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60 design criteria and the limits of their applicability (e.g., shear select the criteria was based on the results of impact assess- connector design criteria, limits of applicability of empirical ment using Process 12-50, which is described next. deck design methods, and transverse load distribution factors for line-girder analyses). For this study, it was assumed that current AASHTO criteria for such concerns apply, including 3.4 IMPACT ASSESSMENT OF CANDIDATE skew corrections. DESIGN CRITERIA The 12-50 Process (NCHRP, 2003) was originally used for 3.3 DESIGN CRITERIA DEVELOPMENT the validation of bridge software. Other possible uses of this process are to determine whether the proposed code changes Candidate design criteria were derived by performing accomplish the desired objectives and to prevent problems regression analyses based on the beff /b values extracted from from arising because of changes made by specification writ- the finite element parametric study in the vicinity of the ers. The potential benefit of this process comes from specific maximum positive and negative moment sections. Candidate test computations on real and derived bridges before imple- effective slab width criteria for positive moment sections menting specification changes. Because flexural design of the were derived initially from the simple-span cases, while the section is the primary focus of interest when considering effec- candidate effective slab width criteria for negative moment tive width, the sectional flexural capacity and stress in flanges sections were derived from the multiple-span continuous would be the major parameters in test computations. For this cases. The beff /b values from positive moment sections of the reason, the familiar notion of rating factor (RF) is the mea- multiple-span continuous cases were used to validate the can- sure taken to quantify the effect of proposed changes to didate effective slab width design criteria obtained from the effective width provisions. simple-span positive moment cases. The 12-50 process was used not only to assess the effects of The parameters appearing in the regression equations were the final recommended provisions but also to narrow the selec- indeed the main variables of interest in the parametric study: tion process among various different proposed provisions. The winnowing process was based on balancing the degree of effect against the simplicity of the proposed provisions. Span length L (exterior span length L1 in continuous- span bridges), Span ratio L2 /L1 in continuous bridges, where L2 is the length of the interior span, 3.4.1 Process 12-50 Girder spacing S, and Skew angle . In the 12-50 process, the bridge analysis and design process is divided into manageable computational domains. Within each of these smaller subdomains, the task is described in Various regression equations were generated for interior parametric form. Therefore, the main procedure in each sub- and exterior girders (separately and with the data combined) domain involves generation of required data for given input using various subsets of the above set of parameters. These parameters. regression equations were generated using the general-purpose Bridges in the test suite are selected and their ratings are cal- statistical software package SPSS. Comparisons between culated on the basis of current and proposed effective flange these various equations and the FEM-extracted values of effective width ratio beff /b are given in Appendix K. For the width provisions. The two corresponding rating factors are suite of continuous bridges, candidate criteria (regression compared to investigate the significance of code change at equations) appear as most unconservative in the case of the critical sections in each bridge. The method of comparison is CS-75 bridge, which has a short span length, wide girder based on the percentage difference between two results. The spacing, and high skew angle. existing and new criteria generate results (e.g., stress and Results of bridges from the validation cases described in moment) at n points in a girder, which in general are termed Appendix J are also compared with the various candidate as ai and bi (i = 1,2,..., n). In the present study, the ai repre- effective width criteria. The span ratio parameter, L2 /L1, is sents a rating factor based on existing effective width crite- found in all cases to have minimal effect. Thus it can be ria, and the bi represents a rating factor based on proposed removed entirely from the candidate regression criteria. Sift- new criteria. At each point, the absolute average quantity, mi, ing through the large set of possible criteria and narrowing is calculated as the list of candidates down to the criteria proposed subse- quently required a sound methodology and rationale that could ai + bi mi = identify the best design criteria. Accordingly, the approach to 2

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61 The difference between ai and bi can be calculated by two Thus, when the Service II limit state is applied, the fol- methods. The first method ( p1) uses the absolute average at lowing equation will be used: that point. The second method ( p2) uses the maximum absolute average, M, for the calculation: C - 1.0 DC - 1.0 DW RFLRFR = 1.3 LL (1 + IM ) M = max ( mi ) i =1,K,n ai - bi For the Strength I limit state, inventory-based load factors p1 (%) = 100 are used with C = 1.0 and S = 1.0. Therefore, the resulting mi equation is ai - bi p2 (%) = 100 mi C - 1.25 DC - 1.5 DW RFLRFR = 1.75 LL (1 + IM ) Therefore, if p1 or p2 is larger than the threshold accept- able percentage ( pallow), then the two results are concluded The effective flange width of a composite girder increases as different. as stress at the section increases. This is the rationale for Comparisons based on p1 are tallied in Appendix L. These developing proposed provisions based on the service limit tallies show that p1 values based on full width are very close state at the positive moment section. Consequently, Service to p1 values based on more accurate (and more complex) can- II limit state based rating values are used for impact assess- didate formulations for effective width. These tallies also ment, in particular, at positive moment sections. This section show that all effects are rather minimal except for a few wide- is generally designed as a compact section, and stress of the girder spacing configurations in negative moment regions. bottom flange at the Service II limit state typically governs the design. For the design of negative moment sections, gen- erally noncompact sections are used. Therefore, stress devel- oped for the Strength I limit state governs the design of neg- 3.4.2 Rating Factor in LRFR ative moment sections. Rating factors for