THREE-SPAN CONTINUOUS STRAIGHT COMPOSITE I GIRDER Load and Resistance Factor Design (Third Edition -- Customary U.S. Units)

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1 EXAMPLE 1: THREE-SPAN CONTINUOUS STRAIGHT COMPOSITE I GIRDER Load and Resistance Factor Design (Third Edition -- Customary U.S. Units) by Michael A. Grubb, P.E. Bridge Sotware Development International, Ltd. Cranberry Township, PA and Robert E. Schmidt, E.I.T. SITE-Blauvelt Engineers Pittsburgh, PA

2 Disclaimer All data, speciications, suggested practices, and drawings presented herein, are based on the best available inormation and delineated in accordance with recognized proessional engineering principles and practices, and are published or general inormation only. Procedures and products, suggested or discussed, should not be used without irst securing competent advice respecting their suitability or any given application. Publication o the material herein is not to be construed as a warranty on the part o the National Steel Bridge Alliance or that o any person named herein that these data and suggested practices are suitable or any general or particular use, or o reedom rom inringement on any patent or patents. Further, any use o these data or suggested practices can only be made with the understanding that the National Steel Bridge Alliance makes no warranty o any kind respecting such use and the user assumes all liability arising thererom

3 LRFD rd Edition Table o Contents 1. INTRODUCTION OVERVIEW OF LRFD ARTICLE DESIGN PARAMETERS STEEL FRAMING Span Arrangement Bridge Cross-Section Cross-Frames Field Section Sizes PRELIMINARY GIRDER SIZES Girder Depth Cross-section Proportions LOADS Dead Loads Live Loads Design Vehicular Live Load (Article.6.1.) Loading or Optional Live-Load Delection Evaluation (Article.6.1..) Fatigue Load (Article.6.1.4) Wind Loads Load Combinations STRUCTURAL ANALYSIS Multiple Presence Factors (Article ) Live-Load Distribution Factors (Article 4.6..) Live-Load Lateral Distribution Factors - Positive Flexure Interior Girder - Strength Limit State Exterior Girder - Strength Limit State Distribution Factors or Fatigue Limit State Distribution Factor or Live-Load Delection Live-Load Lateral Distribution Factors - Negative Flexure Interior Girder - Strength Limit State Distribution Factors or Fatigue Limit State Dynamic Load Allowance: IM (Article.6.) ANALYSIS RESULTS Moment and Shear Envelopes Live Load Delection LIMIT STATES Service Limit State (Articles 1... and 6.5.) Fatigue and Fracture Limit State (Articles 1... and 6.5.) Strength Limit State (Articles and 6.5.4) Extreme Event Limit State (Articles and 6.5.5) SAMPLE CALCULATIONS Section Properties Section Eective Flange Width (Article ): Section Elastic Section Properties: Section Plastic Moment: Section Yield Moment: Section Section Eective Flange Width (Article ): Section Minimum Negative Flexure Concrete Deck Reinorcement (Article ) Elastic Section Properties: Section May, 004 i

4 LRFD rd Edition 10.. Exterior Girder Check: Section Constructibility (Article 6.10.) Deck Placement Analysis Deck Overhang Loads Wind Loads Flexure (Article )... 5 Top Flange... 5 Local Buckling Resistance (Article )... 5 Lateral Torsional Buckling Resistance (Article )... 5 Web Bend-Buckling Resistance (Article ) Bottom Flange Shear (Article ) Concrete Deck (Article ) Service Limit State (Article ) Elastic Deormations (Article ) Permanent Deormations (Article ) Concrete Deck (Article ) Fatigue And Fracture Limit State (Article ) Load Induced Fatigue (Article ) Top-Flange Connection-Plate Weld Bottom-Flange Connection-Plate Weld Stud Shear-Connector Weld Distortion Induced Fatigue (Article ) Fracture (Article 6.6.) Special Fatigue Requirement or Webs (Article ) Strength Limit State (Article ) Flexure (Article ) Nominal Flexural Resistance (Article ) Shear ( ) End Panel (Article ) Interior Panels (Article ) Exterior Girder Check: Section Strength Limit State (Article ) Flexure (Article )... 7 Bottom Flange Lateral Torsional Buckling Resistance (Article ) Elastic Section Properties: Flange transition Local Buckling Resistance (Article ) Stress Check Bottom Flange... 8 Top Flange Shear ( ) Service Limit State (Article ) Permanent Deormations (Article ) Fatigue And Fracture Limit State (Article ) Load Induced Fatigue (Article ) Special Fatigue Requirement or Webs (Article ) Constructibility (Article 6.10.) Flexure (Article ) Web Bend-Buckling Shear (Article ) Shear Connector Design (Article ) Stud Proportions Pitch (Article ) Fatigue Limit State Strength Limit State (Article ) ii May, 004

5 LRFD rd Edition Exterior Girder: Field Section Transverse Intermediate Stiener Design (Article ) Projecting Width (Article ) Moment o Inertia (Article ) Area (Article ) Exterior Girder: Abutment Bearing Stiener Design (Article ) Projecting Width (Article ) Bearing Resistance (Article ) Axial Resistance (Article ) Bearing Stiener-to-Web Welds Exterior Girder: Design Example Summary Positive-Moment Region, Span 1 (Section 1-1) Constructibility (Slender-web section) Service Limit State Fatigue and Fracture Limit State Strength Limit State (Compact Section) Interior-Pier Section (Section -) Strength Limit State (Slender-web section) Service Limit State Fatigue and Fracture Limit State Constructibility (Slender-web section) Appendix A: Elastic Eective Length Factor or Lateral Torsional Buckling... A1 Appendix B: Moment Gradient Modiier, C b... B1 Appendix C: Lateral Torsional Buckling Resistance o Stepped Flanges...C1 May, 004 iii

