Effective Slab Width for Composite Steel Bridge Members (2005)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

2CHAPTER 1 INTRODUCTION AND RESEARCH APPROACH 1.1 PROBLEM STATEMENT AND PROJECT OBJECTIVES The phenomenon of shear lag is shown in Figure 1a. Shear lag can result in underestimating the deflections and stresses at the web-flange intersections of a girder in calculations based on line-girder analysis and the elementary theory of bending, which assumes that plane cross sections remain plane. It is traditional to obtain correct values of maximum deflection or stress from the elementary theory by using an effective slab width concept in which the actual width of each flange is replaced by an appropriate reduced (“effective”) width (Moffatt and Dowling, 1978; ASCE, 1979; Garcia and Daniels, 1971), labeled beff in Figure 1b. The determination of effective slab width directly affects the computed moments, shears, torques, and deflections for the composite section and also affects the proportions of the steel section and the num- ber of shear connectors required. The effective slab width is thought to be particularly important for serviceability checks (e.g., fatigue, overload, and deflection), which can often gov- ern the design. Figure 2 summarizes the various influences that the effec- tive width beff has in the design and rating of a composite beam. Both sides of the basic LRFD methodology, ΣηiγiQi ≤ φRn, are influenced by the effective width for all limit states involving flexure of a slab-on-girder composite beam. Thus it is not possible by inspection to determine the net effect of any proposed change to effective width for a given bridge, let alone for a suite of bridges. A systematic parametric study is necessary. Just such a study is at the heart of the research results presented herein. In AASHTO bridge design specifications (AASHTO, 2004), the effective slab width for interior girders of all types of composite bridge superstructures, except for orthotropic deck and segmental concrete structures, is specified as the least of the following: (1) one-quarter of the effective span length, (2) 12.0 times the average depth of the slab plus the greater of web thickness or one-half the top flange width, and (3) the average spacing of adjacent beams. These criteria cur- rently apply to all types of composite interior and exterior steel bridge members with any combination of the following: • Conventional or High-Performance Steel Girder System: – Tub-girder – Two-girder system – Conventional multi-girder system • Deck System: – Conventional Cast-in-Place • Conventional concrete (e.g., f ′c = 21 MPa or 28 MPa) • High-Performance Concrete (HPC) – Prestressed, either constant depth or variable depth, and often prestressed longitudinally as well as trans- versely, on potentially very wide girder spacings • Alignment: – Right – Skew • Span Location: – Positive Moment Region – Negative Moment Regions considered composite where sufficient shear studs and longitudinal rein- forcing steel are supplied • Applicable Limit State, e.g., – Service II and Fatigue (elastic), and – Strength I and perhaps Strength II (possibly inelastic). For girder spacings 2.4 m (8 ft) or less, the effective width computed according to the current AASHTO provisions gen- erally includes all of the deck. With the increasing use of wider girder spacing, however, the contribution of the addi- tional width of deck is not fully recognized by the current cri- teria. The AASHTO Guide Specifications for Segmental Con- crete Bridges recognize the entire deck width to be effective, unless shear lag adjustments become necessary. Field mea- surements of modern composite steel bridges indicate that recognition of more of the concrete deck is often necessary to better correlate actual with calculated deflections. The above criteria apply to all types of composite interior and exterior steel bridge members. In addition to their com- mon use on multi-girder bridges, composite deck systems can participate structurally with tied arches or cable-stayed bridges. Thus, the effective width of the slab may well differ among some of these cases from more conventional multi- stringer I-girder bridges. The effective width of decks using high-strength concrete may also be affected by the larger elastic and shear moduli of the concrete. Distinctions for the effective width of slab to be used may be needed • In positive and negative bending, • At the AASHTO serviceability and strength limit states,

3• Considering both conventionally reinforced and pre- stressed decks. In accordance with the NCHRP 12-58 Project Statement, the objectives of the research undertaken were to investigate both new and existing approaches for effective slab width and to develop and validate the most promising of these. The research products consist of criteria, recommended specifi- cations and commentary, and worked examples addressing applicable AASHTO LRFD limit states in AASHTO LRFD format. 