Guidelines for Analysis Methods and Construction Engineering of Curved and Skewed Steel Girder Bridges (2012)

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.

A P P E N D I X B Task 9 Report—Recommendations for Construction Plan Details and Level of Construction Analysis

N a t i o N a l c o o p e r a t i v e H i g H w a y r e s e a r c H p r o g r a m project no. NcHrp 12-79 Recommendations for Construction Plan Details and Level of Construction Analysis TASK 9 REPORT Prepared for NCHRP Transportation Research Board Of The National Academies Brandon W. Chavel HDR EnginEERing, inc. Chicago, IL Domenic Coletti HDR EnginEERing, inc. Raleigh, NC Donald W. White gEoRgia institutE of tEcHnology Atlanta, GA February 29, 2012 TRAnsPoRTAT ion ReseARCh BoARD WAshingTon, D.C. 2006 www.TRB.org

C o n t e n t s B-1 summary B-2 Chapter 1 introduction B-2 1.1 Problem Statement B-2 1.2 Objectives B-2 1.3 Organization B-3 Chapter 2 Recommendations for Construction Plan Details B-3 2.1 Introduction B-3 2.2 Erection Procedure Drawings Recommendations B-8 2.3 Erection Plan and Procedures Checklist B-9 Chapter 3 Recommendations for Methods of structural Analysis and Calculations B-9 3.1 Introduction B-9 3.2 Recommendations on Methods of Analysis B-18 3.3 Guidelines on Calculations for Structural Adequacy and Stability B-22 3.4 Structural Adequacy of Temporary Components B-22 3.5 Miscellaneous Calculations and Recommendations B-24 3.6 Calculation Checklist B-24 3.7 Problematic Characteristics and Details to Avoid B-26 References

B-1 s U M M A R Y Difficulties can arise during the construction of curved and skewed steel girder bridges when an erection plan does not contain sufficient details or when the construction analy sis does not properly account for the three-dimensional behavior of the structure. The erection plan, con- struction analysis, and other computations for curved and skewed steel girder bridges must be sufficient to account for the complex behavior of these bridge types. This document provides recommendations regarding the content of construction plans for curved and skewed steel I-girder bridges. Guidelines for selecting the appropriate methods of analysis for the construction analysis of I-girder and tub-girder bridges are also provided. The guidelines for selecting the appropriate methods of analysis focus on commonly used 1D, 2D, and 3D analytical approaches in current structural engineering practice (2011). Guidelines per- taining to the calculations developed to support the erection plan and procedures also are pro- vided within this document. This document focuses on the plans, analysis methods, and other calculations conducted for the construction engineering of curved and/or skewed steel girder bridges. It does not address the wide range of additional overall considerations in the complete design and analysis of these types of bridges, such as the design of the structure in its final con- structed condition for vehicular live load effects. The major objectives of these recommendations are to help engineers: 1. Ensure that construction plans, methods of analysis, and other calculations for curved and/ or skewed steel girder bridges, as affected by the structure’s geometry and other construction conditions, are generally sufficient for predicting the constructed geometry (to facilitate fit-up), 2. Ensure stability during all stages of erection, and 3. Achieve better consistency in construction plans, methods of analysis, and other calculations for a given degree of the bridge’s geometric, structural, and construction complexity. Contractors and Contractors’ Engineers can use this document as a guide in developing con- struction plans, performing calculations, and selecting the appropriate analysis methods. Bridge Owners can use this document as a checklist to verify that the Contractor and the Contractor’s Engineer have developed an appropriate construction plan and calculation submittal. Recommendations for Construction Plan Details and Level of Construction Analysis

B-2 C H A P t e R 1 1.1 Problem Statement In current practice (2011), the construction of curved and/or skewed steel girder bridges is sometimes hampered by insufficient erection plans and procedures or computations. Within the industry, little has been published in the way of guidelines or recommendations on the level of detail for construction plans for curved and/or skewed steel girder bridges, or on the level of detail regarding engineering calculations for the construction engineering. Furthermore, the industry is lacking guidelines on choosing the proper analytical methods for investigating the steel erection sequence of curved and/or skewed steel girder bridges. 1.2 Objectives This document outlines key recommendations regarding the level of effort for development of construction plans and calculations for curved and/or skewed steel girder bridges at the construction engineering stage. This document also provides recommendations regarding the appropriate methods of structural analysis for evaluating the structural behavior and predicted geometry of the bridge during the various stages of construction. This document is written in an effort to make the development of construction plans, calcu- lations, and methods of analysis more consistent for curved and/or skewed steel girder bridges. Contractors and Contractors’ Engineers can use this document to guide them in developing con- struction plans, performing calculations, and selecting the appropriate analysis methods. Bridge Owners can use this document as a checklist to verify that the Contractor and the Contractor’s Engineer have developed an appropriate construction plan and calculation submittal. 1.3 Organization This report is divided into two main sections. Section 2 provides recommenda tions regarding the level of detail that should be used in the development of erection plans and procedures for curved and/or skewed steel girder bridges. This section is written in a style and format similar to design code provisions, including the development of Commentary sections for many of the erection plan recommendations. Section 3 defines the levels of construction analysis that should be considered for curved and skewed steel girder bridges based upon the complexity of the structure. These guidelines are summarized from the studies conducted as part of NCHRP Project 12-79, “Guidelines for Ana- lytical Methods and Erection Engineering of Curved and Skewed Steel Deck-Girder Bridges.” This section also provides details regarding particular calculations for consideration by engi- neers developing construction plans and procedures. introduction

B-3 C H A P t e R 2 2.1 Introduction The AASHTO/NSBA Steel Bridge Collaboration document S10.1, “Steel Bridge Erection Guide Specification,” (AASHTO/NSBA, 2007) highlights the minimum requirements for the develop- ment of steel girder erection procedures, including steel erection drawings and calculations. The recommendations provided herein use and build upon this AASHTO/NSBA document based on studies conducted as part of NCHRP Project 12-79. Contractors and Engineers developing erection plans for steel erectors are encouraged to use these recommendations so that erection plans are uniform and complete. Bridge Owners are encouraged to adopt these recommenda- tions as a guide to verify that erection plans submitted by the Contractor contain the necessary details and procedures. 2.2 Erection Procedure Drawings Recommendations 2.2.1 General The Contractor shall submit a detailed erection plan and procedures to the Owner for each structural unit, prepared by or under the supervision of a licensed Professional Engineer (or a qualified Structural Engineer where applicable). The detailed erection plan and procedures shall contain drawings and calculations (see Section 3) that support the erection plan and procedures. The plan and procedures shall address all requirements for erection of the structural steel into the final designed configuration and satisfy all written Owner comments prior to the start of erection. As a minimum, the erection plan and procedures shall include the items cited in the sections that follow. 2.2.1.1 General—Commentary The qualifications of the Engineer preparing the erection plan and procedures should reflect knowl- edge, training, and experience in steel erection, and demonstrated abilities to resolve problems related to steel bridge erection. Complex or monumental structures should have specific requirements noted in the Contract. The erection procedure should be submitted as soon as possible after the Contract award. The submission dates and review period should be agreed upon by the Owner and the Contractor as soon as possible after the Contract award, so that sufficient time is allotted for review by the Owner. Erectors are encouraged to attend prebid and preconstruction meetings to help understand the com- plexities associated with the steel erection well in advance. Projects that involve complex erection or multi-agency reviews can be expected to require additional time for review of the submitted erection plan and procedure. In these cases, submission dates and review periods should be agreed upon by the Contractor and all agencies conducting reviews. Furthermore, in some cases, coordination with the Fabricator and Detailer may be necessary, as the preparation of shop detailing drawings and geomet- ric calculations will be delayed until the erection plan and procedure is approved. Recommendations for Construction Plan Details