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7 LRFD rd Edition 1. INTRODUCTION In 199, the American Association o State Highway and Transportation Oicials (AASHTO) adopted the Load and Resistance Factor Design (LRFD) speciications or bridge design. The First Edition o the design speciications was published by AASHTO in The publication o a Second Edition ollowed in 1998, along with the publication o the First Edition o a companion document the AASHTO LRFD Bridge Construction Speciications. The design speciications are available in either customary U.S. units or in SI (metric) units, whereas the construction speciications are currently only available in SI units. The LRFD speciications were approved by AASHTO or use as alternative speciications to the AASHTO Standard Speciications or Highway Bridges The LRFD speciications evolved in response to a high level o interest amongst the AASHTO Subcommittee on Bridges and Structures in developing updated AASHTO bridge speciications together with accompanying commentary. The goal was to develop more comprehensive speciications that would eliminate any gaps and inconsistencies in the Standard Speciications, incorporate the latest in bridge research, and achieve more uniorm margins o saety or reliability across a wide variety o structures. The decision was made to develop these new speciications in an LRFD-based ormat, which takes the variability o the behavior o structural elements into account through the application o statistical methods, but presents the results in a manner that is readily usable by bridge designers. A detailed discussion o the evolution o the LRFD design speciications and commentary is presented in NCHRP Research Results Digest 198 (available rom the Transportation Research Board) and elsewhere, and will not be repeated herein. The design o steel structures is covered in Section 6 o the AASHTO LRFD Bridge Design Speciications and only straight steel bridges are covered in the provisions as o this writing. The Third Edition o the design speciications, to be published in 004, will contain a complete set o new provisions or the design o straight steel I- and box-section lexural members within Articles 6.10 and 6.11, respectively. These new provisions have been structured to simpliy their logic, organization and application, while also improving their accuracy and generality. More importantly, the new provisions lay the necessary groundwork or a potential uture uniied design approach or both straight and horizontally curved girders within a single speciication, which will urther streamline and improve the overall eiciency o the design process or bridges that contain both straight and curved spans. The basic application o these new provisions to the design o straight steel I-section section lexural members is illustrated through the design example presented herein. The example illustrates the design o a typical three-span continuous straight steel I-girder bridge with spans o Speciically, the example illustrates the design o selected critical sections rom an exterior girder at the strength, service and atigue limit states. Constructibility checks, stiener and shear connector designs are also presented.. OVERVIEW OF LRFD ARTICLE 6.10 The design o I-section lexural members is covered within Article 6.10 o the AASHTO LRFD Bridge Design Speciications. The new provisions o Article 6.10 contained in the Third Edition o the LRFD speciications have been organized to correspond more closely to the general low o the calculations necessary or the design o I-section lexural members. Each o the sub-articles are written such that they are largely sel-contained, thus minimizing the need or reerence to multiple sub-articles to address any o the essential design considerations. Many o the individual calculations and equations have been streamlined and selected resistance equations have been updated to improve their accuracy and generality. The Commentary to the provisions also covers a number o areas in which the previous speciications have been largely silent. The sub-articles within the Third Edition Article 6.10 are organized as ollows: General Cross-section Proportion Limits May, 004 Page 1 o 1

8 LRFD rd Edition Constructibility Service Limit State Fatigue and Fracture Limit State Strength Limit State Flexural Resistance - Composite Sections in Positive Flexure Flexural Resistance - Composite Sections in Negative Flexure and Noncomposite Sections Shear Resistance Shear Connectors Stieners Cover Plates In addition, our new appendices to Section 6 relevant to the design o lexural members are provided as ollows: Appendix A - Flexural Resistance - Composite Sections in Negative Flexure and Noncomposite Sections with Compact or Noncompact Webs Appendix B - Moment Redistribution rom Interior-Pier Sections in Continuous-Span Bridges Appendix C - Basic Steps or Steel Bridge Superstructures Appendix D - Fundamental Calculations or Flexural Members For composite I-sections in negative lexure and noncomposite I-sections, the provisions o Article limit the nominal lexural resistance to a maximum o the moment at irst yield. As a result, the nominal lexural resistance or these sections is conveniently expressed in terms o the elastically computed lange stress. When these sections satisy speciic steel grade requirements and have webs that are classiied as either compact or noncompact, the optional provisions o Appendix A may be applied instead to determine the lexural resistance, which may exceed the moment at irst yield. Thereore, the lexural resistance is expressed in terms o moment in Appendix A. The provisions o Appendix A are a direct extension o and are ully consistent with the main provisions o Article The previous Speciications deined sections as either compact or noncompact and did not explicitly distinguish between a noncompact web and a slender web. The proposed provisions make explicit use o these deinitions or composite I-sections in negative lexure and noncomposite I-sections because the noncompact web limit serves as a useul anchor point or a continuous representation o the maximum potential section resistance rom the nominal yield moment up to the plastic moment resistance. Because sections with compact or nearly compact webs are less commonly used, the provisions or sections with compact or noncompact webs have been placed in an appendix in order to simpliy and streamline the main provisions. The main provisions within the body o Article 6.10 may be used or these types o sections to obtain an accurate to somewhat conservative determination o the lexural resistance calculated using Appendix A. For girders that are proportioned with webs near the noncompact web slenderness limit, the provisions o Article 6.10 and Appendix A produce the same strength or all practical purposes, with the exception o cases with large unsupported lengths sometimes encountered during construction. In these cases, Appendix A gives a larger more accurate lexural resistance calculation. In the example to ollow, a slender-web section is utilized or both the composite section in regions o negative lexure and or the noncomposite section in regions o positive lexure beore the concrete deck has hardened. As a result, the main provisions o Article 6.10 must be applied or the strength limit state and constructibility checks or those sections and the optional Appendix A is not applicable. Minor yielding at interior piers o continuous spans results in redistribution o the moments. For straight continuous-span lexural members that satisy certain restrictions intended to ensure adequate ductility and robustness o the pier sections, the optional procedures o Appendix B may be used to calculate the redistribution moments at the service and/or strength limit states. These provisions replace the ormer ten-percent redistribution allowance as well as the ormer inelastic analysis procedures. They provide a simple calculated percentage redistribution rom interior-pier sections. This approach utilizes elastic Page o 1 May, 004

