Report No. CCEER 13-15 SEISMIC DESIGN AND NONLINEAR EVALUATION OF STEEL I-GIRDER BRIDGES USING CONVENTIONAL AND DUCTILE SUPPORT CROSS-FRAMES Ahmad M. Itani Eric V. Monzon Michael A. Grubb Ebrahim Amirihormozaki Center for Civil Engineering Earthquake Research University of Nevada, Reno September 2013 Abstract The AASHTO Guide Specifications for LRFD Seismic Bridge Design define three Global Seismic Design Strategies based on the expected behavior characteristics of bridge systems. The Type 2 design strategy is dedicated to an essentially elastic substructure with a ductile superstructure. This category applies to steel superstructures where the nonlinear response is achieved by providing ductile elements in the interior pier support cross-frames. However, the current guide specifications do not provide bridge engineers with a complete design procedure for achieving the desired performance when utilizing this strategy. In an attempt to overcome this shortcoming, this report presents a proposed Force-Based design procedure that will achieve an essentially elastic substructure and ductile superstructure. The proposed language and modifications are based on the ASSHTO LRFD Specifications. The flexural resistance of the reinforced concrete (R/C) substructure is based on the longitudinal seismic forces that are determined from the design spectrum using a force reduction factor equal to 1.5. Meanwhile, the shear resistance of the substructure is conservatively based on assumed plastic hinging of the substructure, which is not expected to occur. The pier support cross frames are designed and detailed to achieve a ductile response. The horizontal resistance of these cross frames is based on the nominal shear resistance of the substructure in the transverse direction divided by a response modification factor equal to 4. This will ensure that the superstructure will act as a ‗fuse‘ and will not subject the substructure to forces that may cause a nonlinear response in the transverse direction. The shear resistance of the substructure is also checked based on the expected lateral resistance of fully yielded and strain hardened pier support cross frames. In order to achieve a ductile response of the pier support cross frames, the diagonal members, which are expected to undergo inelastic response, are detailed to satisfy more stringent width-to-thickness and slenderness ratio limits. The diagonal member connections and other cross frame members are designed for fully yielded and strain hardened diagonal members. Three example bridges were selected to illustrate the proposed design procedure for the Type 2 design strategy. The substructure of these bridges was varied to examine single-column piers, two-column piers, and wall piers. Examples showing the design of these bridges using the more conventional Type 1 design strategy are also shown. Thus, a total of six bridge design examples are shown in this report. The seismic performance of these design examples was then evaluated through nonlinear response history analysis using ground motions representing the design and maximum considered earthquakes. The results of the nonlinear analysis for the Design and the MCE Levels earthquakes showed that the proposed strategy indeed achieved an essentially elastic substructure and the inelasticity was concentrated at the pier cross-frames as intended. Using the proposed design strategy resulted in an increase in the size of the substructure; however the seismic performance was greatly enhanced with minimal post-earthquake damage. The damage was limited to the diagonals of the pier support cross frames. These members can be easily replaced after large earthquake without interruption of the traffic. Meanwhile in conventional design, the size of the pier cross frames and the bearings were significantly larger than those in bridge designed according to the proposed strategy. Furthermore, as intended, the damage was concentrated in the substructure which will require substantial repair after major earthquakes. It is important to note here that for bridges with pier walls designed according to the conventional seismic design, the pier cross frames buckled under the design level earthquake. This damage is not intended to occur and may have detrimental effect on the performance of connections and the bearings. i Acknowledgement The work on this report was funded by American Iron and Steel Institute, AISI, contract CC-3070. Mr. Dan Snyder was the contract manager. The authors sincerely appreciate his support and collaboration. The authors appreciate the comments by a task group funded by AASHTO to support HSCOBS Technical Committee on Seismic Design. The chair of this group is Dr. Lee Marsh. The authors wish to thank the following individuals for their help and suggestions: Mr. Richard Pratt, Mr. Greg Perfetti, Prof. Ian Buckle, Dr. John Kulicki, Dr. Elmer Marx, Dr. Lian Duan, Mr. Keith Fulton, and Dr. Gichuru Muchane. Disclaimer The materials set fourth here in are for general information only. They are not a substitute for competent professional assistance. The opinions expressed in this report are those of the authors and do not necessarily represents the views of the University of Nevada, Reno, the American Iron and Steel Institute and the individuals who kindly provided the authors information and comments. ii Table of Contents Abstract .......................................................................................................................................................... i Acknowledgement ........................................................................................................................................ ii Disclaimer ..................................................................................................................................................... ii Table of Contents ......................................................................................................................................... iii Chapter 1 Introduction ............................................................................................................................... 