B-4 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges 2.2.2 Plan of Work Area The erection plan shall contain a plan of the work area showing the bridge, the permanent support structures (piers and abutments), roads, railroad tracks, waterways (including dimen- sions for navigational channel, and navigational clearance required during construction), over- head and underground utilities, structures and conditions that may limit access, right-of-way and property lines, material (steel) storage areas, and other information that may be pertinent to the steel erection. 2.2.2.1 Plan of Work Area—Commentary The plan of work area drawing should provide a general overview of the area where the bridge is to be erected. It allows all involved to see site conditions, access routes and staging areas, as well as utilities, roadways, existing structures, or other possible site constraints and better understand why a certain procedure or detail is specified within the erection plans and procedures. 2.2.3 erection sequence The erection plan shall contain the erection sequence for all members noting the use of tem- porary support conditions, such as holding crane positions, temporary supports, falsework, etc. The erection sequence shall be shown in an illustrative plan view of the bridge for each erection stage, highlighting the structural components to be erected, lifting crane locations for primary member picks, and any temporary support conditions that are necessary during the particular stage. The illustrative plan view shall be accompanied with a written narrative of the procedure to be followed by the steel erector, which shall clearly state items such as structural components to be erected, use of temporary supports, use of temporary bracing, hold cranes, etc. Member reference marks, when reflected on the erection plan, should be the same as used on the shop detail drawings. 2.2.3.1 Erection Sequence—Commentary The erection sequence should clearly indicate specific structural components to be erected at a given stage, such as the girders, cross frames, lateral bracing, etc. The erection sequence should also clearly indicate lifting crane positions, as well as any temporary support conditions necessary to facilitate a certain erection stage, such as temporary supports, holding crane positions, tie-down stability provisions, blocking of the bearings, etc. The erection sequence drawings should be treated as the detailed instructions for construction of the bridge and should be written as, and followed as, mandatory directives. If an item is not clearly shown or described, problems could arise during steel erection. 2.2.4 Delivery Location The erection plan shall indicate the primary member delivery location and orientation. 2.2.4.1 Delivery Location—Commentary The maximum crane lift radius is often controlled by the material delivery location, hence it is necessary to indicate the delivery location on the erection plan. 2.2.5 Crane information The erection plan shall show the location of each crane to be used for each primary member pick (see Section 2.2.3), the crane type, the crane pick radius, the crane support methods (mats, barges, etc.), and the means of attachment to the girders being lifted or supported.

Appendix B B-5 The erection drawings also shall show a capacity chart or table for each crane configuration, boom length, counterweight requirements, and pick weights required to do the proposed work. The erection drawings also shall indicate any potential obstructions to crane operations such as existing structures, utilities, etc. Any calculations related to evaluation of crane capacity and crane stability also shall be included. The crane types shall be agreed upon by the Contractor and Contractor’s Engineer, to ensure that the crane types are available to the Contractor and can access the work site. 2.2.5.1 Crane Information—Commentary When the steel erection takes place on a navigable waterway, the configuration of the barge(s), loading sequence, and stability provisions (tie-downs, piles, etc.) shall be provided in the erection plan. Communication between the Contractor and the Contractor’s Engineer is vital to ensure the cranes assumed by the Engineer are available to the Contractor. Providing the crane types, pick radii, pick weight, boom lengths, possible obstructions, etc., in the erection plans will help to prevent crane interferences, overloads, or failures during the steel erection. 2.2.6 Primary Member Crane Pick information The erection plan shall include the lifting weight of the primary member picks, including all rigging and pre-attached elements (such as cross-frames or splice plates). The erection plan shall also include the approximate center of gravity locations for the primary member picks of curved girders and assemblies. 2.2.6.1 Primary Member Crane Pick Information—Commentary The lifting weights and the approximate centers of gravity for each pick will provide the steel erector with necessary information to safely lift various components. The centers of gravity provided on the plans should be taken as approximate locations, as these are typically calculated assuming nominal material sizes and approximations of minor items such as bolted connections, etc. The actual center of gravity locations should reasonably match these approximate locations and will aid the steel erector in determining the proper lifting location in the field. 2.2.7 Lifting Devices and special Procedures The erection plan shall include the details, weight, capacity, and arrangement of all rigging (beam clamps, lifting lugs, etc.) and all lifting devices (such as spreader and lifting beams) required for lifting primary members. The erection plan also shall specify whether rigging or lifting devices are to be bolted or welded to permanent members, including the method and time (shop or field) of attachment and capacity, as well as methods, time, and responsibility for removal. As necessary, the erection plan shall provide special lifting/handling procedures for any pri- mary member with potential stability or slenderness issues. 2.2.7.1 Lifting Devices and Special Procedures—Commentary Assumptions regarding the weight of rigging, spreader beams, etc., should be included in the erection plan. Explicitly indicating all details related to rigging and spreader or lifting beams will help to ensure that the appropriate devices are being properly used in the field. Straight slender beams, traditionally defined as those having a length of the shipping piece to flange width ratio (L/b) greater than 85, are prone to lateral torsional buckling and require particu- lar attention during lifting/handling operations. This limiting length to flange width ratio for curved beams is smaller than 85, and in some cases has been taken as low as a value of 10. The flange width

B-6 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges (b) should be taken as the smallest width flange within the field section being lifted. Other types of structural members also may have slenderness and/or stability issues that should be addressed in the erection plans as appropriate. 2.2.8 Bolting Requirements The erection plan shall indicate the bolting requirements for field splices and cross-frame (or diaphragm) connections. For bolted splice connections of primary members, and bolted connections of diaphragms or cross frames that brace I-girders, fill at least 50 percent of holes in the connection prior to crane release with either erection bolts in a snug tight condition, or full-size erection pins (a.k.a., “drift pins”), using bolts for at least half of the filled holes (i.e., at least 25 percent of all holes). Sufficient erection pins shall be used near the outside corners of splice plate and at member ends near splice plate edges to ensure alignment. The filled holes shall be uniformly distributed across the connection. 2.2.8.1 Bolting Requirements—Commentary Steel I-girders depend on their connections to adjacent girders through bracing members for their stability and stiffness during steel erection. This is especially true for curved steel girders, as the cross frames serve as primary load carrying members. Therefore, loosely connected cross frames should not be used during steel girder bridge erection, as this may compromise the girder alignment (geometry control) and stability. The bolting requirements for girder field splices during steel erection need to be considered as well. In accordance with the AASHTO LRFD Bridge Construction Specifications, Article 11.6.5, “splices and field connections shall have one-half of the holes filled with bolts and cylindrical erection pins (half bolts and half pins) before installing and tightening the balance of the high strength bolts.” In addition, the Contractor’s Engineer developing the erection plan must ensure that the number of bolts or erection pins to be used provides enough capacity for transfer of loads for the given stage of steel erection. 2.2.9 Bearing Blocking and Tie-Down Details The erection plan shall indicate the blocking and/or tie-down details for the bridge bearings, as necessary. 2.2.9.1 Bearing Blocking Details—Commentary Depending on their details, bridge bearings may allow movement (translation) in any direction and/or rotation about any axis. During steel erection, in addition to other stability provisions, the bearings may require blocking to prevent or limit the translational movements and rotations. In addition, bearings may need temporary tie-downs to prevent uplift at various stages during construction. The Contractor’s Engineer (CE) should determine the blocking and/or tie down requirements such that the structure remains stable during all stages of erection and such that the behavior of the physical structure is consistent with the behavior assumed in the analysis and the erection plans. The CE should ensure that the bearings are not overloaded or over-rotated at any stage during the construction. 2.2.10 Load Restrictions Restrictions regarding wind and construction dead and live loadings shall be included on the erection plan, as necessary.

Appendix B B-7 2.2.10.1 Load Restrictions—Commentary Limits may be placed on wind velocities during lifting of girder field pieces or during various stages of erection when the structure is only partially complete. The limitations on wind velocities are intended to prevent girder overstress and/or instabilities that could be caused by certain wind speeds and the associated wind pressure loading. Calculations may show that a girder or girder system may not be stable at a certain wind velocity, and this needs to be communicated to the Contractor and Steel Erector via the erection plan. If appropriate, the erection plans should include instructions and details for temporary support or tie-down of partially completed structures during high wind conditions. The erection plans should also explicitly state restrictions on construction live loads (vehicles, equipment, personnel, etc.) and construction dead loads (formwork/falsework, stored materials, etc.). Inadvertent overloading by construction loads can affect the geometry control and also can lead to structural collapse. 2.2.11 Temporary supports The erection plan shall include the location of any temporary support structures (see Sec- tion 2.2.3), as well as details of the temporary support structure itself. If the temporary sup- port is to be prefabricated (selected from a supplier’s catalogue), the type and capacity shall be clearly defined in the erection plan; lateral capacity as well as vertical capacity requirements shall be considered as appropriate. If the temporary support is to be constructed by the Con- tractor on site, a complete design with full details, including member sizes, connections, and bracing elements, shall be provided in the erection plans. In either case, details regarding the upper grillage and temporary bearing assembly (i.e., details of how the steel girders will bear on the temporary support) also shall be included in the erection plan. In addition, all founda- tion requirements for temporary support structures shall be provided in the erection plan. The erection plan shall indicate the location of hold cranes used to provide temporary support to the steel assembly (see Sections 2.2.3 and 2.2.5). The hold crane type, capacity, boom lengths, pick radius, and means of attachment to the girders also shall be indicated in the erection plan. The erection plan shall include the location and details for temporary tie-downs that are required to facilitate the steel erection. At a minimum, the details shall include the tie-down, girder attachment devices, and anchoring devices. 2.2.11.1 Temporary Supports—Commentary In many cases, temporary supports are essential for the construction of a steel girder bridge. As such, they should be clearly detailed in the erection plan, whether the support is a falsework tower, hold crane, tie-down, bearing blocking, or other support. 2.2.12 Jacking Devices The erection plan shall indicate jacking devices required to complete the steel erection. Their location, type, size, and capacity shall be clearly indicated on the erection plan, as well as their intended use, sequence of engagement, load level, and any other key parameters of their operation. 2.2.12.1 Jacking Devices—Commentary In some cases, jacking devices may be required at temporary support structures, or at the permanent supports, for alignment of the structure during the erection process. If the erection plan does indeed require jacking devices, they should be clearly indicated in the erection plan to alert the Contractor to their need, and their intended use should be explicitly presented.