9 LRFD rd Edition moment envelopes and does not require the direct use o any inelastic analysis. As such, the new procedures are substantially simpler and more streamlined than the inelastic analysis procedures o the previous Speciications. Where appropriate, these provisions make it possible to use prismatic sections along the entire length o the bridge or between ield splices, which can improve overall atigue resistance and provide signiicant abrication economies. Although the necessary steps could be taken to allow moment redistribution in the example presented herein, the provisions o Appendix B are not applied. Flow charts or lexural design o I-sections according to the new provisions, along with a revised outline giving the basic steps or steel-bridge superstructure design, are provided in Appendix C. Fundamental section property calculations or lexural members have been relocated rom the speciication to a new Appendix D. The provisions o Article 6.10 and the optional Appendices A and B provide a uniied approach or consideration o combined major-axis bending and lange lateral bending rom any source in both straight and horizontally curved I-girders. As such, general design equations are provided that include the consideration o both major-axis bending and lange lateral bending. For straight girders, lange lateral bending is caused by wind and by torsion rom various origins. Sources o signiicant lange lateral bending due to torsion include eccentric slab overhang loads acting on cantilever orming brackets placed along exterior members, staggered cross-rames, and signiicant support skew. When the above eects are judged to be insigniicant or incidental, the lange lateral bending term,, is simply set equal to zero in the appropriate equations. The ormat o the equations then simply reduces to the more conventional and amiliar ormat or checking the nominal lexural resistance o I-sections in the absence o lange lateral bending. The example to ollow considers the eects o lange lateral bending caused by wind and by torsion due to the eects o eccentric slab overhang loads. Finally, it should be noted that the new Article 6.10 provisions do not incorporate all the necessary requirements or horizontally curved I-girder bridge design as o this writing. It is anticipated that these requirements will soon be incorporated under the work o NCHRP Project 1-5, and that some additional restrictions will be placed on the application o the provisions in Article 6.10 to curved bridge design. However, the new provisions lay the necessary groundwork or accomplishing that eort in an eicient manner, which was the primary impetus or the extensive revisions.. DESIGN PARAMETERS The ollowing data apply to this example design: Speciications: 004 AASHTO LRFD Bridge Design Speciications, Customary U.S. Units, Third Edition Structural Steel: AASHTO M 70 Grade HPS 70W (ASTM A 709 Grade HPS 70W) uncoated weathering steel with F y = 70 ksi (or the langes in regions o negative lexure) AASHTO M 70, Grade 50W (ASTM A 709, Grade 50W) uncoated weathering steel with = 50 ksi (or all other girder and cross-rame components) The example design utilizes uncoated weathering steel. Where site conditions are adequate or successul application, uncoated weathering steel is the most cost-eective material choice in terms o savings in both initial and uture repainting costs. In the years since its introduction into bridge construction by the Michigan DOT in the 1960's, uncoated weathering steel has become widely accepted as cost-eective, currently representing about 45 percent o the steel-bridge market. However, it has also requently been misused because o inexperience or ignorance about the properties o the material. To counter this and increase the conidence in its perormance, the FHWA issued a Technical Advisory (T5140.) in 1989 F y May, 004 Page o 1

