Steel Bridge Design Handbook Vol. 21

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U.S. Department of TransportationFederal Highway AdministrationSteel Bridge Design HandbookDesign Example 2A:Two-Span Continuous StraightComposite Steel I-Girder BridgePublication No. FHWA-HIF-16-002 - Vol. 21December 2015

FOREWORDThis handbook covers a full range of topics and design examples intended to provide bridgeengineers with the information needed to make knowledgeable decisions regarding the selection,design, fabrication, and construction of steel bridges. Upon completion of the latest update, thehandbook is based on the Seventh Edition of the AASHTO LRFD Bridge Design Specifications.The hard and competent work of the National Steel Bridge Alliance (NSBA) and primeconsultant, HDR, Inc., and their sub-consultants, in producing and maintaining this handbook isgratefully acknowledged.The topics and design examples of the handbook are published separately for ease of use, andavailable for free download at the NSBA and FHWA websites: http://www.steelbridges.org, andhttp://www.fhwa.dot.gov/bridge, respectively.The contributions and constructive review comments received during the preparation of thehandbook from many bridge engineering processionals across the country are very muchappreciated. In particular, I would like to recognize the contributions of Bryan Kulesza withArcelorMittal, Jeff Carlson with NSBA, Shane Beabes with AECOM, Rob Connor with PurdueUniversity, Ryan Wisch with DeLong’s, Inc., Bob Cisneros with High Steel Structures, Inc.,Mike Culmo with CME Associates, Inc., Mike Grubb with M.A. Grubb & Associates, LLC, DonWhite with Georgia Institute of Technology, Jamie Farris with Texas Department ofTransportation, and Bill McEleney with NSBA.Joseph L. Hartmann, PhD, P.E.Director, Office of Bridges and StructuresNoticeThis document is disseminated under the sponsorship of the U.S. Department of Transportation inthe interest of information exchange. The U.S. Government assumes no liability for use of theinformation contained in this document. This report does not constitute a standard, specification,or regulation.Quality Assurance StatementThe Federal Highway Administration provides high-quality information to serve Government,industry, and the public in a manner that promotes public understanding. Standards and policiesare used to ensure and maximize the quality, objectivity, utility, and integrity of its information.FHWA periodically reviews quality issues and adjusts its programs and processes to ensurecontinuous quality improvement.

Technical Report Documentation Page1. Report No.2. Government Accession No.FHWA-HIF-16-002 - Vol. 214. Title and SubtitleSteel Bridge Design Handbook Design Example 2A: Two-SpanContinuous Straight Composite Steel I-Girder Bridge7. Author(s)Karl Barth, Ph.D. (West Virginia University)9. Performing Organization Name and AddressHDR, Inc.11 Stanwix StreetSuite 800Pittsburgh, PA 1522212. Sponsoring Agency Name and AddressOffice of Bridges and StructuresFederal Highway Administration1200 New Jersey Avenue, SEWashington, D.C. 205903. Recipient’s Catalog No.5. Report DateDecember 20156. Performing Organization Code8. Performing Organization Report No.10. Work Unit No.11. Contract or Grant No.DTFH6114D0004913. Type of Report and Period CoveredTechnical ReportFinal ReportDecember 2014 – November 201514. Sponsoring Agency Code15. Supplementary NotesThe previous version of this Handbook was published as FHWA-IF-12-052 and was developed to be current with the AASHTOLRFD Bridge Design Specifications, 5th Edition with the 2010 Interims. FHWA-HIF-16-002 was updated in 2015 by HDR,Inc., to be current with the AASHTO LRFD Bridge Design Specifications, 7th Edition.16. AbstractThe purpose of this example is to illustrate the use of the AASHTO LRFD Bridge Design for the design of a continuous two spansteel I-girder bridge. The design process and corresponding calculations for steel I-girders are the focus of this example, withparticular emphasis placed on illustration of the optional moment redistribution procedures. All aspects of the girder design arepresented, including evaluation of the following: cross-section proportion limits, constructibility, serviceability, fatigue, andstrength requirements. Additionally, the weld design for the web-to-flange joint of the plate girders is demonstrated along withall applicable components of the stiffener design and cross frame member design.17. Key WordsSteel Bridge, Steel I-Girder, AASHTO LRFD, MomentRedistribution, Cross Frame Design19. Security Classif. (of this report)UnclassifiedForm DOT F 1700.7 (8-72)18. Distribution StatementNo restrictions. This document is available to the public throughthe National Technical Information Service, Springfield, VA22161.20. Security Classif. (of this page)Unclassified21. No of Pages22. PriceReproduction of completed pages authorized