B-8 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges 2.3 Erection Plan and Procedures Checklist •• Plan of Work Area – Permanent and temporary structures shown – All roads, railroad tracks, waterways, clearances, utilities, potential conflicts shown – Material (steel) storage areas shown •• Erection Sequence – Step-by-step procedure–figures and narrative dictating work – Delivery location of components shown – Crane locations shown – Temporary support, hold cranes, blocking, tie-downs shown – Load restrictions for certain stages (i.e., wind) •• Crane Information – Crane type, pick radii, boom length shown – Approximate crane pick points shown – Crane pick weights shown – Hold crane loads •• Details of Lifting Devices and Special Procedures •• Bolting Requirements •• Bearing Blocking and Tie-Down Details •• Temporary Supports – Details of structure shown – Load capacities •• Jacking Devices and Procedures

B-9 C H A P t e R 3 3.1 Introduction Calculations by the Contractor’s Engineer investigating the steel erection sequence are required to substantiate the erection plan and procedures submitted for a given project. This section pres- ents guidelines regarding these calculations. It also provides recommendations on the appropri- ate methods of analysis to employ when investigating the adequacy of the erection sequence of a curved or skewed steel girder bridge. These guidelines and recommendations are a synthesis of studies conducted as part of NCHRP Project 12-79, “Guidelines for Analytical Methods and Erec- tion Engineering of Curved and Skewed Steel Deck-Girder Bridges.” Detailed background to these guidelines can be found in the Task 8 report of Project 12-79, “Guidelines for Selecting Analytical Methods for Construction Engineering of Curved and Skewed Steel Girder Bridges.” 3.2 Recommendations on Methods of Analysis A substantial number of studies were conducted as part of NCHRP Project 12-79 to determine the ability of approximate 1D and 2D methods of analysis to capture the behavior predicted by refined 3D finite element models. To evaluate 1D methods, a commonly available commercial line-girder analysis program, STLBRIDGE (Bridgesoft, 2010), was used to analyze the behavior of straight skewed I- and tub-girder bridges. The 1D analysis of curved, and curved and skewed, I-girder bridges was based on the V-load method (Richardson, Gordon & Associates, 1976; United States Steel, 1980) using the software VANCK (NSBA, 1996). The 1D analysis of curved, and curved and skewed, tub-girder bridges was based on a line-girder analysis coupled with additional calculations based on the M/R method (Tung and Fountain, 1970). To evaluate 2D methods, two commercially available software programs, typically employed by bridge designers, were used to investigate the behavior of these same bridges: the software MDX (MDX, 2011) for analysis using a conventional 2D-grid approach and the capabilities of LARSA-4D (LARSA, 2010) for analysis using a conventional 2D-frame approach. To evaluate linear elastic 3D finite element analysis methods, the software program ABAQUS was used to investigate the behavior of these same bridges. The 1D, 2D, and linear elastic 3D analysis results were compared to benchmark nonlin- ear “simulation” 3D finite element analysis solutions, also prepared using the software program ABAQUS, including the modeling of 2nd-order effects (geometric nonlinearity). Where possible, extant bridges were evaluated and if those bridges had been instrumented, the nonlinear simula- tion benchmark analysis results were validated against measured responses. 3.2.1 i-Girder Bridges A quantitative assessment of the analysis accuracy was obtained by identifying error measures that compared the approximate (1D and 2D methods) solutions to the 3D FEA benchmark Recommendations for Methods of structural Analysis and Calculations

B-10 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges solutions. Using the quantitative assessments, the various methods of analysis were ranked based on a scoring system developed to provide a comparative evaluation of each analysis method with regard to the accuracy of its analysis predictions for various structural responses. Table 3.1 summarizes the scoring system for the various methods and behaviors monitored. The scoring criteria are as follows: •• A grade of A is assigned when the normalized mean error is less than or equal to 6 percent, reflecting excellent accuracy of the analysis predictions. •• A grade of B is assigned when the normalized mean error is between 7 percent and 12 per- cent, reflecting a case where the analysis predictions are in “reasonable agreement” with the benchmark analysis results. Traditional 2D-Grid 1D-Line Girder Traditional 2D-Grid 1D-Line Girder C ( I C < 1) B B A B C ( I C > 1) D C B C S ( I S < 0.30) B B A A S (0.30 < I S < 0.65) B C B B S ( I S > 0.65) D D C C C&S ( I C > 0.5 & I S > 0.1) D F B C C ( I C < 1) B C A B C ( I C > 1) F D F C S ( I S < 0.30) B A A A S (0.30 < I S < 0.65) B B A B S ( I S > 0.65) D D C C C&S ( I C > 0.5 & I S > 0.1) F F F C C ( I C < 1) C C B B C ( I C > 1) F D C C S ( I S < 0.30) NA a NA a NA a NA a S (0.30 < I S < 0.65) F b F c F b F c S ( I S > 0.65) F b F c F b F c C&S ( I C > 0.5 & I S > 0.1) F b F c F b F c C ( I C < 1) C C B B C ( I C > 1) F D C C S ( I S < 0.30) NA d NA d NA d NA d S (0.30 < I S < 0.65) F b F e F b F e S ( I S > 0.65) F b F e F b F e C&S ( I C > 0.5 & I S > 0.1) F b F e F b F e C ( I C < 1) NA f NA f NA f NA f C ( I C > 1) NA f NA f NA f NA f S ( I S < 0.30) B A A A S (0.30 < I S < 0.65) B B A B S ( I S > 0.65) D D C C C&S ( I C > 0.5 & I S > 0.1) F F F C Response Geometry Worst-Case Scores Mode of Scores Major-Axis Bending Stresses Vertical Displacements Cross-Frame Forces Flange Lateral Bending Stresses Girder Layover at Bearings a Magnitudes should be negligible for bridges that are properly designed & detailed. The cross-frame design is likely to be controlled by considerations other than gravity-load forces. b Results are highly inaccurate due to modeling deficiencies addressed in Ch. 6 of the NCHRP 12-79 Task 8 report. The improved 2D-grid method discussed in this Ch. 6 provides an accurate estimate of these forces. c Line-girder analysis provides no estimate of cross-frame forces associated with skew. d The flange lateral bending stresses tend to be small. AASHTO Article C6.10.1 may be used as a conservative estimate of the flange lateral bending stresses due to skew. e Line-girder analysis provides no estimate of girder flange lateral bending stresses associated with skew. f Magnitudes should be negligible for bridges that are properly designed & detailed. table 3.1 Matrix for recommended Level of Analysis – I-Girder Bridges.

