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Effective Slab Width for Composite Steel Bridge Members (2005)

Chapter: Chapter 3 - Interpretation, Appraisal, and Applications

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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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Page 63
Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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Suggested Citation:"Chapter 3 - Interpretation, Appraisal, and Applications." National Academies of Sciences, Engineering, and Medicine. 2005. Effective Slab Width for Composite Steel Bridge Members. Washington, DC: The National Academies Press. doi: 10.17226/13853.
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59 CHAPTER 3 INTERPRETATION, APPRAISAL, AND APPLICATIONS 3.1 INTRODUCTION The objectives of this study were to propose criteria for effective width provide recommended specifications and commentary and provide worked examples illustrating the use of those proposed new criteria. Draft criteria were devel- oped based on applying regression approaches and account- ing for the different subsets of the parameters varied in the parametric study described in Chapter 2. Effects of those criteria were assessed, using the Rating Factor (RF) as the measure of effect. Based on the assessment, draft criteria are recommended and illustrated in the context of positive and negative moment region worked examples. 3.2 ASSUMPTIONS AND IMPLICATIONS Some key, almost paradoxical, assumptions underlie the use of the notion of effective slab width, e.g., 1. Even with the sophisticated computer-aided analysis available for bridge design in the 21st century, tradi- tional line-girder analysis provides an ongoing useful context for analyzing steel girders acting compositely with concrete decks. 2. Given that the context of analyses based on effective width is single member line-girder analysis, analyses based on effective width are not appropriate for use in situations where a line-girder analysis is insufficient and a system analysis is thus considered necessary. 3.2.1 Some Implications of Line-Girder Analysis Limitations Beyond line-girder analysis, system analysis is generally considered necessary in the following kinds of situations: • Highly skewed and curved girder bridge analysis and design, • After-fracture redundancy and load redistribution analy- sis where required (e.g., Daniels et al., 1989), and • Detailed design stages for systems where second-order effects can be important, e.g., cable-stayed bridges. Given that a simplistic line-girder analysis is insufficient for such situations, the use of idealizations that inherently assume line-girder analysis (such as effective slab width) may be considered questionable at best in these kinds of situations. 3.2.2 Some Implications of Wide Girder Spacing The 12t limitation clearly can be removed. Given that the challenge to the 12t limitation arises, for typical deck thick- nesses, in the context of girder spacings wider than 3 m (10 ft) or so, additional implications of wide girder spacings are also of interest. Some of these implications are as follows: • The empirical method of deck design is prohibited by AASHTO for use beyond a girder spacing of 4.1 m (13.5 ft.) [AASHTO LRFD S9.7.2.4]. Thus, methods of traditional design, prestressed design, and system analy- sis of decks that go beyond line-girder analysis (e.g., grillage and finite strip) must be used to design the actual decks. Given that these methods typically go beyond line-girder analysis, some may ask why it should still be permissible to use line-girder analysis for the in-plane analysis of the composite girders supporting the result- ing decks. • The use of the line-girder-oriented distribution factor for- mulas is prohibited by AASHTO for use beyond a girder spacing of 4.9 m (16.0 ft) [AASHTO LRFD S4.6.2.2]. • The possible interaction of plate bending with in-plane “effective width” behavior increases. This interaction is a possible explanation of the “negative shear lag” evi- dent in some of the cable-stayed bridge analysis results presented in Chapter 2. • Longitudinal shear forces that get “funneled” into the shear connectors increase. Whether the current AASHTO shear stud design criteria still apply, in HPS and HPC composite combinations, may need to be revisited. Some of these implications of the use of wider girder spac- ings in conjunction with high-performance steels and con- cretes point to the need to re-examine existing AASHTO

