck thickness as well as both moment and width, based on regression analysis, that intentionally force equivalence between the finite element model and span the gamut between simplicity and accuracy; the line-girder idealization wherein beff is used; · Applying Process 12-50 in a systematic assessment of · Performing judicious finite element modeling and analy- impact of those various candidate criteria in order to sis, using appropriate levels of detail (e.g., approximat- recommend which criteria were most appropriate; ing "smeared" rather than discrete deck rebar and crack- · Proposing specific draft code and commentary language ing, yet explicitly representing deck thickness using four for implementing those criteria in AASHTO LRFD Arti- brick elements through the thickness); cle 188.8.131.52.1, for consideration by the AASHTO Sub- · Corroborating that finite element modeling approach committee on Bridges and Structures; and with experimental data produced by others as well as by · Illustrating the use of the recommended criteria in the form the authors; of comprehensive worked design calculation examples.