Appendix B B-11 •• A grade of C is assigned when the normalized mean error is between 13 percent and 20 per- cent, reflecting a case where the analysis predictions start to deviate “significantly” from the benchmark analysis results. •• A grade of D is assigned when the normalized mean error is between 21 percent and 30 per- cent, indicating a case where the analysis predictions are poor, but may be considered accept- able in some situations. •• A grade of F is assigned if the normalized mean errors are above the 30 percent limit. At this level of deviation from the benchmark analysis results, the subject approximate analysis method is considered unreliable and inadequate for design. The normalized mean error is calculated as 1 • max 1N R ee FEA ii N∑µ = = where N is the total number of sampling points along the length in the approximate model, RFEAmax is the absolute value of the maximum response obtained from the FEA, and ei is the absolute value of the error relative to the 3D FEA benchmark solution evaluated at point i: e R Ri approx FEA= − The summation in the above is computed for each girder line along the full length of the bridge, and the largest resulting value is reported as the normalized mean error for the bridge. The error measure µe is useful for the overall assessment of the analysis accuracy since this mea- sure is insensitive to isolated discrepancies, which can be due to minor shifting of the response predictions, etc. The normalized local maximum errors, ei /RFEAmax are generally somewhat larger than the normalized mean error. Also, in many situations, unconservative error at one location in the bridge leads to comparable conservative error at another location. Hence, it is simpler to not consider the sign of the error as part of the overall assessment of the analysis accuracy. In Table 3.1, the scoring for the various measured responses is subdivided into six categories based on the bridge geometry. These bridge categories are defined as follows: •• Curved bridges with no skew are identified in the Geometry column by the letter “C.” •• The curved bridges are further divided into two subcategories, based on the connectivity index, IC defined as: I R n m C cf = +( ) 15000 1 where R is the minimum radius of curvature, ncf is the number of intermediate cross-frames in the span, and m is a constant taken equal to 1 for simple-span bridges and 2 for continuous- span bridges. In bridges with multiple spans, IC is taken as the largest value obtained from any of the spans. •• Straight-skewed bridges with no curvature are identified in the geometry column by the letter “S.” •• The straight-skewed bridges are further divided into three subcategories, based on the skew index, IS. where IS is taken as: I w L S s = tanθ where w is the width of the bridge measured between fascia girders, q is the skew angle mea- sured from a line perpendicular to the tangent of the bridge centerline, and Ls is the span

B-12 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges length at the bridge centerline. In bridges with unequal skew at the bearing lines, q is taken as the angle of the bearing line with the largest skew. •• Bridges that are both curved and skewed are identified in the geometry column by the letters “C&S.” Two letter grades are indicated for each of the cells in Table 3. The first letter grade corresponds to the worst-case results encountered from either of the two 2D-grid solutions considered in the NCHRP Project 12-79 studies, or from the 1D-line girder calculations, within each of the speci- fied categories. The second letter grade indicates the mode of the letter grades for that category, i.e., the letter grade encountered most often for that category. Table 3.1 can be used to determine when a certain analysis method can be reasonably expected to produce acceptable results. The following two examples illustrate how Table 3.1 is to be used. 3.2.1.1 I-Girder Bridge Level of Analysis Example 1 Consider a horizontally curved steel I-girder bridge with radial supports, “regular” geometry (constant girder spacing, constant deck width, relatively uniform cross-frame spacing, etc.), and IC < 1, for which the engineer wants to perform a traditional 2D-grid analysis to determine the forces and displacements during critical stages of the erection sequence. (It should be noted that if IC is calculated for an intermediate stage of the steel erection in which some of the cross-frames have not yet been placed, the number of intermediate cross-frames ncf in Eq. 8 should be taken as the number installed in the erection stage that is being checked. In addition, the radius of curva- ture R and the constant m should correspond to the specific intermediate stage of construction being evaluated, not the bridge in its final erected configuration.) For the girder major-axis bending stresses and vertical displacements (fb and D), the results are expected to deviate somewhat from those of a 3D analysis in general, because a worst-case score of B is assigned in Table 3.1 for all of these response quantities. The worst-case normalized mean error in these results from the 2D-grid analysis will typically range from 7 to 12 percent, as compared to the results from a refined geometric nonlinear 3D FEA. However, one can expect that for most bridges, the errors will be less than or equal to 6 percent, based on the mode score of A for both of these responses. Therefore, in this example, if the major-axis bending stress results and vertical displacement results are of prime interest, a 2D-grid model should be sufficient if worst-case errors of approxi- mately 12 percent are acceptable. Given that the bridge has very “regular” geometry, it is likely that the fb and D errors are less than or equal to 6 percent. (The worst-case score is considered as the appropriate one to consider when designing a bridge with complicating features such as a poor span balance, or other “less regular” geometry characteristics.) It is important to note that the engineer can “compensate” for potential unconservative major- axis bending stress errors in the design by adjusting the target performance ratios desired for the construction engineering analysis. For example, with the above bridge, the engineer may require that the performance ratio be less than or equal to 1/1.12 = 0.89 or 1/1.06 = 0.94 for the girder flexural resistance checks to gain some further confidence in the adequacy of the analysis. Conversely, over-prediction and under-prediction of the vertical displacements can be equally bad. Nevertheless, 12 percent or 6 percent displacement error may be of little consequence if the magnitude of the displacements is relatively small, or if the deflections are being calculated at an early stage of the steel erection and it is expected that any resulting displacement incompat- ibilities or loss of geometry control can be subsequently resolved. However, if the magnitude of the displacements is large, or if it is expected that the resulting errors or displacement incompat- ibilities may be difficult to resolve, the engineer should consider conducting a 3D FEA of the subject construction stage to gain further confidence in the calculated displacements. This step

Appendix B B-13 in the application of Table 3.1 is where the bridge span length enters as an important factor, since longer-span bridges tend to have larger displacements. It should be noted that compared to the creation of 3D FEA models for overall bridge design, including calculation of live load effects, the development of a 3D FEA model for several specific construction stages that may be of concern involves a relatively small amount of effort. This is particularly the case with many of the modern software interfaces that facilitate the definition of the overall bridge geometry. For calculation of the girder flange lateral bending stresses and the cross-frame forces in the above example bridge, the worst-case errors are expected to be larger, on the order of 13 percent to 20 percent (corresponding to a grade of C for both of these responses). However, the mode score is B, and since the bridge has very regular geometry, it is likely that the normalized mean error in the flange lateral bending stresses and cross-frame forces is less than 12 percent. If these errors are acceptable in the engineer’s judgment, then the 2D-grid analysis should be acceptable for the construction engineering calculations. As noted above, the engineer can compensate for these potential errors by reducing the target performance indices. With respect to the flange lateral bending stress, it should be noted that the fl values are multiplied by 1⁄3 in the AASHTO 1⁄3 rule equations. Therefore, the errors in fl have less of an influence on the performance ratio errors than errors in fb. When checking the AASHTO flange yielding limit for constructability, both fl and fb have equal weights though. Based on these considerations, the best way to com- pensate for different potential unconservative errors in the fl and fb values is to multiply the cal- culated stresses from the 2D-grid analysis by 1.20 and 1.12 (or 1.12 and 1.06) respectively prior to checking the performance ratios. 3.2.1.2 I-Girder Bridge Level of Analysis Example 2 Consider a straight steel I-girder bridge with skewed supports and a skew index, Is = 0.35 (cor- responding to the intermediate erection stage being evaluated), for which the engineer wants to perform a traditional 2D-grid analysis to determine the forces and displacements during critical stages of the erection sequence. After reviewing Table 3.1, it is observed that for major-axis bending stresses and vertical deflec- tions, a worst-case score of B is shown for straight skewed I-girder bridges with 0.30 < IS ≤ 0.65. Furthermore, it can be observed that the mode of the scores for these bridge types is a B for the major-axis bending stresses and an A for the vertical displacements. Therefore, a properly pre- pared conventional 2D-grid analysis would be expected to produce major-axis bending stress and vertical deflection results that compare reasonably well with the results of a second-order elastic 3D FEA, such that the normalized mean error would be expected to be less than or equal to 12 percent. If the layout of the cross-frames in the skewed bridge is such that overly stiff (nuisance) trans- verse load paths are alleviated, the engineer may expect that the error in the displacement calcu- lations may be close to 6 percent or less. In this case, the engineer should be reasonably confident in the 2D-grid results for the calculation of these responses. As noted in the previous example, the potential unconservative errors in the stresses can be compensated for in the construction engineering design checks; however, positive or negative displacement errors are equally bad. The girder layover at the skewed bearing lines is often of key interest in skewed I-girder bridges. Table 3.1 shows that the girder layover calculations have essentially the same magnitude of errors and resulting grades as the girder vertical displacements. This is because the skewed bearing line cross-frames are generally relatively rigid in their own planes compared to the stiffness of the girders. Hence, the girder layovers are essentially proportional to the girder major-axis bending rotations at the skewed bearing lines.