Steel Bridge Design Handbook Design Example 2A:Two-Span Continuous Straight Composite SteelI-Girder BridgeTable of Contents1.0INTRODUCTION . 12.0DESIGN PARAMETERS . 23.0GIRDER GEOMETRY . 43.1 Web Depth . 43.2 Web Thickness . 43.3 Flange Geometries . 54.0LOADS . 84.1 Dead Loads . 84.1.1Component Dead Load (DC) . 84.1.2Wearing Surface Dead Load (DW). 94.2 Vehicular Live Loads . 94.2.1General Vehicular Live Load (Article 3.6.1.2) . 104.2.2Optional Live Load Deflection Load (Article 3.6.1.3.2) . 104.2.3Fatigue Load (Article 3.6.1.4). 114.3 Wind Loads . 114.4 Load Combinations . 115.0STRUCTURAL ANALYSIS. 135.1 Multiple Presence Factors (Article 3.6.1.1.2) . 135.2 Live-Load Distribution Factors (Article 4.6.2.2) . 135.2.1Live-Load Lateral Distribution Factors – Positive Flexure . 135.2.1.1Interior Girder – Strength and Service Limit States . 155.2.1.1.1 Bending Moment . 155.2.1.1.2 Shear . 165.2.1.2Exterior Girder – Strength and Service Limit States . 16i

5.2.1.2.1 Bending Moment . 165.2.1.2.2 Shear . 195.2.1.3Fatigue Limit State . 205.2.1.3.1 Bending Moment . 205.2.1.3.2 Shear . 205.2.1.4Distribution Factor for Live-Load Deflection. 216.05.2.2Live-Load Lateral Distribution Factors – Negative Flexure. 215.2.3Dynamic Load Allowance . 23ANALYSIS RESULTS . 246.1 Moment and Shear Envelopes . 246.2 Live Load Deflection . 297.0LIMIT STATES . 307.1 Service Limit State (Articles 1.3.2.2 and 6.5.2). 307.2 Fatigue and Fracture Limit State (Article 1.3.2.3 and 6.5.3) . 307.3 Strength Limit State (Articles 1.3.2.4 and 6.5.4) . 307.4 Extreme Event Limit State (Articles 1.3.2.5 and 6.5.5) . 308.0SAMPLE CALCULATIONS . 318.1 Section Properties . 318.1.18.1.2Section 1 – Positive Bending Region. 318.1.1.1Effective Flange Width (Article 4.6.2.6) . 318.1.1.2Elastic Section Properties: Section 1 . 328.1.1.3Plastic Moment: Section 1 . 338.1.1.4Yield Moment: Section 1 . 34Section 2 – Negative Bending Region . 358.1.2.1Effective Flange Width (Article 4.6.2.6) . 358.1.2.2Minimum Negative Flexure Concrete Deck Reinforcement (Article6.10.1.7) 358.1.2.3Elastic Section Properties: Section 2 . 368.1.2.4Plastic Moment: Section 2 . 388.1.2.5Yield Moment: Section 2 . 398.2 Exterior Girder Check: Section 2 . 408.2.1Strength Limit State (Article 6.10.6) . 41ii