1 1.1 Background ................................................................................................................................... 1 1.2 Proposed Draft AASHTO Specifications for the Type 2 Design Strategy ................................... 1 1.3 Seismic Design Examples ........................................................................................................... 16 1.3.1 Set I Bridges ........................................................................................................................ 16 1.3.2 Set II Bridges ...................................................................................................................... 17 1.3.3 Set III Bridges ..................................................................................................................... 18 1.4 Seismic Design Methodology ..................................................................................................... 18 1.5 Presentation of Design Examples ............................................................................................... 20 1.6 Analytical Model ........................................................................................................................ 20 1.6.1 Material Properties .............................................................................................................. 20 1.6.2 Superstructure ..................................................................................................................... 21 1.6.3 Support Cross-Frames ......................................................................................................... 23 1.6.4 Pier Caps and Columns ....................................................................................................... 23 1.6.5 Abutment Backfill Soil ....................................................................................................... 24 1.7 Design Loads .............................................................................................................................. 24 1.8 Seismic Evaluation of Design Examples .................................................................................... 28 1.8.1 Ground Motions .................................................................................................................. 28 Chapter 2 Example I-1: Bridge with Single-Column Piers Designed using the Type 1 Strategy ........... 32 2.1 Bridge Description ...................................................................................................................... 32 2.2 Computational Model ................................................................................................................. 32 2.3 Analysis....................................................................................................................................... 33 2.3.1 Gravity Loads – DC and DW .............................................................................................. 33 2.3.2 Earthquake Loads – EQ ...................................................................................................... 35 2.3.3 Design Loads ...................................................................................................................... 38 2.4 Design of Columns ..................................................................................................................... 39 2.5 Seismic Design of Support Cross-Frames................................................................................... 41 iii 2.6 Cross-Frame Properties for Nonlinear Analysis ......................................................................... 44 2.7 Design Summary ......................................................................................................................... 46 2.8 Nonlinear Evaluation of Seismic Design .................................................................................... 47 2.8.1 Response under Design Earthquake .................................................................................... 47 2.8.2 Response under Maximum Considered Earthquake ........................................................... 47 Chapter 3 Example I-2: Bridge with Single-Column Piers Designed using the Type 2 Strategy ........... 50 3.1 Bridge Description ...................................................................................................................... 50 3.2 Computational Model ................................................................................................................. 50 3.3 Analysis....................................................................................................................................... 51 3.3.1 Gravity Loads – DC and DW .............................................................................................. 51 3.3.2 Earthquake Loads – EQ ...................................................................................................... 53 3.3.3 Design Loads ...................................................................................................................... 55 3.4 Design of Columns ..................................................................................................................... 56 3.5 Design of Support Ductile End Cross-Frames ............................................................................ 59 3.6 Cross-Frame Properties for Nonlinear Analysis ......................................................................... 62 3.7 Design Summary ......................................................................................................................... 63 3.8 Nonlinear Evaluation of Seismic Design .................................................................................... 64 3.8.1 Response under Design Earthquake .................................................................................... 64 3.8.2 Response under Maximum Considered Earthquake ........................................................... 