10 LRFD rd Edition entitled Uncoated Weathering Steel in Structures. The guidelines contained in this document, developed in cooperation with the steel industry, are a valuable source o inormation on the proper environments or the use o weathering steel. The guidelines also suggest good detailing practice to help ensure successul application o the material. In regions o negative lexure, the example design utilizes a hybrid section consisting o ASTM A 709 Grade HPS 70W high-perormance steel (HPS) langes and an ASTM A 709 Grade 50W web. Grade HPS 70W was developed in the early 1990s under a successul cooperative research program between the Federal Highway Administration, the U.S. Navy, and the American Iron and Steel Institute. Grade HPS 70W possesses superior weldability and toughness compared to conventional steels o this strength range. Grade HPS 70W is currently produced by quenching and tempering (Q&T) or by thermo-mechanicalcontrolled-processing (TMCP). TMCP HPS is available in plate thicknesses up to inches and in maximum plate lengths rom approximately 600 to 1500 inches depending on weights. Q&T HPS is available in plate thicknesses up to 4 inches, but because o the urnaces that are used in the tempering process, is subject to a maximum plate-length limitation o 600 inches or less depending on weights. Thereore, when Q&T HPS is used, the maximum plate-length limitation should be considered when laying out lange and web transitions. Current inormation on maximum plate length availability can be obtained by contacting a steel producer. Guidelines or abrication using Grade HPS 70W steel are available in the AASHTO Guide Speciications or Highway Bridge Fabrication with HPS 70W Steel (Second Edition to be published in 004). HPS is inding increasing application in highway bridges across the U.S., with hybrid designs utilizing Grade HPS 70W langes in conjunction with a Grade HPS 50W web being the most popular application. Concrete: Slab Reinorcing Steel: c = 4.0 ksi AASHTO M 1, Grade 60 (ASTM A 615, Grade 60) with F y = 60 ksi Permanent steel deck orms are assumed between the girders; the orms are assumed to weigh 15.0 ps. The girders are assumed to be composite throughout. For the atigue design, the Average Daily Truck Traic (ADTT) in one direction, considering the expected growth in traic volume over the 75-year atigue design lie, is assumed to be,000 trucks/day. 4. STEEL FRAMING 4.1. Span Arrangement Proper layout o the steel raming is an important part o the design process. The example bridge has spans o , with the span lengths arranged to give similar positive dead load moments in the end and center spans. Such balanced span arrangements (i.e. end spans approximately 0.8 o the length o the center spans) in multiple continuous-span steel bridges result in the largest possible negative moments at the adjacent piers, along with smaller concomitant positive moments and girder delections. As a result, the optimum depth o the girder in all spans will be nearly the same resulting in a much more eicient design. Steel has the lexibility to be utilized or most any span arrangement. However, in some competitive situations, steel has been compelled to use a particular span arrangement that has been optimized or an alternate design. In a competitive situation, i the pier locations are lexible and i the spans have been optimized or the alternate design, the span arrangement or the steel design almost certainly will be dierent and must also be optimized. In situations where there are severe depth restrictions or where it is desirable to eliminate center piers (e.g. certain overpass-type structures), it may be desirable to provide short end spans. However, in cases where there are no such restrictions or needs, it will likely be more economical to extend the end spans to provide a balanced span ratio. This will avoid the costs associated with the possible need or tie-downs at the end bearings, ineicient girder depths and additional moment Page 4 o 1 May, 004

11 LRFD rd Edition in some spans. In curved structures, extension o the end spans may also permit the use o radial supports where skewed supports might otherwise have been necessary. It should be noted that the most eicient and cost-competitive steel bridge system can result only when the substructure or the steel design is evaluated and designed concurrently with the superstructure. Although the superstructure and substructure act in concert, each is oten analyzed or separate loads and isolated rom the other as much as possible both physically and analytically. Substructure costs represent a signiicant portion o the total bridge cost. The orm chosen or the substructure, oten based on past experience or the desire to be conservative, may unknowingly lead to an ineicient steel design. Substructure orm also has a marked eect on the overall aesthetic appeal o the structure. When the site dictates diicult span arrangements and pier designs, steel is oten the only material o choice. However, its eiciency oten suers when designed to conorm to oundations developed or other materials. For major projects, superstructure and substructure cost curves should be developed or a series o preliminary designs using dierent span arrangements. Since the concrete deck costs are constant and independent o span length, they need not be considered when developing these curves. The optimum span arrangement lies at the minimum o the sum o the superstructure and substructure costs. These curves should always be regenerated to incorporate changes in unit costs that may result rom an improved knowledge o speciic site conditions. While it is recognized that the locations o piers cannot be varied in many instances, or cases where pier locations are lexible, the use o poorly conceived span arrangements and/or substructure orm can have the greatest total cost impact on a steel-bridge design. 4.. Bridge Cross-Section The example bridge cross-section consists o our (4) girders spaced at 1-0 centers with -6 deck overhangs and an out-to-out deck width o 4-0. The 40-0 roadway width can accommodate up to three 1-oot-wide design traic lanes. The total thickness o the cast-in-place concrete deck is 9½ including a ½ -thick integral wearing surace. The concrete deck haunch is ½ deep measured rom the top o the web to the bottom o the deck. The width o the deck haunch is assumed to be 16.0 inches. Deck parapets are each assumed to weigh 50 pounds per linear oot. A uture wearing surace o 5.0 ps is also assumed in the design. A typical cross-section is shown in Figure 1: Figure 1: Typical Bridge Cross-Section The deck overhangs are approximately 9 percent o the girder spacing. Reducing the girder spacing below 1-0 would lead to an increase in the size o the deck overhangs, which may lead to larger May, 004 Page 5 o 1