8.2.1.1Flexure (Appendix A6) . 418.2.1.2Moment Redistribution (Appendix B6, Articles B6.1 – B6.5) . 488.2.1.2.1 Web Proportions . 488.2.1.2.2 Compression Flange Proportions . 488.2.1.2.3 Compression Flange Bracing Distance . 498.2.1.2.4 Shear . 498.2.1.3Moment Redistribution - Refined Method (Appendix B6, Article B6.6)528.2.1.48.2.28.2.3Constructibility (Article 6.10.3) . 548.2.2.1Flexure (Article 6.10.3.2). 558.2.2.2Shear (Article 6.10.3.3) . 55Service Limit State (Article 6.10.4) . 568.2.3.18.2.4Shear (6.10.6.3) . 54Permanent Deformations (Article 6.10.4.2) . 56Fatigue and Fracture Limit State (Article 6.10.5) . 598.2.4.1Load Induced Fatigue (Article 6.6.1.2) . 598.2.4.2Distortion Induced Fatigue (Article 6.6.1.3) . 618.2.4.3Fracture (Article 6.6.2) . 618.2.4.4Special Fatigue Requirement for Webs (Article 6.10.5.3). 618.3 Exterior Girder Check: Section 1 . 618.3.1Constructibility (Article 6.10.3) . 618.3.1.1Deck Placement Analysis . 618.3.1.1.1 Strength I. 638.3.1.1.2 Special Load Combination (Article 3.4.2.1) . 638.3.1.2Deck Overhang Loads. 638.3.1.2.1 Strength I. 678.3.1.2.2 Special Load Combination (Article 3.4.2.1) . 688.3.1.3Flexure (Article 6.10.3.2). 698.3.1.3.1 Compression Flange: . 708.3.1.3.2 Tension Flange: . 738.3.1.4Shear (Article 6.10.3.3) . 738.3.2Service Limit State (Article 6.10.4) . 738.3.2.1Elastic Deformations (Article 6.10.4.1) . 748.3.2.2Permanent Deformations (Article 6.10.4.2) . 74iii

8.3.38.3.4Fatigue and Fracture Limit State (Article 6.10.5) . 758.3.3.1Load Induced Fatigue (Article 6.6.1.2) . 758.3.3.2Special Fatigue Requirement for Webs (Article 6.10.5.3). 76Strength Limit State (Article 6.10.6) . 768.3.4.1Flexure (Article 6.10.6.2). 768.3.4.2Ductility Requirement (6.10.7.3) . 778.3.4.3Shear (6.10.6.3) . 788.4 Cross-frame Design . 798.4.1Intermediate Cross-frame Design . 798.4.1.1Bottom Strut . 808.4.1.1.1 Combined Axial Compression and Bending. 828.4.1.2Diagonals . 838.4.2End Cross-frame Design . 848.4.2.1Top Strut . 858.4.2.1.1 Strength I:. 878.4.2.1.2 Strength III: . 908.4.2.1.3 Strength V: . 928.4.2.2Diagonals . 928.4.2.2.1 Strength I:. 938.4.2.2.2 Strength III: . 938.4.2.2.3 Strength V: . 938.4.2.2.4 Combined Axial Compression and Flexure . 948.5 Stiffener Design . 968.5.1Bearing Stiffener Design. 968.5.1.1Projecting Width (Article 6.10.11.2.2) . 988.5.1.2Bearing Resistance (Article 6.10.11.2.3) . 988.5.1.3Axial Resistance of Bearing Stiffeners (Article 6.10.11.2.4) . 998.5.1.4Bearing Stiffener-to-Web Welds . 1018.6 Flange-to-Web Weld Design . 1019.08.6.1Steel Section: . 1028.6.2Long-term Section: . 1028.6.3Short-term Section: . 102References . 105iv

List of FiguresFigure 1 Sketch of the Typical Bridge Cross Section . 2Figure 2 Sketch of the Superstructure Framing Plan . 3Figure 3 Sketch of the Girder Elevation . 4Figure 4 Sketch of Section 1, Positive Bending Region . 14Figure 5 Sketch of the Truck Location for the Lever Rule . 17Figure 6 Sketch of the Truck Locations for the Special Analysis . 19Figure 7 Sketch of Section 2, Negative Bending Region . 22Figure 8 Dead and Live Load Moment Envelopes . 24Figure 9 Dead and Live Load Shear Envelopes. 25Figure 10 Fatigue Live Load Moments . 25Figure 11 Fatigue Live Load Shears . 26Figure 12 AASHTO LRFD Moment-Rotation Model. 52Figure 13 Determination of Mpe Using Refined Method . 53Figure 14 Determination of Rotation at Pier Assuming No Continuity . 54Figure 15 Deck Placement Sequence . 62Figure 16 Deck Overhang Bracket Loads . 64Figure 17 Intermediate Cross Frame. 79Figure 18 Single Angle for Intermediate Cross Frame . 80Figure 19 End Cross Frame . 85Figure 20 Live load on Top Strut. 87v