1.2 RESEARCH TASKS The set of research tasks in the original solicitation for the NCHRP Project 12-58 investigation was augmented to incor- porate the following: • Conduct experimental investigations of scale-model slab- on-girder bridge structures to complement the finite element-based parametric study, • Conduct several analysis cases of cable-stayed bridges, • Explore impacts of proposed changes to effective width code provisions (“Process 12-50”), • Analyze additional cases required by the DOE (Design of Experiments) approach that were not contained in the original scope of work, • Analyze a few prestressed concrete girder cases to investigate whether changes proposed for effective slab width in composite steel bridge members could reason- ably be applied to bridges supported by prestressed con- crete girders, and • Revise the MathCad worksheets developed for use in presenting illustrative design examples to reflect the substantive changes to S6.10 and S6.11 in the 3rd Edi- tion AASHTO LRFD code, published in 2004. The resulting amended task descriptions were as follows: Task 1. Review domestic and foreign field and laboratory test results, analytical studies, and specifications regarding the effective slab widths for all types of steel and concrete composite structures. Task 2. Using the findings from Task 1, summarize applic- able methodologies for determining the effective slab width (a) (b) (c) Figure 1. Effective width for the positive moment section. Effective Width beff Moment of Inertia I Plastic Moment Mp Depth of Compressive Portion of Web Dc First Moment for Horizontal Shear Q Horizontal Shear Transfer VQ I Moment on Composite Section MLL+IM, MDC2, MDW (Stiffness Attracts Load in Continuous Spans) Bending Stress fb Compactness of Web c w D t Nominal Flexural Resistance Mn, Fn Limiting Web Stress Fcrw Compressive Stress in Web fcw Factored Applied Moment Mu Figure 2. Design parameters influenced by effective width.

for different types of composite steel bridge superstructures typical of those in use today. As a minimum, I-girder and tub- girder cross-sections should be considered. Both interior and exterior girders should be considered. Composite floor sys- tems that participate structurally with tied arches, cable-stayed bridges, and deck or through trusses should also be consid- ered, along with variable- or constant-depth composite, pre- cast post-tensioned decks. Consider the effects of the larger elastic and shear moduli of high-strength deck concrete on the computed effective width. Task 3. Prepare an interim report documenting the find- ings from Tasks 1 and 2. Provide practical recommenda- tions for promising methodologies to determine effective slab width that can be further developed and validated. Pre- pare an expanded work plan for the remainder of the project describing the type of investigations needed to develop and validate the recommended methodologies. Task 4. Develop and validate the methodologies for deter- mining effective slab width using finite element analysis. Task 5. Verify the finite element analysis through a program of laboratory testing of reduced scale structures as approved by the project panel. Task 6. Perform parametric studies of different composite steel-bridge superstructure configurations using the current provisions of the AASHTO LRFD Bridge Design Specifica- tions and the proposed effective-width criteria. At least 100 cases shall be considered. In addition, a limited set of concrete girders should be investigated to determine the applicability of the criteria and several cable-stayed bridges designed by oth- ers shall be investigated for axial and flexural effective width. Task 7. Propose recommended revisions to the specifica- tions and provide design examples demonstrating their use. For each case considered, develop suggested general guide- lines for designing the slab reinforcement and shear connec- tors to transfer the calculated shear forces effectively between the girder and slab at each limit state. The design examples shall conform to the provisions of the 2004 AASHTO LRFD Specifications. Task 8. Perform impact testing to compare rating factors resulting from the recommended revisions with those of the LRFD Specifications. The method for impact testing devel- oped in NCHRP Project 12-50 is recommended. Task 9. Submit a final report documenting the entire research effort. The recommended specifications shall be provided in an appendix to the report and must be in a format suitable for consideration by the AASHTO Highway Sub- committee on Bridges and Structures. 1.3 RESEARCH APPROACH Key specific aspects of the above research tasks are further described below. Tasks 1 through 3 involved not only an extensive literature review of both analytical and experi- mental explorations of effective slab width and associated slab-on-girder bridge studies but also a survey of effective 4 slab width criteria and maximum girder spacings used by the various states, documented in Appendix A (provided on the accompanying CD-ROM). In addition, international prac- tice was surveyed and the various effective width provisions compared. The literature review is contained in Appendix B (provided on the accompanying CD-ROM). Task 4 involved an implementation of finite element mod- eling techniques at an appropriate level of detail to predict both linear and nonlinear (post-cracking and post-yielding) behavior of composite steel bridge member superstructures. In order to determine what level of detail was appropriate, an extensive review of the shear lag phenomenon and effec- tive width definitions was conducted along with new defi- nitions for effective width beff developed herein. The details of this review and the new definitions are