12 LRFD rd Edition loading on the exterior girders. The eect o a wider girder spacing would have to be evaluated with respect to any potential increase in the cost o the concrete deck. Wide girder spacings oer the advantages o ewer girders and pieces to abricate, inspect, ship and erect, and ewer bearings to purchase and set. 4.. Cross-Frames Cross-rames provide lateral stability to the top and bottom langes o the girder, distribute vertical dead and live loads applied to the structure, transer lateral wind loads rom the bottom o the girder to the deck and rom the deck to the bearings, reduce any lange lateral bending eects and transverse deck stresses and provide adequate distribution o load to ensure relatively equal girder delection during construction. Cost-eective design o steel-bridge superstructures requires careul attention to details, including the design o diaphragms and cross-rames. Although these members account or only a small percentage o the total structure weight, they usually account or a signiicant percentage o the total erected steel cost. Cross-rames in steel-girder bridges, along with the concrete deck, provide restoring orces that tend to make the steel girders delect equally. During erection and prior to curing o the deck, the cross-rames are the only members available to provide the restoring orces that prevent the girders rom delecting independently. The restoring orces will be very small i the stinesses o the adjacent girders at the cross-rame connection points are approximately equal and the applied loads to each girder are approximately the same. For the more general case where the girders delect by dierent amounts, the cross-rames and concrete deck will develop larger restoring orces, with the magnitude being dependent on the relative girder, cross-rame and deck stinesses. With ewer cross-rame lines, the orce in each cross-rame member will increase to some degree since the total restoring orce between two adjacent girders is the same regardless o the number o crossrames that are provided. Stresses in the concrete deck will also increase to a degree. For a tangent composite bridge with a regular raming plan, which is the case in this particular design example, the increases in these orces and stresses will typically be o less concern; particularly at the cross-rame spacings chosen or this example. However, the designer should be at least cognizant o these eects when ewer cross-rame lines are provided, especially or more irregular raming plans and when the bridge is non-composite. When reined methods o analysis are used and the cross-rames are included in the structural model to determine orce eects, the cross-rame members are to be designed or the calculated orce eects. When approximate methods o analysis are used (e.g., lateral distribution actors), cross-rame orce eects due to dead and live loads generally cannot be easily calculated. Thus, as a minimum, crossrames are designed to transer wind loads and to meet all applicable slenderness and minimum material thickness requirements. For the most part, such an approach has proven successul on tangent bridges without skewed supports or with small skews. For tangent bridges with moderate to highly skewed supports, where the eects o dierential delections between girders become more pronounced, and or all curved bridges, closer scrutiny o cross-rame orce eects is warranted. Since 1949, the AASHTO Standard Speciications or steel design have speciied a limit o 5'-0" on the longitudinal diaphragm or cross-rame spacing or I-girder bridges. While this limit has ensured satisactory perormance o these structures over the years, it is essentially an arbitrary limit that was based on the experience and knowledge that existed at that time. This arbitrary requirement has been removed in the LRFD speciications. Instead, the need or cross-rames at all stages o construction and the inal condition is to be established by rational analysis (Article ). Article urther states that the investigation should include, but not be limited to, consideration o the transer o lateral wind loads rom the bottom o the girder to the deck and rom the deck to the bearings, the stability o bottom langes or all loads when subject to compression, the stability o top langes in compression prior to curing o the deck and the distribution o vertical dead and live loads applied to the structure. Diaphragms or cross-rames required or conditions other than the inal condition may be speciied to be Page 6 o 1 May, 004

13 LRFD rd Edition temporary bracing. Based on the preceding considerations, the cross-rame spacings shown on the raming plan in Figure were chosen or this example. Although the AASHTO design speciications are generally member based, the overall behavior o the entire bridge system must also be considered, particularly during the various stages o construction. As will be demonstrated later on in the design example, the noncomposite bridge structure acts as a system to resist wind loads during construction. The example calculations will illustrate how a couple o panels o top lateral bracing, as shown in the interior bays adjacent to the interior piers in Figure, can be added, i necessary, to provide a stier load path or wind loads acting on the noncomposite structure during construction. The lateral bracing helps to reduce the lateral delections and lateral lange bending stresses due to the wind loads. A rational approach is presented to help the Engineer evaluate how many panels o lateral bracing might be necessary to reduce the lateral delections and stresses to a level deemed acceptable or the situation under consideration. Such a system o lateral bracing adjacent to supports can also help provide additional rigidity to an I-girder bridge system to help prevent signiicant relative horizontal movements o the girders that may occur during construction, particularly in longer spans (e.g. spans exceeding approximately 00 eet). Unlike building columns, which are restrained against the ground by gravity and cannot translate with respect to each other, bare steel bridge girders are generally ree to translate longitudinally with respect to adjacent girders. Lateral bracing provides a triangulation o the members to help prevent the rectangles ormed by the girders and cross-rames rom signiicantly changing shape and moving longitudinally with respect to each other. Bottom lateral bracing can serve similar unctions to those described above, but unlike top bracing, would be subject to signiicant liveload orces in the inished structure that would have to be considered should the bracing be let in place Field Section Sizes Field section lengths are generally dictated by shipping weight and length considerations. The Engineer should consult with abricators regarding any speciic restrictions that might inluence the ield-splice locations. For the example design, there is one ield splice assumed in each end span and two ield splices assumed in the center span resulting in ive (5) ield sections in each line o girders, or 0 ield sections or the bridge (Figure ). Figure : Framing Plan May, 004 Page 7 o 1