64 Chapter 4 Example II-1: Bridge with Two-Column Piers Designed using the Type 1 Strategy ............. 69 4.1 Bridge Description ...................................................................................................................... 69 4.2 Computational Model ................................................................................................................. 69 4.3 Analysis....................................................................................................................................... 70 4.3.1 Gravity Loads – DC and DW .............................................................................................. 70 4.3.2 Earthquake Loads – EQ ...................................................................................................... 72 4.3.3 Design Loads ...................................................................................................................... 75 4.4 Design of Columns ..................................................................................................................... 76 4.5 Seismic Design Support of Cross-Frames................................................................................... 81 4.6 Cross-Frame Properties for Nonlinear Analysis ......................................................................... 83 4.7 Design Summary ......................................................................................................................... 84 4.8 Performance Assessment ............................................................................................................ 85 4.8.1 Response under Design Earthquake .................................................................................... 85 4.8.2 Response under Maximum Considered Earthquake ........................................................... 85 iv Chapter 5 Example II-2: Bridge with Two-Column Piers Designed using the Type 2 Strategy ............. 89 5.1 Bridge Description ...................................................................................................................... 89 5.2 Computational Model ................................................................................................................. 89 5.3 Analysis....................................................................................................................................... 90 5.3.1 Gravity Loads – DC and DW .............................................................................................. 90 5.3.2 Earthquake Loads – EQ ...................................................................................................... 92 5.3.3 Design Loads ...................................................................................................................... 94 5.4 Design of Columns ..................................................................................................................... 95 5.5 Design of Support Ductile Cross-Frames ................................................................................... 99 5.6 Cross-Frame Properties for Nonlinear Analysis ....................................................................... 102 5.7 Design Summary ....................................................................................................................... 103 5.8 Performance Assessment .......................................................................................................... 104 5.8.1 Response under Design Earthquake .................................................................................. 104 5.8.2 Response under Maximum Considered Earthquake ......................................................... 104 Chapter 6 Example III-1: Bridge with Wall Piers Designed using the Type 1 Strategy ....................... 108 6.1 Bridge Description .................................................................................................................... 108 6.2 Computational Model ............................................................................................................... 108 6.3 Analysis..................................................................................................................................... 111 6.3.1 Gravity Loads – DC and DW ............................................................................................ 111 6.3.2 Earthquake Loads – EQ .................................................................................................... 111 6.3.3 Design Loads .................................................................................................................... 114 6.4 Design of Wall Pier ................................................................................................................... 115 6.5 Seismic Design of Support Cross-Frames................................................................................. 118 6.6 Cross-Frame Properties for Nonlinear Analysis ....................................................................... 120 6.7 Design Summary ....................................................................................................................... 121 6.8 Performance Assessment .......................................................................................................... 122 6.8.1 Response under Design Earthquake .................................................................................. 122 6.8.2 Response under Maximum Considered Earthquake ......................................................... 122 Chapter 7 Example III-2: Bridge with Wall Piers Designed using the Type 2 Strategy ....................... 127 7.1 Bridge Description .................................................................................................................... 127 7.2 Computational Model ............................................................................................................... 127 7.3 Analysis..................................................................................................................................... 