positive moment sections are calcu- The general expression for rating factor in LRFR is as lated using MathCad worksheets developed for design of follows: the bridges (Appendix O). For negative moment sections, the OPIS program is used in which BRASS-GIRDER (AASHTO, C - DC DC - DW DW p P 2004) performs the actual analyses. RFLRFR = L LL (1 + IM ) 3.4.3 Positive Moment Regions where C capacity (C = C s R: Strength limit state, C = fR: Eight simple-span bridges were selected for the impact Service limit state) investigation in positive moment regions. Service II rating fR allowable stress specified in the LRFD code factors of interior and exterior girders were calculated for R nominal member resistance five different candidate effective width provisions. Based on DC dead-load effect due to structural components and calculated p1 values, the impact in positive moment regions attachments is not significant. The maximum p1 value for interior gird- DW dead-load effect due to wearing surface and utilities ers is 3.5 percent, and the maximum for exterior girders is P permanent load other than dead loads 2.9 percent--where both these maximum values occur for LL live-load effect the full width candidate. That is, more complicated curvefit IM dynamic load allowance expressions have less error. Details on these results appear in DC LRFD load factor for structural components and Appendix L. attachments DW LRFD load factor for wearing surfaces and utilities 3.4.4 Negative Moment Regions P LRFD load factor for permanent loads other than dead loads (1.0) Sixteen bridges were selected for the impact investigation L evaluation live-load factor in negative moment regions. Strength I and Service II rating C condition factor factors were calculated for eight different candidate effective S system factor width provisions. Service II rating factors, as in the positive LRFD resistance factor moment region, show minimal impacts as measured by p1.

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62 But a few of the Strength I based rating factors show signif- inventory have girder spacings that wide as well as com- icant reductions in p1. This is the first of two concerns that posite design in the negative moment region. arise in negative moment regions but have no counterpart in Negative moment regions of plate girder bridges designed positive moment regions. according to industry guidelines would normally have At the Strength I limit state, whether the rating factor noncompact webs anyway. increases or decreases depends on whether a section that was compact (under the old beff /b criteria) stays compact Thus, there are believed to be few if any existing bridges (using widened value of beff /b) or whether it becomes non- whose ratings would suddenly be reduced by imposing a wider compact. Under service conditions, a widened effective effective width. width results in an increased rating factor for both compact and noncompact sections. At the Strength I limit state, how- ever, what happens to the rating factor depends on whether the section becomes noncompact only using a widened effec- 3.4.4.2 To Stud or Not To Stud tive width. The second concern is whether the section is considered as Although one of the experimental specimens investigated composite and how that compositeness is provided. These in this study deliberately omitted the placement of shear con- two concerns are described next. nectors in the negative moment region, there are at least the following reasons to install shear studs in the negative moment regions of composite girders: 3.4.4.1 Webs Made Noncompact To maintain consistent design philosophy and practice regarding "composite" design, and The impact on a strength-based rating factor is substantial To resist transverse seismic loads reliably. when a web that is compact according to the current AASHTO criteria for effective width becomes noncompact according Composite Design Philosophy and Practice. For the slab to to the proposed full width for effective width. The reasons for be acting (such that part of it can be "effective"), it must be this substantial impact are that acting compositely with the steel girder. Thus, the funda- mental premise of this entire investigation ("Effective Slab Compact sections can use the full plastic moment for Width of Composite Steel Bridge Members") has been that their nominal moment strength and behavior is composite. Designers naturally and properly con- Noncompact sections are limited to an elastic stress dis- sider this composite action to be delivered by shear connec- tribution as the basis for their nominal moment strength. tors. Conversely, configurations without the shear connectors are naturally and properly considered to be noncomposite. Paradoxically, the result is that by adding material (to the Thus, even to consider the notion of effective slab width effective width), flexural resistance has actually decreased-- in negative moment regions without shear studs makes all because a previously compact section is caused to become no sense. noncompact by virtue of the raising of the neutral axis which Complicating this issue is the ambiguity of the current AASHTO specifications on whether negative moment regions in turn is caused by the widened effective slab width. This is without continuous shear connectors can be considered to by far the most significant downside impact of the prospect be composite when longitudinal deck reinforcing steel is of having widened effective width. There is no correspond- developed and anchored to clusters of shear connectors in ing impact when comparing service rating factors because at moment inflection regions. The negative moment subassem- service, the stress distribution on the cross section is, of course, blage experiment conducted in this study further suggests that always based on elastic analysis. composite behavior can be attained in such cases, but it is only This downside impact, however, is not considered a com- one specimen. pelling reason to avoid changing the effective width criteria. The following reasons exist for proceeding with a liberalized Transmission of Transverse Seismic Loads. It is critically effective width criterion: important that a load path be provided in a steel slab-on- girder bridge that will allow seismic damage to be limited to The downside impact occurs only for the bridges in the well-confined plastic hinges in the columns (current AASHTO parametric study that have very wide girder spacings design philosophy as expressed in Art. 4.6.2.8) or in redun- [S = 4.8 m (16 ft)]. dant components of a bridge superstructure such as the end Based on the results of the survey reported in Appen- cross frames (NCHRP Project 12-49 design philosophy). In dix A, probably no existing bridges in the nationwide either case, given that the bulk of the superstructure mass is