14 LRFD rd Edition 5. PRELIMINARY GIRDER SIZES 5.1. Girder Depth The proper girder depth is another extremely important consideration aecting the economy o steelgirder design. In the absence o any depth restrictions, Article provides suggested minimum span-to-depth ratios. From Table , the suggested minimum depth o the steel section in a composite I-section in a continuous span is given as 0.07L, where L is the span length in eet. Using the longest span o 175-0, the suggested minimum depth o the steel section is: 0.07(175.0) = 4.75 t = 56.7 in. Since there are no depth restrictions in this case, a deeper steel section is desired to provide greater stiness to the girders in their noncomposite condition during construction (it should be noted that the optimum web depth is usually also greater than the suggested minimum web depth). Thereore, the suggested minimum overall depth o the composite I-section in a continuous span, equal to 0.0L, rom Table will be used here or the steel section: 0.0(175.0) = 5.60 t = 67. in. A web depth o 69 inches is used. 5.. Cross-section Proportions Cross-section proportion limits or webs o I-sections are speciied in Article In the span ranges given or this example, the need or longitudinal stieners on the web is not anticipated. For webs without longitudinal stieners, webs must be proportioned such that: Rearranging: D 150 Eq. ( ) t w D 69 ( t w ) = = =0.46 in. min Because o concerns about the web bend-buckling resistance at the service limit state in regions o negative lexure and also the higher shears in these regions, try a web thickness o inches in regions o negative lexure and a web thickness o 0.5 inches in regions o positive lexure. Note that the AASHTO/NSBA Steel Bridge Collaboration Guidelines or Design or Constructibility (hereater reerred to as the Guidelines - to be published in 004 and endorsed by the AASHTO T-14 Technical Committee or Structural Steel Design) recommend a minimum web thickness o inches, with a minimum thickness o 0.5 inches preerred. Cross-section proportion limits or langes o I-sections are speciied in Article The minimum width o langes is speciied as: Thereore: ( b ) min. The minimum thickness o langes is speciied as: Or: b D6 Eq. ( ) = D 6=69 6=11.5 in. t 1.1t ( t ) ( ) min w =1.1t = =0.6 in. w Eq. ( ) Page 8 o 1 May, 004

15 LRFD rd Edition However, the Guidelines recommend a minimum lange thickness o 0.75 inches. Thereore, use (t ) min = 0.75 inches. For the top lange in regions o positive lexure in composite girders, Article C provides the ollowing additional guideline or the minimum compression-lange width. This guideline is intended to provide more stable ield pieces that are easier to handle during erection without the need or special stiening trusses or alsework, and to help limit out-o-plane distortions o the compression lange and web during the deck-casting operation: L bc Eq. (C ) 85 where L is the length o the girder shipping piece in eet. From Figure, the length o the longest ield piece, which is assumed to also equal the length o the longest shipping piece in this case, is 100 eet. Thereore, or this particular shipping piece: L 100 ( b c ) = = =1.176 t=14.1 in. min Based on the above minimum proportions, the trial girder shown in Figure is assumed or the exterior girder, which is assumed to control. Because the top lange o the exterior girders will be subject to lange lateral bending due to the eect o the eccentric deck overhang loads, and also due to wind loads during construction, top-lange sizes slightly larger than the minimum sizes are assumed in regions o positive lexure. The bottom lange plates in regions o positive lexure in this example are primarily sized based on the lange-stress limitation at the service limit state speciied in Article However, in the end spans, the size o the larger bottom-lange plate in this region is controlled by the stress-range limitation on a cross-rame connection plate weld to the tension lange at the atigue and racture limit state, as will be demonstrated later. The bottom-lange sizes in regions o negative lexure are assumed controlled by either the lange local buckling or lateral torsional buckling resistance at the strength limit state. Top-lange sizes in these regions are assumed controlled by tension-lange yielding at the strength limit state. At this stage, the initial trial plate sizes in regions o negative lexure are primarily educated guesses based on experience. Because the girder is assumed to be composite throughout, the minimum one-percent longitudinal reinorcement required in Article will be included in the section properties in regions o negative lexure. As a result, a top lange with an area slightly smaller than the area o the bottom lange can be used in these regions. Recall that the langes in regions o negative lexure are assumed to be Grade HPS 70W steel in this example. Because the most economical plate to buy rom a mill is between 7 and 96 inches wide, an attempt was made in the design to minimize the number o thicknesses o plate that must ordered or the langes. As recommended in the Guidelines, lange thicknesses should be selected in not less than 1/8-inch increments up to ½ inches in thickness and ¼-inch increments over ½ inches in thickness. Note that individual lange widths are kept constant within each ield piece, as recommended in the Guidelines. The Guidelines contain more detailed discussion on speciic issues pertinent to the sizing o girder langes as it relates to the ordering o plate and the abrication o the langes. Fabricators can also be consulted regarding these issues and all other abrication-related issues discussed herein. Flange transitions, or shop-welded splices, are located based on design considerations, plate length availability (as discussed earlier) and the economics o welding and inspecting a splice compared to the cost o extending a thicker plate. The design plans should consider allowing an option or the abricator to eliminate a shop splice by extending a thicker lange plate subject to the approval o the Engineer. Usually, a savings in weight o between 800 to 1000 pounds should be realized in order to justiy a lange butt splice. Again, the Guidelines contain more detailed discussion regarding this particular issue. At May, 004 Page 9 o 1