B-14 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges For the calculation of the cross-frame forces and/or the girder flange lateral bending stresses in the above example, one can observe that the conventional 2D-grid procedures are entirely unreliable. That is, the scores in Table 3.1 are uniformly an F. The reason for this poor per- formance of the traditional 2D-grid methods is the ordinary modeling of the girder torsional properties using only the St. Venant torsional stiffness GJ/L. The physical girder torsional stiffnesses are generally much larger due to restraint of warping, i.e., flange lateral bending, effects. In addition, for wide skewed bridges and/or for skewed bridges containing specific overly stiff (nuisance) transverse load paths, the limited accuracy of the cross-frame equiva- lent beam stiffness models used in conventional 2D-grid methods may lead to a dramatic loss of accuracy in the cross-frame forces. Lastly, conventional 2D-grid methods generally do not include any calculations of the girder flange lateral bending stresses due to skew. Hence, the score for the calculation of the flange lat- eral bending stresses is also an F in Table 3.1. Chapter 6 of the NCHRP 12-79 Task 8 report, “Guidelines for Selecting Analytical Methods for Construction Engineering of Curved and Skewed Steel Girder Bridges,” recommends several important modifications to conventional 2D-grid procedures that are relatively simple for soft- ware providers to implement yet provide substantial improvements in the analysis accuracy. To realize the benefits of these improvements in typical bridge design practice it will be necessary for commercial 2D-grid software providers to implement these types of improvements, since manual implementation of the improvements tends to be cumbersome and time consuming for the engineer. Therefore, this document focuses solely on the accuracy of conventional 2D-grid and 1D line-girder procedures. 3.2.2 Tub-Girder Bridges Similar to the I-girder bridges, a quantitative assessment of the analysis accuracy of tub-girder bridges was obtained by focusing first on the normalized mean errors in the approximate (1D and 2D method) solutions for the girder major-axis bending stresses, internal torques, and verti- cal displacements, compared to benchmark 3D FEA results. Using the quantitative assessments, the various methods of analysis were assigned scores in the same manner as the scoring discussed in Section 3.1.1 for the I-girder bridge responses. Table 3.2 summarizes the scores for the above responses in tub-girder bridges. It is interesting that the Table 3.2 scores for the major-axis bending stresses and vertical dis- placements are relatively good. However, the worst-case scores for the internal torques are gener- ally quite low. These low scores are largely due to the fact that the internal torques in tub-girder bridges can be sensitive to various details of the framing, such as the use and location of external intermediate cross-frames or diaphragms, the relative flexibility of these diaphragms as well as the adjacent internal cross-frames within the tub-girders, skewed interior piers without external cross-frames between the piers at the corresponding bearing line, incidental torques introduced into the girders due to the spe cific orientation of the top flange lateral bracing system members (particularly for Pratt-type TFLB systems), etc. Jimenez Chong (2012) pro vides a detailed evalu- ation and assessment of the causes for the errors in the girder internal torques for the tub-girder bridges considered in the NCHRP Project 12-79 research. Similar to the considerations for I-girder bridges, the external diaphragms and/or cross- frames typically respond relatively rigidly in their own plane compared to the torsional stiffness of the girders. Therefore, the girder layovers at skewed bearing lines tend to be proportional to the major-axis bending rotation of the girders at these locations. As a result, the errors in the girder layover calculations obtained from the approximate methods tend to be similar to the errors in the major-axis bending displacements.

Appendix B B-15 The connectivity index, IC does not apply to tub-girder bridges, since this index is primarily a measure of the loss of accuracy in I-girder bridges due to the poor modeling of the girder torsion properties. For tub-girder bridges, the conventional St. Venant torsion model generally works well as a characterization of the torsional response of the pseudo-closed section tub-girders. Hence, IC is not used for characterization of tub-girder bridges in the table. Furthermore, there is only a weak correlation between the accuracy of the simplified analysis calculations and the skew index IS for tub-girder bridges. Therefore, the skew index is not used to characterize tub-girder bridges in Table 3.2 either. Important differences in the simplified analysis predictions do exist, however, as a function of whether the bridge is curved, “C,” straight and skewed, “S,” or curved and skewed “C&S.” Therefore, these characterizations are shown in the table. In addition, to the above quantitative assessments, the calculation of bracing component forces in tub-girder bridges is assessed separately in Table 3.3. It is useful to address the accuracy of these response calculations separately from those shown in Table 3.2 since the simplified bracing component force calculations take the girder major-axis bending moments, torques, and applied transverse loads as inputs and then apply various useful mechanics of materials approximations to obtain the force estimates. That is, there are two distinct sources of error in the bracing component forces relative to the 3D FEA benchmark solutions: 1. The error in the calculation of the input quantities obtained from the 1D line-girder or the 2D-grid analysis, and 2. The error introduced by approximations in the component force equations. Chapter 2 of the NCHRP Project 12-79 Task 8 report provides an overview of the most com- monly employed bracing component force equations evaluated here. It should be noted that the calculation of the top flange lateral bending stresses in tub girders is included as one of the bracing component force calculations. This is because these stresses are influenced significantly by the interaction of the top flanges with the tub-girder bracing systems. The NCHRP Project 12-79 research observed that in many situations the bracing component force estimates are conservative relative to the 3D FEA benchmark solutions. Therefore, it is use- ful to consider a signed error measure for the bracing component force calculations. In addition, the bracing component dimensions and section sizes often are repeated to a substantial degree throughout a tub-girder bridge for the different types of components. Therefore, it is useful to Traditional 2D-Grid 1D-Line Girder Traditional 2D-Grid 1D-Line Girder S B B A B C B C A B C&S B C B B S F F D F C D D A B C&S F F A B S B B A A C A B A A C&S B B A A S B B A A C NAa NAa NAa NAa C&S B B A A Girder Torques Vertical Displacements Girder Layover at Bearing Lines a Magnitudes should be negligible where properly designed and detailed diaphragms or cross-frames are present. Response Geometry Worst-Case Scores Mode of Scores Major-Axis Bending Stresses table 3.2 Matrix 1 for recommended Level of Analysis – tub-Girder Bridges.

B-16 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges quantify the analysis error as the difference between the maximum of the component forces determined by the approximate analysis minus the corresponding estimate from the 3D FEA benchmark, i.e.: e R R Rapprox FEA FEAmax = −( )• • •max max max for a given type of component. The grades for these responses were then assigned based on the same scoring system as that used for the assessments based on normalized mean error with one exception: Separate grades were assigned for the positive (conservative) errors and for the nega- tive (unconservative) errors in Table 3.3. In situations where no negative (unconservative) errors were observed in all of the bridges considered in a given category, the symbol “—” is shown in the cells of the matrix and the cells are unshaded. The mode of the grades is shown only for the top flange diagonal bracing forces in Table 3.3. The mode of the grades for the other component force types are not shown because of substantial positive and negative errors in the calculations that were encoun tered in general for the tub-girder bridges, and because, in cases where a clear mode for the grades existed, the mode of the grades was the same as the worst-case grade. In addition to the above considerations, it should be noted that current simplified estimates of the tub-girder bridge bracing component forces are generally less accurate for bridges with Pratt-type top flange lateral bracing (TFLB) systems compared to Warren and X-type systems. A small number of tub-girder bridges with Pratt-type TFLB systems were considered in the NCHRP Project 12-79 research. Therefore, the composite scores for these bridges are reported separately in Table 3.3. 3.2.2.1 Tub-Girder Bridge Level of Analysis Example Consider a horizontally curved steel tub-girder bridge with a Warren top flange lateral bracing system and skewed supports for which the engineer wants to perform a traditional 2D-grid anal- ysis to determine the forces and displacements during critical stages of the erection sequence. The bridge has “regular” geometry (constant girder spacing, constant deck width, a relatively uniform top flange lateral bracing [TFLB] system and internal cross-frame spacing, solid plate end diaphragms, single bearings for each girder, etc.). A properly prepared 2D-grid analysis would be expected to produce major-axis bending stresses and vertical deflections with mean errors less than 12 percent relative to a rigorous 3D FEA solution, since the worst-case score assigned for both of these quantities is a B in Table 3.2 for the subject “C&S” category. Furthermore, it can be observed that the mode of the scores for the vertical displacements is an A, and hence, given the “regular” geometry of the above bridge, it is expected that the vertical displacements most likely would be accurate to within 6 percent. Unfortunately, the worst-case score is an F for the 2D-grid estimates of the internal torques in the “C&S” bridges. As noted previously, this low score is due to the fact that the internal torques in tub-girder bridges can be very sensitive to various details of the framing, such as the use and location of external intermediate cross-frames or diaphragms, the relative flexibility of these diaphragms as well as the adjacent internal cross-frames within the tub-girders, skewed interior piers without external cross-frames between the piers at the corresponding bearing line, inciden- tal torques induced in the girders due to the specific orientation of the top flange lateral bracing system members (particularly for Pratt-type TFLB systems), etc. Fortunately though, the web and bottom flange shear forces due to the internal torques are often relatively small compared to the normal stresses due to the major-axis bending response of the girders. Furthermore, the mode of the scores for the internal torques is an A from Table 3.2. Therefore, the engineer must exercise substantial judgment in estimating what the expected error may be for the internal