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

The difference between ai and bi can be calculated by two methods. The first method (p1) uses the absolute average at that point. The second method (p2) uses the maximum absolute average, M, for the calculation: Therefore, if p1 or p2 is larger than the threshold accept- able percentage (pallow), then the two results are concluded as different. Comparisons based on p1 are tallied in Appendix L. These tallies show that p1 values based on full width are very close to p1 values based on more accurate (and more complex) can- didate formulations for effective width. These tallies also show that all effects are rather minimal except for a few wide- girder spacing configurations in negative moment regions. 3.4.2 Rating Factor in LRFR The general expression for rating factor in LRFR is as follows: where C capacity (C = φCφsφ × R: Strength limit state, C = fR: Service limit state) fR allowable stress specified in the LRFD code R nominal member resistance DC dead-load effect due to structural components and attachments DW dead-load effect due to wearing surface and utilities P permanent load other than dead loads LL live-load effect IM dynamic load allowance γDC LRFD load factor for structural components and attachments γDW LRFD load factor for wearing surfaces and utilities γP LRFD load factor for permanent loads other than dead loads (1.0) γL evaluation live-load factor φC condition factor φS system factor φ LRFD resistance factor RF C DC DW P LL IMLRFR DC DW p L = − − ± +( ) γ γ γ γ 1 M m p a b m p a b i n i i i i i = ( ) ( ) = − × ( ) = − = max % % , ,1 1 2 100 K i im × 100 61 Thus, when the Service II limit state is applied, the fol- lowing equation will be used: For the Strength I limit state, inventory-based load factors are used with φC = 1.0 and φS = 1.0. Therefore, the resulting equation is The effective flange width of a composite girder increases as stress at the section increases. This is the rationale for developing proposed provisions based on the service limit state at the positive moment section. Consequently, Service II limit state based rating values are used for impact assess- ment, in particular, at positive moment sections. This section is generally designed as a compact section, and stress of the 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- ative moment sections. Rating factors for positive moment sections are calcu- lated using MathCad worksheets developed for design of the bridges (Appendix O). For negative moment sections, the OPIS program is used in which BRASS-GIRDER (AASHTO, 2004) performs the actual analyses. 3.4.3 Positive Moment Regions Eight simple-span bridges were selected for the impact investigation in positive moment regions. Service II rating factors of interior and exterior girders were calculated for five different candidate effective width provisions. Based on calculated p1 values, the impact in positive moment regions is not significant. The maximum p1 value for interior gird- ers is 3.5 percent, and the maximum for exterior girders is 2.9 percent—where both these maximum values occur for the full width candidate. That is, more complicated curvefit expressions have less error. Details on these results appear in Appendix L. 3.4.4 Negative Moment Regions Sixteen bridges were selected for the impact investigation in negative moment regions. Strength I and Service II rating factors were calculated for eight different candidate effective width provisions. Service II rating factors, as in the positive moment region, show minimal impacts as measured by p1. RF C DC DW LL IMLRFR = − × − × × +( ) 1 25 1 5 1 75 1 . . . RF C DC DW LL IMLRFR = − × − × × +( ) 1 0 1 0 1 3 1 . . .