List of TablesTable 1 Section 1 Steel Only Section Properties . 15Table 2 Positive Bending Region Distribution Factors (lanes) . 21Table 3 Section 2 Steel Only Section Properties . 22Table 4 Negative Bending Region Distribution Factors . 23Table 5 Unfactored and Undistributed Moments (kip-ft) . 26Table 6 Unfactored and Undistributed Live Load Moments (kip-ft) . 27Table 7 Strength I Load Combination Moments (kip-ft) . 27Table 8 Service II Load Combination Moments (kip-ft) . 27Table 9 Unfactored and Undistributed Shears (kip) . 28Table 10 Unfactored and Undistributed Live Load Shears (kip) . 28Table 11 Strength I Load Combination Shear (kip). 28Table 12 Section 1 Short Term Composite (n) Section Properties (Exterior Girder) . 32Table 13 Section 1 Long Term Composite (3n) Section Properties (Exterior Girder) . 32Table 14 Section 2 Short Term Composite (n) Section Properties . 37Table 15 Section 2 Long Term Composite (3n) Section Properties . 37Table 16 Section 2 Steel Section and Longitudinal Reinforcement Section Properties . 38Table 17 Moments from Deck Placement Analysis (kip-ft) . 62vi

1.0 INTRODUCTIONThe purpose of this example is to illustrate the use of the Seventh Edition of the AASHTO LRFDBridge Design Specifications [1], referred to herein as AASHTO LRFD (7th Edition, 2014) forthe design of a continuous steel I-girder bridge. The design process and correspondingcalculations for steel I-girders are the focus of this example, with particular emphasis placed onillustration of the optional moment redistribution procedures. All aspects of the girder design arepresented, including evaluation of the following: cross-section proportion limits, constructibility,serviceability, fatigue, and strength requirements. Additionally, the weld design for the web-toflange joint of the plate girders is demonstrated along with all applicable components of thestiffener design and cross-frame design.The moment redistribution procedures allow for a limited degree of yielding at the interiorsupports of continuous-span girders. The subsequent redistribution of moment results in adecrease in the negative bending moments and a corresponding increase in positive bendingmoments. The current moment redistribution procedures utilize the same moment envelopes asused in a conventional elastic analysis and do not require the use of iterative procedures orsimultaneous equations. The method is similar to the optional provisions in previous AASHTOspecifications that permitted the peak negative bending moments to be decreased by 10% beforeperforming strength checks of the girder. However, in the present method this empiricalpercentage is replaced by a calculated quantity, which is a function of geometric and materialproperties of the girder. Furthermore, the range of girders for which moment redistribution isapplicable is expanded compared to previous editions of the specifications, in that girders withslender webs may now be considered. The result of the use of these procedures is considerableeconomical savings. Specifically, inelastic design procedures may offer cost savings by (1)requiring smaller girder sizes, (2) eliminating the need for cover plates (which have unfavorablefatigue characteristics) in rolled beams, and (3) reducing the number of flange transitions withoutincreasing the amount of material required in plate girder designs, leading to both material and,more significantly, fabrication cost savings.1