130 7.3.1 Gravity Loads – DC and DW ............................................................................................ 130 v 7.3.2 Earthquake Loads – EQ .................................................................................................... 130 7.3.3 Design Loads .................................................................................................................... 132 7.4 Design of Wall Pier ................................................................................................................... 133 7.5 Design of Support Ductile Cross-Frames ................................................................................. 135 7.6 Cross-Frame Properties for Nonlinear Analysis ....................................................................... 138 7.7 Design Summary ....................................................................................................................... 139 7.8 Performance Assessment .......................................................................................................... 140 7.8.1 Response under Design Earthquake .................................................................................. 140 7.8.2 Response under Maximum Considered Earthquake ......................................................... 140 Chapter 8 Summary of Designs and Nonlinear Evaluation ................................................................... 143 8.1 Overview ................................................................................................................................... 143 8.2 Design Summary ....................................................................................................................... 143 8.3 Summary of Nonlinear Design Evaluation ............................................................................... 145 References ................................................................................................................................................. 150 vi Chapter 1 Introduction 1.1 Background A ductile superstructure with an essentially elastic substructure commonly known as Type 2 Design Strategy may be used as an alternative to the conventional seismic design strategy of providing an elastic superstructure and a ductile substructure. The ductile superstructure elements must be specially designed and detailed to undergo large cyclic deformations without premature failure. The inelastic activity in these elements will dissipate seismic energy and will limit the seismic forces transferred to the substructure. In this design strategy, special cross-frames are provided at the interior-pier supports. The substructure in this case is designed to be essentially elastic in the longitudinal and transverse directions of the bridge. Ideally, ductile superstructures have shown the most effectiveness when used with stiff substructures. Flexible substructures will attract smaller seismic forces and, thus, the support cross-frames will be subjected to low seismic forces and will be less effective (Alfawakhiri and Bruneau, 2001; Bahrami et al., 2010). The special ductile support cross-frames are designed with an R factor equal to 4.0. Thus, the diagonal members of these cross frames will undergo a nonlinear response and will limit the seismic forces in the transverse direction. Experimental investigations were conducted on diagonal cross-frame members and subassemblies to determine the nonlinear response of single angles to ensure that they will be able to withstand large cyclic deformations without premature failure. These experiments also provided the physical data needed to establish the overstrength factor for the diagonal members and their failure mode (Carden et al., 2006). Nonlinear response history analyses conducted on 3D bridge models confirmed the seismic response predicted by the proposed seismic design procedure. 1.2 Proposed Draft AASHTO Specifications for the Type 2 Design Strategy The following are proposed force-based draft specifications for possible consideration and evaluation that would incorporate the Type 2 Design Strategy in Article 6.16 of the AASHTO LRFD Bridge Design Specifications. Revisions to the AASHTO Guide Specifications for LRFD Seismic Bridge Design, which are displacement based specifications, are not proposed herein: 6.16.4.5Ductile Superstructures 6.16.4.5.1General C6.16.4.5.1 For a ductile superstructure, special support cross- A ductile superstructure with an essentially elastic frames, designed as specified in Article 6.16.4.5.2, shall be substructure may be used as an alternative to an elastic provided at all interior supports. The substructure shall be superstructure in combination with a ductile designed to be essentially elastic as specified in Article substructure. Ductile superstructures must be specially 4.6.2.8.2. designed and detailed to dissipate seismic energy. In 1 The seismic design forces for the diagonal members of ductile superstructures, special support cross-frames are the special support cross-frames shall be taken as the to be provided at all interior supports and must be unreduced elastic seismic forces divided by a response detailed and designed to undergo significant inelastic modification factor, R, which shall be taken equal to 4.0. activity and dissipate the seismic input energy without The superstructure drift,  determined as the ratio of premature failure or strength degradation in order to the relative lateral displacement of the girder top and limit the seismic forces on the substructure. The bottom flanges to the total depth of the steel girder, shall substructure in this case is designed to be essentially not exceed 4%. The drift shall be determined from the elastic as specified in Article 4.6.2.8.2 and described in results of an elastic analysis. Article C6.16.4.1. This strategy has been analytically and experimentally validated using subassembly and shake table experiments on steel I-girder bridges with no skew or horizontal curvature. Ideally ductile superstructures have shown the most effectiveness when utilized in conjunction with stiff substructures. Flexible substructures will attract smaller seismic