16 LRFD rd Edition Figure : Elevation o Exterior Girder Page 10 o 1 May, 004

17 LRFD rd Edition 6. LOADS lange splices, the cross-sectional area o the thinner plate should not be less than one-hal the crosssectional area o the thicker plate. Article contains two additional lange proportion limits as ollows: b t 1.0 Eq. ( ) Iyc Eq. ( ) I where: I yc = moment o inertia o the compression lange o the steel section about the vertical axis in the plane o the web (in 4 ) I yt = moment o inertia o the tension lange o the steel section about the vertical axis in the plane o the web (in 4 ) These criteria are each checked or the most critical case (reer to Figure ): ( ) All other langes have a ratio o b /t less than 10.. yt b 18 = = 10.< 1.0 ok t ( ) Iyc 1 yt 116 = = 0.51 I ( ) 1 0.1< 0.51< 10 ok At all other sections, the ratio o I yc /I yt is greater than 0.51 and less than Dead Loads As speciied in Article.5.1, dead loads are permanent loads that include the weight o all components o the structure, appurtenances and utilities attached to the structure, earth cover, wearing suraces, uture overlays and planned widenings. In the LRFD speciication, the component dead load DC is assumed to consist o all the structure dead load except or any non-integral wearing suraces and any speciied utility loads. For composite steelgirder design, DC is assumed divided into two separate parts: 1) DC acting on the non-composite section (DC 1 ), and ) DC acting on the composite section (DC ). As speciied in Article a, DC 1 represents permanent component load that is applied beore the concrete deck has hardened or is made composite, and is assumed carried by the steel section alone. DC represents permanent component load that is applied ater the concrete deck has hardened or is made composite, and is assumed carried by the long-term composite section. For computing stresses rom moments, the stiness o the long-term composite section in regions o positive lexure is calculated by transorming the concrete deck using a modular ratio o n to account in an approximate way or the eect o concrete creep (Article b). In regions o negative lexure, the long-term composite section is assumed to consist o the steel section plus the longitudinal reinorcement within the eective width o the concrete deck (Article c). As discussed previously, cross-rames in steel-girder bridges, along with the concrete deck, provide restoring orces that tend to make the steel girders delect equally. Under the component dead load, DC 1, May, 004 Page 11 o 1

18 LRFD rd Edition applied prior to hardening o the deck or beore the deck is made composite, the cross-rames are the only members available to provide the restoring orces that prevent the girders rom delecting independently. Thereore, aside rom delections resulting rom elastic shortening o the cross-rames, which are generally negligible, it is reasonable to assume or typical deck overhangs and or bridges with approximately equal girder stinesses at points o connection o the cross-rames (e.g. straight bridges with approximately equal-size girders and bearing lines skewed not more than approximately 10 rom normal) that all girders in the cross-section will resist the DC 1 loads equally. This assumption has been borne out analytically and in the ield. Other assumptions may potentially lead to problems in the ield, particularly when the DC 1 delections are large. Thereore, in this example, the total DC 1 load will be assumed equally distributed to each girder in the cross-section. Note that Article permits the permanent load o the deck to be distributed uniormly among the girders when certain speciied conditions are met. In the ollowing, the unit weight o concrete is taken equal to kc (Table.5.1-1), the concrete deck haunch width is taken equal to 16.0 inches, and the deck haunch thickness is conservatively taken equal to.75 inches (reer also to Figure 1): Component dead load (DC 1 ): Concrete deck = 9.5 ( 4.0 )( ) =5.106 kips/t (includes IWS) 1 Concrete deck overhang tapers = ( ) =0.14 kips/t 1 1 Concrete deck haunches = 16(.75) 4 ( ) =0.18 kips/t 144 Stay-in-place orms = (0.015)=0.480 kips/t 1 Cross-rames and details = 0.10 kips/t DC 1 load per girder = 6.01 kips/t 4 girders = kips/t plus girder sel-weight DW in the LRFD speciication consists o the dead load o any non-integral wearing suraces and any utilities. DW is also assumed carried by the long-term composite section. DC and DW are separated because dierent permanent-load load actors γ p (Table.4.1-) are applied to each load. In this example, the wearing surace load, DW, is assumed applied over the 40-0 roadway width and equally distributed to each girder, which has been the customary practice or many years and is also permitted in Article or bridges satisying speciied conditions. Over time, there has been a signiicant increase in the use o large concrete barriers that are oten placed at the outer edges o the concrete deck. When reined methods o analysis are employed, these concrete barrier loads (the DC loads in this case) should be applied at their actual locations at the outer edges o the deck, which results in the exterior girders carrying a larger percentage o these loads. Thus, in this example, the weight o each concrete barrier will be distributed equally to an exterior girder and the adjacent interior girder. The PennDOT DM-4 Design Manual ollows such a practice (others have assigned 60 percent o the barrier weight to the exterior girder and 40 percent to the adjacent interior girder, while others continue to distribute the barrier weight equally to each girder). In this particular case, with only our girders in the cross-section, this is equivalent to equal distribution o the total barrier weight to all the girders, but this would not be the case when there are more girders in the cross-section. Thereore, the DW and DC loads on a single exterior girder are computed as ollows or this particular example: Wearing surace load (DW) = [0.05 x 40.0]/4 girders = 0.50 kips/t Component dead load -- Barrier load (DC ) = 0.50/ = 0.60 kips/t Page 1 o 1 May, 004