2.0 DESIGN PARAMETERSThe bridge cross-section for the tangent, two-span (90 ft - 90 ft) continuous bridge underconsideration is given below in Figure 1. The example bridge has four plate girders spaced at10.0 ft and 3.5 ft overhangs. The roadway width is 34.0 ft and is centered over the girders. Thereinforced concrete deck is 8.5 inch thick, including a 0.5 inch integral wearing surface, and hasa 2.0 inch haunch thickness.The framing plan for this design example is shown in Figure 2. As will be demonstratedsubsequently, the cross frame spacing is governed by constuctibility requirements in positivebending and by moment redistribution requirements in negative bending.The structural steel is ASTM A709, Grade 50W, and the concrete is normal weight with a 28-daycompressive strength, f′c, of 4.0 ksi. The concrete slab is reinforced with nominal Grade 60reinforcing steel.The design specifications are the AASHTO LRFD (7th Edition, 2014) Bridge DesignSpecifications. Unless stated otherwise, the specific articles, sections, and equations referencedthroughout this example are contained in these specifications.The girder design presented herein is based on the premise of providing the same girder designfor both the interior and exterior girders. Thus, the design satisfies the requirements for bothinterior and exterior girders. Additionally, the girders are designed assuming composite actionwith the concrete slab.Figure 1 Sketch of the Typical Bridge Cross Section2

Figure 2 Sketch of the Superstructure Framing Plan3

3.0 GIRDER GEOMETRYThe girder elevation is shown in Figure 3. As shown in Figure 3, section transitions are providedat 30% of the span length (27 feet) from the interior pier. The design of the girder from theabutment to 63 feet from the abutment is primarily based on positive bending moments; thus, thissection of the girder is referred to as either the “positive bending region” or “Section 1”throughout this example. Alternatively, the girder geometry at the pier is controlled by negativebending moments; consequently the region of the girder extending from 0 to 27 feet on each sideof the pier will be referred to as the “negative bending region” or “Section 2”. The rationale usedto develop the cross-sectional geometry of these sections and a demonstration that this geometrysatisfies the cross-section proportion limits specified in Article 6.10.2 is presented herein.3.1 Web DepthSelection of appropriate web depth has a significant influence on girder geometry. Thus, initialconsideration should be given to the most appropriate web depth. In the absence of other criteriathe span-to-depth ratios given in Article 2.5.2.6.3 may be used as a starting point for selecting aweb depth. As provided in Table 2.5.2.6.3-1, the minimum depth of the steel I-beam portion of acontinuous-span composite section is 0.027L, where L is the span length. Thus, the minimumsteel depth is computed as follows.0.027(90 ft)(12 in./ft) 29.2 inchesPreliminary designs were evaluated for five different web depths satisfying the aboverequirement. These web depths varied between 36 inches and 46 inches and in all cases girderweight decreased as web depth increased. However, the decrease in girder weight became muchless significant for web depths greater than 42 inches.Figure 3 Sketch of the Girder Elevation3.2 Web ThicknessThe thickness of the web was selected to satisfy shear requirements at the strength limit statewithout the need for transverse stiffeners. This resulted in a required web thickness of 0.5 inch at4

the pier and 0.4375 inch at the abutments. The designer may also want to examine the economyof using a constant 0.5 inch web throughout.In developing the preliminary cross-section it should also be verified that the selecteddimensions satisfy the cross-section proportion limits required in Article 6.10.2. The requiredweb proportions are given in Article 6.10.2.1 where, for webs without longitudinal stiffeners, theweb slenderness is limited to a maximum value of 150.D 150twEq. (6.10.2.1.1-1)Thus, the following calculations demonstrate that Eq. 6.10.2.1.1-1 is satisfied for both thepositive and negative moment regions of the girder, respectively.D42 96 150t w 0.4375(satisfied)D 42 84 150t w 0.5(satisfied)3.3 Flange GeometriesThe width of the compression flange in the positive bending region was controlled byconstructibility requirements as the flange lateral bending stresses are directly related to thesection modulus of the flange about the y-axis of the girder as well as the cross-frame spacing.Various cross-frame distances were investigated and the corresponding flange width required tosatisfy constructibility requirements for each case was determined. Based on these efforts it wasdetermined that a minimum flange width of 14 in. was needed to avoid the use of additionalcross-frames. Thus, this minimum width was used for the top flanges.All other plate sizes were iteratively selected to satisfy all applicable requirements whileproducing the most economical girder