Appendix B B-17 torque from a 2D-grid analysis, and in assessing the impact of this error on the bridge design. As noted previously in Section 3.2.1.1 and 3.2.1.2 for I-girder bridges, one can compensate for any anticipated potential unconservative error in the internal force or stress response quantities by scaling up the corresponding responses by the anticipated error, or by adjusting the target values of the performance ratios. Based on Table 3.3, the worst-case score for the positive (conservative) error in the calculation of the TFLB diagonal forces in the above example bridge is a D whereas the mode of the scores is Traditional 2D-Grid 1D-Line Girder Traditioal 2D-Grid 1D-Line Girder S D D D C C D F B F C&S D a F B F Pratt TFLB System C F A F S F b C C -- c -- C&S -- -- Pratt TFLB System -- -- S C C C F F C&S F F d Pratt TFLB System F F S C C C -- A C&S -- C Pratt TFLB System D D S NA e NA e C F F C&S F F Pratt TFLB System -- F f S NA e NA e C -- -- C&S -- D Pratt TFLB System B -- S C C C F F C&S F F d S C C C -- A C&S -- C c The symbol "--" indicates that no cases were encountered with this score. d Modified from a B to an F considering the grade for the C bridges. e For straight-skewed bridges, the internal intermediate cross-frame diagonal forces tend to be negligible. f Modified from an A to an F considering the grade for the C and C&S bridges. b Large unconservative error obtained for bridge ETSSS2 due to complex framing. If this bridge is considered as an exceptional case, the next worst-case unconservative error is -15 % for NTSSS2 (grade = C). a Modified from a C to a D considerting the grade for the C and the S bridges. Response Sign of Error Geometry Worst-Case Scores Mode of Scores TFLB Diagonal Force Positive (Conservative) Negative (Unconservative) Top Flange Lateral Bending Stress (Warren TFLB Systems) Positive (Conservative) Negative (Unconservative) TFLB & Top Internal CF Strut Force Internal CF Diagonal Force Positive (Conservative) Negative (Unconservative) Positive (Conservative) Negative (Unconservative) table 3.3 Matrix 2 for recommended Level of Analysis – tub-Girder Bridges.

B-18 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges a B. The table shows that no unconservative errors were encountered in this calculation for the tub-girder bridges studied in NCHRP Project 12-79. Since the example bridge is “very regular,” the engineer may assume that the TFLB diagonal force calculations are conservative, but reason- ably accurate, relative to the refined 3D FEA benchmark values. For both the TFLB and top internal cross-frame strut forces and the internal cross-frame diagonal forces in “C&S” bridges, Table 3.3 shows a grade of F for the conservative error. Also, the table shows that no unconservative errors were encountered in the NCHRP Project 12-79 calculations for these responses. Therefore, the engineer can assume that the forces for these components, as determined from a 2D-grid analysis plus the bracing component force equa- tions, are highly conservative. It should be noted that the forces in the top struts of the internal cross-frames at exterior diaphragm or exterior cross-frame locations can be very sensitive to the interaction of the external diaphragm or cross-frame with the girders. These forces should be determined based on consideration of statics at these locations given the forces transmitted to the girders from the external diaphragm or cross-frame components. NCHRP Project 12-79 did not consider these component forces in its error assessments. Lastly, Table 3.3 shows that the tub-girder top flange lateral bending stresses tend to be esti- mated with a high degree of conservatism by 2D-grid methods combined with the bracing com- ponent force equations. In addition, no unconservative errors were encountered in the tub-girder bridges studied by NCHRP Project 12-79 for the top flange lateral bending stresses. Therefore, the engineer also can assume that these stress estimates are highly conservative. 3.3 Guidelines on Calculations for Structural Adequacy and Stability Calculations to substantiate the structural adequacy and stability of the bridge system for each step of the steel erection should be submitted with the erection plan. The calculations should be done in accordance with design criteria established by the Owner, or as stated in the contract plans. This section provides guidelines regarding these calculations. These guidelines should by no means be construed as providing a comprehensive “checklist” of items needing evaluation for erection of any steel girder bridge; each project is unique and may have particular issues requir- ing the attention of the Contractor’s Engineer. Only basic guidelines and suggested evaluation items are presented herein. 3.3.1 Design Criteria The calculations supporting the erection plan and procedures should be completed in accor- dance with the AASHTO LRFD Bridge Design Specifications, the AASHTO LRFD Bridge Con- struction Specifications, and the AASHTO Guide Design Specifications for Bridge Temporary Works, unless otherwise directed by the Owner or the contract documents. 3.3.2 Loads and Load Combinations The calculations supporting the erection plan and procedures shall consider all applicable loads. Typical load considerations include permanent dead load, construction dead load, con- struction live load, and wind loads. Permanent dead loads typically include the self-weight of the structural members and detail attachments. Construction dead and live loads may consist of deck placement machinery, Con- tractor’s equipment, deck overhand brackets, concrete formwork, or other similar attachments applied in the appropriate sequence.

Appendix B B-19 Wind loads shall be considered in each step of the steel erection analysis and are to be com- puted in accordance with the established design criteria. Provisions should be made by the Con- tractor’s Engineer to ensure that girders are stable in wind events. It is permissible to set limits on maximum wind velocities during steel erection, but these limits must be clearly stated in the erection plan. In some cases, it may be advisable and/or necessary to include provisions in the erection plan for temporary supports and/or tie-downs to address high wind conditions. Load combinations should be in accordance with the project design criteria, and typically in accordance with the AASHTO LRFD Bridge Design Specifications, unless otherwise agreed to by the Owner. 3.3.3 Girder and system stability The calculations supporting the erection plan and procedures shall verify the stability both of individual girders and of the entire erected steel framing for each step of the bridge erection. These calculations are highly dependent upon the particular features of the bridge being erected and also of the particular sequence of erection of each part of the bridge. The assumptions used in the analysis should directly and fully conform to all steps and all details in the erection plan. The constructability provisions of Article 6.10.3 of the AASHTO LRFD Bridge Design Speci- fications should be referenced by the Contractor’s Engineer when investigating structural adequacy and stability during steel erection. A partial list of suggested evaluation items and guidelines regarding appropriate investigations are as follows. 3.3.3.1 Single Girder Stability Particular attention should be given to the lateral torsional buckling capacity of a singly erected I-girder. One of the most critical stages during I-girder erection is when the first girder has been erected but not yet connected to adjacent girders in the cross section. Assuming the girder is adequately braced at the supports, and there is no additional bracing within the span, the unbraced length for the girder will be the distance between supports. Long unbraced lengths typically correspond to very low lateral torsional buckling capacity of the girder. Tub-girders typically have much higher lateral torsional buckling capacity, but only if provided with a properly designed top flange lateral bracing system that provides for quasi-closed section behavior of the girder. Global overturning stability is also a concern for single curved girders, whether I- or tub-girders. The offset of the center of gravity of the girder from a chord line drawn between the support points results in an overturning moment. Single girders are typically afforded little or no torsional restraint at their supports unless tie downs or bracing, or temporary shoring or hold cranes, are provided. 3.3.3.2 Multi-Girder (Global) Stability A girder system may be vulnerable to global buckling during the steel erection sequence and/ or during deck placement. Narrow, long span segments during steel erection are the most sus- ceptible to this global buckling phenomenon. Methods to investigate the global stability of girder systems are available (Yura et al., 2008). 3.3.3.3 Second-Order Amplification Estimates Second-order amplification of the girder lateral-torsional stresses may cause a loading condition that exceeds the design capacity of the girders or other components. In this situation, the lateral- torsional displacement of the girder results in additional torsional loading in a nonlinear manner. In addition, the displacement amplifications may complicate the prediction and control the struc- ture’s geometry during erection. Although second-order amplification should be considered in the