19 LRFD rd Edition 6.. Live Loads In the LRFD speciications, live loads are assumed to consist o gravity loads (vehicular live loads, rail transit loads and pedestrian loads), the dynamic load allowance, centriugal orces, braking orces and vehicular collision orces. Live loads o interest in this example are the basic design vehicular live load, a speciied loading or optional live-load delection evaluation, and a atigue load, with the appropriate dynamic load allowance included. Live loads are considered to be transient loads that are assumed applied to the short-term composite section. For computing stresses rom moments, the short-term composite section in regions o positive lexure is calculated by transorming the concrete deck using a modular ratio o n (Article b). In regions o negative lexure, the short-term composite section is assumed to consist o the steel section plus the longitudinal reinorcement within the eective width o the concrete deck (Article c), except as permitted otherwise at the atigue and service limit states (see Articles and ) and when computing longitudinal lexural stresses in the concrete deck (see Article d) Design Vehicular Live Load (Article.6.1.) The basic design vehicular live load in the LRFD speciications is designated as HL-9 and consists o a combination o the ollowing placed within each design lane: a design truck or design tandem. a design lane load. This represents a deviation rom the traditional AASHTO approach in which the design truck or tandem is applied independently rom the lane load. In the AASHTO Standard Speciications, the lane load is treated as a separate loading and one or two single concentrated loads are superimposed onto the lane loading to produce extreme orce eects. The design truck (Article.6.1..) is equivalent to the current AASHTO HS0 truck with the spacing between the kip rear-axle loads varied between 14 and 0 t to produce extreme orce eects (Figure ). The 8 kip ront axle is located at a constant distance o 14 t rom the closest rear axle. The transverse spacing o the wheels is 6 t. The truck is assumed to occupy a design lane 1 t in width with only one truck to be placed within each design lane (except as discussed below). The truck is to be positioned transversely within a lane to produce extreme orce eects; however, the truck is to be positioned no closer than t rom the edge o the design lane. For the design o the deck overhang, the truck is to be positioned no closer than 1 t rom the ace o the curb or railing (Article ). The design tandem (Article.6.1..) consists o a pair o 5 kip axles spaced 4 t apart with a transverse spacing o wheels equal to 6 t. The design lane load (Article ) consists o a 0.64 kips/t uniormly distributed load occupying a 10 t lane width positioned to produce extreme orce eects. The uniorm load may be continuous or discontinuous as necessary to produce the maximum orce eect. For continuous spans, live-load moments in regions o positive lexure and in regions o negative lexure outside the points o permanent-load contralexure are computed using only the HL-9 loading. For computing live-load moments in regions o negative lexure between the points o permanent-load contralexure, a special negative-moment loading is also considered. For this special negative-moment loading, a second design truck is added in combination with the design lane load (Article ). The minimum headway between the lead axle o the second truck and the rear axle o the irst truck is speciied to be 50 t (a larger headway may be used to obtain the maximum eect). The distance between the two kip rear axles o each o the design trucks is to be kept at a constant distance o 14 t. In addition, all design loads (truck and lane) are to be reduced to 90 percent o their speciied values. The live-load negative moments between points o permanent-load contralexure are then taken as the larger o the moments caused by the HL-9 loading or this special negative-moment loading. The speciication May, 004 Page 1 o 1

20 LRFD rd Edition is currently silent regarding spans without points o permanent-load contralexure. It is presumed that the special negative-moment loading should be considered over the entire span in such cases. Live-load shears in regions o positive and negative lexure are to be computed using the HL-9 loading only. However, interior-pier reactions are to be calculated based on the larger o the shears caused by the HL-9 loading or the special negative-moment loading. In all cases, axles that do not contribute to the extreme orce eects under consideration are to be neglected. For strength limit state and live-load delection checks, a percent dynamic load allowance (or impact actor) is applied only to the design truck or tandem portion o the HL-9 design live load or to the truck portion o the special negative-moment loading (Article.6.). The dynamic load allowance is not to be applied to the lane portion o the loadings. As a result, the dynamic load allowance implicitly remains a unction o the span length, although the span length is not explicitly used to compute the allowance. The live-load models discussed above are not intended to represent a particular truck, but rather they are intended to simulate the moments and shears produced by groups o vehicles routinely permitted on highways o various states under "grandather" exclusions to weight laws. The moment and shear eects rom these notional live-load models were compared to selected weigh-in-motion data, the results o truck weight studies, the Ontario Highway Bridge Design Code live-load model, and statistical projections o 75-year vehicles, and were ound to be representative when scaled by appropriate load actors. The current HS0 and HS5 vehicles by themselves were not considered to be accurate representations o the exclusion loads over a wide range o spans that were studied Loading or Optional Live-Load Delection Evaluation (Article.6.1..) The vehicular live load or checking the optional live-load delection criterion speciied in Article is taken as the larger o: the design truck alone. 5 percent o the design truck along with the design lane load. These loadings are used to produce apparent live-load delections similar to those produced by AASHTO HS0 design live loadings. It is assumed in the live-load delection check that all design lanes are loaded and that all supporting components are assumed to delect equally (Article.5..6.). The appropriate multiple presence actors speciied in Article (discussed later) are to be applied. For composite design, Article also permits the stiness o the design cross-section used or the determination o the delection to include the entire width o the roadway and the structurally continuous portions o any railings, sidewalks and barriers. The bending stiness o an individual girder may be taken as the stiness, determined as described above, divided by the number o girders. Live-load delection is checked using the live-load portion o the SERVICE I load combination (Table.4.1-1), including the appropriate dynamic load allowance Fatigue Load (Article.6.1.4) The vehicular live load or checking atigue in steel structures in the LRFD speciications consists o a single design truck (without the lane load) with a constant rear-axle spacing o 0 t (Article ). The atigue load is used to represent the variety o trucks o dierent types and weights in actual traic. The constant rear-axle spacing approximates that or the 4- and 5-axle semi-trailers that do most o the atigue damage to bridges. The AASHTO atigue-design procedures given in the Standard Speciications do not accurately relect actual atigue conditions in bridges; these procedures combine an artiicially high atigue stress range with an artiicially low number o stress cycles to achieve a reasonable design. The speciied atigue load in the LRFD speciications produces a lower calculated stress range than produced by the loadings in the Page 14 o 1 May, 004

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