forces, and thus, the special support cross-frames will also be subjected to smaller seismic forces and will be less effective (Alfawakhiri and Bruneau, 2001). Bridge dynamic analyses conducted according to the provisions of Article 4.7.4 can provide insight on the effectiveness of special support cross-frames (Alfawakhiri and Bruneau, 2001; Bahrami et al., 2010; and Itani et al., 2013). The R factor of 4.0 specified for the design of the special support cross-frame diagonal members in a ductile superstructure is the result of nonlinear time history analyses conducted on 3D bridge models (Bahrami et al., 2010 and Itani et al., 2013). For these nonlinear analyses, the deck and steel plate girders were modeled with shell elements, while the cross-frames, cap beams and columns were modeled with nonlinear frame elements. The drift, , of the superstructure is to be determined from an elastic structural analysis without the use of an R value. 6.16.4.5.2Special Support Cross-Frames C6.16.4.5.2 Special support cross-frames shall consist of top and Concentric support cross-frames are those in which bottom chords and diagonal members. The diagonal the centerlines of members intersect at a point to form a members shall be configured either in an X-type or an truss system that resists lateral loads. Concentric inverted V-type configuration. Only single angles or configurations that are permitted for special support double angles with welded end connections shall be cross-frames in ductile superstructures are X-type and permitted for use as members of special support cross- inverted V-type configurations. The use of tension-only frames. bracing in any configuration is not permitted. V-type In an X-type configuration, diagonal members shall be configurations and solid diaphragms are also not connected where the members cross by welds. The welded permitted. Members other than single-angle or double- connection at that point shall have a nominal resistance angle members are not currently permitted, as other equal to at least 0.25 times the tensile resistance of the types of members have not yet been sufficiently studied diagonal member, P, determined as specified in Article for potential use in special support cross-frames (AISC, t 6.16.4.5.2c. 2010b and Bahrami et al., 2010). In both configurations, the top chord shall be designed The required resistance of the welded connection at for an axial force taken as the horizontal component of the the point where diagonal members cross in X-type tensile resistance of the diagonal member, P, determined configurations is intended to permit the unbraced length t 2 as specified in Article 6.16.4.5.2c. for determining the compressive buckling resistance of In an inverted V-type configuration, the top chord and the member to be taken as half of the full length (Goel the concrete deck at the location where the diagonals and El-Tayem, 1986; Itani and Goel, 1991; Carden et al., intersect shall be designed to resist a vertical force, V, 2005a and 2005b, and Bahrami et al., 2010). t taken equal to: Inverted V-type configurations exhibit a special problem that sets them apart from X-type configurations. V  P  0.3P sin (6.16.4.5.2-1) Under lateral displacement after the compression t t nc diagonal buckles, the top chord of the cross-frame and the concrete deck will be subjected to a vertical where: unbalanced force. This force will continue to increase until the tension diagonal starts to yield. This unbalanced  = angle of inclination of the diagonal member with force is equal to the vertical component of the difference respect to the horizontal (degrees) between the tensile resistance of the diagonal member and the absolute value of 0.3P . 0.3P is taken as the nc nc Pnc = nominal compressive resistance of the diagonal nominal post-buckling compressive resistance of the member determined as specified in Article member (Carden et al., 2006a). A similar overstrength 6.16.4.5.2c (kip) factor is applied in the design of the welded end connections for special support cross-frame members in Pt = tensile resistance of the diagonal member Article 6.16.4.5.3, and in determining the transverse determined as specified in Article 6.16.4.5.2c seismic force on the piers/bents for the design of the (kip) essentially elastic substructure in Article 4.6.2.8.2. During a moderate to severe earthquake, special Members of special support cross-frames in either support cross-frames and their end connections are configuration shall satisfy the applicable requirements expected to undergo significant inelastic cyclic specified in Articles 6.16.4.5.2a through 6.16.4.5.2e. The deformations into the post-buckling range. As a result, welded end connections of the special support cross-frame reversed cyclic rotations occur at plastic hinges in much members shall satisfy the requirements specified in Article the same way as they do in beams. During severe 6.16.4.5.3. earthquakes, special support cross-frames are expected to undergo 10 to 20 times the yield deformation. In order to survive such large cyclic deformations without premature failure, the elements of special support cross- frames and their connections must be properly designed (Zahrai and Bruneau, 1999a and 1999b; Zahrai and Bruneau, 1998; Carden et al., 2006, and Bahrami et al., 2010). The requirements for the seismic design of special support cross-frames are based on the seismic requirements for Special Concentric Braced Frames (SCBFs) given in AISC (2010b). These requirements are mainly based on sections and member lengths that are more suitable for building construction. However, Carden et al. (2006) and Bahrami et al. (2010) tested more typical sections and member lengths utilized in bridge construction and verified that the AISC seismic provisions for SCBFs can be used for the seismic design of special support cross-frames. These studies, in addition to other analytical and experimental investigations conducted by numerous researchers, have identified three key parameters that affect the ductility of cross-frame members:  Width-to-thickness ratio;  Slenderness ratio; and  End conditions. 3