B-20 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges erection analysis of any steel girder bridge, structures that are more susceptible to second-order amplification include widening of an existing bridge with one, two, or a few girders, pedestrian bridges with two-girder systems, phased construction where the various phases may have only one, two, or a few girders erected, and the interim stages of erection of larger bridges where only a few girders are in place in a given erection stage. A relatively simple method for identifying potentially adverse response amplifications due to second-order effects was developed as part of NCHRP Project 12-79. In this method, the linear response prediction obtained from any first-order analysis is multiplied by the following ampli- fication factor (AFG): AF M M G G cr G = − 1 1 max where MmaxG is the maximum total moment supported by the bridge unit for the loading under consideration, equal to the sum of all the girder moments, and McrG is the elastic global buckling moment of the bridge unit, which may be estimated using the equation M C sE L I IcrG b s ye x= pi2 2 (Yura et al., 2008). In this equation, Cb is the moment gradient modification factor applied to the full bridge cross-section moment diagram, s is the spacing between the two outside girders of the unit, E is the modulus of elasticity of steel, I I b c Iye yc yt= + is the effective moment of inertia of the individual I-girders about their weak axis, where I yc and Iyt are the moments of inertia of the compression and tension flanges about the weak axis of the girder cross-section respectively, b and c are the distances from the mid-thickness of the ten- sion and compression flanges to the centroidal axis of the cross-section, and Ix is the moment of inertia of the individual girders about their major-axis of bending (i.e., the moment of inertia of a single girder). Yura et al. (2008) provide a number of examples illustrating the calculation of McrG. 3.3.3.4 Cantilever Girders During the various stages of erection of most steel girder bridges there are often cases where field sections of girders are supported in a cantilevered position. Typically, these intermediate canti- lever conditions were not addressed by the Design Engineer during the original bridge design, so it is incumbent on the Contractor’s Engineer to investigate these conditions. For long canti- levers, lateral torsional buckling will typically govern over yielding of the section. To examine cantilevers, the lateral torsional buckling capacity can be estimated using the procedures pro- vided in Galambos (1998), Ziemian (2010), or a similar appropriate method. For curved girders, additional consideration needs to be given to the torsional forces that develop due to the offset centroid of the cantilever. 3.3.4 Uplift Uplift at temporary and permanent supports during steel erection should be accounted for in the development of the erection plan and procedures. Typically, uplift is undesirable and should be prevented, either by changing the erection plan or by providing tie-down restraints. If uplift

Appendix B B-21 is indicated in the analysis but no tie-down restraint is provided, then the analysis should rec- ognize the absence of vertical restraint at that particular support by modeling the boundary condition appropriately. Curved or skewed I-girder bridge systems are particularly susceptible to uplift during various stages of steel erection due to the torsional twisting of the system caused by curvature and/or skew. Incorrect consideration of uplift invalidates the analysis; if not considered correctly, uplift can result in girder alignment and/or other problems as steel erection progresses. 3.3.5 Temporary hold Cranes The computations for hold crane loads (if hold cranes are used) should be included in the erection plan calculations. Hold cranes are used to apply an upward load at some location with the span of a girder, thereby reducing the load carried by the girder. Oftentimes, the hold crane load is used to reduce the girder flexural moment due to self-weight (and any other applied loads) to a level at which the moment is less than the lateral-torsional bucking capacity. Typically, a hold crane should not be considered as a brace point in the evaluation of the lateral torsional buckling capacity of a girder; in most cases, the crane cable and crane system are flexible and not capable of providing the lateral resistance necessary to be considered as a brace point. 3.3.6 Temporary support Loads The erection plan calculations should include computations for the loads on temporary sup- ports provided at critical stages of the erection sequence. These loads may include vertical and lateral reactions from the superstructure, self-weight of the temporary support, wind loads on the temporary support, etc. 3.3.7 Bearings Computed bearing rotations during construction should not exceed the rotational capacity of the bearing. The erection plan calculations should include these bearing rotations. Skewed bridges are particularly vulnerable to twisting about the longitudinal axis of the girder. During steel erection, the girder could be rotated beyond the rotational capacity of the bearing, regard- less of the vertical load on the bearing. 3.3.8 Cross Frames and Bracing The placement of the cross frames and other bracing members should be substantiated through calculations that support the erection plan and procedures. The required number of cross frames to be installed before the girders are released from the lifting crane should be veri- fied with calculations and clearly indicated in the erection plan. The cross frames and bracing members and their associated connections must be structurally adequate, and they must also provide sufficient stiffness to the bridge system. The presence, and correct installation of, cross frames in curved or skewed steel I-girder bridge erection is an important issue. During steel erection, the erector may choose to install the mini- mum required number of cross frames when initially erecting the girders, so as to decrease erec- tion time, allowing a follow-up crew to install the remaining cross frames later. Therefore, correct determination of the minimum number of required cross frames to prevent lateral torsional buckling of the girders is critical to ensuring the stability of the girders during erection. Yura (1998) provides a general method to check whether cross frames in a girder system provide suf- ficient bracing for the girders. Additional calculations may be required to check that individual cross frame members and connections have adequate capacity.

B-22 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges 3.4 Structural Adequacy of Temporary Components Calculations to substantiate the structural adequacy and stability of any and all temporary support components for each step of the steel erection should be submitted with the erection plan. Additionally, calculations supporting the use of lifting beams, lifting devices (rigging), and jacking devices should be included in the calculation submittal. The calculations should be done in accordance with design criteria established by the Owner, or as stated in the con- tract plans. 3.4.1 Temporary supports Calculations indicating the load capacity and verifying the stability of any temporary supports should be included in the computations supporting the erection plan and procedures. Tempo- rary support structures should be designed to carry vertical and lateral loads resulting from the proposed erection sequence. As necessary, calculations for the design of an upper grillage, tem- porary bearings, and foundations should also be included. The elevation of the bearing support (bearing seat elevation) at the top of the temporary support structure should be computed and provided in the erection plan. The bearing seat elevations at the temporary supports can aid the steel erector in controlling the geometry of the structure during steel erection. 3.4.2 Girder Tie-Downs Calculations indicating the load capacity of girder tie-downs at any location should be included in the computations supporting the erection plan and procedures. The tie-downs may be used to resist wind loads, uplift, lateral dead load forces resulting from horizontal cur- vature, or other loads. 3.4.3 Lifting Beams and Devices Calculations verifying the load capacity of Contractor-fabricated lifting devices such as lifting beams, spreader beams, welded lugs, beam clamps, etc., should be provided in the computations supporting the erection plan and procedures. When applicable, manufacturers’ certification or catalog cuts for pre-engineered devices should be included with the calculations. 3.4.4 Jacking Devices Calculations for jacking devices, including jacking loads, jack type, etc., should be included with the erection plan calculations. Also, a detailed jacking procedure should be developed and included in the erection plan. 3.5 Miscellaneous Calculations and Recommendations 3.5.1 Crane Pick Locations The Contractor’s Engineer often provides calculations for the approximate pick locations for girder erection. These approximate crane pick locations should be determined with consider- ation of the centroid of the entire assembly being lifted into place, including the girder as well as any attached cross frames, splice plates, stiffening trusses, or other attached items. Figure 3.1 provides equations helpful in the computation of the centroids of various curved shapes.

Appendix B B-23 3.5.2 Alignment of Field splice Connections Using the erection analysis results, the Contractor’s Engineer should evaluate the lateral and vertical displacements and rotations at field splice locations of previously erected girders in rela- tion to the next girder segment being erected. Oftentimes, the field splice location will be at the end of the girder that is cantilevered over an interior support, and displacements and rotations may be significant enough to hinder the Contractor’s attempts to align bolt holes in bolted field splice connections. Vertical displacements and end rotations at the end of the previously placed, cantilevered section may result in the end of the girder being out of position and out of align- ment relative to the next field section being erected, which is often in a level, neutral position when being lifted. Lateral displacements are caused by the natural behavior of a curved steel girder to rotate outward from the radius of curvature. Since the next girder piece being lifted into place will typically be in a vertically plumb position, laterally displaced cantilever tips of the previously erected girder could cause alignment issues. 3.5.3 Alignment of Cross Frame Connections Using the erection analysis results, the Contractor’s Engineer should verify that the lateral displacements and girder rotations do not cause problems in erecting cross frames, whether cross frames are installed before or after girders are released from the lifting crane. Long unbraced girder lengths may result in significant out-of-plane rotations and displacements of the top and bottom flanges. Curvature and skew also produce potentially significant girder displacements and rotations. If the rotations and displacements are too large, the Contractor may have difficulty aligning connections. Contractors typically use various methods to correct these types of misalignments, including the use of temporary hold cranes, jacks, come-alongs, or other means. In certain situations, these means may prove insufficient. In extreme cases, the inherent stiffness of the girders is such that enough force cannot be practically applied to pull the connections into alignment, or alternately the amount of force required to pull the connections into alignment would damage the structure. 3.5.4 support Conditions The boundary (support) conditions assumed in the erection analysis should accurately reflect the actual support conditions in the structure at all stages of erection (including accurate consid- eration of any and all temporary supports). If the character of the support at a location changes during the steel erection, this should be accurately addressed in the analysis model. Improper modeling of boundary conditions leads to erroneous results and invalidates the analysis. (a) (b) Figure 3.1 Center of gravity for approximate pick points during lifting: (a) circular arc, (b) sector of annulus.