contained in Appendix C (provided on the accompanying CD-ROM), while the finite element modeling and the verifications thereof are described in detail in Appendix D (provided on the accompanying CD-ROM). Task 5, laboratory testing, was conducted of a two-span con- tinuous one-quarter-scale slab-on-girder bridge structure and is documented in Appendix E (provided on the accompanying CD-ROM). Testing of two one-half-scale subassemblages of the negative moment region portion of such structures is doc- umented in Appendix F (provided on the accompanying CD- ROM). These experiments were used to help establish the cred- ibility of the finite element modeling approaches developed in Task 4 so that these approaches could be used for parametric studies of various bridge configurations in Task 6. Task 6 pursued a systematic set of analyses of finite element models representing bridges with various span lengths (15 m to 60 m), girder spacings (2.4 m to 4.8 m), skew angles (0 to 60 deg), and (in the cases of continuous bridges) span length ratios (from 1.0 to 1.5). Both single-span and three-span con- tinuous configurations were the focus of the systematic set. The set was assembled using “design of experiments” (DOE) concepts (Montgomery, 2001). Effective width according to the new definitions developed in Task 4 was extracted from the finite element analysis results considering both interior and exterior girders, service and strength limit states, positive and negative moment regions, and both right and skew alignments. Details of the “design of experiments” background, the finite element modeling, and the suite of bridges analyzed in the parametric study along with the analysis results are presented in Appendix G (provided on the accompanying CD-ROM). The bridges modeled in this parametric investigation needed to be designed first. Industry guidelines were carefully followed in the design of these bridges. These guidelines and the resulting bridge parameters (e.g., girder sizes) are described in further detail in Appendix H (provided on the accompanying CD-ROM). In addition to the parametric study set of bridges, various bridge configurations that go beyond the parametric limits were investigated. These included some of cable-stayed bridges, described in Appendix I (provided on the accompanying

CD-ROM). Other bridges beyond the parametric limits include a limited number of prestressed-concrete bridges, two-girder bridges with girders spaced as widely as 7.6 m, tub-girder, hybrid, and prestressed-slab bridges. Finite element analy- sis results for these “validation cases” are documented in Appendix J (provided on the accompanying CD-ROM). Task 7 involved the development of curve-fit expressions for predicting effective width based on the results of the finite element analyses. Development and comparison of various such curve-fit expressions are documented in Appendix K (provided on the accompanying CD-ROM). Task 8 addressed evaluating the impact of these candidate beff expressions as compared with the current AASHTO pro- visions. The basis for this evaluation of impact was taken to be the Rating Factor, considering both service and strength limit states, and was documented in Appendix L (provided on the accompanying CD-ROM). The culmination of this effort was the draft code and commentary language for pro- posed new effective width provisions, which were docu- mented along with their underlying rationale in Appendix M (provided in print herein and on the accompanying CD-ROM). Appendix N (provided on the accompanying CD-ROM) contains information about the finite element modeling of the prestressed girder bridge structures investigated in this study, while Appendix O (provided in print herein and on the accom- panying CD-ROM) presents worked design examples illus- trating the use of the new proposed provisions for effective slab width. The scope of the investigation excludes consideration of the following: 5 • Horizontally curved bridges, for which a system analy- sis is recommended instead of a line-girder approach for which effective width is traditionally applied; • Segmental bridges; and • Tied-arch bridges, with net tension added to flexure on the cross section. 1.4 ORGANIZATION OF THIS REPORT This report consists of four chapters as well as the afore- mentioned appendixes (provided on CRP-CD-56). This chap- ter provides the introduction and research approach, describes the research objectives, and outlines the scope of the study. Chapter 2 describes the findings of the survey and literature review, new definitions for effective width, verifications of the FEM (Finite Element Method) modeling approaches employed, highlights of results from the FEM-based para- metric study, and insights from the experiments performed. Chapter 3 summarizes the development of candidate design criteria and impact assessment of these criteria using a straight- forward application of Process 12-50 to show that the subtle differences among the various possible curve-fit expressions are, for all practical purposes, negligible. This observation leads to a recommendation of simplified design criteria for effective width. Highlights of the worked example illustrat- ing the use of these simplified design criteria are summa- rized. Chapter 4 then summarizes the conclusions of this study and presents suggestions for future research.