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

in the deck, shear studs in the negative moment regions pro- vide an essential element of the required load path (Carden et al., 2003). Concerns about fatigue in the shear stud welds in negative moment regions need not prevent welding to the top flange altogether. 3.4.5 Shear Connector Impact At first glance, one might expect a wider effective slab width to cause more demands on the shear connectors, in order to develop that wider effective slab. The impact of wider beff on shear connector layout, however, is surprisingly minimal. The reason for this minimal impact apparently stems from offsetting effects. Shear connectors are designed to resist the longitudinal shear flow and are typically governed by fatigue rather than strength. At the fatigue limit state, elastic analy- sis is performed, where the longitudinal shear flow is given by the familiar equation VQ/I, where I is the moment of iner- tia of the short-term composite section and Q is the first moment of the transformed area of the slab. A wider beff increases both Q and I, thus producing offsetting effects. Several bridges with wide (4.8 m = 16 ft) girder spacings were investigated regarding their shear connector layout in Appendix L. The most significant impact on shear stud lay- out was for the longest spans investigated (60 m = 200 ft). Even in this case, however, the required shear stud pitch decreased only 10 percent. 3.5 PROPOSED DESIGN CRITERIA 3.5.1 Slab-on-Girder Bridges Based on the impact assessment of various candidate effective width criteria according to Process 12-50 principles using Rating Factor as the measure of comparison, the addi- tional accuracy achieved by the more complicated formula- tions is minimal. Thus, this simple formulation is recom- mended instead: “for both interior and exterior girders designed to be composite sections, the effective flange width may be assumed equal to the physical flange width.” This recommendation should be limited to the parameter range used in the parametric study on which it is based: • Girder spacing S ≤ 4.8m (16 ft) • Span Length L ≤ 60m (200 ft) • Skew Angle θ ≤ 60° The skew angle θ here is defined as it is in AASHTO LRFD Chapter 4, such that 0 deg skew is a right bridge align- ment. Further discussion of the rationale and justification for this recommendation is provided in Appendix M. 63 Bridge engineers may encounter situations beyond the range of values investigated in the parametric study. The fol- lowing brief discussion addresses these situations. 3.5.1.1 Span Length L > 60 m (200 ft) There is no reason to expect that spans longer than 60 m (200 ft) would not behave similarly to 200 ft spans. The span length limit could be relaxed, since in the parametric study presented herein it was found that the longer the span (or, more accurately, the greater the length/width ratio), the more we can be sure that the full width is effective. The reason for specifying the 60 m (200 ft) span length as a limit is that the parametric study did not consider longer spans. 3.5.1.2 Girder Spacing S > 4.8 m (16 ft) In the parametric study conducted herein, a small number of cases were analyzed with S > 4.8 m (up to S = 7.6 m). For those few cases, there was no indication that effective width should be taken as less than full width. However, they were only a few cases. 3.5.1.3 Skew Angle θ > 60º In the parametric study, no cases were analyzed with skews greater than 60 degrees. What happened with the 60-degree skews analyzed was that although effective width was typi- cally somewhat less than full width, moments extracted from the FEM model were less than moments that would be pre- dicted by a line-girder analysis (with AASHTO 2004 skew correction factors for the transverse live-load distribution fac- tors). Thus, if the designer assumed full width but also used line-girder analysis, there were offsetting errors. The small impact of these offsetting errors on rating factor were such that they allowed use of full effective width. Presumably, such off- setting errors could reasonably be expected for skews greater than 60 degrees. Of course, if the ongoing NCHRP Project 12-62 develops more significant skew correction factors for the AASHTO LRFD transverse live-load distribution factors, then there may not be such offsetting effects. 3.5.2 Cable-Stayed Bridges In light of the results tallied in Table 11 for the first four ana- lyzed cable-stayed bridges and the longitudinal variation of effective slab width seen in Figures 62 through 72, a reason- able and conservative lower bound set of effective width val- ues for cable-stayed bridges may be summarized as follows:

• 0.90 for regions away from the towers, and • 0.70 for regions close to the towers. The above values are suitably conservative for the verifi- cation case (Cooper River Bridge) as illustrated in Figure 73. For Cooper River as in Byers’ bridges, there was high nor- malized effective width (close or equal to 1) in most regions away from the towers and a bit lower (but still high—higher than 0.70) in regions close to the pylons. The above values are recommended for use in cable-stayed bridges with the characteristics of those analyzed in this work. This means that they address bridges with the follow- ing characteristics: • Semi-harp cable pattern with two planes of cables; • Relatively thin concrete slab (approximate thickness 240 to 250 mm, 9.5 to 10 in.); • Cable spacing approximately 10 percent of the back span length; and • Floorbeam spacing approximately one-third of the cable spacing. 3.6 IMPLEMENTATION EXAMPLE Two worked examples of design calculations based on AASHTO LRFD provisions were prepared to illustrate use of the proposed new effective width criteria based on full width. One of these was in the positive moment region of a continu- ous hybrid girder, while the other was in the negative moment region of a hybrid girder. Both examples are provided in Appendix O. Table 12 summarizes flexural performance ratios associ- ated with the limit state checks that are influenced by the effective width. By “flexural performance ratio” is meant the ratio of applied bending stress (or moment) to resisting bend- ing stress (or moment) capacity, at applicable limit states. 64 The last column of the table lists the performance ratios for 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 1 m to the effective width of the slab specified by current AASHTO LRFD provisions, in both the positive and nega- tive moment regions. The effect of this increase in effective width can be assessed by comparing the last two columns of the table, which were both computed for the same trial steel section. Overall, the comparison suggests that the effect of the increase in effec- tive width for this example is minimal—safety margins are 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- alized effective width. Interestingly, even the web bend- buckling performance ratio is not adversely affected in the negative moment region. Evidently, the increase in the moment of inertia I (which reduces the applied web stress fcrw) more than offsets the increase in the depth of the com- pression portion of the web Dc (which reduces the web bend-buckling strength Fcrw). 3.7 SUMMARY The full width being proposed here for composite bridge members subject to the limits of the parametric study (S ≤ 4.8 m, L ≤ 60m, θ ≤ 60°) is in fact the most liberal of all effec- tive width provisions in all known international codes. This proposal is based on an extensive and systematic investigation of bridge finite element models that are more sophisticated than the models upon which other codes are based, that are cor- roborated by experimental results both by others and by the authors, and that explicitly investigate the negative moment region much more extensively than previous researchers have done. Limit State Region Component Proposed Current Top Flange 64.7% 69.1% Positive Bottom Flange 92.9% 93.8% Top Flange 55.5% 58.6% Bottom Flange 66.3% 67.7% Service II Negative Web-Bend-Buck 87.2% 89.0% Positive (Compact) 90.2% 91.3% Top Flange 92.3% 96.7% Strength I Negative Bottom Flange 95.8% 96.7% TABLE 12 Flexural performance ratios in worked examples

In summary, the process that has been followed in arriv- ing at the proposed full width criteria has involved each of the following: • Formulating a new definition of effective width which for the first time accounts for the variation of stresses through the deck thickness as well as both moment and force equivalence between the finite element model and the line-girder idealization wherein beff is used; • Performing judicious finite element modeling and analy- sis, using appropriate levels of detail (e.g., approximat- ing “smeared” rather than discrete deck rebar and crack- ing, yet explicitly representing deck thickness using four brick elements through the thickness); • Corroborating that finite element modeling approach with experimental data produced by others as well as by the authors; 65 • Designing a suite of bridges according to industry guide- lines to support the parametric study; • 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 could be methodically extracted; • Formulating various candidate criteria for effective width, based on regression analysis, that intentionally span the gamut between simplicity and accuracy; • Applying Process 12-50 in a systematic assessment of impact of those various candidate criteria in order to recommend which criteria were most appropriate; • Proposing specific draft code and commentary language for implementing those criteria in AASHTO LRFD Arti- cle 4.6.2.6.1, for consideration by the AASHTO Sub- committee on Bridges and Structures; and • Illustrating the use of the recommended criteria in the form of comprehensive worked design calculation examples.

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 543: Effective Slab Width for Composite Steel Bridge Members examines recommended revisions to the American Association of State Highway and Transportation Officials’ specifications for the effective slab width of composite steel bridge members. The report’s recommended specifications are applicable to all types of composite steel bridge superstructures and are suitable for design office use. Accompanying CRP-CD-56 contains extensive supporting information, including the recommended specifications and design examples.

The supporting information associated with NCHRP Report 543 are available in an ISO format. Links to instructions on buring an .ISO CD-ROM and the download site for the .ISO CD-ROM are below.

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