B-24 Guidelines for Analysis Methods and Construction engineering of Curved and skewed steel Girder Bridges 3.6 Calculation Checklist •• Complete analysis of erection sequence – Proper level of analysis used – Support conditions modeled appropriately at all stages •• Correct design criteria employed •• Correct loads investigated •• Complete checks of structural adequacy of bridge components •• Complete checks of stability of girder and bridge system •• Second-order amplification effects addressed as needed •• Girder reactions checked for uplift •• Temporary hold crane loads computed •• Temporary support loads computed •• Bearing capacity and rotation checks •• Cross frame and bracing placement •• Checks of structural adequacy of temporary supports and devices – Falsework towers – Girder tie-downs – Lifting beams – Jacking devices •• Crane pick location calculations •• Checks of displacements at field splices •• Checks of displacements for cross frame placement 3.7 Problematic Characteristics and Details to Avoid 3.7.1 oversized or slotted holes The use of oversized or slotted holes in gusset and connection plates can decrease significantly the stability bracing efficiency of cross-frames. In addition, the control of the deformed bridge geometry can also be affected since cross-frames are necessary to integrate the girders and make them deform as a unit rather than as inde pendent components. Therefore, it is not recommended to use this scheme as a solution to erecting cross-frames at stiff locations such as the regions near skewed supports. 3.7.2 narrow Bridges or Bridge Units In some cases, I-girder bridges can be susceptible to large response amplifications due to global second-order effects. Widening projects of existing bridges, pedestrian bridges with twin girders, phased construction, and erection stages where only a few girders of the bridge are in place, are some examples of structures that can be susceptible to considerable global second- order amplifications. When potential amplifications of the system stress and displacement responses are a concern, it is recommended to study the structure with refined 3D FEA or an approximate method based on amplified responses of a linear analysis solution. 3.7.3 V-Type Cross-Frames without Top Chords Cross-frames are needed to stabilize I-girders prior to hardening of the concrete deck. In some cases, V-type cross-frames without top chords may not be able to perform this function. The flex- ural stiffness of this type of cross-frame is substantially smaller than other configurations (i.e. X-type or V-type with top chord). Therefore, its ability to provide stability bracing needs to be con-

Appendix B B-25 sidered carefully during design. Studies conducted on an existing structure that uses V-type cross- frames without top chords illustrates the importance of including the top chord (Sanchez, 2011). 3.7.4 Bent-Plate Connections in i-Girder Bridges Bent-plate details can introduce excessive flexibility in the system, affecting the stability brac- ing capacity of skewed cross-frames. Due to this limitation, designers should consider the use of other connection details that do not represent a detriment to the system performance. Details such as the half-pipe stiffener and the reinforced bent-plate are options that can be used to con- nect skewed cross-frames at angles larger than 20°. 3.7.5 Long-span i-Girder Bridges without Top Flange Lateral Bracing systems Flange level lateral bracing systems are recommended for long-span bridges since second- order amplification and global flange lateral bending effects can be more critical for longer spans as the stresses are more dominated by dead load effects. Flange level lateral bracing systems help to control the bridge geometry and eliminate the second-order effects as these systems cause portions of the structure to act as pseudo-box girders. 3.7.6 Partial-Depth end Diaphragms in Tub-Girder Bridges Partial-depth end diaphragms often are used when they are the only solution due to the proj- ect geometric constraints. When possible, such a detail should be avoided in the practice because it changes the local and global behavior of the system. At the local level, the top flange lateral bracing system will lose continuity close to the end diaphragm. This results in a redis- tribution of forces through a different load path to reach the end of the girder. Also, the end panel will experience comparatively more deformation with respect to the adjacent panels, thus having a direct impact in the adjacent elements that control the cross section distortion, such as the internal cross-frames. The global consequences include a significant increase of the girder deflections and rotations due to the increased flexibility caused by partial-depth end diaphragms. If partial-depth end diaphragms are used, the resulting behavior of the sys- tem needs to be carefully investigated and, in many cases, will require a more refined analysis. 3.7.7 non-Collinear external intermediate Diaphragms in Tub-Girder Bridges When tub-girder bridges require external intermediate cross-frames or support diaphragms to control differential displacements between girders, or reaction force distribution, the inter- nal and external components should be collinear to avoid undesired behavior at the connect- ing locations. 3.7.8 Two-Bearing system at Tub-Girder support The use of twin bearing support under a single tub-girder typically requires a more refined analysis and, in general, should be avoided for curved and/or skewed bridges. In the curved and/or skewed bridges, an ideal twin bearing system could be used to transfer part or all of the associated torque to the support rather than follow the end diaphragm mechanism. In most cases, common bridge bearings are not able to resist upward forces and, consequently, the bridge could experience uplift at one of the twin bearings while the other bearing could be subjected to the entire vertical load, possibly exceeding the bearing design force.

B-26 References AASHTO/NSBA Steel Bridge Collaboration (2007). Steel Bridge Erection Guide Specification, American Associa- tion of State Highway and Transportation Officials/National Steel Bridge Alliance, Washington, D.C. AASHTO (2008). Guide Design Specifications for Bridge Temporary Works, 1st edition with Interim Revisions through 2008, American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO, LRFD Bridge Design Specifications (2010). 5th edition, American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO, LRFD Bridge Construction Specifications (2010). 3rd edition, American Association of State Highway and Transportation Officials, Washington, D.C. Bridgesoft, Inc. (2010). “STLBRIDGE, Continuous Steel Bridge Design,” http://bridgesoftinc.com/ Galambos, T.V. (1998). Guide to Stability Design Criteria for Metal Structures, 5th edition, Wiley, New Jersey. Jimenez Chong, J.M. (2012). “Construction Engineering of Steel Tub-Girder Bridge Systems for Skew Effects,” Ph.D. dissertation, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, 276 pp. LARSA (2010). “LARSA 4D, The Complete Software for Bridge Engineering,” http://www.larsa4d.com/products/ larsa4d.aspx MDX (2011). “MDX Software, The Proven Steels Bridge Design Solution,” http://www.mdxsoftware.com/ NSBA (1996). “V-Load Analysis and Check (VANCK), User Manual, Version 1.0,” National Steel Bridge Alliance and American Institute of Steel Construction. Quadrato, C., Battistini, A., Frank, K., Helwig, T., and Engelhardt, M. (2010). “Improved Cross-Frame Connection Details for Steel Bridges with Skewed Supports,” Transportation Research Record 2200, 29-35, Transportation Research Board, Washington, D.C. Richardson, Gordon, & Associates (1976) (now Pittsburgh office of HDR, Inc.), FHWA Curved Girder Workshop Manual. Sanchez, T.A. (2011). “Influence of Bracing Systems on the Behavior of Steel Curved and/or Skewed I-Girder Bridges during Construction,” Ph.D. dissertation, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, 2011. Tung, D.H.H. and Fountain, R.S. (1970). “Approximate Torsional Analysis of Curved Box Girders by the M/R Method,” AISC Engineering Journal, Vol. 7, No. 3, 1970. United States Steel Corporation (1984). V-Load Analysis (ADUSS 88-8535-01). Yura, J., (1993). “Fundamentals of Beam Bracing,” Is Your Structure Suitably Braced? – Structural Stability Research Council Annual Stability Conference Proceedings, Milwaukee, WI, April 6-7: 1-1.20. Yura, J., Helwig, T., Herman, R., and Zhou, C., (2008). “Global Buckling of I-Shaped Girder Systems,” Journal of Structural Engineering, ASCE, 134(9), 1487-1494. Ziemian, R. (2010). Guide to Stability Design Criteria for Metal Structures, 6th edition, Wiley, New Jersey.

Abbreviations and acronyms used without definitions in TRB publications: AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S.DOT United States Department of Transportation